Mechanics lies at the heart of many of the underpinnings of modern technological civilization: materials, infrastructure, transportation, health and security. The mechanics of dynamic failure processes also has a major bearing on the potential catastrophes that threaten civilization, including airbursts and major asteroid impacts. Recent events (such as the Chelyabinsk meteoroid) have demonstrated the need to understand major impact and fragmentation events. Many of the fundamental problems of current interest in national security also involve impact and fragmentation, typically studied through large-scale computational simulations. In the Murray lecture, these issues were addressed by describing fundamental high-strain-rate experiments, high-speed visualization, theoretical and computational modeling of failure processes, and simulations of asteroid damage and disruption. This paper focuses on experimental results on meteorites and a basalt.
Protection materials are continuously facing higher velocity threats; characterizing their response to these threats is necessary to improve performance. We have previously examined failure of boron carbide and magnesium systems at strain rates of up to 105 per second [12,13]. To study dynamic deformation at higher strain rates closer to the hypervelocity regime, we use micro-flyers to impact target materials. Over the last two decades, pulsed lasers have proven to be effective drivers for micro-flyers when achieving hypervelocity impacts. However, control of the experiment requires good characterization of the flyer behavior [11] and velocities. Here, we explore the velocity regime for a tabletop laser-driven flyer system as a function of laser pulse conditioning (fluence, pulse duration, etc.),and launch package materials. We modify an established model to inform the selection of launch package substrates and configuration in a lens-coupled micro-flyer apparatus. We use Photon Doppler Velocimetry (PDV) to obtain velocity histories of the flyers [10]. Comparisons between flyer data from our launcher system and the model predictions uncover the important parameters controlling launcher performance.
Journal of the Mechanics and Physics of Solids 2017 Volume 106(Volume 106) pp:
Publication Date(Web):1 September 2017
DOI:10.1016/j.jmps.2017.05.020
A minor error was present in one equation in the original paper, “Multi-scale defect interactions in high-rate brittle material failure. Part I: Model formulation and application to AlON” and in the corresponding computational implementation. The correction is provided here. None of the primary conclusions of the original paper are affected.
Co-reporter:Neha Dixit, Kelvin Y. Xie, Kevin J. Hemker, K.T. Ramesh
Acta Materialia 2015 Volume 87() pp:56-67
Publication Date(Web):1 April 2015
DOI:10.1016/j.actamat.2014.12.030
Abstract
The mechanical behavior of extruded pure magnesium was studied experimentally under high strain rate ) compression loading in the extrusion direction. Electron back scattered diffraction was used to examine the changes in the texture and transmission electron microscopy was used to investigate the dislocation structures in the material. Extensive grain reorientation due to extension twinning is observed. Dislocation activity is observed inside the parent region (〈a〉 slip) as well as the twinned region (〈c+a〉 slip). The high degree of strain hardening observed is postulated to be due to the texture hardening associated with extension twinning coupled with significant increase in the dislocation density with strain. In compression along the extrusion direction, extension twinning and dislocation activity are both needed to accommodate plastic deformation.
A universal scaling relationship is developed that describes the dynamic compressive strength of brittle solids. The scaling is based on the micromechanics of the growth of cracks from populations of initial flaws, and captures the fundamental dynamics of rapidly growing and interacting cracks. A characteristic stress and a characteristic strain rate are defined in terms of material and microstructural properties. The resulting model compares well with the available experimental data for ceramics and geologic materials, and demonstrates specific scaling of strength with strain rate for compressive behavior.
Uniaxial quasi-static, uniaxial dynamic and confined dynamic compression experiments have been performed to characterize the failure and deformation mechanisms of a sintered polycrystalline aluminum nitride using a servohydraulic machine and a modified Kolsky bar. Scanning electron microscopy and transmission electron microscopy (TEM) are used to identify the fracture and deformation mechanisms under high rate and high pressure loading conditions. These results show that the fracture mechanisms are strong functions of confining stress and strain rate, with transgranular fracture becoming more common at high strain rates. Dynamic fracture mechanics and micromechanical models are used to analyze the observed fracture mechanisms. TEM characterization of fragments from the confined dynamic experiments shows that at higher pressures dislocation motion becomes a common dominant deformation mechanism in AlN. Prismatic slip is dominant, and pronounced microcrack–dislocation interactions are observed, suggesting that the dislocation plasticity affects the macroscopic fracture behavior in this material under high confining stresses.
Biomechanics and Modeling in Mechanobiology 2012 Volume 11( Issue 1-2) pp:245-260
Publication Date(Web):2012 January
DOI:10.1007/s10237-011-0307-1
Computational models are often used as tools to study traumatic brain injury. The fidelity of such models depends on the incorporation of an appropriate level of structural detail, the accurate representation of the material behavior, and the use of an appropriate measure of injury. In this study, an axonal strain injury criterion is used to estimate the probability of diffuse axonal injury (DAI), which accounts for a large percentage of deaths due to brain trauma and is characterized by damage to neural axons in the deep white matter regions of the brain. We present an analytical and computational model that treats the white matter as an anisotropic, hyperelastic material. Diffusion tensor imaging is used to incorporate the structural orientation of the neural axons into the model. It is shown that the degree of injury that is predicted in a computational model of DAI is highly dependent on the incorporation of the axonal orientation information and the inclusion of anisotropy into the constitutive model for white matter.
High temperature (298 K–573 K) and high strain rate (4000 s−1) compression experiments were performed on a cryomilled ultra-fine grained (UFG) Al-5083 using a modified Kolsky bar with a heating system designed to reduce “cold contact” time. The resulting stress strain curves show a reduction in strength of approximately 300 MPa at the highest temperature tested. This softening has been related to a thermally activated deformation mechanism. In addition, an experimental procedure was developed to investigate the microstructure evolution during the preheating, prior to mechanical loading, so as to identify the intrinsic mechanical response of the material at high temperatures. The results of this procedure are in good agreement with a TEM study on material that has been heated but not loaded.
Scripta Materialia 2007 Volume 57(Issue 6) pp:481-484
Publication Date(Web):September 2007
DOI:10.1016/j.scriptamat.2007.05.028
We discuss the dynamic failure of armor-grade hot-pressed boron carbide (B4C) under loading rates ∼5 × 10−6 to 200 MPa μs−1. High-speed photography is used in conjunction with real-time stress measurement during high-rate loading. Compressive strength of this ceramic is found to be relatively rate-insensitive over this range of loading rates. We use crack growth dynamics to compare the behavior with that of hot-pressed SiC–N and sintered α-SiC and find that the defect density has a strong influence on rate dependence.
A hierarchically designed Al-5083 composite achieves dramatic mechanical properties at impact rates of deformation through a combination of three micro-structural length scales: strengthening through a nanocrystalline core architecture and through length-scale dependent reinforcement with μ-sized ceramic particles, and enhanced ductility through the incorporation of a certain volume fraction of microscale grains (see fig.).
Traditionally, Kolsky bars are used to study the dynamic response of hard materials in uniaxial compression, tension or torsion. We present modifications to the technique that allow loading of a soft tissue specimen in (a) hydrostatic compression and (b) simple shear. The first modification is designed to determine the pressure vs. volume behavior of each material, and thence to extract a measure of the dynamic compressibility or equivalently of the bulk modulus. The second modification is designed to develop the shear stress versus shear strain behavior for a near-simple shear experiment. The critically important questions of the proper acquisition of human tissue samples and protocols for appropriate experimentation have also been addressed. The experimental techniques and the results are discussed in detail and the results compared to finite element simulations. We present examples of the dynamic response of typical tissue simulants as well as human liver and stomach tissues.
Co-reporter:H. Zhang, B.E. Schuster, Q. Wei, K.T. Ramesh
Scripta Materialia 2006 Volume 54(Issue 2) pp:181-186
Publication Date(Web):January 2006
DOI:10.1016/j.scriptamat.2005.06.043
We investigate (via finite-element analyses) the factors that may affect the accuracy of micro-compression measurements (see, e.g., Uchic et al. [Uchic MD, Dimiduk DM, Florando JN, Nix WD. Science 2004;305:986]). Based on these simulations, we suggest guidelines for the development of accurate micro-compression experiments in terms of fillet to post radius ratio, post aspect ratio, post taper, and system alignment.
Materials Science and Engineering: A 2004 Volume 382(1–2) pp:162-170
Publication Date(Web):25 September 2004
DOI:10.1016/j.msea.2004.04.062
The mechanical response of a metal–matrix composite to dynamic shearing deformations has been measured, using a new design of the thin-walled tubular specimen for the torsional Kolsky bar experiment that allows working with these difficult-to-machine materials. The advantages of using the new specimen design are as follows: (i) the thickness of the thin wall along the axial direction is very uniform; (ii) specimen machining is extremely simple; (iii) the cost of specimen machining is greatly reduced. The approach has been used to characterize the high shear strain rate (103 s−1) behavior of an A359/SiCp composite and its corresponding A359 monolithic alloy with the torsion Kolsky bar. The experimental results show that the flow stress of the composite in shear increases in the presence of SiC particles, whereas the failure strain is reduced. The shear failure strains of both the A359/SiCp composite and the A359 monolithic alloy appear to increase with increasing strain rate. Previous observations have shown that particle fracture develops during compressive deformations of this material. However, particle fracture is not a significant damage mode during the shearing deformations of the composite, and this is reflected in differences between the torsional and tension behaviors of the material.
Materials Science and Engineering: A 2004 Volume 384(1–2) pp:26-34
Publication Date(Web):25 October 2004
DOI:10.1016/j.msea.2004.05.027
Aluminum 6092/B4Cp (boron carbide) metal-matrix composites (MMC) fabricated by two different powder consolidation routes, extrusion and sintering/hot isostatic-pressing (HIPing), were made and tested over a wide range of strain rates (10−4 to 104 s−1). The strength of these MMCs increases with increasing volume fraction of particulate reinforcement. Strain hardening is observed to increase with increasing volume fraction of reinforcement at lower strains (<5%), but tends to be insensitive to volume fraction at higher strains. The composites show significant strain rate dependence. The fabrication route affects the strength of the matrix material, as reflected in the microstructure, and this effect carries on into the corresponding composites. The composites made by the extrusion route show similar strain rate hardening for all volume fractions studied, while the composites produced via sintering/HIPing demonstrate increased strain rate hardening at the higher reinforcement volume fractions. Particle size effect is not significant for the particle size range (>5 μm) considered. Finally, the Li–Ramesh model captures the observed high-rate behavior exhibited by these powder-consolidated composites.
The mechanical behaviors of consolidated iron with average grain sizes from tens of nanometers to tens of microns have been systematically studied under uniaxial compression over a wide range of strain rates. In addition to the well-known strengthening due to grain size refinement, grain size dependence is observed for several other key properties of plastic deformation. In contrast with conventional coarse-grained Fe, high-strength nanocrystalline and submicron-grained Fe exhibit diminished effective strain rate sensitivity of the flow stress. The observed reduction in effective rate sensitivity is shown to be a natural consequence of low-temperature plastic deformation mechanisms in bcc metals through the application of a constitutive model for the behavior of bcc Fe in this strain rate and temperature regime. The deformation mode also changes, with shear localization replacing uniform deformation as the dominant deformation mode from the onset of plastic deformation at both low and high strain rates. The evolution and multiplication of shear bands have been monitored as a function of plastic strain. The grain size dependence is discussed with respect to possible enhanced propensity for plastic instabilities at small grain sizes.
Materials Science and Engineering: A 2000 Volume 276(1–2) pp:9-21
Publication Date(Web):15 January 2000
DOI:10.1016/S0921-5093(99)00517-1
The thermomechanical response of commercially pure polycrystalline tungsten was investigated over a wide range of strain rates and temperatures. The material was examined in two forms: one an equiaxed recrystallized microstructure and the other a heavily deformed extruded microstructure that was loaded in compression along the extrusion axis. Low strain rate (10−3–100 s−1) compression experiments were conducted on an MTS servohydraulic load frame equipped with an infra-red furnace capable of sustaining specimen temperatures in excess of 600°C. High strain rate (103–104 s−1) experiments were performed on a compression Kolsky bar equipped with an infra-red heating system capable of developing specimen temperatures as high as 800°C. Pressure–shear plate impact experiments were used to obtain shear stress versus shear strain curves at very high rates (∼104–105 s−1). The recrystallized material was able to sustain very substantial plastic deformations in compression (at room temperature), with a flow stress that appears to be rate-dependent. Intergranular microcracks were developed during the compressive deformations. Under quasi-static loadings a few relatively large axial splitting cracks were formed, while under dynamic loadings a very large number of small, uniformly distributed microcracks (that did not link up to form macrocracks) were developed. The rate of nucleation of microcracks increased dramatically with strain rate. The extruded tungsten is also able to sustain large plastic deformations in compression, with a flow stress that increases with the rate of deformation. The strain hardening of the extruded material is lower than that of the recrystallized material, and is relatively insensitive to the strain rate. High-temperature experiments at low and high strain rates show that the strain hardening is also insensitive to the temperature over this temperature range. The flow stress is shown to be strongly temperature-dependent at low homologous temperatures.
International Journal of Impact Engineering (October–November 2009) Volume 36(Issues 10–11) pp:1242-1249
Publication Date(Web):1 October 2009
DOI:10.1016/j.ijimpeng.2009.05.007
An inherently rate dependent material model is used to model the nucleation and growth of voids in metals, leading to spall fracture. Intrinsic material rate dependence introduces a third time scale in addition to those introduced by rates of nucleation and growth. Material rate dependence does increase the spall strength of metals, but it is not nearly as important as local inertia in doing so.
Journal of the Mechanics and Physics of Solids (October 2014) Volume 70() pp:262-280
Publication Date(Web):1 October 2014
DOI:10.1016/j.jmps.2014.05.018
Here we examine the role of dislocation kinetics and substructure evolution on the dynamic growth of voids under very high strain rates, and develop a methodology for accounting for these effects in a computationally efficient manner. In particular, we account for the combined effects of relativistic dislocation drag and an evolving mobile dislocation density on the dynamics of void growth. We compare these effects to the constraints imposed by micro-inertia and discuss the conditions under which each mechanism governs the rate of void growth. The consequences of these constraints may be seen in a number of experimental observations associated with dynamic tensile failure, including the extreme rate-sensitivity of spall strength observed in laser shock experiments, an apparent anomalous temperate dependence of spall strength, and some particular features of void size distributions on spall surfaces.
Journal of the Mechanics and Physics of Solids (May 2011) Volume 59(Issue 5) pp:1076-1093
Publication Date(Web):1 May 2011
DOI:10.1016/j.jmps.2011.02.003
Uniaxial quasi-static compression, uniaxial dynamic compression and confined dynamic compression experiments were performed to characterize the failure of Aluminum Nitride (AlN) using a servo hydraulic machine and a modified Kolsky bar set-up respectively. High-speed digital cameras are used to visualize the failure processes. A summary of the available experimental results, including that in the literature, shows that the compressive strength of the AlN is sensitive to strain rate in the range from 10−3 to 103 s−1, and that the deviatoric strength of AlN is linearly dependent on pressure at low pressures and nearly independent of pressure above a transitional pressure (about 2 GPa). TEM characterization of fragments obtained after dynamic loading is used to characterize the deformation mechanisms in the AlN for varying confinement. The transition in the pressure dependent behavior is shown to be the result of a change of deformation mechanism. Classical wing crack micromechanics is used to predict the transition in the deformation mechanism, and to explain the observed behavior at low pressure.
Journal of the Mechanics and Physics of Solids (March 2008) Volume 56(Issue 3) pp:896-923
Publication Date(Web):1 March 2008
DOI:10.1016/j.jmps.2007.06.012
A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.
Journal of the Mechanics and Physics of Solids (January 2016) Volume 86() pp:117-149
Publication Date(Web):1 January 2016
DOI:10.1016/j.jmps.2015.10.007
Highlights•Develop an approach to create a statistical realization of a microcrack distribution.•Model generates observed variability and strain rate sensitivity of the strength.•Simulate an edge on impact experiment and discuss the interaction of multiple mechanisms.Within this two part series we develop a new material model for ceramic protection materials to provide an interface between microstructural parameters and bulk continuum behavior to provide guidance for materials design activities. Part I of this series focuses on the model formulation that captures the strength variability and strain rate sensitivity of brittle materials and presents a statistical approach to assigning the local flaw distribution within a specimen. The material model incorporates a Mie–Grüneisen equation of state, micromechanics based damage growth, granular flow and dilatation of the highly damaged material, and pore compaction for the porosity introduced by granular flow. To provide initial qualitative validation and illustrate the usefulness of the model, we use the model to investigate Edge on Impact experiments (Strassburger, 2004) on Aluminum Oxynitride (AlON), and discuss the interactions of multiple mechanisms during such an impact event. Part II of this series is focused on additional qualitative validation and using the model to suggest material design directions for boron carbide.
Journal of the Mechanics and Physics of Solids (January 2016) Volume 86() pp:94-116
Publication Date(Web):1 January 2016
DOI:10.1016/j.jmps.2015.10.005
Our traditional view of void nucleation is associated with interface debonding at second-phase particles. However, under extreme dynamic loading conditions second-phase particles may not necessarily be the dominant source of void nucleation sites. A few key experimental observations of laser spall surfaces support this assertion. Here, we describe an alternative mechanism to the traditional view, namely shock-induced vacancy generation and clustering followed by nanovoid growth mediated by dislocation emission. This mechanism only becomes active at very large stresses. It is therefore desirable to establish a closed-form criterion for the macroscopic stress required to activate dislocation emission in porous materials. Following an approach similar to Lubarda and co-workers, we derive the desired criterion by making use of stability arguments applied to the analytic solutions for the elastic interactions of dislocations and voids. Our analysis significantly extends that of Lubarda and co-workers by accounting for a more general stress state, finite porosity, surface tension, as well as temperature and pressure dependence. The resulting simple stress-based criterion is validated against a number of molecular dynamics simulations with favorable agreement.
Journal of the Mechanics and Physics of Solids (January 2016) Volume 86() pp:237-258
Publication Date(Web):1 January 2016
DOI:10.1016/j.jmps.2015.10.006
Highlights•We provide further validation of the Tonge–Ramesh model for Boron Carbide.•We simulate the sphere on cylinder simplified ballistic loading geometry.•The granular flow of the comminuted material effects the performance of the material.•The damage model controls the peak strength under uniaxial dynamic compression.Micromechanics based damage models, such as the model presented in Part I of this 2 part series (Tonge and Ramesh, 2015), have the potential to suggest promising directions for materials design. However, to reach their full potential these models must demonstrate that they capture the relevant physical processes. In this work, we apply the multiscale material model described in Tonge and Ramesh (2015) to ballistic impacts on the advanced ceramic boron carbide and suggest possible directions for improving the performance of boron carbide under impact conditions. We simulate both dynamic uniaxial compression and simplified ballistic loading geometries to demonstrate that the material model captures the relevant physics in these problems and to interrogate the sensitivity of the simulation results to some of the model input parameters. Under dynamic compression, we show that the simulated peak strength is sensitive to the maximum crack growth velocity and the flaw distribution, while the stress collapse portion of the test is partially influenced by the granular flow behavior of the fully damaged material. From simulations of simplified ballistic impact, we suggest that the total amount of granular flow (a possible performance metric) can be reduced by either a larger granular flow slope (more angular fragments) or a larger granular flow timescale (larger fragments). We then discuss the implications for materials design.
International Journal of Impact Engineering (April 2007) Volume 34(Issue 4) pp:784-798
Publication Date(Web):1 April 2007
DOI:10.1016/j.ijimpeng.2005.12.002
In this paper, a simple and effective technique is described for measurement of the viscoplastic tensile strains of specimens in the tension Kolsky bar experiment. The technique uses a Laser Occlusive Radius Detector (LORD) to directly measure the local diametral strain. To verify the accuracy of this technique, comparative tests of an A359 aluminum alloy were performed in which the strains in the specimens were simultaneously determined using the LORD approach and on-specimen strain gauges. Full numerical simulations of the tension Kolsky bar experiment were also performed for a variety of specimen geometries and material properties to evaluate the domains of accuracy of each measure of specimen strain. The experimental and numerical results show that (i) the strain measured using the LORD approach is in very good agreement with that measured using on-specimen strain gauges; (ii) the LORD approach continues to provide strain measurements after failure of the on-specimen strain gauges; (iii) the strain measured using conventional approaches is different from the strain measured using either the LORD or the on-specimen strain gauges.
While computational models of impact events have the potential to accelerate the design cycle, one's confidence in a material model should be related to the extent of validation work that has been performed for that model. Quantities of interest used for validation are often either scalar volume-averaged quantities (such as the average density, or the force applied to a boundary) or field quantities (such as the strain field obtained from digital image correlation, or density maps computed from X-ray computed tomography (XCT)). Volume averaged quantities are easy to compare quantitatively since they are either a single value or a simple time series. However, these averaged quantities do not capture differences in the failure process within a material and can be blunt instruments for validation efforts. Field quantities provide spatial information, but are difficult to reduce to a scalar that quantifies the goodness of a particular model with respect to another model. This work describes an approach to using XCT data to quantify how well a particular simulation agrees with simulation data while accounting for the statistical nature of failure in brittle materials.
