•A new model is developed to predict the growth of primary α phase of Ti-alloys.•Soft impingement and thermal history are considered in diffusion field.•Precipitation of secondary α phase affects the growth kinetics of primary α phase.Volume fraction of primary alpha is an important microstructure feature and can be changed by controlling its diffusive growth during heat treatment of two-phase Ti-alloys. A model for predicting its growth is urgently needed to realize microstructure control. Classical diffusion model based on additivity rule causes a significant underestimation of volume fraction of primary alpha phase. In present work, a diffusion-controlled growth model is developed to predict the evolution of phase fraction with temperature in the finite beta matrix, by solving the 3-dimensional diffusion equation with moving boundary conditions. By introducing a thermal history-related function and considering soft impingement, the prediction precision of present model is improved notably. Moreover, by considering the effect of secondary alpha precipitation on the far-field matrix composition and thus matrix supersaturation, the maximum error is almost one third of that by classical diffusion model when applied to TA15 and Ti-6Al-4V alloys. The results show that the volume fraction of primary alpha phase is overestimated in the later stage due to the effect of secondary alpha which is not captured by classical model. Combining the calculated length of diffusion field with metallographic analysis, the present model slightly underestimates the volume fraction of primary alpha in the initial stage due to the overestimation of soft impingement.

It is critical to precisely control the tri-modal microstructure during the isothermal local loading forming of titanium alloy to obtain high-performance components. To this end, the effect of local loading processing parameters on the development of tri-modal microstructure were experimentally investigated. The key influence factors and laws are revealed as follows. In the first loading step, the deformation temperature plays a decisive role in the volume fraction of equiaxed α, which decreases with the increase of temperature. While, the deformation amount and cooling mode present little effects on the microstructure evolution. In the second loading step, the deformation temperature and amount mainly influence the volume fraction, spatial orientation distribution and globularization of lamellar α. The volume fraction of lamellar α increases with the temperature decreasing. The spatial orientation distribution of lamellar α gradually changes from homogeneous distribution to concentrated distribution with the increase of deformation amount. Besides, the dynamic globularization fraction of lamellar α producing in the second loading step increases with the deformation amount, and their relationship can be well fitted by Avrami type equation. Moreover, higher temperature in the second loading step is beneficial to decrease the critical strain for the initiation of dynamic globularization and promote the kinetic rate of dynamic globularization. On the other hand, the deformation amount of the second loading step has after-effects on the static globularization of lamellar α in the annealing treatment. If the deformation amount exceeded the critical strain for the initiation of dynamic globularization, the static globularization of lamellar α would produce in the annealing, and the static globularization fraction increases with the deformation amount of the second loading step.

The dependences of microstructures and properties on initial tempers of 7050 aluminum alloy under creep age forming (CAF) conditions are investigated by using transmission electron microscope (TEM), scanning electron microscope (SEM), mechanical property tests and corrosion resistance tests. Three tempers are selected as the initial tempers for CAF, viz., solution, retrogression and re-solution. The constant-stress creep aging tests are conducted under simulated CAF conditions at 165 °C and 250 MPa for 18 h. TEM observations show that there are obviously different initial microstructures in the alloy with various initial tempers. After creep aging, a lot of fine and homogeneous transgranular precipitates with continuous grain boundary precipitates are found in the specimen with initial temper of solution; for retrogression temper, the transgranular precipitates grow up and the spacing of discontinuous grain boundary precipitates become wider; the transgranular re-precipitation and the biggest grain boundary precipitates with the widest spacing are observed in the specimen with initial temper of re-solution. Due to the fine transgranular precipitates, the creep aged specimens with initial tempers of solution and re-solution exhibit higher mechanical properties than that of retrogression with coarse transgranular precipitates. Both the creep aged specimens with initial tempers of retrogression and re-solution have lower corrosion susceptibility due to their discontinuous grain boundary structures, while the continuous grain boundary precipitates reduce the corrosion resistance of the creep aged specimen with initial temper of solution. Combining both mechanical properties and corrosion resistances into account, under the given thermal-mechanical conditions, the re-solution temper may be a preferable choice to achieve high performance of the components beyond the precise shape in CAF.

The deformation inhomogeneity of transitional region plays a great role in both the macro and micro forming qualities in the local loading forming. In this work, the dependence of deformation inhomogeneity of transitional region on the die parameters in the local loading forming of Ti-alloy rib-web component was studied based on finite element (FE) simulation. To evaluate the deformation inhomogeneity, an area-weighted strain inhomogeneity index was employed, which is calculated through the user subroutine of FE software (DEFORM-2D). It is found that there exist two kinds of strain concentration areas contributing to the deformation inhomogeneity of transitional region. One kind is the almost symmetric strain concentration area at the non-partitioned ribs, which is essentially related to the filling of rib. Another kind is the slant strain concentration area at the partitioned rib, which is caused by the multi-step loading during local loading forming. Besides, the effects of die parameters on the deformation inhomogeneity of transitional region were studied by the combination of orthogonal experiment design and FE simulation. The results suggest that the draft angle of the right rib is the most significant factor for both the deformation inhomogeneities of the partitioned rib region and whole transitional region. And, these two deformation inhomogeneities both decrease with the draft angle of the right rib decreasing. Furthermore, the relationship between die parameters and deformation inhomogeneity of transitional region is developed using the response surface methodology (RSM). Based on the RSM model, the die parameters were optimized to improve the deformation homogeneity of transitional region. The results will provide basis for the design of die parameters to improving the deformation and microstructure homogeneities in the isothermal local loading forming of Ti-alloy rib-web component.

The Cu–10 %Fe–1.5 %Ag in situ composite with high strength, high conductivity and low cost was prepared, and its hot deformation behavior was investigated by isothermal compression test with true strain of 0.69, temperature range of 750–950 °C and strain rate of 0.002–1.000 s−1. The flow stress–strain response shows the characterization of dynamic recrystallization (DRX), and the peak stress increases gradually with deformation temperature decreasing and strain rate increasing. The deformation activation energy of the composite for DRX is calculated as 241.864 kJ·mol−1. The constitutive relation of the composite was got by Arrhenius equation. Furthermore, according to the dynamic material modeling and Kumar–Prasad’s instability criteria, the processing map was constructed and the unsafe regions for hot deformation were analyzed. Based on the processing map and microstructural evolution, the optimal parameter range for hot deformation processing is 750–863 °C at the strain rate of 0.002–0.013 s−1.

•SRS varies from negative to positive then to negative with increased strain rate.•Dislocation substructure transformation and defects evolution lead to this.•New model of SRS built based on thermal activated dislocation movements.The significant variation of strain rate sensitivity (SRS), i.e. the non-linear characteristics of SRS, within wide strain and strain rate ranges in high strain rate forming (HSRF) leads to the complexity of constitutive behaviors of aluminum alloys. Therefore, in order to achieve accurate simulation of HSRF process, a panoramic description of the SRS variation and related mechanisms are required within wide ranges. To address this problem, taking 5A06 aluminum alloy as an example, three distinct SRS zones were determined at 0.001 s−1–5000 s−1 in the present work, including quasi-static negative SRS zone (Zone-I), positive SRS zone at dynamic strain rate (Zone-II) and negative SRS zone at high strain and strain rate (Zone-III). Then, the mechanism for that in Zone-II is attributed to the conversion from dislocation glide to viscous drag through thermal activation analysis. In Zone-III, the dominant mechanisms are the change of dislocation configuration from dislocation cells and dislocation bands to subgrains in adiabatic shear bands in compression and to the increasing volume fraction of voids in tension, respectively, which is proved by SEM and TEM observations. Consequently, the effect of dislocation evolution on the SRS was quantitatively characterized and the nonlinear rate dependent stress responses of the aluminum alloy in a wide strain rate range were captured.

•Formation mechanism of flat, zig-zag and mixed αGB was revealed via experiment.•A unified growth model was proposed by considering critical length Lc of flat αGB.•Lc lies on GB characteristic and energy, αGB VS, and chemical driving force.•Inhomogeneous nucleation on HAGB and deviated growth result in zig-zag αGB.•Nucleation at TJ and β GB simultaneously and competitive growth lead to mixed αGB.The growth mechanisms of the flat, zig-zag and mixed secondary grain boundary α (αGB) phase in TA15 Ti-alloy were investigated through heat treat experiment (cooled from β-phase field at a constant rate combined with interrupted water quenching). A unified growth model was proposed by introducing the relationship between the critical length of flat αGB (Lc) and β grain boundary (GB) length. The Lc is related to the characteristic and energy of the host GB, possible variants and habit plane of αGB, and chemical driving force. αGB preferentially nucleates at a triple junction (TJ) and extends on one side of β GB to form the flat morphology. Deviated growth of the heterogeneously and separately nucleated αGB on a high-angle grain boundary results in zia-zag morphology. The driving force and time available for αGB growth on the undecorated β GB determines its type, connected or unconnected. The flat and zig-zag αGB showed a competitive growth, and if αGB nucleated at the TJs and in the middle of the β GB simultaneously, the mixed αGB would appear.

•A process for equal-thickness in-plane ring roll-bending of a metal strip is presented.•Tangential velocity of the conical roll affects greatly ring formation.•The coupled influence of tangential velocity and deformation zone was found.•Positive and negative spread appears at the inner and outer half, respectively.•Adjustable parameters and small spread contribute to precise process control.A flexible and precise forming technology for low-cost, high-efficient and high-quality manufacture of equal-thickness rings is urgently required. To this end, a novel technique for equal-thickness in-plane ring roll-bending of a metal strip (ET-IRS) by twin conical rolls is presented. In this process, the twin conical rolls are placed to form an equal-thickness roll gap. The rolls rotate in opposite directions with identical angular velocity. The strip is bitten into the roll gap by frictional force and compressed equally across its width. Under the varying boundary conditions supported by the varying tangential velocity (VTV) of the rolls and varying deformation zone (VDZ) across the strip width, monotonically varying elongation of the strip is obtained, the coordination of which creates an equal-thickness ring. The results show that the VTV of the rolls plays a major part in ring formation, whereas the VDZ has little influence. However, remarkable coupling effects of VDZ with VTV exist. In comparison with the tangential velocity of the roll, the outlet velocity at the inner half of the strip is larger, but the velocity at the outer half is smaller. As a result, the inner half and the outer half experience frictional drag and traction, respectively, which produces a bending moment acting on the strip. The deformation characteristics of ET-IRS studied by simulation and experiment demonstrate that gradients exist in the radial and hoop strain components and outlet velocity of the strip across its width. Positive radial strain at the inner rim of the strip and negative strain at the outer rim result in positive and negative spread, respectively, leading to minimal resultant spread of the formed ring. The independently adjustable parameters, such as initial position of the strip z0, the roll gap t, the friction coefficient μ, the strip width b0 and the cone-apex angle α, affect the deformation. The gradient of radial strain increases with decreasing z0 and t and increasing μ and α, and the spread increases with increasing z0 and α and decreasing t and b0. The results indicate the forming mechanism and characteristics of ET-IRS are considerably different from existing processes.

•Growth models for grain boundary and intragranular Widmanstatten α were proposed.•Clustered lamellar αWGB grows via adjacent lamellae merging and subsequent coarsening.•Holes in thick lamellae expand and further fracture result in forked αWI.•Merger of residual thick αWI with thin tertiary parallel αWI results in double forked αWI.The morphology evolution and growth mechanism of secondary Widmanstatten α phase in the TA15 Ti-alloy, including the clustered grain boundary Widmanstatten α (αWGB), and forked intragranular Widmanstatten α (αWI), were investigated and the growth model were proposed. Results indicate that the clustered lamellar αWGB grows via the merger of adjacent thin lamellae and subsequent coarsening. Two types of forked αWI exist: a forked αWI with short and thick branches, and a forked αWI with thin and long branches. They results of the fracture of thick lamellar αWI and merger of residual thick αWI with the newly precipitated thin lamellar αWI, which showed a clustered distribution and paralleled the residual thick αWI, respectively.

Dynamic and post dynamic recrystallization in primary working of a coarse grained two-phase TA15 titanium alloy were investigated. It is found that in β deformation, dynamic recrystallization (DRX) can be triggered at a low strain. The low nucleation rate retards DRX. It is prone to producing a duplex grain structure. During post-deformation holding, both meta-dynamic recrystallization (MDRX) and static recrystallization (SRX) occur. The average recrystallized grain size increases sharply in the early stage of holding due to MDRX but varies slightly after SRX occurs. Post dynamic recrystallization can be finished in a short time and additional β annealing after deformation is unnecessary. Refining the initial structure can accelerate recrystallization and decrease the recrystallized grain size.

•Reveal action of temperature drop before WQ on formation of tri-modal microstructure.•Get tri-modal microstructure in TA15 via near-β forging (AC + WQ) + HLT.•Toughening temperature determines mainly volume fractions of αp and αs.•Morphology and size of αp and αs lie on both toughening and strengthening treatments.•Get reasonable toughening and strengthening conditions for tri-modal microstructure.For Ti-alloy tri-modal microstructure can be obtained by the near-β forging (water quenching, WQ) + high temperature toughening and low temperature strengthening treatment (HLT) method. However in actual production, it is hard to accomplish water quenching after near-β forging immediately. In this paper a short time of air cooling (AC) after near-β forging was introduced to consider the temperature drop during the forgings transferring in actual production. For TA15 alloy the formation process of tri-modal microstructure in near-β forging (AC + WQ) + HLT was studied. Under the given near-β forging condition, the influences of the subsequent toughening and strengthening treatment on the obtained tri-modal microstructure were revealed as well as on the corresponding mechanical properties. Then the reasonable HLT route for tri-modal microstructure with excellent comprehensive properties was determined.

For TA15 Ti-alloy, conventional forging combined with subsequent heat treatment provides a new method to obtain a tri-modal microstructure (consisting of about 20% equiaxed αp, 50–60% lamellar αs and transformed β matrix) possessing attractive comprehensive properties, and it is expected to solve the problems (such as, deformation temperature control, microstructure coarsening, or special requirement for the original microstructure) caused by using the existing method. In this paper, the forming process and principle of obtaining a tri-modal microstructure under conventional forging combined with given subsequent near-β and two-phase field heat treatments (NTH, i.e. 975 °C/30 min/WQ + 930 °C/100 min/AC) were investigated. Meanwhile, taking the volume fraction and morphology of equiaxed αp and lamellar αs as targets, the tri-modal microstructure evolution under different conventional forging conditions (deformation temperatures, deformation degrees, strain rates, cooling modes) and significance of influencing factors were revealed.

Springback after unloading is an issue that directly reduces the accuracy of bent tubes, especially for Ti-alloy tubes which are of high strength and low Young’s modulus. The Young’s modulus, E; wall thickness, t; and neutral layer, De, of a tube vary during the bending process. These variations may influence the bending deformation of components, thus on springback. Considering these variations, an analytic elastic-plastic tube bending springback model was established in this study based on the static equilibrium condition. When these variations were considered individually or combined, the resulting springback angles were all larger and closer to the experimental results than the results when variations were not considered for a D6 mm × t0.6 mm Ti-3Al-2.5V Ti-alloy tube. The t variation contribution is the largest and decreases the prediction error by 41.2%–45.3%. De variation ranks second and decreases the error by 21.2%-25.3%. E variation is the least significant, decreasing the error by only 2.4%. Furthermore, the influence of the stable Young’s modulus Ea on the springback is larger than the initial Young’s modulus E0. Therefore, for the bending springback of tubes with a small difference between E0 and Ea and under a normal bending radius, E variation effects can be neglected. While for tubes with large differences between E0 and Ea, and high springback prediction requirements, the E variation should be replaced by Ea. The influences of the initial tube sizes, material properties and bent tube sizes of the Ti-3Al-2.5V tube on springback were obtained using the newly developed model.

Warm rotary draw bending provides a feasible method to form the large-diameter thin-walled (LDTW) TC4 bent tubes, which are widely used in the pneumatic system of aircrafts. An accurate prediction of flow behavior of TC4 tubes considering the couple effects of temperature, strain rate and strain is critical for understanding the deformation behavior of metals and optimizing the processing parameters in warm rotary draw bending of TC4 tubes. In this study, isothermal compression tests of TC4 tube alloy were performed from 573 to 873 K with an interval of 100 K and strain rates of 0.001, 0.010 and 0.100 s−1. The prediction of flow behavior was done using two constitutive models, namely modified Arrhenius model and artificial neural network (ANN) model. The predictions of these constitutive models were compared using statistical measures like correlation coefficient (R), average absolute relative error (AARE) and its variation with the deformation parameters (temperature, strain rate and strain). Analysis of statistical measures reveals that the two models show high predicted accuracy in terms of R and AARE. Comparatively speaking, the ANN model presents higher predicted accuracy than the modified Arrhenius model. In addition, the predicted accuracy of ANN model presents high stability at the whole deformation parameter ranges, whereas the predictability of the modified Arrhenius model has some fluctuation at different deformation conditions. It presents higher predicted accuracy at temperatures of 573–773 K, strain rates of 0.010–0.100 s−1 and strain of 0.04–0.32, while low accuracy at temperature of 873 K, strain rates of 0.001 s−1 and strain of 0.36–0.48. Thus, the application of modified Arrhenius model is limited by its relatively low predicted accuracy at some deformation conditions, while the ANN model presents very high predicted accuracy at all deformation conditions, which can be used to study the compression behavior of TC4 tube at the temperature range of 573–873 K and the strain rate of 0.001–0.100 s−1. It can provide guideline for the design of processing parameters in warm rotary draw bending of LDTW TC4 tubes.

For TA15 Ti-alloy two types of tri-modal microstructures with excellent comprehensive mechanical properties were obtained via a new approach, near-β forging combined with the solution and aging treatments (SAT), regardless of whether there was a short time of air cooling (AC) during forgings transferring in practice before water quenching. Performance of tri-modal microstructure, with different morphologies and contents of constituent phases (primary equiaxed αp and secondary lamellar αs), was investigated. More and larger αp contributes to higher plasticity, while more and thicker αs benefits for room and high temperature strengths and impact toughness. The formation of tri-modal microstructure via near-β forging+SAT was investigated. AC may change the formation process of lamellar αs and the stored distortion energy in as-forged specimen, and further results in more and larger αp and fewer and thinner αs in final tri-modal microstructure, leading to lower strength but higher plasticity and fracture toughness. The dependences of near-β forging conditions on the obtained tri-modal microstructure via near-β forging and SAT were revealed. The tri-modal microstructure and its performance for service need can be adjusted via control of air-cooling time before water quenching combined with near-β forging conditions selection.

Rolling-spinning of titanium alloy tubes is an advanced plastic forming technology that has been developed due to the urgent need for light-weight, high-precision, and high-reliability components in high-tech fields, such as aviation and aerospace. However, due to the complexity of the rolling-spinning process and the sensitivity of titanium alloy to temperature and strain rate, it is easy to crack, which severely restricts the improvement of the forming quality and forming limit of components. In this study, the critical deformation of Ti-6Al-2Zr-1Mo-1V was obtained by a hot compression test under various temperatures and strain rates. The damage threshold was obtained through FE simulation for the hot compression process under these temperatures and strain rates. The relationship among damage threshold, temperature, and strain rate was established by introducing the Zener-Hollomon factor. A thermal damage model for Ti-6Al-2Zr-1Mo-1V was established by combining the Oyane ductile fracture criterion with the relationship among damage threshold, temperature, and strain rate. By coupling this thermal damage model into the FE model for rolling-spinning of a Ti-6Al-2Zr-1Mo-1V tube, the damage prediction for the process was realized. The results show that the stress triaxiality at the top and bottom ends of the rolling zone is positive, the accumulation of damage is fast, and the strain rate is large in the zone. Thus, these ends are the zones most prone to damage in rolling process. The stress triaxiality at the local inner surface area of the spinning region is positive, the accumulation of damage is fast, and the strain rate is large in the zone. Therefore, the inner surface of the spinning region is the zone most prone to damage.

Temperature rise is a significant factor influencing microstructure during (α + β) deformation of TA15 titanium alloy. An experiment was designed to explore microstructure evolution induced by temperature rise due to deformation heat. The experiment was carried out in (α + β) phase field at typical temperature rise rates. The microstructures of the alloy under different temperature rise rates were observed by scanning electron microscopy (SEM). It is found that the dissolution rate of primary equiaxed α phase increases with the increase in both temperature and temperature rise rate. In the same temperature range, the higher the temperature rise rate is, the larger the final content and grain size of primary equiaxed α phase are due to less dissolution time. To quantitatively depict the evolution behavior of primary equiaxed α phase under any temperature rise rates, the dissolution kinetics of primary equiaxed α phase were well described by a diffusion model. The model predictions, including content and grain size of primary equiaxed α phase, are in good agreement with experimental observations. The work provides an important basis for the prediction and control of microstructure during hot working of titanium alloy.

The microstructure evolution and mechanical properties in different loading regions during isothermal near-β local forging were investigated using three TA15 Ti-alloy workpieces of different sizes, namely, a cylindrical sample, a quadrate billet, and a bulkhead component. Reasons for differences in the microstructure and mechanical properties were determined. Fine primary equiaxed α and clustered acicular secondary α were obtained for the small cylindrical sample, and the different loading regions exhibited good uniformity in microstructural morphology and size. Significant differences in microstructure existed between the first and second loading regions for the quadrate billet and bulkhead component, especially in the secondary lamellar α, which resulted in different mechanical properties. Specifically, coarse primary equiaxed α and straight and thin clustered lamellar α existed in the first loading region, and less coarse primary equiaxed α and thickened and globularized secondary lamellar α with short rod-like or equiaxed shape existed in the second loading region. The holding time and different cooling rates caused by the workpiece sizes resulted in differences in their primary equiaxed α and secondary lamellar α size. The combined effects of strain history, holding time, and cooling rate led to microstructural differences in different regions for the quadrate billet and bulkhead component, whereas the effect of strain history was reduced for the cylindrical sample because of the short holding time and fast cooling rate, and little difference existed between the first and second loading regions.

Forming quality of transitional region determines the performance of titanium alloy large-scale rib-web component under isothermal local loading forming. As folding defect is the most sensitive defect in transitional region, its prediction is very critical to the precision shape forming in isothermal local loading forming. In this paper, a quick prediction model for the folding defect in transitional region was established to replace the traditional defect prediction method by time-consuming FE simulation. First of all, the FE model of local eigen model of transitional region during local loading forming of large-scale rib-web component was established and validated by physical experiment. Then, an adaptive folding index was proposed to measure the possibility and severity of folding defect based on the mechanism that there exists a local increase of strain rate when a folding tends to appear. Availability of the adaptive folding index was checked by large numbers of uniform experiments designed by the space-filling Maximin Latin hypercube designs (maximin LHDs). Furthermore, a judging criterion for folding defect based on the folding index was developed and validated by random samples. Subsequently, the folding index was correlated with the geometrical characteristic parameters of transitional region model by RSM model, through which the folding index can be predicted quickly without the time-consuming FE simulation. Finally, a quick prediction model was established for folding defect judgment under various geometrical parameters by combination of the RSM model for folding index and proposed judging criterion. Prediction results are quite consistent with the results of FE simulation and experiment. The folding prediction model can greatly facilitate the design space exploration and engineering design thereby providing guideline to the precision shape forming. Besides, the adaptive folding index and corresponding judging criteria for folding defect put forward in this work have reference significance to the study on folding defect in other forging processes.

The forming quality of transitional region plays a key role in the performance of titanium alloy large-scale rib-web component under isothermal local loading forming. In this work, a local eigen model of transitional region in the local loading forming of large-scale rib-web component is extracted so as to catch the detail-forming characteristics of transitional region with low computation time in simulation and experiment cost. Then, based on the local eigen model, the mechanism of forming defects in transitional region and their dependence on processing parameters are studied by the combination of physical experiment and verified finite element (FE) simulation. It is found that the second loading step can be divided into two forming stages according to the material flow pattern: (1) the transverse flow stage and (2) the stable forming stage. In the transverse flow stage, there exists long-range transverse flow of web material and excessive transverse flow would lead to the formation of folding and cavum defects. Moreover, the severities of defects are well correlated with the quantity of material transferred into the first-loading region in this stage. For a certain reduction amount, decreasing spacer block thickness and increasing friction both can decrease the quantity of transferred material and then suppress the development of folding and cavum defects, while the deformation temperature and loading speed have little effect on the quantity of transferred material and defects. In the end, an effective way is put forward to suppress and prevent the defects in transitional region during the local loading forming of titanium alloy large-scale rib-web component.

Incremental in-plane bending (IIB) is a new and advanced flexible manufacturing technology for small-lot production of strip with various bending radii. The strip of sheet metal is bent incrementally by a beating inclined punch. The bending radius is strongly affected by mechanical properties of the material, geometry of the strip, and processing parameters. It is difficult to predict the bending radius due to the complex synergistic effects of the controlling parameters. How to predict the bending radius accurately has therefore become a key point to be urgently solved in the development of this advanced forming technology. In this paper, a model based on a back propagation neural network (BPNN) is introduced to reveal the relationship of bending radius with angle of die α, indentation s, pitch p, and width of strip w. Out of 14 different BPNN architectures trained, the 4-9-9-1 BPNN with two hidden layers having nine neurons trained with the Levenberg-Marquardt algorithm (trainlm) is found to be the optimum network model, and the prediction error is less than 2 % on average. Otherwise, a 1-9-9-4 reverse BPNN is developed to build the processing window for a given bending radius. Meanwhile, taking section moment of inertia I as a quantitative index of forming stability, α, p, s, w0 are optimized as design variables in order to make objective functions of I maximized simultaneously. Finally, to verify its predictive capability, the present approach is applied to a case study, and the optimal combination of parameters for stable forming during IIB is obtained.

The under-filling defect is prone to occur in the forging of large-scale titanium alloy rib-web components (LTRC). A rigorous preform design with accurate volume distribution is required for a desirable LTRC. The unequal thickness billet (UTB) design divides the preform into multiple regions of varying thickness and can not only adjust the volume distribution effectively but also control forming defects with low cost and high efficiency. The purpose of this paper is to attain LTRC without any under-filling defects using the UTB methodology. Firstly, cross sections are extracted from a desirable LTRC so as to create the initial UTB according to the calculated neutral layer of material flow between ribs. Then a finite element (FE) model is established, using the Deform-3D software for the isothermal closed-die forging to study the material flow and die cavity filling. Finally, three schemes to modify the initial UTB are proposed for those areas where there is under-filling: (I) increase the number of regions in affected areas, (II) adjust the size parameters of the regions around affected areas, and (III) increase the thickness of the regions in affected areas. In conclusion, it is found that scheme I and scheme II are based on the constancy of volume principle and can be adopted if the distribution of the ribs on those affected areas is quite simple. However, scheme I increases the complexity of the UTB, so scheme II is preferred. Alternatively, if the distribution of ribs on those regions is more complicated, scheme III can be adopted. Although the volume of the UTB is increased slightly, all ribs can be completely filled, allowing the most accurate LTRC to be produced.

The intrinsic multi-heat unequal deformation behavior of the local loading forming requires a through-process macro–micro model to characterize the microstructure evolution during the forming process. In the present work, the phenomena and mechanisms of microstructural developments in local loading forming of titanium alloys are summarized. Mechanism-based unified material models, which characterize the through process microstructure evolution, are developed for integrated prediction of constitutive behavior and microstructure. A through-process macro–micro finite element model is established for the local loading forming of large scale complex titanium alloy component. The model can predict the microstructure evolution as well as macroscopic deformation in multi-step local loading forming process. Model predictions are in good agreement with experimental results. The microstructure evolution in local loading forming is investigated by the established finite element model. It is found that the thermo-mechanical processing route greatly affects the volume fraction of primary alpha but has little influence on the grain size in local loading forming

•Dual indexes are used to represent multi-instability constrained bending limits of tube.•Intrinsic factor dependent bending limits of tube are established under various conditions.•A conceptual multiple defect-constrained bending limit diagram against D/t is presented.•A stepwise method for improving tube bending limits is proposed considering coupling effects of multiple forming parameters.Understanding the bending limits is critical to extract the forming potential and to achieve precision tube bending. The most challenging task is the development of the tube bending limits in the presence of unequal deformation induced multiple instabilities and multi-factor coupling effects. Using analytical and 3D-FE methods as well as experiments, a comprehensive map of the tube bending limits during rotary draw bending is provided under a wide range of tube sizes, material types and processing parameters. The major results show: (1) For each instability, the intrinsic factors (tube geometrical parameters, D and t, and mechanical properties, m) dependent bending limits are clarified, and evident interactive or even conflicting effects are observed. (2) Under mandrel bending, the significant effects of the intrinsic factors on the wrinkling limit are reduced, the neglected effects of D/t on the thinning limit are magnified; the significant influences of D/t on the flattening limit even become contrary, and the effects of m on wrinkling and thinning limit are opposite to that on the flattening limit. (3) Taking D/t as the basic design parameter, a conceptual multiple defect-constrained bending limit diagram (BLD) is constructed, and a knowledge-based stepwise method for determining and improving tube bending limits is proposed, considering coupling effects of multiple forming parameters, e.g., intrinsic factors, tooling/processing parameters and uncertainties. (4) The method is experimentally verified by several practical bending scenarios for different kinds of tubular materials with extreme size.

•A hybrid method is proposed for prediction of multiple instability modes in IRS.•4 buckling modes are obtained by eigenvalue buckling analysis and analytical solution.•An appropriate imperfection and an optimal scaling factor Ai are obtained.The in-plane roll-bending of strip (IRS) is a flexible forming process to produce ring parts with advantages of low forming forces, low material waste and good flexibility. However, if deformation condition is inappropriate, it results in several instability modes including external wrinkling, internal wrinkling, turning-I and turning-II. Solely using pure analytical solution, implicit finite element method (FEM) or explicit FEM cannot predict all these instability modes of the strip. In this study, a new hybrid method is proposed to accurately predict all these instability modes in IRS. First, using two analytical models with two simple support conditions to simplify the actual roll-bending conditions, the eigenvalue buckling analysis and the analytical solution analysis are conducted to generate four kinds of buckling modes, respectively, and a series of imperfections are defined in the shapes of these buckling modes. Second, assigning these geometrical imperfections into the perfect geometry of strip, a series of hybrid FE models for IRS are established. Four specific case studies of external wrinkling, internal wrinkling, turning-I and turning-II are carried out. By comparing with corresponding experimental results, an appropriate imperfection and an optimal scaling factor Ai are obtained. Third, to validate our proposed method, the hybrid method is applied to five cases of arbitrary experimental condition. The comparisons between the predicted results and experiments show that the proposed method is reliable to accurately predict all instability modes in IRS.

For isothermal local loading process by means of partitioned die, the partition at a rib is generally adopted in order to reduce the disadvantageous influence of loading area on unloaded area. In the local loading process, some metal (flow-into metal) in loading area flow into unloaded area due to the local loading characteristic. The distribution of the metal flowing into unloaded area plays an important role in analyzing the forming process, controlling the metal flow, and improving the forming quality. The distribution of flow-into metal coming from loading area is mainly determined by the shape of the unloaded area and the geometric parameters near the die partitioning boundary. If the unloaded area is a formed area then some of the flow-into metal will fill the cavity of partitioning rib. A predicted model for the ratio of flow-into metal distributed to cavity of partitioning rib has been established by using partial least squares regression. The numerical simulation result indicates that the analysis on distribution of flow-into metal and the predicted model are reasonable.

•The Q-value of 6005A aluminum alloy is −211.7485 kJ/mol in 623–773 K.•The Q-value of 6005A aluminum alloy is −368.5722 kJ/mol in 573–623 K.•The constitutive equations are extracted as follows:ε̇=4.28×1015[sinh(0.0191σ)]7.58exp-2.11×105RTε̇=2.59×1026[sinh(0.0195σ)]7.38exp-3.68×105RTin 623–773 K and 573–623 K, respectively.The 6005A aluminum alloy is one of the most widely used alloys in aeronautic and railway industries, yet its plastic deformation behavior under hot compression is still not fully understood. Isothermal compression tests of 6005A aluminum alloy were performed using a Gleeble-1500 device, up to a 70% height reduction of the sample at strain rates ranging from 0.01 s−1 to 10 s−1, and deformation temperatures ranging from 573 K to 773 K. Several modeling approaches, including flow stress–strain curves, a constitutive Arrhenius-type equation model, and processing maps were used to characterize the deformation behavior of the isothermal compression of 6005A aluminum alloy in this study. The related material constants (i.e. A, β and α) as well as the activation energy Q for 623–773 K and 573–623 K temperature regimes were determined. Two sets of constitutive exponent-type equations for the 6005A aluminum alloy were proposed. Furthermore, a change in deformation mechanism occurred when changing the temperature range from 623–773 K to 573–623 K.

Understanding the mechanism of high temperature deformation is important for controlling the forming quality of the titanium alloy forgings. In the present work, the flow softening mechanism in subtransus deformation of titanium alloys with equiaxed structure was investigated by interrupted isothermal compression tests. The results show that limited strain hardening followed by continuous flow softening occurs in high temperature deformation of a two-phase TA15 titanium alloy. The flow softening can not be rationalized by dynamic recrystallization. Instead, the increase of mobile dislocations during deformation is an important reason for flow softening. The grain boundaries (including the α-β interfaces) act as an important source for the generation of mobile dislocations. The continuous flow softening results from the significant deformation heterogeneity in subtransus working.

Radial-axial ring rolling process is an irreplaceable metal forming technology for manufacturing various seamless rings. However, during the process, there exists complex interaction of deformations in the radial and axial directions of the ring, so the coordinate deformation between radial and axial directions has crucial influences on the quality of the rolled ring. In this paper, a reliable FE model based on in-process control for the radial-axial ring rolling process has been established under the ABAQUS/Explicit platform. In this model, the motions of the rolls are real-time controlled based on in-process measurement. Then, taking the ratio of axial to radial feed amount as the key parameter, we explored the effects of the coordinate deformation between radial and axial directions on the radial-axial rolling of sleeve-type rings by FE simulations. It is found that the rational diameter growth rates become fewer for making the sleeve-type ring roundness stay well as the ratio of axial to radial feed amount decreases. The ratio of axial to radial feed amount has slight effects on the precision of the ring diameter when the diameter growth rate is large. With the ratio of axial to radial feed amount increasing, the deformation of the sleeve-type ring becomes more nonuniform, while the temperature distribution becomes more uniform.

Investigation of macro–micro dynamic mechanical behavior of aluminum alloys is crucial to understand and model high velocity forming processes, e.g. the electromagnetic forming. Therefore, this work presents the experimental investigation of the macro–micro dynamic deformation behavior and related mechanisms of 5A0X alloys. With increasing strain rate, notable hardening and serrated flow curves are observed for both 5A06 and 5A02 alloys; the flow softening ratio increases from 10.59% to 15.56% for 5A06 alloy, while increasing up to 34.55% at a strain rate of 3000 s−1 for 5A02 alloy. High velocity deformation enhances the ductility of both the alloys via slowing down the neck development rather than suspending the onset of necking. Comparative study in dynamic tensile/compressive behavior of 5A06 alloy indicates a similar hardening rule in these two loading conditions, however, more obvious softening is found in tension than that in compression. The difference can be attributed to the different microstructure-related characteristics, namely, the diffuse necking related to void evolution in tension and the adiabatic shear bands (ASB) in compression. In addition, a mathematical model is used in this work to corroborate the occurrence of ASBs and to predict the half width of ASBs, which is proved reliable by experiments.

The heat rotary draw bending of large-diameter thin-walled (LDTW) commercial pure titanium (CP-Ti) tube is a highly nonlinear thermo-mechanical coupled physical process. Developing a reliable finite element (FE) model for this process is an effective way to investigate the heat loading and the complex bending behaviors. In this study, considering the characteristics of multi-die constraints and local heating, a thermo-mechanical 3D-FE model was established for preheating and heat bending of LDTW CP-Ti tube in terms of both accuracy and efficiency. First, using the static implicit algorithm, a preheating model was developed to predict the temperature distribution of bending tools. In this model, the key issues such as the full-sized geometry modelling, thermal interaction definition, and automatic heating control were solved to increase the simulation accuracy and efficiency. Then, introducing the predictions of preheating model and using the dynamic explicit algorithm, a thermo-mechanical coupled 3D-FE model was established for the heat bending simulation via the geometry modelling simplification, temperature definition of bending tools, realization of non-uniform temperature distribution, etc. Considering the temperature history of bending tools and wall thickness changing of bent tube, the reliability of preheating model and heat bending model was verified by several experiments. The results showed that the maximum relative errors of both predicted temperature and wall thickness changing degree were less than 9 %. Based on the reliable models, the effects of preheating temperature on the temperature distribution of bending tools and wall thickness changing of tube were numerically evaluated. The established model provides the scientific basis for the prediction and control of bending qualities of the heat RDB process, and the modeling method is also of general significance to the other heat-aided forming process.

Quantitative characterization of lamellar and equiaxed alpha phases in (α + β) titanium microstructures is needed to investigate how the microstructure affects the mechanical properties. However, the complex touching features between the lamellar and equiaxed alpha of the microstructure make quantitative analysis challenging. To overcome this problem, a four-level procedure for separating touching features, which includes image pre-processing, concave points detection, splitting line determination, and lamellar and equiaxed alpha discrimination, has been proposed to automatically process many microstructures. Moreover, a set of criteria was established for each level to handle various problems caused by the complexity of how lamellar and equiaxed alpha can touch each other. The result on a representative microstructure of a (α + β) titanium alloy, a tri-modal microstructure, shows that the approach works well and is robust. Based on this effort, the phase distributions of the tri-modal microstructure were quantified through two-point and lineal-path correlation functions based on the newly developed, efficient algorithms. Significant heterogeneity and morphological anisotropy in different directions and ranges of the lamellar and equiaxed alpha were quantitatively measured.Highlights► A novel four-level approach to automatically split touching features was proposed. ► Lamellar and equiaxed alpha touching in complex manner were separated automatically. ► Anisotropy in morphology and distribution of lamellar and equiaxed alpha was quantified.

This paper investigates the substructure and texture evolution of a near-α titanium alloy Ti–6Al–2Zr–1Mo–1V (TA15) during isothermal hot compression in an α + β two-phase field. The microstructures of deformed samples were analyzed using an electron backscatter diffraction (EBSD) technique to study the effects of process parameters on the evolution of substructure and texture. The activated energy and the stress exponent were calculated to identify the deformation behaviors and the softening mechanisms. The experimental results showed that the transformation of low angle boundaries (LABs) to high angle boundaries (HABs) was sensitive to strain rate, strain and temperature. The volume fraction of the HABs increased with the increasing strain rate or strain but decreased with increasing temperature. During the transformation process, the dislocations inside the subgrains and around the subgrain boundaries were annihilated by dislocation reaction and absorption. The transformation of the LABs into HABs significantly influenced the flow stress during the thermomechanical processing. With the increase of strain or temperature, the texture in the alpha phase became weaker and the pyramidal slip systems began to be activated, while the texture in the beta phase tended to be stronger with more plastic deformation.

Grain coarsening of titanium alloys takes place easily at high temperatures, which significantly affects the mechanical properties of the material. In this study, the coarsening mechanisms and kinetics of the Ti-6Al-2Zr-1Mo-1V (TA15) alloy in the (α + β) two-phase field were investigated by heat treatment experiments. The experimental results showed that the microstructural morphology evolved from the cuboidal, rod-like, or plate-like at the initial stages to the equiaxed or spherical. The coarsening mechanism was different at different temperature. At lower temperature (900 °C), the coarsening exponent (n) was close to 4.1. This indicated that the coarsening process was controlled by diffusion along grain boundaries. At higher temperatures (940 and 970 °C), the values of n were equal to 3.2 and 3.3, respectively. It could be concluded that the coarsening processes were mainly controlled by diffusion through the matrix. Furthermore, the activation energy of diffusion (Qact) and the coarsening rate constant (K) were calculated and compared with the theoretic values. That confirmed the coarsening mechanism mentioned above.

Large diameter thin-walled (LDTW) commercial pure titanium (CP-Ti) bent tubes are widely used in the pneumatic system of commercial airplane. Understanding and modeling the temperature and strain rate dependent quasi-static tensile behaviors are fundamentals for the improvement of bending formability of LDTW CP-Ti tubes. With the LDTW CP-Ti tube of 76.2 mm×1.07 mm (D×t, D-outer diameter, t-wall thickness, D/t=71.2) as the objective, uniaxial tensile tests were conducted under various temperatures (298–873 K) and different strain rates (10−3–10−2 s−1). The major results show that: (1) The flow stress of LDTW CP-Ti tube becomes less temperature dependent at 473–573 K, and the positive effect of strain rate on the flow stress is not obvious at 523–773 K. These results are interpreted in terms of dynamic strain ageing. (2) The fracture elongation of LDTW CP-Ti tube can be greatly improved at 873 K, but the ductility decreases with the increase of temperature at 573–773 K, which is considered as “blue brittle” phenomenon. (3) The strain hardening exponent of the LDTW CP-Ti tube increases from 0.073 to 0.155 as the temperature increases from 373 K to 573 K, and the increased strain hardening exponent has positive effect on the improvement of bending formability of the LDTW CP-Ti tube. Then, at the temperature range of 298–573 K, by introducing a quadratic function of the reciprocal of temperature and the semi-log scale of strain rate, a group of new equations for strain hardening exponent, strain rate sensitivity parameter and strength coefficient were proposed based on Fields–Bachofen(FB) equation; comparing the predicted results with the experimental data, the proposed constitutive models present a good estimate of the quasi-static flow stress for the CP-Ti tube, and the largest mean error is 3.66%.

A cellular automata (CA) method was employed to model static coarsening controlled by diffusion along grain boundaries at 1173 K and through the bulk at 1213 and 1243 K for a two-phase titanium alloy. In the CA model, the coarsening rate was inversely proportional to the 3rd power of the average grain radius for coarsening controlled by diffusion along grain boundaries, and inversely proportional to the 2nd power of the average grain radius for coarsening controlled by diffusion through the bulk. The CA model was used to predict the morphological evolution, average grain size, topological characteristics, and the coarsening kinetics of the Ti-6Al-2Zr-1Mo-1V (TA15) alloy during static coarsening. The predicted results were found to be in good agreement with the corresponding experimental results. In addition, the effects of the volume fraction of the α phase (Vf) and the initial grain size on the coarsening were discussed. It was found that the predicted coarsening kinetic constant increased with Vf and that a larger initial grain size led to slower coarsening.

Substructure evolution significantly influences the flow behavior of titanium alloys in isothermal hot compression. This paper presents a physical experiment (isothermal hot compression and electron backscatter diffraction, EBSD) and a cellular automaton (CA) method to investigate the substructure evolution of a near-α titanium alloy Ti-6Al-2Zr-1Mo-1V (TA15) isothermally compressed in the α + β two-phase region. In the CA model, the subgrain growth, the transformation of low angle boundaries (LABs) to high angle boundaries (HABs) and the dislocation density evolution were considered. The dislocation density accumulating around the subgrain boundaries provided a driving force and made the transformation of the LABs to HABs. The CA model was employed to predict the substructure evolution, dislocation density evolution and flow stress. In addition, the effects of strain, strain rate and temperature on the relative frequency of the HABs were analyzed and discussed. To verify the CA model, the predicted results including the relative frequency of the HABs and the flow stress were compared with the experimental values.

The static globularization behavior and mechanism of transformed structure during heat-treatment of hot worked TA15 alloy were investigated. It is found that boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. Boundary splitting is significant in the initial stage of annealing while coarsening occurs throughout the annealing process. Static globularization kinetics increases with annealing temperature and prestrain, but is independent on strain rate. The rate of static globularization kinetics decreases with annealing time. The asymptotic equation can be used to model the static globularization kinetics.Highlights► Boundary splitting and microstructure coarsening are two competing mechanisms for static globularization. ► Static globularization kinetics is found to increase with annealing temperature and prestrain, but to be less dependent on strain rate ► The asymptotic equation can be used to model the static globularization kinetics.

Hot ring rolling is a preferred technology for manufacturing high-quality titanium alloy rings. During the process, the material undergoes complex microstructure evolution which determines the mechanical properties of the rolled ring. In this study, an internal state variable microstructure model for the hot working of TA15 titanium alloy is implemented into the 3D-FE model of hot ring rolling process under ABAQUS environment to realize multi-scale simulation of the process. Then the effects of deformation degree and initial forming temperature on the microstructure of TA15 titanium alloy in hot ring rolling are investigated numerically. The results show that: (1) with increasing deformation degree, the volume fraction and grain size of primary α phase in the ring both decrease, and the primary α phase distribution becomes more nonuniform while the primary α grain size distribution becomes more uniform; (2) with increasing initial forming temperature, the volume fraction and grain size of primary α phase both decrease, and the uniformity of primary α phase distribution gets better first and then worse while the uniformity of primary α grain size distribution gets better; and (3) in order to obtain uniform distributions of both primary α phase and grain size, an optimum process condition for hot ring rolling of TA15 titanium alloy is suggested to be the deformation degree of 0.25–0.35 and the initial forming temperature of 930–940 °C. The results can serve as a guide to the microstructure control, blank size design and processing parameter optimization for hot ring rolling of titanium alloy.Highlights► α phase distribution of ring becomes more nonuniform with deformation degree. ► α grain size distribution becomes more uniform with deformation degree. ► There is optimum initial forming temperature for obtaining uniform microstructure. ► α grain size distribution becomes more uniform with initial forming temperature.

In this paper, the microstructure evolution and processing–microstructure relationship in the non-isothermal local loading forming of TA15 titanium alloy were studied through an analog experiment. Some new microstructural mechanisms are found, which are different from those under isothermal local loading forming. In the non-isothermal local loading forming, the tri-modal microstructure consisted of equiaxed primary α, lamellar α and β transformed matrix is achieved. The lamellar α, not produced under isothermal condition, is generated by β → α transformation due to the decrease of component temperature. With the same processing parameters, the volume fraction and grain size of primary α are both greater than those processed isothermally. The content of lamellar α decreases with heating temperature decreasing and little lamellar α can be found when the heating temperature drops to 930 °C. Under small deformation degree, the lamellar α distributes randomly in each feature region. As deformation increases, the lamellar α in transitional region and second-loading region present a preferred orientation perpendicular to the compression direction. The primary α content almost decreases linearly with heating temperature, which is different from the regular that under isothermal condition. Non-isothermal local loading forming with a higher heating temperature (near-β region) offers a cost-efficient way for the manufacture of TA15 titanium alloy large-scale integral components.Highlights► Tri-modal microstructure is obtained in the non-isothermal local loading forming. ► The lamellar α content decreases with the heating temperature decreasing. ► The primary α content almost decreases linearly with the heating temperature. ► Non-isothermal local loading of TA15 alloy should be conducted in near-β region.

The constraining effects of the weld and heat-affected zone (HAZ) material in welded tube numerical control (NC) bending process are key problem to be solved in the research, development and application of thin-walled welded tubes. To investigate the constraining effects of the weld and HAZ material on the tube bend formability, finite element (FE) model with weld and subdivided HAZs, model with weld-only and model with parent metal alone under ABAQUS platform are employed. The results show that: (1) the weld and HAZ material have obvious constraining effects on the strain distributions in weld and HAZ as the weld line locates on the outside and inside of the bend, meanwhile, the cross-sectional deformation becomes more severe as the weld line locates on the outside; (2) as the weld line locates on the outside, the constraining effects of the weld and HAZ material make the tangent strain and thickness strain decrease, the hoop strain increase in the weld and HAZ, the cross-sectional deformation increase and the wall thinning decrease as compared with model that contains parent metal alone; (3) the constraining effects of the weld and HAZ material are minimal as the weld line locates on the middle of the bend.Highlights► The implementation of weld and HAZ in FE model can reflect the constraining effect. ► Constraining effect of weld joint is great as weld locates in large strain region. ► Constraining effect increases with larger bending angle and bending radius. ► Constraining effect of weld joint makes the cross-sectional deformation decrease.

Stress-relieved Ti–3Al–2.5V bent tube in hydraulic bleeding systems improves the overall performance of advanced aircraft and spacecraft due to its unique high specific strength. However, the high ratio of yield strength to Young's modulus may induce significant elastic recovery after unloading. The precision bending of the high strength Ti-tube (HSTT) depends on the understanding of the springback features and mechanisms. Using the plasticity deformation theory, the explicit/implicit 3D-FE and the physical experiments, the springback behaviors of the HSTT under multi-die constrained cold rotary draw bending (RDB) are addressed. The results show that: 1) The elastic recovery of the HSTT should be characterized by the significant angular springback, the radius growth and the sectional springback; Both the angular and radius springback should be compensated, while the sectional one decreases the cross-section flattening; 2) Among multiple parameters, both the material properties (Young's modulus, strength coefficient and anisotropy exponent) and the geometrical dimensions (bending angle and bending radius) dominate the unloading; Both the angular and radius springback values decrease with the smaller bending radii; The angular springback increases linearly with the larger bending angles, while the radius growth fluctuates little with the increasing of the bending angles at the later bending stages; Both the springback values of the HSTT are far larger than the ones of the 5052O Al-alloy tube and the 1Cr18Ni9Ti tube; The maximum variations of the angular and radius springback with changing of the processing parameters are 78% and 62.5% less than the maximum ones under different material properties and geometrical ones, respectively. 3) A two level springback compensation methodology is proposed to achieve the precision bending in terms of both springback angle and radius.Graphical abstractTwo level springback compensation methodology for HSTT in RDB.Highlights► The significant springback is studied for high-strength Ti–3Al–2.5V tube (HSTT) in cold bending. ► The springback of HSTT should be characterized by angular, radius and cross-section springback. ► Both the material properties and the geometrical dimensions dominate the unloading. ► The contribution of the processing parameters on springback is relatively little. ► A two level springback compensation method is proposed to achieve the precise bending.

Isothermal local loading (ILL) forming technology provides a new way to form largescale rib-web (LSRW) components of Ti-alloy, widely used in the aero-space fields as key load-bearing structures. However, the metal undergoes complex plastic inhomogeneous deformation and microstructural evolution, this will lead to macroscopical forming defects and further damage due to multi-process parameters and local loading method, making the process and forming quality hard to control. Using numerical simulation, combined with experiment, influences of various process parameters on forming process, inhomogeneous deformation and damage have been explored for ILL of LSRW components, such as the types of die-forging mode, frictional conditions, and local loading parameters (partitioning of the loading zone, constraint conditions, and loading pass). Then the reasonable forming conditions for LSRW components of Ti-alloy to be studied are proposed. The practical forming experiment of TA15 LSRW component was achieved successfully and the forging with good forming quality, excellent microstructure, and comprehensive mechanical properties was obtained, which indicates the reliability and practical value of results obtained in this article.

Control of microstructure morphology in isothermal local loading of titanium alloys is important to obtaining high performance components. To this end, the effect of thermo-mechanical processing on the microstructure development of TA15 alloy during isothermal local loading was experimentally investigated. It is found that bi-modal or equiaxed microstructure can be achieved when the heating temperature of the last loading step is not lower than that of the previous loading step. The volume fraction of primary alpha phase and the morphology of transformed beta matrix are determined by heating temperature and cooling rate in the last loading step, respectively. Tri-modal structure can be achieved by near-beta forging followed by conventional forging in the last loading pass. The volume fraction of each constituent phase in tri-modal structure is determined by the heating temperatures of the last two loading steps. The emergence of secondary alpha platelets in beta phase is promoted by increasing the heating temperature or cooling rate of the last loading step. Globularization of alpha lamellae can be avoided by thickening the alpha laths or decreasing the deformation degree in the last loading pass.Highlights► Equiaxed, bi-modal and tri-modal structures can be obtained in local loading. ► Increasing temperature or cooling rate promotes formation of secondary α in β phase. ► Heating temperatures of the last two steps determine the fraction of each phase. ► Decreasing deformation in the last step prevents globularization of α lamellae.

Static coarsening is an important physical phenomenon that influences microstructural evolution and mechanical properties. How to simulate this process effectively has become an important topic which needs to be dealt with. In this paper, a new cellular automaton (CA) model, which considers the effect of solute drag and anisotropic mobility of grain boundaries, was developed to simulate static grain coarsening of titanium alloys in the beta-phase field. To describe the effect of the drag caused by different solute atoms on coarsening, their diffusion velocities in beta titanium were estimated relative to that of titanium atoms (Ti). A formula was proposed to quantitatively describe the relationship of the diffusion velocity of Ti to that of solute atoms; factors influencing the diffusion velocity such as solute atom radius, mass, and lattice type were considered. The anisotropic mobility of grain boundaries was represented by the parameter c0, which was set to 1 for a fully anisotropic effect. These equations were then implemented into the CA scheme to model the static coarsening of titanium alloys Ti-6Al-4V, Ti17 (Ti-5Al-4Mo-4Cr-2Sn-2Zr, wt%), TG6 (Ti-5.8Al-4.0Sn-4.0Zr-0.7Nb-1.5Ta-0.4Si-0.06C, wt%) and TA15 (Ti-6Al-2Zr-1Mo-1V, wt%) in the beta field. The predicted results, including coarsening kinetics and microstructural evolution, were in good agreement with experimental results. Finally, the effects of time, temperature, and chemical composition on grain coarsening and the limitations of the model were discussed.

In this paper, an analogue experiment was carried out to study the effect of processing parameters including deformation temperature, deformation degree, cooling mode and loading pass on the microstructure of transitional region under isothermal local loading forming of TA15 titanium alloy. The volume fraction, grain size and aspect ratio of primary α phase of transitional region were quantitatively characterized. It is found that deformation temperature and deformation degree also have interaction on the microstructure evolution of transitional region under isothermal local loading forming. At a certain deformation degree, primary α grain size increases first and then decreases with increasing temperature. However, primary α grain size varies little with deformation degree at higher temperature (in upper two phase region) but increases firstly and then decreases with deformation degree at lower temperature (in lower two phase region). Primary α aspect ratio increases with deformation degree at lower temperature but varies little at higher temperature. The morphology of transformed structure in β matrix is greatly influenced by deformation temperature and less influenced by deformation degree under air-cooling. The precipitated Widmanstatten α phase in β matrix is in lamellar form and arranges in colonies under air-cooling, but it is in thinner acicular form and distributes disorderly under water quenching. Loading pass has little influence on the morphology of microstructure.Research highlights► Local deformation path has little effect on microstructure morphology and features. ► Deformation temperature and degree have interaction on the microstructure evolution. ► Cooling mode has effect on the morphology of transformed structure in β matrix.

The rolls and stand deflections induced by rolling force lead to a significant decrease in the radius prediction accuracy of the ring product in the in-plane roll-bending of strip. To precisely predict the deflections and control the radius, a new analytical model is developed. Numerical implementation is presented to solve the theoretical rolling force, the deflections as well as the inherent force–deflection relationship considering the interactions of the strip workpiece, the rolls and the stand. A series of profile measurements of the formed ring parts are made to assess the accuracy of the predicted deflections. Different control approaches are used in the experiments to validate the radius control model. The experimental results show that the model is reliable to control the radii with a maximum relative error of 10.4% deviating from the desired ones. By considering the rolls and stand deflections, the prediction accuracy of the radii of most aluminum alloy AA-3003O rings is improved by 65.9–159.9%.Highlights► An analytical model for precision control of the radius in in-plane roll-bending of strip considering the rolls and stand deflections is developed. ► The force–deflection relationship is determined with considering the interactions of the strip workpiece, the rolls and the stand. ► Almost 65.9–159.9% improvement in prediction accuracy of the radii of most aluminum alloy AA-3003O rings is achieved by applying the radius control model.

The mechanical characteristics of the weld joint were investigated by tensile test, microstructure test, and microhardness test. The welded tube NC bending tests were carried out to evaluate the weld on the formability of the QSTE340 welded tube. The results show that the wall thinning degree, cross-sectional deformation and springback angle increase significantly as the weld line is located on the outside of the bend compared with that located on the middle and inside, and the welded tubes produce nearly identical performance as the weld line is located on the middle and inside. The wall thickening degree decreases much as the weld line is located on the inside of the bend. So the welded tube can acquire good bending formability as the weld line is located in the region away from the outside of the bend.

Cellular automata (CA) algorithm has become an effective tool to simulate microstructure evolution. This paper presents a review on CA modeling of microstructural evolution, such as grain coarsening, recrystallization and phase transformation during metal forming process which significantly affects mechanical properties of final products. CA modeling of grain boundary motion is illustrated and several aspects of recrystallization are described, e.g. nucleation and growth, the development of static and dynamic recrystallization. For phase transformation, attention is paid to such key factors as solute element diffusion and change of systemic chemical free energy. In view of the reviewed works, several open questions in the field of further development of CA simulation are put forward and recommendations to them are given.

The rapid development of aviation and aerospace technologies has led to increased interest in the application of numerically controlled (NC) technology for bending light-weight titanium alloy tubes. In order to study and develop advanced NC bending technology, it is necessary to understand the bending performance of medium strength TA18 (Ti-3Al-2.5V, ASTM Gr. 9) titanium alloy tubes during NC bending under different die sets. This paper focuses on the bending performance of medium strength TA18 tubes under different NC bending die sets, including the variations in the stress, strain, wall thickness, cross sectional deformation, and defects. The results show that adding a wiper die to the base die set decreases the radial, hoop, and tangential compressive stress and the tangential compressive strain, and adding a mandrel to the base die set also decreases these stresses, but increases the radial and hoop tensile stress and decreases the hoop compressive strain obviously, and brings about a three-dimensional tensile stress concentration where the mandrel provides support. For the NC bending of medium strength TA18 tubes, the flattening of cross section is more sensitive index than the thinning of wall thickness. Introducing a mandrel can improve the flattening of cross section obviously but it has a little worse effect on the thinning of wall thickness, and adding a wiper die to the base die set can inhibit the occurrence of the inside bulge but worsen the flattening of the cross section remarkably. Considering the above effects of the mandrel and wiper die on bending performance, it is reasonable to apply the die set comprising a bending die, clamp die, and pressure die for tubes with a small diameter and the die set including an appropriate mandrel additionally for tubes with a larger diameter, in order to bend the medium strength TA18 tubes with high quality and at low cost.

AbstractThe rotary draw bending(RDB) of large diameter thin-walled (LDTW) tube needs the strict cooperation of multiple processing parameters to avoid possible multiple defects. Due to the specific properties, the bending behaviors of LDTW commercial pure titanium (CP-Ti) tube are much more complex to achieve precise deformation. With the CP-Ti tube of 50.8 mm (out diameter, D)×0.508 mm (wall thickness, t)×101.6 mm (bending radius, R) as a representative component, the bending behaviors of LDTW CP-Ti tube under different processing conditions were investigated. With experiments and analytical analysis, the bending characteristics of the CP-Ti tube were identified. Then, based on the orthogonal experimental design, a series of three-dimensional FE models of RDB for LDTW CP-Ti tube were established, and the effects of processing parameters on the bending behaviors were numerically investigated. The results show that: 1) Wrinkling is the primary behavior for the LDTW CP-Ti tube in RDB, and the larger the difference between the maximum wall thickening and the maximum wall thinning degrees of the bent tube, the larger the wrinkling tendency; 2) The bending behaviors of the LDTW CP-Ti tube are very sensitive to the some processing parameters, and the wrinkling is significantly affected by the mandrel shank diameter, while the wall thinning is remarkably affected by the clearance between wiper die and tube, mandrel shank diameter. The qualified bent tube with the wall thinning of 11.43%, the cross-section distortion of 2.69% and the wrinkling height less than 2% is then obtained.

A large-scale rib-web component may be considered as a combination of many T-shaped components which can reflect forming characteristics of large-scale rib-web components by local loading. So exploring the material flow and filling law of the T-shaped components local loading forming is important for parameter optimization and process control of local loading forming processes of rib-web components. With the help of reasonable assumptions and simplifications, the slab method (SM) is used to analyze the isothermal forming process of titanium-alloy T-shaped components under local loading in this paper. The process of local loading forming and the characteristics of material deformation are analyzed, and two deformation patterns under local loading are found by using the physical experiment. Mathematical models of loading force, rib height (depth of cavity filling) and the position of neutral layer in loading process are established by using the slab method. Calculation-program for models is developed under MATLAB environment, and then the loading force, rib height and position of neutral layer are predicted. The comparison of the SM results with the experimental and FEM results indicates that the models established based on the slab method are reliable. The reasonable parameters determined by using the mathematical models, such as the width of punch, the thickness of billet, the reduction amount etc., may provide a basis for analysis of local loading forming for large-scale rib-web components.

By using FE method combined with experimental method, the power spinning processes of conical parts with transverse inner rib under different processing parameters are investigated. It is found that three kinds of typical plastic deformation behaviors, namely, under-filled, full-filled and unstable plastic deformation behavior occur in the forming process; the under-filled plastic deformation behavior has two different deformation modes; clearance between forming roller and mandrel and feed rate of forming roller are the two decisive factors influencing the plastic deformation behavior. Based on the study of plastic deformation behaviors, reasonable range of processing parameters for obtaining desired transverse inner rib is determined. Further, combining with the effects of processing parameters on the degree of inhomogeneous deformation and surface quality of finished spun parts, the rules for selecting reasonable processing parameters in power spinning process of conical parts with transverse inner rib are established for the first time. Then, reasonable values of processing parameters for a given process are determined, and desired spun parts with transverse inner rib are successfully obtained in experiment.

With increasing diameters of aluminum alloy thin-walled tubes (AATTs), the tube forming limits, i.e. the minimum bending factors, and their predictions under multi-index constraints including wrinkling, thinning and flattening have been being a key problem to be urgently solved for improving tube forming potential in numerical control (NC) bending processes of AATTs with large diameters. Thus in this paper, a search algorithm of the forming limits is put forward based on a 3D elastic-plastic finite element (FE) model and a wrinkling energy prediction model for the bending processes under axial compression loading (ACL) or not. This algorithm enables to be considered the effects of process parameter combinations including die, friction parameters on the multi-indices. Based on this algorithm, the forming limits of the different size tubes are obtained, and the roles of the process parameter combinations in enabling the limit bending processes are also revealed. The followings are found: the first, within the appropriate ranges of friction and clearances between the different dies and the tubes enabling the bending processes with smaller bending factors, the ACL enables the tube limit bending processes after a decrease of the mandrel ball thickness and diameters; then, without considering the effects of the tube geometry sizes on the tube constitutive equations, the forming limits will be decided by the limit thinning values for the tubes with diameters smaller than 80 mm, while the wrinkling for the tubes with diameters no less than 80 mm. The forming limits obtained from this algorithm are smaller than the analytical results, and reduced by 57.39%; the last, the roles of the process parameter combinations in enabling the limit bending processes are verified by experimental results.

Hot rolling of a large ring of titanium alloy (LRT) is a highly nonlinear incremental forming process with coupled mechanical and thermal behaviors (MTBs) which significantly affect microstructure and properties of the ring. In the study, a 3D coupled thermo-mechanical FE model of the process is developed and validated. Reasonable ranges of key process parameters are determined for successful simulation. Investigation and comparison are performed regarding the MTBs of LRTs with different blank sizes and the dependence of the MTBs on key process parameters using dynamic explicit FE simulation. The results obtained show that: (1) at the stable forming stage, along the radial direction of an LRT, the largest equivalent plastic strain (PEEQ) is found on the inside or outside surface, depending on the distribution ratio of feed amount. The smallest PEEQ appears in the middle layer. The highest temperature occurs in the interior of the inside or outside layer, depending on the mechanical behavior. The lowest temperature is found on the inside or outside surface, or on the end plane of the middle layer. (2) For LRTs with different blank sizes, effects of key process parameters on their MTBs are similar under different forming conditions, i.e., under the stable forming condition, a smaller n1, a larger v, or a higher T0 contributes to more uniform strain and temperature distributions.

With respect to wrinkling, wall thinning and cross section deformation, combined with analytical description, the deformation behaviors of thin-walled tube NC bending with large diameter D/t (50.0–87.0) and small bending radius Rd/D   (1.0–2.0) are explored via a series of reliable 3D-FE models under ABAQUS platform. The results show that: (1) The segmentation feature is observed for the deformation fields such as effective compressive/tensile regions τc/τtτc/τt, stress/strain distributions, wrinkling tendency, wall thinning and cross section deformation. With smaller Rd/D  , the tangent stress increases and becomes more inhomogenous. The maximum tangent stress σφσφ at the intrados increases by 46% with Rd/D   from 2.0 to 1.2. While the distributions of σφσφ are nearly similar with larger D/t. With smaller Rd/D and larger D/t  , the velocity variation of tube materials becomes more obvious. (2) The wrinkling tendency and cross section deformation degree ΔDΔD increase with smaller Rd/D and larger D/t; With smaller Rd/D, both the wall thinning and thickening degrees increase. The maximum wall thinning and thickening degrees increase by 24.0% and 52.5%, respectively. However, with larger D/t, the wall thinning degree increases, while the thickening degree decreases significantly. The maximum wall thinning degree increases by 31.3%, while the maximum thickening one decreases by 58.9%.

3D-FE simulation has become an indispensable approach to develop advanced ring rolling technologies, and a perfect 3D-FE ring rolling model is the basic demand of the simulation. How to control the movement of guide rolls reasonably in the model is one of the key problems urgently to be solved, particularly for rings complicated in shape or large in dimension or with high precision. In this paper, a method to control the guide rolls by the hydraulic adjustment mechanism is explored and realized in 3D-FE ring rolling model for the first time, and the key technologies, such as the parameter design of the linkage assembly and critical pressure of the hydraulic ram, are also proposed. Moreover, the difficulty in determining the liquid flow rate out of the hydraulic ram is solved by combining dichotomy with numerical simulation results. Based on the elastic–plastic dynamic finite element method under the ABAQUS software environment, the 3D-FE cold ring rolling model with hydraulic adjustment mechanism has been built, and the side spread of rectangular-section rings and the final section configuration of T-shaped ring have been analyzed. Good agreements between the calculating results and experimental ones prove the validity of the improved cold ring rolling model, and consequently the developed guide roll control method is also valid. Meanwhile, the circularity and oscillation of ring show that the rings are kept circular and stable very well during the process. Therefore the guide roll control method developed is suitable and reliable, particularly for rings complicated in shape or large in dimension or with high precision.

Backward simulation using the finite element method (FEM) is an important approach for preform design. Different preforms can be obtained by imposing different dynamic boundary conditions in the backward simulation. In this paper, boundary conditions in the backward simulation are controlled by altering the time of boundary node separating from dies. And the relative non-uniform deformation degree is adopted to assess the preform design for deformation uniformity. Preform designs for the forging process of an airfoil section blade were obtained by using backward simulation approach and the influence of dynamic boundary conditions on preform design for deformation uniformity was investigated. The results are the followings: (1) shorting the separating time by a constant proportion leads to the slight change of the relative non-uniform deformation degree, which has a little effect on preform design for deformation uniformity; (2) decreasing the separating time of the nodes with large equivalent strain and increasing the separating time of the nodes with small equivalent strain simultaneously lead to the decrease of the relative non-uniform deformation degree, which may benefit the preform design.

The splitting spinning which is designed to split a rotational disk blank into two flanges, is one of newly rising, green flexible forming technologies, and it can be widely applied to manufacture a whole pulley or wheel in fields of aerospace, automobile and train. The investigation of forming parameters influencing on splitting spinning force can provide the foundation for the choice of equipments, the design of dies and the determination of processing parameters. This paper aims at developing a reasonable formula between splitting spinning force and forming parameters by the principal stress method, and then the reliability of the formula is verified by the comparisons with experimental data. Meanwhile, both a reasonable method of calculating the three-dimensional projected areas and a more effective method of solving the average angle in the deformation zone are presented. Furthermore, based on the formula, the laws of initial thickness and initial diameter of workpiece, diameter and splitting angle of splitting roller and feed ratio of splitting spinning influencing on splitting spinning force are investigated. The achievements may serve as an important guide for the determination and optimization of forming parameters of splitting spinning.

In this paper, based on the establishment of a reasonable mechanics model for a typical draw-spinning, research on the first pass of the spinning process is carried out with an elasto-plastic FEM method. The distributions of the stress and strain are obtained under three types of roller-trace curves: straight lines, involute curves and quadratic curves. The distribution laws of the radial and tangential stress that are obtained can serve as a significant guide to determining the forming limits in multi-pass conventional spinning under different roller-traces. Comparison of the distributions of strain and stress of three roller-traces could provide a theoretical basis for selecting a reasonable roller-trace in multi-pass conventional spinning.

•A unified model considers interaction of stress response and micro-defects evolution in HSRF.•Defects-related softening was modeled with evolutions of ASBs and voids.•Competition between thermal activated hardening and defects-induced softening was quantified.•Low or negative strain rate sensitivity was captured under high-strain-rate deformation.High strain rate forming (HSRF) is promising to break through the conventional forming limit of materials and thus to form hard-to-deform components. During HSRF process, long-lasting micro-defects before fracture, i.e. adiabatic shear bands (ASBs) in compression and voids in tension, are significant characteristics existing in a large strain range. These defects bring about the non-destructive softening of stress and continuous exertion of ductility, in return, the stress responses affect the evolution of micro-defects. However, the interaction between stress responses and defects evolution has not yet been reflected in the existing models, resulting in a limited prediction accuracy. Aiming at this issue, the competition between hardening caused by thermal activated dislocation movements and the flow softening brought by micro-defects evolution was well modeled in this work. During the modeling, the relation between the normal strain and effect zone of ASBs was established via the modification of Bai–Dodd model by considering the geometric features of ASBs. Moreover, by introducing a rate-dependent ASB trace angle, the half width of ASBs was expressed as a function of maximum shear strain and critical instability strain. The effect of strain and strain rate to the evolution of voids under tensile conditions was taken into account by combining Hollomon hardening law with Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. Then, the interactions between micro-defects and structure-related athermal stress were characterized by connecting volume fraction of voids and effective bearing area in tension and the intensity of flow localization with ASBs width in compression. As a consequence, a unified model of constitutive behaviors coupled with micro-defects evolution was established with considering rate-dependent hardening and softening. Applied to aluminum alloys, this model predicts the stress responses, evolution of ASBs and voids, and low or negative strain rate sensitivity with high precision in large ranges of strain (0–0.6) and strain rate (0.001–5000 s−1). The proposed model is thus believed to be with a successful application in precise prediction and optimization of HSRF processes.

•Three slip modes and two twinning modes dominate anisotropy and asymmetry of Ti-tube.•A Knoop indentation-based method for evaluating anisotropic characteristics of tubular materials.•A compression based orthogonal inverse method is used to calibrate VPSC parameters.•Correlation among deformation mode, texture evolution and distorted plasticity is constructed.•Texture evolution is tailored by allocating 3D plastic flow for bespoke tube property.The coupling effects of low asymmetry of HCP structure and transient non-uniform stress/strain states during multi-pass deformation processing cause a great variation in crystallographic orientation of titanium tubes, which may induce anisotropic/asymmetrical behaviors and affect the formability and service performance of the materials. The unique plastic deformation and mechanisms under 3D stress need to be accurately and fully understood for integrated design of fabrication and forming of titanium tubular products achieving shape forming and property tailoring simultaneously. How to address this eluded and tantalized issue, however, is still a bottleneck issue. In tandem with this, taking high strength titanium tube (HSTT) as a case, by using macro/meso scaled hybrid methodology, a correlation among loading condition, distorted plasticity and texture evolution of the material is established and articulated: 1) Via Knoop indentation, tension/compression and EBSD, the distorted plasticity of HSTT is identified, and the coupling of three slip and two twinning modes are found to dominate the inhomogeneous deformation, which must be introduced in viscoplastic self-consistent (VPSC) crystal plasticity; 2) A compression-based orthogonal inverse method is used to calibrate the crystal plasticity parameters and validated from various aspects, and the VPSC-based computation is conducted for tubular materials with six typical initial textures under six fundamental loadings; 3) The remarkable distorted plasticity and evolution in strain hardening, strain flow and yield loci are observed for most cases; The interactions among slipping/slipping, slipping/twinning and twinning/twinning coordinate the anisotropic/asymmetrical behaviors and hence induce the distorted evolution of plasticity; The relationship between deformation modes (strain vectors) and texture evolution is constructed, and the tubes with the desired textures and bespoke properties can be tailored in cold rolling by allocating spatial plastic flow.

•A unified continuum-based discontinuous (CBD) framework introducing SSM and SIM.•Calibrating way for CBD framework related to convergence, overlapping and accuracy.•Combination of implicit algorithm and interpolation approach for CBD implementation.•Evaluation of SSM and SIM-based CBD models on describing distorted yield loci.•Correlation among initial textures, distorted behaviors and non-uniform deformation.Characterizing the anisotropy/asymmetry-induced distortional yielding and subsequent evolution is still a challenge for potential usages of hard-to-deform materials. From perspective of multiple mechanisms, two types of yield functions are classified, viz., the principal shear stress-based models (SSM) and the stress invariants-based models (SIM); then a unified continuum-based discontinuous (CBD) framework is constructed, in which SSM and SIM are introduced to capture the distorted shape of the yielding, and an interpolation approach is adopted to smoothly present the nonlinear evolution of the distorted plasticity in the full stress space. Taking the CPB06 (Cazacu et al., 2006) and Yoon's criteria (Yoon et al., 2014) as typical SSM and SIM, the CBD framework is implemented in the explicit 3D-FE platform for practical usages by combining implicit algorithm and interpolation approach, and the Nelder-Mead (N-M) method and the genetic algorithm (GA) approach are evaluated for calibrating of CBD related to convergence, overlapping and accuracy. The evaluation proves that the GA-based method is suitable for CBD, and the SIM seems to be feasible for embedding into the CBD framework because of its solid physical basis and numerical robustness. Taking high strength titanium alloy tube (HSTT) as a case, the distorted plasticity evolution of the HSTT with six typical initial textures are characterized, then the correlations among initial textures, distorted behaviors and inhomogeneous deformation are quantitatively established to improve the multi-defect constrained formability in uniaxial tension/compression and mandrel bending.

Severe numerical instability in the integration of rate dependent crystal plasticity (RDCP) model is one of the main problems for implementing RDCP into finite element method (FEM), especially for simulating dynamic/transient forming process containing complicated contact conditions under large step length, large strain and high strain rate. In order to overcome the problem, an implicit model is deduced with the primary unknowns of shear strain increments of slip systems under the corotational coordinate system in the paper. The homotopy auto-changing continuation method combined with the Newton–Raphson (N–R) iteration is adopted. The subroutine VUMAT is developed for implementing RDCP model in ABAQUS/Explicit. Simulation results show that the algorithm is stable and accurate in 3D FE simulations on both dynamic simple loading and complicated loading process containing nonlinear contacts under the conditions of the maximal step length of 3.5 × 10−6 s, the maximal strain of 1.05, the maximal loading speed of 120 mm s−1, and the minimal material rate sensitivity coefficient of 0.01. The predictions of the model on crystal behaviors of anisotropy, rate sensitivity and elasticity, as well as ear profiles in deep cup drawing are in agreement with experiments.

•A new idea treating DRX as one intrinsic part of constitutive behavior is proposed.•A 3D microstructure-based CACPFEM is created by the full coupling of CA and CPFEM.•Interaction of deformation-microstructure evolution-mechanical response is captured.Dynamic recrystallization (DRX), heterogeneous deformation and mechanical responses at the levels of single grain and grains aggregate concurrently occur and interact with each other in hot-working processes of titanium alloys. The interaction has been partly taken into account in our previous work by creating a crystal plasticity finite element method (CPFEM) with DRX considered, but the morphological characteristics of DRX that are crucial to the performance of the formed part failed to be captured. In addition, the existing visualization approaches (e.g., cellular automata, CA) for modeling the morphology evolution treated DRX as a product of deformation and thus separated the interaction. To address these issues, combining the advantages of the above two methods, this work proposes a new concept by treating the morphological evolution of DRX as one intrinsic part of the constitutive behavior, which is realized by establishing a 3D CACPFEM model through the full coupling of CA and CPFEM. During the modeling, the CA algorithm accounting for the DRX evolution is built into the CPFEM framework that accounts for multiscale heterogeneous deformation. Based on the microstructure-based 3D grids acting as both finite elements and cells and the explicit consideration of grain boundary softening, the heterogeneous deformation and the induced non-uniform distribution of the dislocation density at the levels of the slip system, grain interior and boundary are calculated with CPFEM. The obtained results dominate the evolution of DRX synchronizing with the deformation, which is calculated with CA through a semi-probabilistic switch rule that considers the effects of the deformed grain morphology and misorientation between the adjacent matrix grain and recrystallized grain. The DRX-induced changes in the dislocation density, grain boundary, and grain size are returned to CPFEM to determine the slip resistance of the dislocations. Consequently, not only the mechanical response but also the subsequent plastic deformation is determined. With this model, the coupled effect of the heterogeneous deformation, mechanical response and DRX microstructural evolution during the isothermal compression of the TA15 alloy is well captured and analyzed, which is verified by experiments. It is shown that the framework of this model allows the integrated prediction of the macroscale forming, mesoscale deformation mechanism and microscale microstructural evolution of materials, and that it is capable of being extended and applied to other problems (e.g., phase transformation and lamellar spheroidization) in the hot-working processes of materials.Download high-res image (312KB)Download full-size image

A new crystal plasticity model was proposed for synchronously responding dynamic recrystallization (DRX) and thermomechanical behavior of wrought two-phase titanium alloys. Within the crystal plasticity framework, the theories for dislocation density evolution and DRX were introduced and modified. The shear strain rate of slip system calculated via crystal plasticity was employed to determine the dislocation density of a grain. Dislocation annihilation caused by dynamic recovery was incorporated. The evolution of the dislocation densities in the matrix grain (M-grain) and the recrystallized grain (R-grain) was considered individually, thus, repeated nucleation of the recrystallized grains was permitted. They were considered to take place once the dislocation density of a grain (M-grain or R-grain) reached a critical value. The equivalent dislocation density of the grains aggregate (R-grains and M-grain) was calculated via a volume-averaged approach using the recrystallized fraction. The recrystallized fraction was updated by accounting for the percentage of the grain boundary density of the unrecrystallized matrix. This model was coded as a VUMAT in ABAQUS/Explicit and embedded in the finite element method for the simulation of isothermal compression on a two-phase titanium alloy. The predictions of the model are in good agreement with experimental data of the IMI834 alloy. The synchronous coupling effects of thermal deformation responses and DRX are accounted for, which improves the accuracy of the simulation results, e.g., the maximal error of the predicted steady stress to experiment is 3.1%. Nucleation rate and R-grains growth are quantified under different deformation conditions. The former is far larger (more than 20 times) in the α + β region than that in the β region, and the latter is about 0.55∼0.75 times in the α + β region of that in the β region. The effects that intergranular non-uniform deformation due to grain orientations and interphase non-uniform deformation due to different properties do on DRX are quantified. Nucleation rate and the recrystallized fraction at phase interface are about 4 and 10 times, respectively, of those within the β phase. Nucleation rate at β-grain boundary seems uniform, while, the recrystallized fraction becomes more and more non-uniform with increasing deformation.•A crystal plasticity model for synchronously accounting for DRX and thermomechanics of titanium.•Effects of dynamic recovery and DRX on dislocation density were considered simultaneously.•Repeated nucleation of the recrystallized grains was taken into accounted.

To control the microstructure and performance of large scale complex titanium alloy component by local loading forming, the effect of processing on microstructure in local loading forming was investigated by a through-process finite element model. It is found that the volume fraction of primary equiaxed α decreases with temperature, deformation speed and loading pass. The distribution of α fraction becomes more uniform with decreasing temperature and increasing deformation speed and loading pass. The α grain size increases with temperature and loading pass but decreases with deformation speed. The homogeneity of the grain size can be improved by increasing deformation temperature and loading pass, or decreasing loading speed.

To satisfy the ever increasing demands of high performance and light weight in high-end equipments, the titanium components are designed to have complex shape and specific performance. Research and development of advanced plastic forming technologies are of great importance to manufacturing these titanium products with low cost and short cycle. The local loading forming technology with advantages in reducing forming load, enlarging forming size and enhancing forming limit and precision through control of unequal deformation provides a feasible way to manufacture the high performance and light weight titanium components (large-scale, integral, complex, thin-walled) widely used in aircrafts and shows a good developing prospect. This paper presents the state of the art of local loading forming technology and its applications in manufacturing titanium components in the authors’ laboratory, including the isothermal local loading forming of large-scale complex TA15 bulkhead, and heat rotary draw bending of large-diameter thin-walled titanium tube.