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REVIEW 4 major objections 5 minor 113 references

Multi-scale modeling of high strain rate deformation and spall fracture in poly-crystalline metals

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A multiscale pipeline that averages atomistic grain-boundary properties predicts the spall strength of polycrystalline aluminum within 2–6 percent across three flyer-plate impact velocities.

desk verdict A competent, already peer-reviewed multiscale spall thesis; the polycrystal AVGFE claim is un-auditable until the averaging rule is actually defined. read the letter →

arxiv 2608.10734 v1 pith:V6HL7CQF submitted 2026-08-11 cond-mat.mtrl-sci

S Madhavan This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords multiscalemodelingspallfracturemoleculardynamicsNucleationandGrowthmodelparticleswarmoptimizationgrainboundariesaluminumflyer-plateimpact
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis is an attempt to prove that polycrystalline spall can be predicted without simulating a full polycrystal atom by atom. The proposed route runs molecular-dynamics simulations of void formation in 23 aluminum bicrystals, fits the five parameters of a continuum Nucleation and Growth fracture model to each boundary using particle-swarm optimization, then blends those parameter sets through an averaging rule called AVGFE into a one-dimensional hydrodynamic shock code. The paper's central evidence is that this pipeline reproduces the measured free-surface velocity history of pure aluminum flyer-plate impacts at 518, 1588, and 2275 m/s, with spall-strength deviations of 2.15%, 2.9%, and 6.0% and spall-thickness deviations of 2.4–4.0%. If that holds, expensive shock experiments for new alloys could be partially replaced by atomistic-to-continuum calculations, and grain-boundary-specific failure physics would be meaningfully transferable to engineering scale.

What carries the argument

The load-bearing object is the Average Void Growth in a Fluid Element (AVGFE) model, an averaging rule that condenses the void-growth behavior of 23 distinct bicrystal grain boundaries into a single NAG fracture parameter set for a hydrodynamic cell. Around it sits the three-stage machinery the thesis uses: MD triaxial-expansion runs at strain rate $5\times10^9$ s$^{-1}$ that track void volume fraction against tensile pressure; a particle-swarm optimizer that fits the five NAG material parameters; and a 1D Lagrangian hydrodynamic code with Steinberg-Guinan strength and NAG damage that outputs free-surface velocity. AVGFE's job is to decide how the individual boundary responses combine, which is the step that the thesis argues makes the difference between single-crystal and polycrystal predictions.

What would settle it

Run full polycrystalline MD simulations of a representative volume with a known grain size distribution and compare the void-volume-fraction-versus-pressure curve at strain rate $5\times10^9$ s$^{-1}$ with the AVGFE-blended NAG prediction; if the curves differ by more than the claimed tolerance, the averaging rule fails. Directly, perform flyer-plate experiments on aluminum samples with strongly different grain size distributions at the same three velocities and check whether a single blended parameter set can fit all of them within 6%.

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Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that a multiscale chain of methods can carry grain-boundary-specific atomistic information into macroscopic hydrodynamics and accurately predict spall. The chain has three links: MD simulations of triaxial expansion of 11 symmetric tilt and 12 symmetric twist aluminum bicrystals provide void-volume-fraction versus pressure data; a particle-swarm optimizer fits the five NAG coefficients for each boundary; and the new Average Void Growth in a Fluid Element rule maps the 23 parameter sets into the single fluid element of a 1D Lagrangian hydrodynamics code with a Steinberg-Guinan strength model and NAG fracture. The validation is flyer-plate impact on aluminum at 518, 1588, and 2275 m/s: the simulated temporal free-surface velocity curves match the measured profiles, with spall strength deviations bounded by 2.15%, 2.9%, and 6.0%. A second claim of the thesis is that for aluminum bicrystals the peak tensile stress is not the same as the spall strength read from the free-surface velocity profile, and that phase transitions near grain boundaries lower spall strength at high particle velocity while grain-boundary plasticity delays spallation.

Load-bearing premise

The load-bearing premise is that the AVGFE averaging rule can represent a polycrystalline hydrodynamic cell by a single blended NAG parameter set from 23 symmetric bicrystals, with no explicit treatment of grain size distribution, triple junctions, or texture.

Editorial extensions

If this is right

  • If the central claim is correct, spall strength and thickness for a polycrystalline aluminum plate can be computed from bicrystal MD data rather than from a new flyer-plate experiment, for impact velocities inside the validated range.
  • The NAG parameter sets for the 23 bicrystals become reusable material data: the same fits can be fed into hydrodynamic simulations with different flyer thicknesses or target geometries.
  • The thesis's demonstration that peak tensile stress overestimates spall strength in Al bicrystals implies that published MD spall studies reporting only peak stress should be treated as upper bounds.
  • The shock-Hugoniot results for Cu, Al, and Ni, mostly under 6% deviation from experiments, support the use of the same EAM potentials for high-pressure, high-strain-rate atomistic studies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the AVGFE rule suggests a testable route to microstructure-aware continuum damage: instead of one blended parameter set per cell, a cell could carry a distribution of NAG sets representing different boundary populations, and the prediction could be compared with the single-set result on the same three experiments.
  • Whether 23 symmetric bicrystals are sufficient for a general polycrystal is an inference the paper does not prove; a natural check is to build bicrystals with random misorientation distributions or explicit triple junctions and see whether AVGFE predictions shift by more than the claimed 2–6%.
  • The transferability of NAG coefficients fitted at constant triaxial strain rate to the one-dimensional-strain shock state is the step most in need of independent testing, for example by feeding the same parameters into 2D or 3D hydrodynamic simulations and comparing spall morphology.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This manuscript (a Ph.D. thesis posted on arXiv) presents a multiscale pipeline that combines molecular dynamics, particle swarm optimization, and one-dimensional hydrodynamics with a nucleation-and-growth (NAG) void model. Chapter 3 validates EAM potentials for Cu, Al, and Ni by comparing MD shock Hugoniots with first-principles data and experiments. Chapter 4 fits NAG parameters from MD triaxial expansion and uses them in hydrodynamic simulations to obtain single-crystal spall strengths. Chapter 5 reports MD flyer-impact simulations across ten Al symmetric tilt and twist bicrystals. Chapter 6 extends the multiscale approach to polycrystalline Al by fitting NAG parameters for 23 bicrystals and introducing the AVGFE averaging scheme, claiming spall-strength deviations of 2.15%, 2.9%, and 6.0% against three flyer-plate experiments and spall-thickness deviations of 2.4–4.0%.

Significance. If the central polycrystal claim holds, the paper would be valuable: it offers a concrete route from atomistic, grain-boundary-specific information to macroscopic spall prediction without fitting directly to the experimental spall strengths. The single-crystal Hugoniot comparisons in Chapter 3 are systematic, the PSO code is validated on standard test functions, and the bicrystal grain-boundary energies reproduce literature values. The single-crystal multiscale simulations also improve on earlier published results for Cu, Nb, and Mo. However, the polycrystal result is not currently assessable because the AVGFE rule, which is the only new element connecting 23 bicrystal parameter sets to one hydrodynamic cell, is never defined. The reported 2–6% agreement therefore cannot yet be distinguished from a posteriori fitting.

major comments (4)
  1. [§6.2/§6.3, Tables 6.2–6.4] The AVGFE model, which is the load-bearing element of the polycrystal claim, is never defined. The text states that "An Average Void Growth in a Fluid Element (AVGFE) model is proposed" but gives no formula, weighting scheme, algorithm, or pseudo-code; Table 6.4 compares AVGFE with AMEAN without defining either method. Since the central 2–6% spall-strength agreement is produced by this averaging step, the reader cannot rule out that the averaging was chosen after seeing the experimental FSV curves. Please provide the explicit AVGFE rule, its derivation or physical motivation, and a demonstration that its parameters (or weights) are not adjusted to force agreement with the three experiments.
  2. [§6.1/§6.3, Table 6.1] The manuscript asserts that 11 STGB and 12 STwGB bicrystals represent the experimental polycrystalline Al, but it gives no justification for this sampling with respect to grain-size distribution, triple junctions, texture, or the relative area/volume of different GB types. Because the AVGFE result depends on which bicrystals are included and how they are combined, the reported accuracy is not a robust prediction unless the sensitivity of the final FSV and spall strength to the GB ensemble is demonstrated. A leave-one-out or re-sampling test over the 23 bicrystals would be appropriate.
  3. [§4.3.3 and §6.3.3, Eq. (4.1b)] The single-crystal Al multiscale simulations in Chapter 4 show a spurious FSV oscillation period, and the authors state that the period deviation "needs further investigation"; large spall-thickness deviations of 22–24% are reported for Cu and Mo. The polycrystal chapter then reports spall-thickness deviations of only 2.4–4.0% using the same hydrodynamic equations and NAG model. Since AVGFE only modifies the five NAG coefficients and cannot change the elastic-wave transit time that controls Tf in Eq. (4.1b), the mechanism by which averaging restores correct FSV timing needs explanation; otherwise the improved thickness numbers may be an artifact of the unstated averaging or of a different fracture-location criterion.
  4. [§4.2.1 and §2.3.3] The NAG parameters are fitted to MD triaxial deformation at a constant strain rate of 5×10^9 s^-1 and then applied to 1D shock hydrodynamic simulations in which the loading is uniaxial and the strain-rate history varies in space and time. The manuscript does not state whether the NAG parameters depend on strain rate or why isotropic-expansion constitutive data transfer to the uniaxial-strain spall plane. Please report the strain-rate history near the spall plane in the HD simulations and show that it overlaps the MD fitting regime, or justify the transfer explicitly through the pressure-threshold structure of the NAG equations.
minor comments (5)
  1. [§3.3.1, Table 3.1] The text says errors are "mostly <6%", but the MD value for Al C is 5777 m/s against an experimental value of 5426 m/s, which is a relative error of about 6.5%; please reconcile or restate the claim as applying to the other parameters.
  2. [§4.3.2 and elsewhere] There are numerous typos, including "molydbenum", "Surace", "coalascence", and "themodynamic"; a careful proofread is needed.
  3. [§5 and §6] The notation for grain-boundary types is inconsistent (STGB/STwGB in Chapter 5 but ASTGB/ASTwGB in the abbreviations list); please unify the terminology.
  4. [Table 6.1] Reporting the number of atoms for each bicrystal simulation would improve reproducibility and allow readers to verify finite-size convergence.
  5. [§2.3.3, Eq. (2.17)] The symbol Vsim is used in the NAG nucleation equation as if it were known to the hydrodynamic code, but Vsim is defined later as the MD simulation volume; please define the corresponding quantity in the hydrodynamic cell and use distinct notation.

Circularity Check

0 steps flagged · score 2.0 of 10

No demonstrated circularity: NAG parameters are fitted to MD void-growth data, not to the experimental spall strengths, but the central AVGFE averaging rule is never defined, leaving the polycrystal validation unauditable.

full rationale

The multiscale chain is not shown to be circular by the paper's own equations. NAG parameters are obtained by PSO fitting to MD triaxial-expansion void-volume/pressure data (Ch. 4, Sec. 4.2.2 and Ch. 6, Sec. 6.3.2), not to the experimental free-surface velocity or spall-strength values. The hydrodynamic simulations then use those NAG parameters in a separate 1D-HD code (Ch. 2, Sec. 2.3) and compare FSV profiles with external experiments (Kanel, Asay, Anton et al.). That is a genuine MD-to-continuum transfer with independent experimental validation, so the main 'prediction' does not reduce by construction to its fitting inputs. The single-crystal results show 8–15% deviations, which further indicates the comparison is not trivially forced. The principal concern is the AVGFE averaging step: it is named in the abstract and Ch. 6 ('An Average Void Growth in a Fluid Element (AVGFE) model is proposed'), and Tables/Figures compare AVGFE with AMEAN (Table 6.4, Fig. 6.8), but no formula, weighting, or algorithm is given in the visible text. Because AVGFE is the load-bearing bridge from 23 bicrystal NAG fits to the polycrystal hydrodynamic cell, the absence of its definition is an omitted-proof/auditability gap: if the averaging weights had been chosen using the three experimental FSV curves, the reported 2.15%, 2.9%, and 6.0% agreement would be partly circular. However, the text contains no quote or equation showing such fitting, so I do not classify it as demonstrated circularity. The self-adaptation of chapters from the author's published works (e.g., Ref. [30], [98]) is normal and not load-bearing in the sense of importing an external uniqueness theorem; the cited works contain the same proposed method rather than an independent justification of it. Overall, the central claim has independent content, but the undefined AVGFE rule prevents full verification that the polycrystal validation is non-circular.

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The central spall predictions depend on NAG coefficients fitted to MD data, on the transferability of those coefficients to hydrodynamics, and on the AVGFE rule for blending grain-boundary behavior. No code or full derivation of AVGFE is provided, so the ledger cannot be fully audited from this edition.

free parameters (4)
  • NAG coefficients (N0_dot, P1, Pn0, Pg0, eta) per crystal = Table 4.1 for single crystals; Table 6.2 for 23 bicrystals
    Fitted by PSO to MD void volume fraction vs pressure curves; these values enter the hydro simulations that produce the spall predictions.
  • Shock Hugoniot coefficients C and S for Cu, Al, Ni = Table 3.1; e.g., Ni S = 1.21
    Linear fits to MD shock data; the Ni slope deviates 16% from experiments, showing the fit is sensitive to the interatomic potential.
  • Strain-rate law coefficients a,b and P0,P1,tau0,epsilon0 = a=0.335, b=0.133; P0=2.76 GPa, P1=5.326 GPa, tau0=1.272e-8 s, epsilon0=2.64
    Fitted in chapter 5 to combined experimental and MD sigma_sp(epsilon_dot) data using GNUplot; these are descriptive fits, not predictive laws.
  • AVGFE averaging weights or rule = Not specified in visible text
    The averaging scheme that maps 23 bicrystal NAG parameter sets into a 1D hydrodynamic cell is the core of the polycrystal claim; its weighting is not auditable from this edition.
assumptions (6)
  • domain assumption EAM potentials transferable to high pressure and high strain rate
    Validated at ambient conditions (table 2.1) then used at pressures up to about 100 GPa and strain rates up to 1e11 s^-1; Ni requires special attention because the slope S deviates 16%.
  • domain assumption NAG/DFRACT model is an adequate macroscopic void-nucleation-growth description
    Underlies eqs. 2.16-2.19 and all hydro spall simulations; ignores coalescence, which the paper excludes from fitting.
  • domain assumption MD triaxial expansion at constant strain rate 5e9 s^-1 captures local tensile loading relevant to plate-impact spall
    The extracted NAG parameters are assumed transferable from this idealized loading to the 1D-strain shock environment.
  • ad hoc to paper AVGFE averaging over GB types reproduces polycrystal behavior
    Proposed in chapter 6; no derivation is shown in the visible text, and the 2-6% agreement rests on this rule.
  • domain assumption Steinberg-Guinan and polynomial EOS coefficients from literature valid for aluminum
    Used in the hydro code; coefficients are taken from refs [68,69] without recalibration.
  • standard math Rankine-Hugoniot and conservation equations
    Eqs. 3.1-3.6 are standard shock physics used to relate shock velocity, particle velocity, pressure, and volume.
invented entities (1)
  • AVGFE (Average Void Growth in a Fluid Element) averaging scheme
    purpose: Maps per-grain-boundary NAG parameters into a single 1D hydrodynamic cell to simulate polycrystalline spall
    It is a methodological construct, not a physical entity; the only evidence is the three-impact-velocity agreement reported in chapter 6, which is not independent if the averaging was tuned to experiments.

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Pith. "Pith review of Multi-scale modeling of high strain rate deformation and spall fracture in poly-crystalline metals." pith.science (2026). https://pith.science/paper/V6HL7CQF

@misc{pith2026260810734,
  author       = {Pith},
  title        = {Pith review of: Multi-scale modeling of high strain rate deformation and spall fracture in poly-crystalline metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6HL7CQF}},
  note         = {Machine review of arXiv:2608.10734}
}
abstract

This thesis utilizes a multiscale method by connecting molecular dynamics (MD) based information to hydrodynamic macroscopic calculations for investigating the shock response and spallation of metals. First, shock propagation in Cu, Al, and Ni single crystals is simulated up to $100$ GPa at strain rates $>10^6$ s$^{-1}$. Shock-Hugoniot ($U_s$-$U_p$) relations agree strongly with experiments (error $<6\%$); the Foiles EAM potential shows the least deviation for Ni. Second, a multiscale framework linking MD atomic void kinetics to hydrodynamic macro-calculations is established. Using particle swarm optimization (PSO), Nucleation and Growth (NAG) parameters are extracted for Cu, Nb, Mo, and Al, yielding free surface velocity (FSV) profiles matching experiments within $8\%$ for Al. Third, deformation across ten Al tilt (STGB) and twist (STwGB) bicrystals at rates of $10^{10}$-$10^{11}$ s$^{-1}$ proves that threshold spallation depends on boundary misorientation. Phase transitions near GBs lower spall strength at high $U_p$, whereas GB plasticity prolongs pull-back and delays spallation (e.g., $14.2^\circ$ STwGB). FSV methods are found to underestimate true peak tensile strength. Fourth, the framework is extended to polycrystals via 11 STGB and 12 STwGB configurations. Voids consistently nucleate at weakened GBs. Unique NAG parameters are fitted using PSO for all 23 bicrystals. An Average Void Growth in a Fluid Element (AVGFE) model is introduced to map these distinct boundary properties into 1D hydrodynamic codes. The combined model is validated against empirical Al flyer impacts at $518$, $1588$, and $2275$ m/s. The simulated temporal FSV curves mirror experiments, with spall strength deviations tightly bounded within $2.15\%$, $2.9\%$, and $6.0\%$, respectively, and spall thickness deviations within $2.4$-$4.0\%$.

Figures

Figures reproduced from arXiv: 2608.10734 by the authors.

Figure 1.1
Figure 1.1. Schematic of flyer-target impact system to generate a planar shock wave. The shock wave is formed in the YZ plane and propagates along the X-direction. Here, the YZ plane is perpendicular to the plane of the paper. This figure is made from the knowledge gained from Meyers [2]. (Fig:Ref. [31]) [PITH_FULL_IMAGE:figures/full_fig_p021_1_1.png] view at source ↗
Figure 2.1
Figure 2.1. Validation of PSO method (developed in-house) with standard multi-dimension mathematical functions as indicated in figures (a) to (d) [PITH_FULL_IMAGE:figures/full_fig_p030_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Pressure vs Shock propagation distance for flyer plate velocity 800 m/s. Continuous lines are from the 1D Hydrodynamic code developed in-house; Points are from KO code by Wilkins [68] Pressure (GPa) Distance (mm) 0 3 6 9 12 15 18 0.5 µs 1D Hydro 0 3 6 9 12 15 18 0.5 µs 1D Hydro KO Wilkins 0 3 6 9 12 15 18 1 µs 0 3 6 9 12 15 18 1 µs 0 3 6 9 12 15 18 2 µs 0 3 6 9 12 15 18 2 µs 0 3 6 9 12 15 18 0 10 20 30 40 50 3 µs 0 … view at source ↗
Figures from the paper (34 more)
Figure 2.3
Figure 2.3. Figure 2.3: Pressure vs Shock propagation distance for flyer plate velocity 2000 m/s. Continuous lines are from the 1D Hydrodynamic code developed in-house; Points are from KO code by Wilkins [68] [PITH_FULL_IMAGE:figures/full_fig_p035_2_3.png]
Figure 2.4
Figure 2.4. Figure 2.4: Validation of Hugoniot calculated from 1D-Hydrodynamic code for Al : Comparing the simulations results with the experimental work of McQueen [71] and Marsh [72] [PITH_FULL_IMAGE:figures/full_fig_p036_2_4.png]
Figure 2.5
Figure 2.5. Figure 2.5: Flowchart- Sequential steps in the Multiscale modelling: (1) MD −→ (2) PSO −→ (3) HD [PITH_FULL_IMAGE:figures/full_fig_p037_2_5.png]
Figure 3.1
Figure 3.1. Figure 3.1: Spatial Pressure Profile along X-direction for Cu flyer with an impact velocity of 3.0 km/sec. This shows Shock wave position at different times. (Fig:Ref. [31]) [PITH_FULL_IMAGE:figures/full_fig_p041_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: Shock velocity(Us) Vs Particle velocity(Up) data obtained from MD are compared with the results of first principles [31] and experiments for Cu (a), Al (b) & Ni (c). MD results are shown with error bars to represent the uncertainty involved in the shock velocity calc…
Figure 3.3
Figure 3.3. Figure 3.3: Pressure vs Specific Volume obtained under Isothermal and Dynamic Shock-Hugoniot States from MD calculation are compared with published results of first principles calculation and experiments; For isotherm states, the comparisons are made for Cu with Akahama Ref.[85]…
Figure 3.4
Figure 3.4. Figure 3.4: Us −Up & P-V Hugoniot obtained for Ni from this work using Foiles’ EAM potential [54] are compared with MD simulations reported independently by Choi, et al. [36] with four different potentials(RW, DWY, ZJW, MFMP); Jarmakani et al. [34]; Liu Hai et al.[35]. The exper…
Figure 3.5
Figure 3.5. Figure 3.5: MD shock Hugoniot obtained for Ni from this work using Foiles’ EAM potential [54] are compared (a) for Us −Up with experimental results reported by [88] for n-Ni (m=2), (b) for P-ρ with experimental results reported by [89] for Ni with porosity m=1, 1.4 & 2 (Y-axis i…
Figure 4.1
Figure 4.1. Figure 4.1: Workflow of Multi-scale modelling consisting of MD simulations of triaxial deformation of bi-crystals to obtain the void nucleation and growth as a function of tensile pressure. This information is used by a particle swarm optimization (PSO) code to fit the parameter…
Figure 4.2
Figure 4.2. Figure 4.2: MD simulation of single crystal Al subjected to high strain rate triaxial deformation (ε˙ = 5×109 s −1 ). Fig.(a) Image of Al-single crystal with nucleated Void, figure (b) Temporal pressure profile that is used to find the NAG parameters of Al [PITH_FULL_IMAGE:figu…
Figure 4.3
Figure 4.3. Figure 4.3: Void Volume fraction as a function of Pressure. Also shown the line fitted to to MD data using PSO method. Under tri-axial tensile force the void volume fraction and the net pressure of single crystal material vary. This phenomena is captured by MD simulations of mol…
Figure 4.4
Figure 4.4. Figure 4.4: (a) shows the shock wave propagation at very early times. Shock wave is created upon the flyer impacting a target and it travels in both the directions from the point of impact which is at a location 2 mm in figure 4.4(a). The left moving wave reflects from the free …
Figure 4.5
Figure 4.5. Figure 4.5: Comparison of the temporal evolution of Free Surace Velocity (FSV) from ‘Multiscale’ simulations for single crystal of Cu with expt. from ref. [14] NAG parameters are obtained newly in this research work for Mo and Al, while for Cu and Nb, they are adapted from the p…
Figure 4.6
Figure 4.6. Figure 4.6: Comparison of Temporal evolution of Free Surace Velocity (FSV) from ‘Multiscale’ simulations for single crystal of Nb & Mo with expt. from ref. [14]. For Nb (B99) and Mo (B80), multiscale results reported by VR Ikkurthi et al. from ref. [28] is also presented. Multis…
Figure 4.7
Figure 4.7. Figure 4.7: Comparison of Temporal evolution of Free Surace Velocity (FSV) from ‘Multiscale’ simulations for single crystal of Al in 3 different configurations: (a) with Baumang-expt. in ref. [7]; (b) & (c): with Assay expt. 28, 8 as in ref. [94] qualitatively no significant dif…
Figure 5.1
Figure 5.1. Figure 5.1: Initial arrangement of the atoms: The flyer, the target with a grain boundary. The planar shock generated by the impact is in the XZ plane and it propagates along the Y-direction. (Fig:Ref. [98]) For the shock impact simulations, the atoms belonging to one-third of t…
Figure 5.2
Figure 5.2. Figure 5.2: MD impact shock simulations : Temporal variation of free surface velocities (FSV) is shown for GB angle, 22.6 ◦ in the case of (a) STGB, (b) STwGB with various particle velocities (Up in km/s). 5.3.1 Temporal FSV for Tilt and Twist GB, 22.6 o with different levels of…
Figure 5.3
Figure 5.3. Figure 5.3: FSV as a function of time for different STGB with various particle velocities (Up) (Fig:Ref. [98]) Mean Square Deviation (RMSD) are calculated. These are shown in figure 5.6. Figures 5.6(a) to 5.6(f) correspond, respectively to the same parameters as used in figures …
Figure 5.4
Figure 5.4. Figure 5.4: FSV as a function of time for different STwGB with various particle velocities (Up) Variation of σsp in terms of (i) varying Up, (ii) GB angles and (iii) GB Energy (i) [PITH_FULL_IMAGE:figures/full_fig_p067_5_4.png]
Figure 5.5
Figure 5.5. Figure 5.5: Comparison of the spall strength (σsp) obtained from MD simulations for various STGBs in figures a,c,e & STwGBs in figures b,d,f. function of STGB and STwGB angles respectively. In the case of STGB angles, for a given Up calculated σsp do not vary much. The maximum v…
Figure 5.6
Figure 5.6. Figure 5.6: Arithmetic mean values of σsp obtained from MD simulations with their respective RMS deviations are shown in figures a,c,e for STGB and b,d,f for STwGB. Figures a to f also show respective values of σT mean and their RMS values. km/s, no trend was seen for the crysta…
Figure 5.7
Figure 5.7. Figure 5.7: (a): Log-Log scale with the functional form 1-(eqn. 5.3). (b): Log-Linear scale with the functional form 2-(eqn. 5.4). Calculated spall strengths (σsp) for various strain rates (ε˙) from MD simulations are compared with experiments. The various strains rates in MD si…
Figure 5.8
Figure 5.8. Figure 5.8: OVITO-based visualization images in YZ plane, showing different phases: FCC (green), BCC (blue) and Unknown (grey) for STGB (22.6 o ) at t=1.65 picosec. Figures a to f correspond to Up=0.5 to 1.75 km/s in steps of 0.25 km/s respectively. The shock propagates along th…
Figure 5.9
Figure 5.9. Figure 5.9: OVITO-based visualization images in YZ plane showing different phases: FCC (green), BCC (blue), HCP (red) and unknown (grey) for STwGB (22.6 o ) at t=1.65 picosec. Figures a to f correspond to Up=0.5 to 1.75 km/s in steps of 0.25 km/s respectively. The shock propagat…
Figure 5.10
Figure 5.10. Figure 5.10: OVITO-based visualization images in YZ plane, to show the dislocation formation for STwGB (14.2 o ) at various times: corresponding Up is 1 km/s (flyer velocity = 2 km/s). Shock propagates along the horizontal Y-axis. rearrangement of atoms. This eventually assists …
Figure 5.11
Figure 5.11. Figure 5.11: Total line length of dislocations for STwGB (14.2 o ) at various Up, calculated by OVITO-based DXA tool. are allowed to move freely along which the plane-wave shock propagates. Periodic boundary conditions are applied along X and Z directions. The target and the fly…
Figure 6.1
Figure 6.1. Figure 6.1: Comparison of grain boundary energy calculated from our simulation, with published results for Al, for various symmetric tilt [100] and symmetric twist [101] angles. (Fig:Ref. [30]) . ( 10.7 ps). Note also that the voids nucleate at the grain boundary, which is expec…
Figure 6.2
Figure 6.2. Figure 6.2: MD simulation of high strain rate triaxial expansion of Al bi-crystal representing an STGB 59.5◦ : (fig. a) Temporal pressure profile, (fig. b) Temporal evolution of the number of voids and (figs. c-h) the MD computational domain in XY Plane showing the nucleation, g…
Figure 6.3
Figure 6.3. Figure 6.3: MD simulation of high strain rate triaxial expansion of Al bi-crystal representing an STwGB 31.8◦ : (fig. a) Temporal pressure profile, (fig. b) Temporal evolution of the number of voids and (figs. c-h) the MD computational domain in XY Plane showing the nucleation, …
Figure 6.4
Figure 6.4. Figure 6.4: (a) Temporal evolution of dislocation density - tilt & twist; Dislocation line length and number of dislocations segments obtained from MD triaxial deformation simulations are shown in fig.(b) for misorientation angle 59.5◦ STGB (7 4 0) and in fig.(c) for 31.8◦ STwGB…
Figure 6.5
Figure 6.5. Figure 6.5: Void Volume Fraction obtained using NAG parameter fitting are compared with MD simulations results for various tilt angles as indicated. (Fig:Ref. [30]) . and experimental spall strength values match very well within the relative error (deviation) of 2.15% for set-1,…
Figure 6.6
Figure 6.6. Figure 6.6: Void Volume Fraction obtained using NAG parameter fitting are compared with MD simulations results for various twist angles as as indicated. (Fig:Ref. [30]) . values for single crystal (SC) aluminum [29] [PITH_FULL_IMAGE:figures/full_fig_p087_6_6.png]
Figure 6.7
Figure 6.7. Figure 6.7: Multiscale model : Calculated time-varying free surface velocity obtained for set-1, set-2 & set-3 described in sec. 6.3.3. For comparison respective results from Expt. No.1 of Owen, ref. [108] and Expt. No. 19 & 26 of Asay, ref. [94] are also shown. (Fig:Ref. [30]) …
Figure 6.8
Figure 6.8. Figure 6.8: Comparison of Free surface velocity obtained from AVGFE, AMEAN and Single Crystal for set-1, set-2 & set-3. (Fig:Ref. [30]) [PITH_FULL_IMAGE:figures/full_fig_p088_6_8.png]

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Works this paper leans on

113 extracted references · 74 canonical work pages

  1. [1]

    Graham, Solids Under High-Pressure Shock Compression, Springer, 1993

    R. Graham, Solids Under High-Pressure Shock Compression, Springer, 1993. ← page 1

    1993

  2. [2]

    M. A. Meyers, Dynamic Behavior of Materials, John Wiley & Sons, Inc., New York, 1994. ←pages 1, 2, 3, 19, 23, 24, 28, 29, 30, 45, 53, 54, and 73

    1994

  3. [3]

    Johnson, W

    G. Johnson, W. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech. 21 (1985) 31–48.←pages 1, 30, and 41

    1985

  4. [4]

    V . E. Fortov, V . V . Kostin, S. Eliezer, Spallation of metals under laser irradiation, Journal of Applied Physics 70 (1991) 4524. doi:10.1063/1.349087. ← pages 1, 2, 41, 52, and 53

    work page doi:10.1063/1.349087 1991

  5. [5]

    Moshe, S

    E. Moshe, S. Eliezer, E. Dekel, A. Ludmirsky, Z. Henis, M. Werdiger, I. B. Goldberg, An increase of the spall strength in aluminum, copper, and metglas at strain rates larger than 107 s−1, Jnl. of Applied Physics 83 (1998) 4004.←pages 1, 2, 41, 52, and 53

    1998

  6. [6]

    Moshe, S

    E. Moshe, S. Eliezer, Z. Henis, M. Werdiger, E. Dekel, Y . Horovitz, S. Maman, I. B. Goldberg, D. Eliezer, Experimental measurements of the strength of metals approaching the theoretical limit predicted by the equation of state, Applied Physics Letters 76 (2000) 1555–1557.←pages 1, 2, 41, 52, and 53

    2000

  7. [7]

    G. I. Kanel, S. V . Razorenov, K. Baumung, J. Singer, Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point, Jnl. of App. Phy. 90 (2001) 136–143. doi:doi.org/10.1063/1.1374478. ← pages 1, 30, 35, 36, 38, 39, 41, 52, and 53

    work page doi:10.1063/1.1374478 2001

  8. [8]

    Seaman, D

    L. Seaman, D. R. Curran, D. A. Shockey, Computational models for ductile and brittle fracture, Jnl. Appl. Phys. 47 (1976) 4814.←pages 1, 30, and 41

    1976

Show all 113 references
  1. [9]

    D. R. Curran, L. Seaman, D. A. Shockey, Dynamic failure of solids, Phys. Rep. 147 (5-6) (1987) 253–388.←pages 1, 13, 30, 33, and 41

    1987

  2. [10]

    J. N. Johnson, G. Gray, N. Bourne, Effect of pulse duration and strain rate on incipient spall fracture in copper, Jnl. Appl. Phys. 86 (1999) 4892–4901.←pages 1, 30, and 41

    1999

  3. [11]

    V . R. Ikkurthi, S. Chaturvedi, Use of different damage models for simulating impact-driven spallation in metal plates, Int. J. Impact Engg. 30 (2004) 275–301. ← pages 1, 2, 30, 33, and 41

    2004

  4. [12]

    I. R. Vatne, A. Stukowski, C. Thaulow, E. Østby, J. Marian, Three-dimensional crack initiation mechanisms in BCC-Fe under loading modes I, II and III, Materials Science and Engineering: A 560 (2013) 306–314. doi:10.1016/j.msea.2012.09.071. ← pages 1 and 41

    2013 doi

  5. [13]

    Madhavan, V

    S. Madhavan, V . Mehra, S. Pahari, S. Ghosh, C. D. Sijoy, S. Chaturvedi, Buckling and longitudinal cracks in electromagnetically accelerated hollow cylinders, International Journal of Fracture 193 (2015) 1–16.doi:10.1007/s10704-015-0010-9.←pages 1 and 41

    2015 doi

  6. [14]

    T. H. Antoun, L. Seaman, D. R. Curran, Dynamic failure of materials: V olume 2-compilation BIBLIOGRAPHY 77 of russian spall data, Tech. Rep. DSWA-TR-96-77-V2, URL active as on 30th Mar 2023 (1998). URL https://apps.dtic.mil/sti/pdfs/ADA362759.pdf← pages 1, 30, 35, 36, 37, 38, ...

    1998

  7. [15]

    H. E. Lorenzana, J. F. Belak, K. S. Bradley, Shocked materials at the intersection of experiment and simulation, Scientific Modelling and Simulations. 15 (2008) 159–186. doi:10.1007/s10820-008-9107-z.←page 1

    2008 doi

  8. [16]

    J. R. Asay, L. M. Barker, Interferometric mmeasurement of shock-induced particle velocity and spatial variations of particle velocity, Journal of Applied Physics 45 (1974) 2540–2546. ←pages 1 and 35

    1974

  9. [17]

    D. D. Bloomquist, S. A. Sheffield, Optically recording interferometer for velocity mea- surements with subnanosecond resolution, Journal of Applied Physics 54 (1983) 1717. doi:10.1063/1.332222.←pages 1 and 35

    1983 doi

  10. [18]

    R. E. Duff, F. S. Minshall, Investigation of a Shock-Induced Transition in Bismuth, Physical Review 108 (5) (1957) 1207–1212.←page 1

    1957

  11. [19]

    S. G. Srinivasan, M. I. Baskes, G. J. Wagner, Spallation of single crystal nickel by void nucleation at shock induced grain junctions, Journal of Materials Science 41 (2006) 7838– 7842.←pages 1 and 41

    2006

  12. [20]

    S. G. Srinivasan, M. I. Baskes, G. J. Wagner, Atomistic simulations of shock induced microstructural evolution and spallation in single crystal nickel, Journal of Applied Physics 101 (2007) 043504.doi:10.1063/1.2423084.←pages 1, 3, 4, 41, 42, 52, and 53

    2007 doi

  13. [21]

    Rawat, M

    S. Rawat, M. Warrier, S. Chaturvedi, V . Chavan, Effect of material damage on the spallation threshold of single crystal copper: a molecular dynamics study, Modelling and Simulation in Material Science and Engineering 20 (2012) 015012.←pages 1, 21, 22, 41, and 60

    2012

  14. [22]

    D. D. Jiang, J. L. Shao, B. Wu, P. Wang, A. M. He, Sudden change of spall strength induced by shock defects based on atomistic simulation of single crystal aluminum, Scripta Materialia 210 (2022) 114474. doi:https://doi.org/10.1016/j.scriptamat.2021. 114474.←pages 1, 4, 41, 51, and 54

    2022 doi

  15. [23]

    S. J. Fensin, S. M. Valone, E. K. Cerreta, G. T. Gray, Influence of grain boundary properties on spall strength: Grain boundary energy and excess volume, Journal of Applied Physics 112 (2012) 083529.←pages 1, 4, 41, and 51

    2012

  16. [24]

    Y . Zhu, J. Hu, S. Huang, J. Wang, G. Luo, Q. Shen, Molecular dynamics simulation on spal- lation of [111] Cu/Ni nano-multilayers: V oids evolution under different shock pulse duration, Computational Materials Science 202 (2022) 110923. doi:10.1016/j.commatsci.2021. 110923.←pa...

    2022 doi

  17. [25]

    M. L. Wilkins, Computer Simulation of Dynamic Phenomena, Springer, 1999. ← pages 2, 12, 13, 19, and 30

    1999

  18. [26]

    W. J. Murphy, A. Higginbotham, G. K. et al., The strength of single crystal copper under uniaxial shock compression at 100 GPa, Journal of Physics: Condensed Matter 22 (6) (2010) 065404.doi:10.1088/0953-8984/22/6/065404.←page 2

    2010 doi

  19. [27]

    Rawat, V

    S. Rawat, V . R. Ikkurthi, M. Warrier, S. Chaturvedi, Multiscale simulations of damage of perfect crystal Cu at high strain rates, PRAMANA Journal of Physics 83 (2) (2014) 265–272. ←pages 2, 3, 7, 33, 61, 68, and 73

    2014

  20. [28]

    ← pages 2, 3, 5, 7, 30, 35, 37, BIBLIOGRAPHY 78 38, 39, 40, 61, 68, and 73

    V .R.Ikkurthi, H.Hemani, R.Sugandhi, S.Rawat, P.Pahari, M.Warrier, S.Chaturvedia, Multi- scale computational approach for modelling spallation at high strain rates in single-crystal materials, Procedia Engineering 173 (2017) 1177–1184. ← pages 2, 3, 5, 7, 30, 35, 37, BIBLIOGRA...

    2017

  21. [29]

    Madhavan, V

    S. Madhavan, V . R. Ikkuthi, P. V . Laxminarayana, M. Warrier, Multiscale modelling to estimate spall parameters in metallic single crystals, in: Proc. ICONS2018, International Conference on Structural Integrity, IITM, Chennai, India, 2018. doi:https://doi.org/ 10.48550/arXiv....

    2018 doi arXiv

  22. [31]

    Madhavan, V

    S. Madhavan, V . Mishra, P. V . L. Narayana, M. Warrier, Dynamic Response of Single Crystal Al, Cu & Ni Upon Impact : MD and Ab-Initio Calculations, Journal of Dynamic Behavior of Materials 9(1) (2023) 24–35. doi:10.1007/s40870-022-00356-5 . ← pages 2, 5, 19, 22, 23, 24, 25, 2...

    2023 doi

  23. [32]

    B. L. Holian, Modeling shock-wave deformation via molecular dynamics, Physical Review A 37 (7) (1988) 2562–2568.doi:10.1103/PhysRevA.37.2562.←pages 3 and 20

    1988 doi

  24. [33]

    E. M. Bringa, J. U. Cazamias, P. Erhart, et. al, Atomistic shock Hugoniot simulation of single-crystal copper, Journal of Applied Physics 97 (7) (2004) 3793–3799. doi:10.1063/ 1.1789266.←pages 3 and 20

    2004

  25. [34]

    H. N. Jarmakani, E. M. Bringa, P. Erhart, B. A. Remington, Y . M. Wang, N. Q. V o, M. A. Meyers, Molecular dynamics simulations of shock compression of nickel: From monocrys- tals to nanocrystals, Acta Materialia 56 (2008) 5584–5604. ← pages 3, 20, 27, 28, 29, and 73

    2008

  26. [35]

    L. Hai, H. Jie, Z. Zhi-xuan, M. Zhao-xia, Atomistic simulations of elastic-plastic deformation in nickel single crystal under shock loading, Procedia Engineering 204 (2017) 397–404. ←pages 3, 20, 27, 28, 29, and 73

    2017

  27. [36]

    J. Choi, S. Yoo, S. Song, J. S. Park, K. Kang, Molecular dynamics study of Hugoniot relation in shocked nickel single crystal, Journal of Mechanical Science and Technology 32 (7) (2018) 7983.←pages 3, 20, 27, 28, 29, and 73

    2018

  28. [37]

    Sugandhi, M

    R. Sugandhi, M. Warrier, S. Chaturvedi, Identification of best parameters of void nucleation and growth model using particle swarm technique., Applied Soft Computing 35 (2015) 113–122.←pages 3 and 10

    2015

  29. [38]

    Adlakha, M

    I. Adlakha, M. A. Tschopp, K. N. Solanki, The role of grain boundary structure and crystal orientation on crack growth asymmetry in aluminum, Materials Science and Engineering: A 618 (2014) 345–354.doi:10.1016/j.msea.2014.08.083.←pages 3, 4, and 41

    2014 doi

  30. [39]

    Zhang, K

    X. Zhang, K. Wang, W. Zhu, J. Chen, M. Cai, S. Xiao, H. Deng, W. Hu, Effect of grain boundaries on shock-induced phase transformation in iron bicrystals, Jnl. of Applied Physics 123 (2018) 045105.doi:10.1063/1.5003891.←pages 4 and 41

    2018 doi

  31. [40]

    X. Long, X. Liu, W. Zhang, Y . Peng, G. Wang, Shock deformation and spallation of Cu bicrystals with (111) twist grain boundaries, Computational Materials Science 173 (2020) 109411.doi:10.1016/j.commatsci.2019.109411.←pages 4, 41, 51, 56, and 59

    2020

  32. [41]

    E. Q. Lin, H. J. Shi, L. S. Niu, E. Z. Jin, Shock response of copper bicrystals with a Σ3 asymmetric tilt grain boundary, Computational Materials Science 59 (2012) 94–100. doi: https://doi.org/10.1016/j.commatsci.2012.02.025.←pages 4, 41, 42, and 51

    2012 doi

  33. [42]

    S. N. Luo, T. C. Germann, D. L. T. Q. An, Shock wave loading and spallation of copper bicrystals with asymmetric Σ3 <110> tilt grain boundaries, Jnl. Appl Phys. 108 (2010) BIBLIOGRAPHY 79 093526.doi:10.1063/1.3506707.←pages 4 and 41

    2010 doi

  34. [43]

    W. Z. Han, Q. An, S. N. Luo, T. C. Germann, D. L. Tonks, W. A. Goddard, Deformation and spallation of shocked Cu bicrystals with Σ 3 coherent and symmetric incoherent twin boundaries, Phys Rev B 85 (2012) 024107. doi:10.1103/Physrevb.85.024107. ← pages 4 and 41

    2012 doi

  35. [44]

    S. J. Fensin, S. M. Valone, E. K. Cerreta, et.al., Effect of grain boundary structure on plastic deformation during shock compression using molecular dynamics, Model Simul Mater Sci. 21 (2013) 015011.doi:10.1088/0965-0393/21/1/015011.←pages 4 and 41

    2013 doi

  36. [45]

    Y . Zhou, Z. Yang, Z. Lu, Dynamic crack propagation in copper bicrystals grain boundary by atomistic simulation, Materials Science and Engineering: A 599 (2014) 116–124. ← pages 4 and 41

    2014

  37. [46]

    L. A. Barrales-Mora, Y . Tokuda, D. A. Molodov, S. Tsurekawa, On incipient plasticity in the vicinity of grain boundaries in aluminum bicrystals: Experimental and simulation nanoindentation study, Materials Science and Engineering: A 828 (2021) 142100. doi: 10.1016/j.msea.2021...

    2021

  38. [47]

    W. W. Pang, P. Zhang, G. Zhang, A. Xu, X. Zhao, Dislocation creation and void nucleation in FCC ductile metals under tensile loading: A general microsopic picture, Scientific Reports 4 (2014) 6981.←page 4

    2014

  39. [48]

    H. V . Swygenhoven, P. M. Derlet, A. G. Froseth, Nucleation and propagation of dislocatiosn in nanocrystalline fcc metals, Acta Materialia 54 (2005) 1975–1983.←pages 4 and 59

    2005

  40. [49]

    D. E. Spearot, K. L. Jacob, D. L. McDowell, Nucleation of dislocations from [001] bicrystal interfaces in aluminum, Acta Materialia 53 (2005) 3579–3589.←pages 4, 56, and 59

    2005

  41. [50]

    Dremov, A

    V . Dremov, A. Petrovtsev, P. Sapozhnikov, M. Smirnova, Molecular dynamics simulations of the initial stages of spall in nanocrystalline copper, Phy. Rev. B 74 (2006) 144110.← pages 4 and 59

    2006

  42. [51]

    Plimpton, Fast parallel algorithms for short range molecular dynamics, Journal of Compu- tational Physics 117 (1995) 1–19.←pages 5, 7, 21, 42, 86, and 87

    S. Plimpton, Fast parallel algorithms for short range molecular dynamics, Journal of Compu- tational Physics 117 (1995) 1–19.←pages 5, 7, 21, 42, 86, and 87

    1995

  43. [52]

    Rawat, Behavior of solids under high strain rate deformation, Ph.D

    S. Rawat, Behavior of solids under high strain rate deformation, Ph.D. thesis, (2012) pp 32-38 chapter 3.3; URL active as on 30th Mar 2023. URL http://www.hbni.ac.in/phdthesis/phys/PHYS01200704031.pdf← pages 7, 9, 30, 33, 35, 39, and 40

    2012

  44. [53]

    Lammps benchmarks, https://www.lammps.org/bench.html, URL active as on 30th Mar 2023.←page 7

    2023

  45. [54]

    S. M. Foiles, M. I. Baskes, M. S. Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt and their alloys, Physical Review B 33 (1986) 7983. ← pages 8, 9, 20, 21, 25, 27, 28, 29, 31, 73, and 87

    1986

  46. [55]

    Interatomic potentials overview, https://www.ctcms.nist.gov/potentials, URL ac- tive as on 30th Mar 2023.doi:10.18434/m37.←pages 8, 87, 88, and 89

    2023 doi

  47. [56]

    Mishin, D

    Y . Mishin, D. Farkas, M. J. Mehl, D. A. Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Physical Review B 59 (5) (1999) 3393–3407.←pages 8, 9, 42, 60, and 89

    1999

  48. [57]

    X. W. Zhou, R. A. Johnson, H. N. G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers, Physical Review B 69 (14) (2004) 144113. doi: {10.1103/physrevb.69.144113}.←pages 8, 9, 31, and 88

    2004 doi

  49. [58]

    Kittel, Introduction to Solid State Physics, 8th Edition, John Wiley & Sons, 2005

    C. Kittel, Introduction to Solid State Physics, 8th Edition, John Wiley & Sons, 2005. ← pages 8 and 9. BIBLIOGRAPHY 80

    2005

  50. [59]

    D. B. Marghitu, Mechanical Engineer’s handbook, Academic Press, 2001. ← pages 8 and 9

    2001

  51. [60]

    Tzanetakis and J

    P. Tzanetakis and J. Hillairet and G. Revel, The Formation Energy of Vacancies in Aluminium and Magnesium, physica status solidi B 75 (2) (1976) 433–439.←page 9

    1976

  52. [61]

    McGervey, W

    J. McGervey, W. Triftshuser, Vacancy-formation energies in copper and silver from positron annihilation, Physics Letters A 44 (1) (1973) 53–54. doi:https://doi.org/10.1016/ 0375-9601(73)90957-2.←page 9

    1973

  53. [62]

    T. R. Mattsson, N. Sandberg, R. Armiento, A. E. Mattsson, Quantifying the anomalous self-diffusion in molybdenum with first-principles simulations, Phys. Rev. B 80 (22) (2009) 224104.doi:10.1103/PhysRevB.80.224104.←page 9

    2009 doi

  54. [63]

    Wolff, M

    J. Wolff, M. Franz, J.-E. Kluin, D. Schmid, Vacancy formation in nickel and α-nickel- carbon alloy, Acta Materialia 45 (11) (1997) 4759–4764. doi:https://doi.org/10. 1016/S1359-6454(97)00112-2.←page 9

    1997

  55. [64]

    K. W. Jacobsen, J. K. Norskov, M. J. Puska, Interatomic interactions in the effective-medium theory, Physical Review B 35 (1987) 7423.←pages 8, 21, 29, 31, and 73

    1987

  56. [65]

    Nordlund, Basics of md, initialization, time step choice, speedup methods, http://beam

    K. Nordlund, Basics of md, initialization, time step choice, speedup methods, http://beam. helsinki.fi/~knordlun/atomistiset/lecture2.ps.gz, URL active as on 30th Mar 2023 (2000).←page 9

    2000

  57. [66]

    Y . Shi, R. Eberhart, A modified particle swarm optimizer, in: Proc. of IEEE international conference on evolutionary computation. IEEE world congress on computational intelligence (Cat. No. 98TH8360), IEEE, 1998, pp. 69–73.←pages 10 and 11

    1998

  58. [67]

    X. S. Yang, Test problems in optimization, John Wiley & Sons, 2010.←page 11

    2010

  59. [68]

    M. L. Wilkins, Calculation of elastic-plastic flow, in: B. Alder (Ed.), Methods in Computa- tional Physics, V ol. 3, 1964, pp. 211–263.←pages 12, 13, 14, 15, 16, and 30

    1964

  60. [69]

    D. J. Steinberg, S. G. Cochran, M. W. Guinan, A constitutive model for metals applicable at high-strain rate, Journal of Applied Physics 51 (3) (1980) 1498–1504. ← pages 13 and 30

    1980

  61. [70]

    D. J. Steinberg, Constitutive model used in computer simulation of time-resolved, shock- wave data, International Journal of Impact Engineering 5 (1) (1987) 603–611, hyperve- locity Impact Proceedings of the 1986 Symposium. doi:https://doi.org/10.1016/ 0734-743X(87)90075-3.←pa...

    1987

  62. [71]

    R. G. McQueen, S. P. Marsh, J. W. Taylor, J. N. Fritz, W. J. Carter, The equation of state of solids from shock wave studies, High velocity impact phenomena 293 (1970) 294–417. ←pages 15 and 17

    1970

  63. [72]

    S. P. Marsh, LASL Shock Hugoniot Data, University of california press, Berkeley, 1980. ←pages 15, 17, 23, 24, 26, 27, 28, and 73

    1980

  64. [73]

    Zel’dovich, Y

    Y . Zel’dovich, Y . Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover Books on Physics, Dover Publications, New York, 2002. URLhttps://books.google.co.in/books?id=zVf27TMNdToC←page 19

    2002

  65. [74]

    A. C. Mitchell, W. J. Nellis, Shock compression of aluminum, copper, and tantalum, Journal of Applied Physics 52 (5) (1981) 3363–3374.←pages 19, 23, 24, 28, 30, and 73

    1981

  66. [75]

    A. D. Chijioke, W. J. Nellis, I. F. Silvera, High-pressure equations of state of Al, Cu, Ta and W, Journal of Applied Physics 98 (2005) 073526.←page 19

    2005

  67. [76]

    M. O. Steinhauser, S. Hiermaier, A review of computational methods in materials science: Examples from shock-wave and polymer physics, Int. J. Mol. Sci. 10 (12) (2009) 5135–5216. ←page 20. BIBLIOGRAPHY 81

    2009

  68. [77]

    Y . Y . Ju, Q. M. Zhang, Z. Z. Gong, G. F. Ji, L. Zhou, Molecular dynamics simulation of shock melting of aluminum single crystal, Journal of Applied Physics 114 (2013) 093507. ←page 20

    2013

  69. [78]

    A. A. Selezenev, V . K. Golubev, A. Y . Aleinikov, O. I. Butney, R. A. Barabanov, B. L. V oronin, Molecular dynamics simulation of shock wave compression of metals, AIP Conference Proceedings 620 (2002) 374–377.←page 20

    2002

  70. [79]

    A. C. Mitchell, W. J. Nellis, J. A. Moriarty, R. A. Heinle, N. C. Holmes, R. E. Tipton, G. W. Repp, Equation of state of Al, Cu, Mo, and Pb at shock pressures up to 2.4 TPa (24 Mbar), Journal of Applied Physics 69 (1991) 2981–2986.←page 20

    1991

  71. [80]

    K. D. Joshi, S. C. Gupta, S. Banerjee, Shock Hugoniot of osmium up to 800 GPa from first principles calculations, J. Phys. Condens. Matter 21 (2009) 415402(1–6).←page 20

    2009

  72. [81]

    Gyanchandani, V

    J. Gyanchandani, V . Mishra, G. K. D. S. K. Sikka, Super heavy element copernicium: Cohesive and electronic properties revisited, Solid State Communications 269 (2018) 16. ←page 20

    2018

  73. [82]

    J. R. Taylor, An introduction to error analysis, 2nd Edition, University Science Books, Sausalito, California, 1997, Ch. 3, pp. 51–53.←page 22

    1997

  74. [83]

    Dewaele, P

    A. Dewaele, P. Loubeyre, M. Mezouar, Equations of state of six metals above 94 GPa, Physical Review B 70 (2004) 094112.←pages 23, 25, and 26

    2004

  75. [84]

    Dewaele, M

    A. Dewaele, M. Torrent, P. Loubeyre, M. Mezouar, Compression curves of transition metals in the mbar range: Experiments and projector augmented-wave calculations, Physical Review B 78 (2008) 104102.←pages 23, 25, and 26

    2008

  76. [85]

    Akahama, M

    Y . Akahama, M. Nishimura, K. Kinoshita, H. Kawamura, Y . Ohishi, Evidence of a fcc-hcp transition in aluminum at multimegabar pressure, Physical Review Letters 96 (2006) 045505. ←pages 23, 25, and 26

    2006

  77. [86]

    J. F. Ziegler, J. P. Biersack, The stopping and range of ions in matter, in Treatise on Heavy-Ion Science, Springer (1985) 93–129.←page 25

    1985

  78. [87]

    D. K. Belashchenko, Computer simulation of nickel and the account for electron contributions in the molecular dynamics method, High Temp. 58 (1) (2020) 64–77.←page 27

    2020

  79. [88]

    A. Y . Dolgoborodov, S. Y . Ananev, V . V . Yakushev, Shock Hugoniot of porous nanosized nickel, J. Appl. Phys. 131 (2022) 125902.←pages 27 and 29

    2022

  80. [89]

    S. A. Kinelovskii, K. K. Maevskii, Estimation of the thermodynamic parameters of a shock-wave action on high-porosity heterogeneous materials, Technical Phys 61 (8) (2016) 1244–1249.←pages 28 and 29

    2016

  81. [90]

    ← pages 28 and 29

    The international shock-wave database (ISWdb), URL active as on 30th Mar 2023. ← pages 28 and 29

    2023

  82. [91]

    J. A. Zukas, Introduction to Hydrocodes, Elsevier, Amsterdam, 2004.←page 30

    2004

  83. [92]

    Eliezer, An Introduction to Equations of State: Theory and Applications, Cambridge University Press, Cambridge, 1986.←page 30

    S. Eliezer, An Introduction to Equations of State: Theory and Applications, Cambridge University Press, Cambridge, 1986.←page 30

    1986

  84. [93]

    S. V . G. Menon, B. Nayak, An equation of state for metals at high temperature and pressure in compressed and expanded volume regions, Condensed Matter 4 (3) (2019) article no. 71. doi:10.3390/condmat4030071.←page 30

    2019 doi

  85. [94]

    X. Chen, J. R. Asay, S. K. Dwivedi, D. P. Field, Spall behavior of aluminum with varying microstructures, Journal of Applied Physics 99 (2006) 023528. doi:10.1063/1.2165409. ←pages 30, 35, 36, 38, 39, 64, 65, 66, and 69

    2006 doi

  86. [95]

    M. R. Fellinger, H. Park, J. W. Wilkins, Force-matched embedded-atom method potential for niobium, Physical Review B 81 (14) (2010) 144119. doi:10.1103/physrevb.81.144119. BIBLIOGRAPHY 82 ←page 31

    2010 doi

  87. [96]

    Hemani, M

    H. Hemani, M. Warrier, N. Sakthivel, S. Chaturvedi, V oxel based parallel post processor for void nucleation and growth analysis of atomistic simulations of material fracture, Journal of Molecular Graphics and Modeling 50 (2014) 134–141.←page 32

    2014

  88. [97]

    M. V . Zhernokletov, B. L. Glushak, Material Properties under Intensive Dynamic Loading, Springer, 2006.←page 41

    2006

  89. [98]

    Madhavan, P

    S. Madhavan, P. V . Laxminarayana, M. Warrier, Spall fracture in aluminum bicrystals: Molecular dynamics study, Materials Today: Proc. 87 (1) (2023) 164–169. doi:10.1016/j. matpr.2023.03.281.←pages 42, 43, 45, 47, 49, and 72

    2023 doi

  90. [99]

    M. A. Tschopp, S. P. Coleman, D. L. McDowell, Symmetric and asymmetric tilt grain boundary structure and energy in Cu and Al (and transferability to other fcc metals), Integrating Materials and Manufacturing Innovation 4 (2015) 176–189. doi:10.1186/ s40192-015-0040-1.←pages 42...

    2015

  91. [100]

    M. A. Tschopp, D. L. Mcdowell, Asymmetric tilt grain boundary structure and energy in copper and aluminium, Philosophical Magazine 87(25) (2007) 3871–3892. ← pages 42, 43, 60, and 62

    2007

  92. [101]

    Q. Yin, Z. Wang, R. Mishra, Z. Xi, Atomic simulations of twist grain boundary structures and deformation behaviors in aluminum, AIP Advances 7 (2017) 015040. ← pages 42, 43, 51, 60, and 62

    2017

  93. [102]

    Smith, J

    J. Smith, J. Lacy, D. Levesque, J. Monchalin, M. Lord, Use of the Hugoniot elastic limit in laser shockwave experiments to relate velocity measurements, V ol. 1706, AIP Conf. Proc., 2016, p. 080005.doi:10.1063/1.4940537.←page 45

    2016 doi

  94. [103]

    W. Li, E. N. Hahn, X. Yao, T. Germann, X. Zhang, Shock induced damage and fracture in SiC at elevated temperature and high strain rate, Acta Materialia 167 (2019) 51–70. doi: https://doi.org/10.1016/j.actamat.2018.12.035.←pages 49, 50, 51, and 52

    2019 doi

  95. [104]

    Williams, C

    T. Williams, C. Kelley, et.al., Gnuplot 4.6: An interactive plotting program (April 2013), http://gnuplot.sourceforge.net, URL active as on 30th Mar 2023.←page 53

    2013

  96. [105]

    A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Modelling and Simulation in Materials Science and Engineering 18 (1) (2009) 015012.←pages 55, 56, and 62

    2009

  97. [106]

    Stukowski, V

    A. Stukowski, V . V . Bulatov, A. Arsenlis, Automated identification and indexing of disloca- tions in crystal interfaces, Modelling and Simulation in Materials Science and Engineering (2012) 085007.←pages 56 and 62

    2012

  98. [107]

    Sansoz, J

    F. Sansoz, J. F. Molinari, Mechanical behavior of Σ tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study, Acta Materialia 53 (7) (2005) 1931–1944.←page 56

    2005

  99. [108]

    C. D. Owen, D. J. Chapman, G. Whiteman, S. M. Millett, S. Johnson, Spall behavior of single crytal aluminum at three principal orientations, Journal of Applied Physics 122 (2017) 155102.←pages 64, 65, 66, and 69

    2017

  100. [109]

    F. J. Zerilli, R. W. Armstrong, Dislocation mechanics based constitutive relations for material dynamics calculations, Journal of Applied Physics 61 (1987) 1816–1825. doi:doi.org/ 10.1063/1.338024.←pages 70 and 75

    1987 doi

  101. [110]

    G. Wang, Y . Xu, Embedded-atom potential for Ni-Al alloy, V ol. 452, IOP Conf. Series: Materials Science and Engineering, 2018, p. 022025. doi:10.1088/1757-899X/452/2/ 022025.←page 89. 86 Appendix A Parameters of EAM potentials used in this work EAM potential can be expressed ...

    2018 doi

  102. [111]

    Introduction Shockwave is produced when a material is subjected to high strain rate ( _e > 10 6/s) impact [1–5]. Computer simulation of shock is extensively performed over the several decades at macroscopic levels, with the assistance of data collected from poly-crystal [4– 6]...

  103. [112]

    Results from the MD andfirst principles calculations and their comparison for shock-Hugoniot condition are discussed in sec. 3. The conclusions are presented in sec. 4. https://doi.org/10.1016/j.matpr.2023.04.543 2214-7853/Copyright�2022 Elsevier Ltd. All rights reserved. Selec...

    2023 doi

  104. [113]

    Upon reaching the free surface, each wave reflects back into the plates as rarefaction waves

    Introduction Metalflyer plate impacting a metal target plate produces shock- waves that travels in both theflyer and the target in opposite directions. Upon reaching the free surface, each wave reflects back into the plates as rarefaction waves. When these two rarefaction waves m...

    2023

  105. [114]

    When two bodies collide shockwaves are generated which travel into both the bodies and reflect as rarefaction waves from the free sur- faces

    Introduction Predicting the dynamic fracture (spall) of materials subjected to high velocity impact or explosion is important for many applications. When two bodies collide shockwaves are generated which travel into both the bodies and reflect as rarefaction waves from the fre...

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