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This work develops RVE-based finite element (FE) models to understand how the microstructure of Ultra-High-Molecular-Weight Polyethylene (UHMWPE) composites affects the overall mechanical behaviour of the laminate. The models represent a [0/90] configuration with a random fibre packing sequence through the thickness of each ply, as well as a variation in the cross-sectional shape of the fibres, both obtained from laminate cross section micrograph images. The uncertainty of interface properties and its effects on the overall mechanical response is also investigated. The response of the fibre is assumed to be viscoelastic-plastic and transversely isotropic and the three-dimensional constitutive behaviour is implemented through a user-defined subroutine in the LS-DYNA explicit FE code. Constituent properties are calibrated using experimental results on UHMWPE single fibres and a generic thermoplastic polyurethane resin material. The numerical results generated by the RVE models are validated against experimental results found in the open literature. Special focus was given to the in-plane shear and out-of-plane compression response of UHMWPE laminates. Our results can be used as inputs in a homogenised continuum level model, to express the effect of uncertainties which propagate from the microstructure to the macro-scale response.

In this work, AgGaS2 thin films are investigated and their applications in photovoltaic cells is attempted. Less porosity and fine grains formed by pulse plating technique compared to dc plating technique. The film thickness measured by surface profilometer and its ranging from 500 to 950 nm with increase in duty cycle. The single-phase polycrystalline nature noticed in X-ray diffraction pattern. Composition of films estimated by Energy dispersive X-ray analysis (EDAX). In XPS studies, peaks in the Ag 3d spectrum at 367.34 eV and 373.42 eV could be the binding energies of Ag3d5/2 and Ag3d3/2, respectively. At 1146 eV and 1118 eV, respectively, the peaks of Ga 2p1/2 and Ga 2p3/2 were noted. At 162.1 eV and 153.1 eV, the sulphur doublet occurred. AFM studies observed that the grain size and surface roughness decreases as the duty cycle increases. The transport properties at room temperature measured, the film resistivity and mobility increased with increase of duty cycle. The carrier density decreases with duty cycle increases. Studies of photo electrochemical cells showed an efficiency of 5.85%. Mott-Schottky plots yield a flat band potential ranging from 0.8 V to 1.00 V in the range of (SCE). The film showed p-type conductivity.

Boron carbide is an excellent protection material but it is also very brittle, and granular flow, triggered by progressive fracture during impact, greatly influences its ballistic performance. Transmission electron microscopy observations of samples recovered from controlled pressure-shear plate impact experiments have elucidated the extent to which local failure mechanisms accompany dynamic granular flow. These observations point to the interplay of quasiplasticity, the formation of nanoscale amorphous bands, cleavage and intragranular cracking. Association of these mechanisms with granular flow and identification of a critical velocity for the onset of amorphization provides a foundation for modeling and predicting armor performance.

This is the first part of a 2-paper series describing a generalized multi-mechanism constitutive model for the dynamic failure of quasi-brittle materials (e.g., ceramics and geomaterials), and focus on the poorly understood mechanism of amorphization. Amorphization has long been recognized as a significant deformation mechanism in a variety of quasi-brittle materials. In this part, we develop an amorphization model based on observations in both experiments and atomistic simulations. We consider the onset of amorphization bands and the deformation of amorphous phases inside the bands. The sliding along amorphization bands introduces damage to the materials, which eventually results in material failure, and the response of the failed material is described as granular flow. Using boron carbide (BC) as a representative material, we determine the material parameters and validate the model using plate impact experiments under different shock conditions. Finally, we use the model to predict the response of BC under dynamic Vickers indentation, and compare the simulation results with experiments from the literature to demonstrate the capability of the proposed model.

We present a hybrid approach for simulating hypervelocity impacts onto asteroids. The overall system response is separated into two stages based on their different characteristic timescales. First, the short-timescale fragmentation phase is simulated using a modified version of the Tonge–Ramesh material model implemented in a Material Point Method framework. Then, a consistent hand-off to an N -body gravity code is formulated to execute the long-timescale gravitational reaccumulation calculation. We demonstrate this hybrid approach by considering the 5 km/s head-on impact of a 1.21 km diameter basalt impactor on a 25 km diameter target asteroid. The impact event resulted in the fragmentation, but not complete disruption, of the entire target. A granular core is observed at the end of the fragmentation simulations, which acts as a gravity well over which reaccumulation occurs in the N -body simulations. Our results suggest that disruption thresholds for rocky asteroids are higher when energy-dissipating mechanisms such as granular flow and pore collapse are included.

An understanding of the dynamic failure of damaged ceramics is important in protection applications, where the interaction of the projectile with cracked material is a contributing factor in the overall system performance. In this paper, we investigate the effects of pre-existing internal cracks on the quasi-static and dynamic compressive behavior of an advanced ceramic. We present experiments on a hot-pressed boron carbide in which internal cracks are generated through thermal shocking after which the initial material damage is quantified. Damage characterization was performed via Resonant Ultrasound Spectroscopy (RUS) and high-resolution Computed Tomography (CT). A computational procedure is developed to determine the three-dimensional structure of the internal crack network in the initially damaged material from a series of CT images. The failure and strength of the material is then evaluated experimentally. The uniaxial compressive strength of the predamaged boron carbide samples is determined under both quasistatic and dynamic loading scenarios and this is correlated with the pre-existing crack structure as determined by CT. Damaged samples were found to have average compressive strength of 1.14 GPa in quasistatic loading and 0.68 GPa in dynamic loading compared to 2.98 ± 0.6 GPa and 3.70 ± 0.3 GPa for pristine material, respectively. High speed photography employed during dynamic testing indicates that pre-existing cracks may lead to different failure mechanisms from what is normally seen in pristine material. Ultimately, these insights can be used to design improved materials that are more resistant to dynamic failure.

The mechanical response of single crystal silicon carbide (SiC) of two hexagonal polytypes (six layer, 6H- and four layer, 4H) was investigated using nanoindentation. Indentations were performed on two specific crystallographic orientations of single crystals i.e., normal to the basal, ( 0001 ) and prismatic, ( 10 1 ¯ 0 ) planes, in the load range between 25 mN and 500 mN. A significant anisotropy in the hardness is observed with the basal orientations showing a higher hardness compared to prismatic orientations. In both orientations, the 6H-SiC polytype exhibits higher hardness than the 4H-SiC polytype. It is also observed that the hardness decreases with increasing indentation load, suggesting that SiC crystals exhibit indentation size effect. However, unlike hardness, elastic modulus is independent of indentation load and the elastic anisotropy is insignificant. Severe cracking, particularly at higher indentation loads is noticed near the edges of the indentation imprints. The indentation fracture toughness, K I C i computed from the imprints shows slightly higher values for 6H-SiC compared to the 4H-SiC. However, for both the polytypes, a slightly higher K I C i is observed for basal indentations compared to the prismatic ones.

A physics-based finite strain crystal plasticity constitutive model for body-centered-cubic (BCC) single crystals is developed to capture the strong temperature, rate, and orientation dependence of mechanical behavior. The key features of the model include twinning-anti-twinning asymmetry of shearing resistance, a yield criterion that incorporates atomistics-informed non-Schmid effects, and a flow rule formulated based on the theory of thermally activated motion of screw dislocations via nucleation of double kinks. The implementation of the constitutive model in a finite-element program is briefly discussed. The material constants in the model are determined by calibrating the model against literature-based experimental data on single-crystal Molybdenum subjected to uniaxial compression and uniaxial tension. Experiments of uniaxial compression on a single crystal specimen with a hole were performed for validation of the calibrated model for BCC Molybdenum. Measurements of deformations in the vicinity of the hole were used to assess the ability of the model in predicting localized deformation patterns around the hole. The model is able to effectively describe the anisotropic and temperature-dependent stress-strain response of a molybdenum crystal up to a homologous temperature of 0.3.

In-situ ultra high speed optical imaging with 200 ns temporal resolution is used to gain insight into the evolution of twinning in single crystal magnesium under dynamic loading. Under compression along the a-axis, nucleation of twins is observed to occur on two conjugate { 10 1 ¯ 2 } twin planes. Twin nucleation appears to be stress-driven with the first twins nucleating at resolved stresses of 5–7 MPa. These first twins propagate across the specimen at very high speeds of the order 1 km/s. After the first twins stop growing, twin boundary growth is observed to be very small and relatively slow. The nucleation of additional twins from the boundaries of pre-existing twins is found to be preferred over twin boundary growth at these rates of loading. As a result, twin nucleation is found to have a dominant contribution to twin volume fraction evolution at later times. Lastly, twinning is found to have a dominant contribution to the net plastic strain at these strain rates.

The distributions of size and chemical composition in the regolith on airless bodies provides clues to the evolution of the solar system. Recently, the regolith on asteroid (25143) Itokawa, visited by the JAXA Hayabusa spacecraft, was observed to contain millimeter to centimeter sized particles. Itokawa boulders commonly display well-rounded profiles and surface textures that appear inconsistent with mechanical fragmentation during meteorite impact; the rounded profiles have been hypothesized to arise from rolling and movement on the surface as a consequence of seismic shaking. We provide a possible explanation of these observations by exploring the primary crack propagation mechanisms during thermal fatigue of a chondrite. We present the in situ evolution of the full-field strains on the surface as a function of temperature and microstructure, and observe and quantify the crack growth during thermal cycling. We observe that the primary fatigue crack path preferentially follows the interfaces between monominerals, leaving them intact after fragmentation. These observations are explained through a microstructure-based finite element model that is quantitatively compared with our experimental results. These results on the interactions of thermal fatigue cracking with the microstructure may ultimately allow us to distinguish between thermally induced fragments and impact products., 23 pages, 7 figures

Magnesium (Mg) and its alloys have been the subject of intensive scientific research and development in the communities of materials science and engineering, mechanical engineering and manufacturing. Considering their light weight and high specific strength, current and potential applications include the aerospace industry, automobiles, and vehicle and personnel armors. This range of applications demands a good understanding of the behavior under extreme conditions such as impact or high strain rate loading. The past two decades have witnessed a surge of studies of the mechanical responses of Mg and its alloys under impact loading, both experimentally and using simulations and modeling at different spatial and temporal scales. Experimental examinations at strain rates up to 1 0 7 s − 1 (shock wave loading) have been published. In terms of simulations and modeling efforts, multi-physics, multi-scale investigations, from first principles calculations (density functional theory, DFT), molecular dynamics (MD), discrete dislocation dynamics (DDD), crystal plasticity (CP) and continuum mechanics have all been explored. To address the challenges in design, manufacturing and application of Mg alloys, the US Army Research Laboratory (US-ARL) created the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) in 2012. The goal of the Metals Program within the MEDE CRA has been to observe, understand, and design the mechanisms active within Mg and Mg alloys in these extreme conditions. In this paper, fundamental aspects of plastic deformation of Mg and Mg-alloys and the history of the research efforts in experiments, modeling, and simulations available in the literature are critically reviewed. Key findings and contributions from the Materials in Extreme Dynamic Environments (MEDE) Metals Collaborative Materials Research Group (CMRG) are presented, followed by summary and future perspectives.

We present a simplified constitutive model, based on the dominant deformation mechanisms, to capture the mechanical behavior of magnesium. This approach takes into account (1) the accumulation and annihilation of 〈 a 〉 and 〈 c + a 〉 dislocations, (2) the volume fraction of extension twins, and (3) two material domains — the parent region and the twinned region. We first show that the model successfully captures the material responses of single crystal magnesium under different loading conditions. We then extend the model for application to a polycrystalline magnesium alloy. The results provide a simple and straightforward approximate model for magnesium and its alloys under various loading conditions.

Based on transmission electron microscopy results from pure Mg single crystal examined in the current work, and Mg alloys and other hexagonal metals in literature, a characteristic dislocation substructure inside 10 1 ¯ 2 twins is identified. Abundant non-basal [c] and ⟨c + a⟩ perfect dislocations, as well as basal I1 stacking faults with widths on the order of 100 nm distributed preferentially in the vicinity of a twin boundary, with a low density zone in the middle of the twin. Considering the ubiquity of 10 1 ¯ 2 twins, this characteristic dislocation substructure should be considered in modeling of hexagonal metal alloy deformation.

A finite deformation mechanism-based thermodynamically consistent constitutive framework is presented for describing the dynamic behaviors of brittle materials under impact loading. The framework is developed based upon a multiplicative decomposition of the deformation gradient in terms of multiple mechanisms, including recoverable elasticity, crack-induced damage, and other inelastic mechanisms such as subgrain and granular plasticity. The finite deformation kinematics that captures the multiple mechanisms is structured within a thermodynamically consistent framework, and the consequent coupling of the various mechanisms is articulated. Specific constitutive equations are formulated for a Mie–Gruneisen equation of state, micromechanics-based dynamic-fracture-induced damage growth, subgrain or lattice plasticity for slip and other deformation modes, and granular plasticity for granular flow and pore collapse post-fragmentation. Using hot-pressed silicon carbide (SiC-N) as the model material, this integrative model is calibrated using available experiments that interrogate specific mechanisms. The effects of loading rate, the influence of confinement, and the path-dependent constitutive behaviors of the material predicted by the model are demonstrated. The model performance at the application scale is then evaluated by simulating previously performed sphere-on-cylinder impact experiments.

Electrical response from dynamic compression tests on x-cut single crystal α-quartz specimens at strain rates of 103 s − 1 reveal nonsimilar stress-charge behavior during damage evolution. Specifically, when quartz is undergoing extensive and irreversible dynamic brittle fracture under a compressive stress impulse of up to 1.8 GPa, the effective piezoelectric stress coefficient (d) exhibits approximately a 24% increase from loading to unloading. The experimental results are examined in the framework of the theory of linear piezoelectricity in order to understand the role of increasing crack density and crystal orientation on electroelastic properties.

Normal plate impact experiments were conducted to study the spall behavior of AMX602 magnesium alloy fabricated via Spinning Water Atomization Process (SWAP), which was followed by cold compaction and hot extrusion. Incipient spall damage in the specimens was measured at different shock conditions using 51 mm and 105 mm diameter bore gas guns. The Hugoniot Elastic Limit (HEL) was measured to be approximately 187 ± 11 MPa. The spall strengths extracted from the free surface velocity profiles of the shocked specimens was found to increase by 8% for shock stresses ranging from 1.61 to 4.53 GPa. The experimental data also revealed some inherent scatter in the spall strength data due to microstructural heterogeneity. Post-test fractographic analysis of the shock-recovered specimens suggests that the initiation of spall was most likely associated with intermetallic Al 2 Ca-bearing precipitates forming during the hot extrusion process. The subsequent spall failure propagated via cavitation events that involved the nucleation of nano- and micrometer-sized voids with very limited plastic growth.

Boron carbide has a wide range of solubility, but the effects of stoichiometry on its microstructure and mechanical response are not well understood. In this study, detailed microstructural characterization was carried out on three hot-pressed B-rich boron carbide samples. Lattice parameter measurements from XRD identified the compositions to be B 4.2 C, B 5.6 C and B 7.6 C. Local substitutional disorder was observed by Raman spectroscopy, particularly for more B-rich samples. Electron energy loss spectroscopy observations suggest that excess boron preferentially substitutes for carbon atoms in the B 11 C icosahedra; after which additional boron modifies the CBC chains. Moreover, the boron content has salient effects on boron carbide densification and microstructure. Improved densification was observed in the more B-rich samples (B 5.6 C and B 7.6 C), and there is a transition from few or no intragranular planar defects (B 4.2 C), to numerous stacking faults (B 5.6 C), to copious twins (B 7.6 C). Nanoindentation experiments revealed that the highest value for B 4.2 C is statistically larger than that for B 5.6 C or B 7.6 C, suggesting that the hardness of boron carbide is reduced by boron substitution.

Single crystals of pure Mg were deformed along the crystallographic 〈 a 〉 axis under normal plate impact loading of microsecond duration. Post-test electron microscopy analyses of the recovered specimens revealed the presence of extension twins. Twins were observed to grow to significant sizes and an estimate of the twin tip velocity was obtained. Secondary extension twinning was also observed.

In this paper, the impact-induced fragmentation of a commercially available hot-pressed boron carbide is explored. Fragmentation has been noted previously by many authors to be important in the impact performance of advanced ceramics, and so this paper seeks to provide some of the first near-complete and detailed measurements of individual fragment size and shape distributions available in the literature. Fragment size and shapes are quantified using methods developed in previous papers by the authors, and results reveal that two distinct fragmentation mechanisms exist as a consequence of the impact failure of boron carbide: one mechanism that creates small fragments that is associated with the coalescence of fractures originating from carbonaceous defects in the material, and one that creates larger fragments that is associated with structural failure (e.g., radial and circumferential cracking). While these mechanisms are similar to those noted for uniaxial compressive failure, results presented here highlight the importance of fragment shape as a consequence of impact failure. Namely, results indicate that both blocky and shard fragments are formed during impact into a boron carbide plate. Blocky and shard fragment types span across both the small and large fragmentation mechanisms. Using Scanning Electron Microscopy, blocky fragments were found to be associated with the predominant growth of cracks parallel to the impact direction, while shard fragments contain fracture surfaces that are associated with crack growth and coalescence in a direction perpendicular to the impact direction. The shards are, thus, believed to be a consequence of structural bending. No amorphous features were found on any blocky or shard fragments observed in this study (determined using Raman Spectroscopy), suggesting brittle fracture may be the dominant mechanisms that creates the shard fragments. Altogether, the implications of these results is that one can control fragment size and shape by controlling the carbonaceous defects population in boron carbide. This should help in the design of next-generation advanced ceramics for personal protection.

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 10 5 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.

Time-resolved normal plate impact experiments and spall recovery experiments were conducted to study the spall behavior of AZ31B-4E magnesium alloy processed via Equal-Channel Angular Extrusion (ECAE). The spall strength and incipient spall damage in the specimens were measured at different shock stresses using 51 mm and 105 mm bore gas guns. The Hugoniot Elastic Limit (HEL) was measured to be approximately 181 ± 3 MPa. The spall strengths extracted from the free surface velocity profiles of the shocked specimens were found to decrease by 5% for shock stresses ranging from 1.7 GPa to 4.6 GPa. However, this reduction in spall strength may fall within the experimental error. Post-test fractographic examinations of recovered specimens revealed that spall failure originated at micrometer-size intermetallic inclusions and propagated through the material by cavitation events with a very limited growth of voids. It was concluded that the strengthening of AZ31B-4E magnesium alloy by the ECAE-process resulted in adverse effects on its microstructure and spall behavior because of the process-induced cracking of intermetallic inclusions and their weak interface strengths.

We investigate the impact history of the Near Earth Asteroid (NEA) Eros 433 using a new material model for brittle materials such as rocks, where initial flaw distributions within the rock are explicitly defined to match what is known about flaw size distributions in rocks. These simulations are limited to the initial impact phase of the crater formation process and use a very crude approximation for the effect of the gravitational overburden pressure. Given these approximations, our simulations of this numerical approximation of Eros suggest that the current observed bulk porosity of about 25% could be consistent with the porosity generated by the formation of the three largest craters observed on Eros indicating that Eros could have started as an intact shard from a prior impact event. Further, we investigate the consequences of two possible internal flaw distributions for the asteroid: a “strong” flaw distribution with shorter crack lengths, that are more difficult to activate during cratering; and a “weak” flaw distribution with longer flaws. The “strong” distribution produces localized deformation regions (lineaments) that are resolved by the simulations, while the “weak” distribution does not produce resolved localized features. For either distribution of internal flaws the initial impact (assumed to be the Himeros forming impact) shatters but does not disrupt the body implying that simulations of asteroid mitigation approaches should assume that asteroids will behave like rubble piles. Subsequent impact events activate linear features created by prior impacts but only change the orientation of the lineament structure near the impact site.

The dynamic rheology of a complex granular material system strongly depends on the imposed stress state. However, drawing a clear physics based picture of dynamic granular flow is challenging due to the heterogeneous nature of granular materials, as well as the overwhelming difficulties in carrying out dynamic experiments. Here, pressure-shear plate impact (PSPI) is utilized to load a granular boron carbide ceramic in a multi-axial fashion with strain rates on the order of 105 s − 1 and pressure levels ranging from 1 to 3 GPa. Comparisons between the shear flow stresses and the superimposed normal stress indicate a strong pressure dependence in the constitutive response, along with an effective friction coefficient measured to be around 0.16. Both the normal and shear stress-strain relations are obtained. Granular boron carbide shows a highly compressible behavior with a significant amount of volume compaction achieved as the result of the large uniaxial normal strain. Due to the compaction, the estimated granular wave speed increases with density. Microstructure characterization of the deformed particles shows that fracture and amorphization are active deformation mechanisms besides the grain-grain frictional interactions and particle rearrangement. This study will contribute to the development of integrative modeling for behavior of granular boron carbide at ultra-high strain rates and confinement pressures.

Dynamic point impact loading is a primary cause of fracture of glass screens on mobile devices. An improved understanding of crack initiation and evolution under high-speed indentation could contribute to the development of materials with better performance, but experimental observations are challenging due to the short timescales and limited depth-of-field of optical microscopy. To address this need, we have observed fracture of a chemically-strengthened glass during dynamic indentation using in situ x-ray phase-contrast imaging (XPCI). Median cracks initiate below the surface of the glass, at a depth approximately corresponding to the depth at which the surface residual compressive stress diminishes to zero. These cracks initially propagate at ∼ 10 m s − 1 , rapidly accelerating to > 100 m s − 1 . We also observe some evidence for rate-dependent behavior, in that indentation at the lowest rates studied here (below about ∼ 0 . 15 m s − 1 ) fails to initiate cracks regardless of the depth of the indentation (up to 18 μ m ), while indentation at higher rates produces median cracks that either arrest or cause complete fracture, depending on the depth of indentation.

Laser-driven micro-flyer plates exhibit high planarity within the first 500 µm of travel, but deform into curved impactors due to loss of flight-driving plasma at the edges of the plate and interaction of the plate with the atmosphere [1, 2]. This time-of-flight based tunability of impactor geometry offers adjustable loading conditions in stress space. Here we explore the dynamic fracture of Boron Carbide under loading at 1100–1200 m/s impact velocities (strain rates up to 107 s − 1 ) from two impactor geometries: (1) a nominally flat aluminum micro-flyer and (2) an Al micro-flyer with a radius of curvature. We compare these results to prior ballistic experiments with a spherical projectile impacting at 930 m/s. In-situ high-speed imaging at 10 million frames-per-second enables characterization of the flyer geometry and identification of active failure mechanisms in the target. Photon Doppler velocimetry provides the target free surface velocity history and allows estimates of the internal stress state during failure. Optical microscopy of the as-received microstructure and generated fragments suggests a link between the microstructure and fragmentation behavior. Statistics from laser-driven fragmentation are similar to ballistic fragmentation experiments, demonstrating the utility of the laser-driven apparatus in fragmentation studies.

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.

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–Gruneisen 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.

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.

The failure and fragmentation of ductile materials through the nucleation, growth, and coalescence of voids is important to the understanding of key structural materials. In this model of development effort, ductile fragmentation of an elastic–viscoplastic material is studied through a computational approach which couples these key stages of ductile failure with nucleation site distributions and wave propagation, and predicts fragment spacing within a uniaxial strain approximation. This powerful tool is used to investigate the mechanical and thermal response of OFHC copper at a strain rate of 105. Once the response of the material is understood, the fragmentation of this test material is considered. The average fragment size as well as the fragment size distribution is formulated.

Knowledge of the relationships between microstructure, stress-state and failure mechanisms is important in the development and validation of numerical models simulating large-scale impact events. In this study, we investigate the effects of microstructural constituent phases and defects on the compressive and tensile strength, failure, and fragmentation of a stony meteorite (GRO 85209). In the first part of the paper we consider the effect of defects on the strength and failure. Strengths are measured and linked with detailed quantification of the important defects in this material. We use the defect statistic measurements in conjunction with our current understanding of rate-dependent strengths to discuss the uniaxial compressive strength measurements of this ordinary chondrite with those of another ordinary chondrite, with a different defect population. In the second part of the paper, we consider the effects of the microstructure and defects on the fragmentation of GRO 85209. Fragment size distributions are measured using image processing techniques and fragments were found to result from two distinct fragmentation mechanisms. The first is a mechanism that is associated with relatively smaller fragments arising from individual defect grains and the coalescence of fractures initiating from microstructure defects. This mechanism becomes more dominant as the strain-rate is increased. The second mechanism is associated with larger fragments that are polyphase and polygrain in character and is dependent on the structural failure mechanisms that are activated during load. In turn, these are dependent on (for example) the strain-rate, stress state, and specimen geometry. The implications of these results are briefly discussed in terms of regolith generation and catastrophic disruption.

Brittle failure in boron carbide has been studied in dynamic uniaxial compression using a Kolsky bar technique. A detailed study of fragments was performed using SEM-EDS, to identify the mechanisms responsible for failure. Microstructural characterization and fracture surface observations revealed that carbon inclusions oriented at certain angles with respect to the direction of loading might act as possible crack initiation sites. Cracks developed from these inhomogeneities had a tensile character, and were linked to the wing crack mechanism.

The quantitative measurement of the spatial and temporal evolution of dynamic damage from impact failure is necessary to provide understanding and accurately predict the overall dynamic mechanical behavior of brittle ceramics. This paper characterizes the spatial and temporal evolution of dynamic damage in synthetic single crystal quartz specimens used as a model material system. Single crystal x-cut α -quartz is impacted using a Kolsky (split-Hopkinson) bar in the [ 1 1 2 ¯ 0 ] and [ 1 0 1 ¯ 0 ] directions. The heterogeneity of the damage evolution presented provides insight into the failure processes, as well as benchmark data for computational simulations of dynamic failure. The results revealed a reduction in the rate of damage near peak loading, and dynamic failure was found to occur preferentially along the second order trigonal–pyramidal or ( 1 1 2 ¯ 2 ) plane. These findings are compared to an existing analytical micromechanical damage model and are discussed in terms of the crystalline anisotropy and general fracture mechanics theory.

We present a validated fully 3D mechanism-based micromechanical constitutive model for brittle solids under dynamic multiaxial loading conditions. Flaw statistics are explicitly incorporated through a defect density, and evolving flaw distributions in both orientation and size. Interactions among cracks are modeled by means of a crack-matrix-effective-medium approach. A tensorial damage parameter is defined based upon the crack length and orientation development under local effective stress fields. At low confining stresses, the wing-cracking mechanism dominates, leading to the degradation of the modulus and peak strength of the material, whereas at high enough confining stresses, the cracking mechanism is completely shut-down and dislocation mechanisms become dominant. The model handles general multiaxial stress states, accounts for evolving internal variables in the form of evolving flaw size and orientation distributions, includes evolving anisotropic damage and irreversible damage strains in a thermodynamically consistent fashion, incorporates rate-dependence through the micromechanics, and includes dynamic bulking based on independent experimental data. Simulation results are discussed and compared with experimental results on one specific structural ceramic, aluminum nitride. We demonstrate that this 3D constitutive model is capable of capturing the general constitutive response of structural ceramics.

The mechanical behavior of extruded pure magnesium was studied experimentally under high strain rate ( 10 3 s - 1 ) 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.

Modeling of catastrophic disruption requires understanding the processes of dynamic failure and fragmentation. This paper summarizes current mechanisms and models for dynamic failure, strength, and fragmentation, reviewing these from a mechanics perspective and with an emphasis on making links to the developing advances in these areas in the engineering and computational mechanics communities. We describe dynamic failure processes, examine size and rate effects, articulate the scaling concepts that arise naturally from these processes, and examine the influences of these processes on effective strength and fragmentation.

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.

Ideas from continuum mechanics are used to derive an elastic stability inequality for a boundary between two different materials under quasi-static, homogeneous conditions. The terms in this inequality are interpreted for the case of an ideal twinning plane between two variants of a face-centered cubic material. High quality potentials for Ni and Cu are used in molecular dynamics calculations to calibrate relevant energies and displacements near the twinning plane. It is found that in comparison with direct molecular dynamics calculations the inequality predicts the critical stress that initiates movement of the twinning plane in Ni within 1.9% and within 1.3% for Cu. Although the predicted and calculated critical stresses are only upper bounds for the more realistic case of an imperfect boundary, the calculations give considerable insight into the interplay of energies that lead to boundary motion.

Plate impact shock and spall recovery experiments were conducted to study the effects of peak shock stress on the substructure evolution and spall response of fully annealed 1100 aluminum. The substructure of the material evolves substantially with increase in peak shock stress ranging from 4 GPa to 9 GPa with dislocation debris uniformly distributed throughout the interior of the subgrain. Observations from substructure evolution in conjunction with spall failure results suggest that ductile fracture by void nucleation, growth, and coalescence was perhaps the dominant fracture mode for shock stresses up to approximately 8.3 GPa. Whereas, beyond 8.3 GPa the material softened possibly due to dislocation reorganization (dynamic recovery) and brittle intergranular fracture by decohesion with isolated pockets of nanovoids was perhaps the dominant fracture mode. The contributions of nanovoids to the dynamic recovery process, if any, were unresolved. Microhardness measurements show an increase in residual hardness throughout the shock stress range studied implying shock hardening up to approximately 8.3 GPa. This observation also suggests that thermal softening was not operative throughout the shock stress range studied. However, dynamic recovery was thermally influenced during shock loading.

In-situ microtensile experiments were conducted on commercially pure polycrystalline magnesium to examine the motion of twin boundaries (TBs) during deformation in a scanning electron microscope. The nature of the boundaries is identified using electron back scattering diffraction (EBSD) analysis. TB displacement is continuously recorded during the deformation and the TB velocity is computed from the real time images and time data. The TB velocity is observed to monotonically increase with the applied stress and eventually reach a speed of 35 nm/s.

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.

Mechanical twinning has been introduced into a body-centered cubic metal, tantalum, through shear-dominant dynamic loading at a high shear strain rate (up to 3 × 104/s) at 77 K. Direct measurement of shear stress combined with transmission electron microscopy (TEM) confirmed the occurrence of deformation twinning at applied global shear stresses of 520 MPa and above. The TEM characterization was focused on nanometer-sized individual twins that are interspersed and aligned in association with slip bands. These small twins belong to the {1 1 2} 〈 1 1 1 ¯ 〉 twinning system but show unusual morphologies and growth characteristics, and are believed to be incipient twins at the early stages of their development. TEM analysis revealed a multifaceted growth characteristic of the incipient twins following at least two {1 1 2} planes in the 〈 1 1 1 ¯ 〉 zone. While the formation of a macroscopic twin is a result of growth and coalescence of an array of small twins, the early stage growth of an incipient twin is rationalized through a slip-assisted double-cross-slip growth mechanism.

A complete description of high-rate dynamic deformation of metals demands, in part, the fundamental understanding and characterization of twin boundary (TB) kinetics. We use molecular dynamics (MD) to characterize the TB kinetics in nickel, which serves as a model material for understanding TB kinetics in face-centered cubic metals. The kinetics of twinning dislocations (TD) fundamentally govern the TB kinetics. Propagation kinetics for a TD shares many common features with full dislocation kinetics, including non-linear kinetics, stable propagation regimes and forbidden velocities. However, a TD experiences an additional drag (as compared to a full dislocation) due to damping interactions with the TB; these characteristics are reflected in the TB kinetics. We show that, in Ni, TB velocities are limited to ∼ 650 m s - 1 , well below the shear wave speed. The insights gained from the MD simulations inform our proposed kinetic relations for TD and TB, and we show how these kinetic relations may be utilized in both macroscopic and crystal plasticity formulations.

This paper presents an enhanced continuum model for a heterogeneous particle arrangement to simulate the variability in the size dependent strengthening of silicon carbide (SiC) ceramic particle reinforced metal matrix composites (MMCs). The model incorporates a size dependent “punched” zone around the particles that is the result of a local increase in dislocation density during thermal processing due to geometrically necessary dislocations generated by the mismatch in coefficients of thermal expansion of the particle and matrix. In this work, these zones are explicitly accounted for in finite element simulations of multiple realizations of representative heterogeneous composite microstructures consisting of randomly distributed particles in a metal matrix. This modeling approach is used to capture the probabilistic response of the material which is linked to stochastic variations in the local microstructure of the material. The model is then used to explore the effects of particle size and volume fraction on the variability of the inelastic deformation response of heterogeneous MMCs. It is shown that the variance of the composite response increases as the particle size decreases and as the volume fraction of reinforcing particles increases. It is also shown that the amount of strain localization in the matrix increases as the particle size decreases.

Deformation twinning was introduced in Ta through dynamic compression shear and uniaxial compression at high strain rates up to ∼10 4 s −1 at low temperatures. Under dominant shear, the specimens showed continuous strain softening at high rates, and the deformation twins showed anomalous and highly irregular morphologies. Under compression, deformation twins appeared as typical straight and thin plates accompanied by considerable strain hardening in mechanical response. The results are correlated with the interplay of slip and deformation twinning unique for body-centered cubic metals.

In this work, we have investigated the effect of low-temperature rolling on the mechanical properties of commercial purity tungsten, particularly the high strain rate (dynamic) behavior of the cold-rolled samples vis-a-vis the as-received coarse-grained material. After rolling, the material was tested under both quasi-static and dynamic (Kolsky bar) uniaxial compression loading conditions. We have found that low-temperature rolling both improves the ductility and the strength of commercial purity tungsten. The rolled tungsten exhibits elastic-nearly perfectly plastic behavior under quasi-static loading, and a strong flow softening tendency with a precipitous stress drop under dynamic loading. Both in situ high speed movie snapshots and post-mortem examination of the dynamic samples suggest that the precipitous stress drop was caused by adiabatic shear banding in the cold-rolled material. The greatly enhanced susceptibility to adiabatic shear banding in the cold-rolled tungsten can either be explained semi-quantitatively based on a mechanistic model or from the rolling texture that leads to geometric softening under dynamic loading.