pith. sign in

arxiv: 2606.28155 · v1 · pith:5Y6UJI42new · submitted 2026-06-26 · ❄️ cond-mat.mtrl-sci

Uniaxial compression of crystalline HCP titanium: an atomistic modelling study of size effects

Fatemeh Safari , Konstantinos Konstantinou This is my paper

Pith reviewed 2026-06-29 03:16 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords titaniummolecular dynamicssize effectsuniaxial compressionHCP structureplastic deformationstrain rate dependencedislocation activity
0
0 comments X

The pith

Molecular dynamics simulations of HCP titanium under compression show that elastic properties are independent of system size and strain rate, while plastic deformation exhibits strong size effects.

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

The paper investigates how the size of the simulated crystal affects the mechanical response of alpha-titanium during uniaxial compression using molecular dynamics. It finds that the elastic stage behaves the same regardless of how large the model is or how fast it is strained, but once plastic deformation begins, larger models produce smoother stress responses, more uniform changes in structure, and steadier movement of dislocations. This coupling between model size and strain rate means that smaller models at slower rates may not reach proper equilibrium. A reader would care because these results help determine the minimum model sizes needed for reliable atomistic predictions of metal plasticity.

Core claim

In this computational study, molecular-dynamics simulations ascertain the impact of model size on the mechanical response of alpha-titanium under compression. The deformation behaviour is investigated as a function of system sizes varied by four orders of magnitude up to 32 million atoms, and strain rates down to 10^8 s^-1. The elastic properties remain independent of both system size and strain rate, whereas marked size effects emerge during plastic deformation. Increasing the system size reduces stress fluctuations, results in more homogeneous structural evolution, and stabilizes dislocation activity. Decreasing the applied strain rate requires a larger system size to achieve equilibration

What carries the argument

Molecular dynamics models of HCP titanium crystals under uniaxial compression, with system sizes from small to 32 million atoms, used to compare elastic and plastic responses including dislocation activity.

If this is right

  • Elastic constants extracted from small simulations remain valid for larger systems.
  • Plastic deformation simulations must use sufficiently large systems to avoid artificial stress fluctuations.
  • Lower strain rates demand proportionally larger models to maintain stable dislocation dynamics.
  • Combined size and rate effects control the homogeneity of structural changes during compression.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar size requirements may apply to simulations of other HCP metals like zirconium or magnesium.
  • Experimental validation at lower strain rates would require even larger computational models than those tested here.
  • These findings suggest that convergence studies with respect to system size are essential before interpreting plastic flow mechanisms from MD results.

Load-bearing premise

The chosen interatomic potential and boundary conditions produce deformation mechanisms representative of real titanium across the varied system sizes and strain rates.

What would settle it

If simulations with systems larger than 32 million atoms at strain rates below 10^8 s^-1 still show the same size-dependent plastic behavior instead of converging, the claim of stabilization with size would be challenged.

Figures

Figures reproduced from arXiv: 2606.28155 by Fatemeh Safari, Konstantinos Konstantinou.

Figure 1
Figure 1. Figure 1: Three Ti crystalline models of different sizes, shown roughly to scale. From left to right, the system size varies by four orders of magnitude with respect to the total number of atoms, while the extent of the dimensions of the simulation boxes is also highlighted. Ti atoms are shown in red, and the black arrow denotes the loading direction (z-axis compression). For all the MD simulations, a time-step of 1… view at source ↗
Figure 2
Figure 2. Figure 2: Stress-strain curves for the seven different Ti modelled structures compressed at a 109 s -1 strain rate with molecular-dynamics simulations performed at 300 K [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dynamic evolution of the different crystal structures in four different Ti models during compression [(a) 32k, (b) 108k, (c) 4M, and (d) 32M], identified using Polyhedral Template Matching (RMSD cutoff = 0.15). Individual atoms are coloured as HCP (red), FCC (green), BCC (blue), and unknown (grey). From left to right, at each panel, snapshots are shown at ε = 0%, 16.5%, 25%, and 40%, and the loading direct… view at source ↗
Figure 4
Figure 4. Figure 4: displays the evolution of all the different crystallographic structure fractions as a function of strain for each Ti model, obtained using a PTM analysis. Atoms labelled as “Other” represent unidentified local environments that do not belong to any of the HCP, FCC, or BCC classifications [47]. All simulated structures remain fully HCP throughout the elastic regime, until a sudden decrease in the HCP fracti… view at source ↗
Figure 5
Figure 5. Figure 5: shows the distributions of all the different dislocation types calculated at the end of the compression simulations (i.e., 40% strain, 10⁹ s⁻¹ strain rate) for three of the modelled systems studied here (108k, 1M, and 4M). The analysis reveals the presence of distinct dislocation types, based on their unique Burgers vectors, in the simulated Ti structures, including 1 3 < 1210 > prismatic dislocations, 1 3… view at source ↗
Figure 7
Figure 7. Figure 7: Stress-strain analysis: (a) at a strain rate of 108 s -1 for three different Ti modelled system sizes (108k, 1M, and 4M); and (b) for the 4M model at three different strain rates (10⁸ s⁻¹, 109 s⁻¹, and 1010 s⁻¹) [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Dynamics of crystallographic structure fractions as a function of strain during the compression simulations of Ti models of three different system sizes (108k, 1M, and 4M atoms) at a 10⁸ s⁻¹ strain rate. The percentages of HCP (a), FCC (b), BCC (c), and Other (d) structures are shown for each model. All the models show a partial recovery of the HCP structure, with the 108k and 1M simulated systems exhibiti… view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of the total dislocation density for the 4M-atom Ti model as a function of strain (%), at three different applied strain rates (10⁸, 10⁹, and 10¹⁰ s⁻¹). During the compression simulations with the 10⁹ and 10⁸ s⁻¹ strain rates a significant increase in the dislocation density after the onset of the plastic deformation is observed in the Ti modelled structure ( [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 11
Figure 11. Figure 11: shows the evolution of dislocation density for each dislocation type at the three different strain rates (10⁸, 10⁹, and 10¹⁰ s⁻¹) for the 4M Ti model. For all the applied strain rates the same dislocation types are found inside the modelled system, with different relative amounts. Also, it can be observed that the “Other” dislocations account for the largest proportion of the total dislocation density, wi… view at source ↗
read the original abstract

Understanding the deformation behaviour of titanium is important not only for technological advances associated with industrially-relevant applications, but also essential to achieve a fundamental understanding of the mechanical properties of the relevant alloys. In this computational study, molecular-dynamics simulations are employed to ascertain the impact of model size on the mechanical response of alpha-titanium under compression. The deformation behaviour of the crystalline models is investigated as a function of different system sizes (varied by four orders of magnitude, up to 32 million atoms), and strain rates (down to 10^8 s^-1). The results show that the elastic properties remain independent of both system size and strain rate, whereas marked size effects emerge during plastic deformation. Increasing the system size of the titanium model reduces stress fluctuations, results in more homogeneous structural evolution, and stabilizes dislocation activity. Decreasing the applied strain rate requires correspondingly a larger system size to achieve equilibration and to ensure a stable behaviour for the simulated structure. The modelling results demonstrate that system size and strain rate are strongly coupled, and their combined effect governs the simulated deformation behaviour of the compressed crystalline material.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript reports molecular-dynamics simulations of uniaxial compression on HCP titanium crystals, varying system size over four orders of magnitude (up to 32 million atoms) and strain rate down to 10^8 s^{-1}. It claims that elastic properties remain independent of both size and rate, while plastic deformation exhibits clear size effects: larger systems reduce stress fluctuations, produce more homogeneous structural evolution, and stabilize dislocation activity. The work concludes that system size and strain rate are strongly coupled and must be considered jointly to obtain equilibrated, stable plastic response.

Significance. If the results hold, the study would be useful for the atomistic modeling of HCP metals by providing concrete evidence that plastic deformation requires substantially larger cells than elastic response and by demonstrating the size-rate coupling at accessible MD scales. The direct simulation of dislocation activity in cells up to 32 M atoms is a technical strength that supplies practical guidance on convergence for similar systems.

major comments (1)
  1. [Methods section] Methods section: the interatomic potential is not identified and no validation is reported against experimental or DFT values for key quantities controlling plastic flow (dislocation nucleation barriers, stacking-fault energies, or cross-slip energetics in HCP Ti). Because the central claim concerns the emergence and stabilization of dislocation-mediated plasticity with increasing cell size, the absence of such validation makes it impossible to determine whether the reported homogenization and rate-size coupling are representative or potential-specific artifacts.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the methods section. We address it point-by-point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods section] Methods section: the interatomic potential is not identified and no validation is reported against experimental or DFT values for key quantities controlling plastic flow (dislocation nucleation barriers, stacking-fault energies, or cross-slip energetics in HCP Ti). Because the central claim concerns the emergence and stabilization of dislocation-mediated plasticity with increasing cell size, the absence of such validation makes it impossible to determine whether the reported homogenization and rate-size coupling are representative or potential-specific artifacts.

    Authors: We agree that the interatomic potential must be explicitly identified and that validation against experimental and DFT data for dislocation nucleation barriers, stacking-fault energies, and cross-slip energetics is necessary to support claims about dislocation-mediated plasticity. In the revised manuscript we will update the Methods section to name the potential and add the requested validation comparisons. This will allow readers to evaluate whether the reported size-rate coupling is representative. revision: yes

Circularity Check

0 steps flagged

No circularity; results are direct outputs of MD simulations

full rationale

The paper presents molecular-dynamics simulation results on HCP titanium under uniaxial compression, varying system size (up to 32 million atoms) and strain rate (down to 10^8 s^-1). Claims that elastic properties are independent of size/rate while plastic deformation exhibits size effects, reduced stress fluctuations, and stabilized dislocation activity are reported as direct simulation outputs, not as predictions derived from equations or fitted parameters. No self-definitional steps, fitted-input predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling appear in the abstract or described methodology. The modeling assumptions (interatomic potential and boundary conditions) are external inputs whose validity is a separate question of model fidelity, not a circular reduction of the reported results to themselves. The derivation chain is therefore self-contained as computational observation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study rests on standard assumptions of classical molecular dynamics; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Newtonian mechanics and periodic boundary conditions govern atomic motion in the simulated crystal
    Invoked implicitly for all MD runs

pith-pipeline@v0.9.1-grok · 5754 in / 1092 out tokens · 68120 ms · 2026-06-29T03:16:57.767106+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 58 canonical work pages

  1. [1]

    Y. Li, C. Yang, H. Zhao, S. Qu, X. Li, Y. Li, New developments of Ti-based alloys for biomedical applications, Materials 7 (2014) 1709–1800. https://doi.org/10.3390/ma7031709

    work page doi:10.3390/ma7031709 2014

  2. [2]

    Pushp, S.M

    P. Pushp, S.M. Dasharath, C. Arati, Classification and applications of titanium and its alloys, Mater. Today Proc. 54 (2022) 537–542. https://doi.org/10.1016/j.matpr.2022.01.008

    work page doi:10.1016/j.matpr.2022.01.008 2022

  3. [3]

    Najafizadeh, S

    M. Najafizadeh, S. Yazdi, M. Bozorg, M. Ghasempour-Mouziraji, M. Hosseinzadeh, M. Zarrabian, P. Cavaliere, Classification and applications of titanium and its alloys: A review, J. Alloys Compd. Commun. 3 (2024) 100019. https://doi.org/10.1016/j.jacomc.2024.100019

    work page doi:10.1016/j.jacomc.2024.100019 2024

  4. [4]

    Leyens, M

    C. Leyens, M. Peters, eds., Titanium and Titanium Alloys, Wiley, 2003. https://doi.org/10.1002/3527602119

    work page doi:10.1002/3527602119 2003

  5. [5]

    Schauerte, Titanium in Automotive Production, Adv

    O. Schauerte, Titanium in Automotive Production, Adv. Eng. Mater. 5 (2003) 411–418. https://doi.org/10.1002/adem.200310094

    work page doi:10.1002/adem.200310094 2003

  6. [6]

    Raabe, B

    D. Raabe, B. Sander, M. Friák, D. Ma, J. Neugebauer, Theory-guided bottom-up design of β-titanium alloys as biomaterials based on first principles calculations: Theory and experiments, Acta Mater. 55 (2007) 4475–4487. https://doi.org/10.1016/j.actamat.2007.04.024. 23

    work page doi:10.1016/j.actamat.2007.04.024 2007

  7. [7]

    D. Ryu, Y. Kim, S. Nahm, L. Kang, Recent developments in plastic deformation behavior of titanium and its alloys during the rolling process: A review, Materials 17 (2024) 6060. https://doi.org/10.3390/ma17246060

    work page doi:10.3390/ma17246060 2024

  8. [8]

    Zheng, M

    X. Zheng, M. Gong, T. Xiong, H. Ge, L. Yang, Y. Zhou, S. Zheng, J. Wang, X. Ma, Deformation induced FCC lamellae and their interaction in commercial pure Ti, Scr. Mater. 162 (2019) 326–330. https://doi.org/10.1016/j.scriptamat.2018.11.037

    work page doi:10.1016/j.scriptamat.2018.11.037 2019

  9. [9]

    Nemat-Nasser, W.G

    S. Nemat-Nasser, W.G. Guo, J.Y. Cheng, Mechanical properties and deformation mechanisms of a commercially pure titanium, Acta Mater. 47 (1999) 3705–3720. https://doi.org/10.1016/S1359-6454(99)00203-7

    work page doi:10.1016/s1359-6454(99)00203-7 1999

  10. [10]

    Zhang, X

    H. Zhang, X. Ou, B. Wei, S. Ni, M. Song, Strain direction dependency of deformation mechanisms in an HCP-Ti crystalline by molecular dynamics simulations, Comput. Mater. Sci. 172 (2020) 109328. https://doi.org/10.1016/j.commatsci.2019.109328

    work page doi:10.1016/j.commatsci.2019.109328 2020

  11. [11]

    Morrow, R.A

    B.M. Morrow, R.A. Lebensohn, C.P. Trujillo, D.T. Martinez, F.L. Addessio, C.A. Bronkhorst, T. Lookman, E.K. Cerreta, Characterization and modeling of mechanical behavior of single crystal titanium deformed by split-Hopkinson pressure bar, Int. J. Plast. 82 (2016) 225–

    2016

  12. [12]

    https://doi.org/10.1016/j.ijplas.2016.03.006

    work page doi:10.1016/j.ijplas.2016.03.006 2016

  13. [13]

    Bishoyi, R.K

    B.D. Bishoyi, R.K. Sabat, S.K. Sahoo, Effect of temperature on microstructure and texture evolutions during uniaxial compression of commercially pure titanium, Mater. Sci. Eng. A 718 (2018) 398–411. https://doi.org/10.1016/j.msea.2018.01.128

    work page doi:10.1016/j.msea.2018.01.128 2018

  14. [14]

    Rawat, N

    S. Rawat, N. Mitra, Evolution of tension twinning in single crystal Ti under compressive uniaxial strain conditions, Comput. Mater. Sci. 141 (2018) 302–312. https://doi.org/10.1016/j.commatsci.2017.09.041

    work page doi:10.1016/j.commatsci.2017.09.041 2018

  15. [15]

    Rawat, P.M

    S. Rawat, P.M. Raole, Molecular dynamics investigation of void evolution dynamics in single crystal iron at extreme strain rates, Comput. Mater. Sci. 154 (2018) 393–404. https://doi.org/10.1016/j.commatsci.2018.08.010

    work page doi:10.1016/j.commatsci.2018.08.010 2018

  16. [16]

    Rawat, N

    S. Rawat, N. Mitra, Twinning assisted α to ω phase transformation in titanium single crystal, AIP Conf. Proc. 1832 (2017) 030018. https://doi.org/10.1063/1.4980197

    work page doi:10.1063/1.4980197 2017

  17. [17]

    H. Zong, X. Ding, T. Lookman, J. Sun, Twin boundary activated α → ω phase transformation in titanium under shock compression, Acta Mater. 115 (2016) 1–9. https://doi.org/10.1016/j.actamat.2016.05.037

    work page doi:10.1016/j.actamat.2016.05.037 2016

  18. [18]

    Salem, S.R

    A.A. Salem, S.R. Kalidindi, R.D. Doherty, Strain hardening of titanium: role of deformation twinning, Acta Mater. 51 (2003) 4225–4237. https://doi.org/10.1016/S1359- 6454(03)00239-8. 24

    work page doi:10.1016/s1359- 2003

  19. [19]

    J. Li, L. Dong, H. Xie, W. Meng, X. Zhang, J. Zhang, W. Zhao, Molecular dynamics simulation of nanocrack propagation mechanism of polycrystalline titanium under tension deformation in nanoscale, Mater. Today Commun. 26 (2021) 101837. https://doi.org/10.1016/j.mtcomm.2020.101837

    work page doi:10.1016/j.mtcomm.2020.101837 2021

  20. [20]

    Ngo, V.-T

    T.-T.B. Ngo, V.-T. Nguyen, T.-H. Fang, Deformation and phase transformation of dual- phase Ti under tension and compression process, J. Mol. Model. 31 (2025) 125. https://doi.org/10.1007/s00894-025-06349-0

    work page doi:10.1007/s00894-025-06349-0 2025

  21. [21]

    Y. Niu, Y. Jia, X. Lv, Y. Zhu, Y. Wang, Molecular dynamics simulations of polycrystalline titanium mechanical properties: Grain size effect, Mater. Today Commun. 40 (2024) 109558. https://doi.org/10.1016/j.mtcomm.2024.109558

    work page doi:10.1016/j.mtcomm.2024.109558 2024

  22. [22]

    Chang, C.-Y

    L. Chang, C.-Y. Zhou, L.-L. Wen, J. Li, X.-H. He, Molecular dynamics study of strain rate effects on tensile behavior of single crystal titanium nanowire, Comput. Mater. Sci. 128 (2017) 348–358. https://doi.org/10.1016/j.commatsci.2016.11.034

    work page doi:10.1016/j.commatsci.2016.11.034 2017

  23. [23]

    M. An, M. Su, Q. Deng, H. Song, C. Wang, Y. Shang, Anisotropic plasticity of nanocrystalline Ti: A molecular dynamics simulation, Chin. Phys. B 29 (2020) 046201. https://doi.org/10.1088/1674-1056/ab7188

    work page doi:10.1088/1674-1056/ab7188 2020

  24. [24]

    J. Ren, Q. Sun, L. Xiao, X. Ding, J. Sun, Size-dependent of compression yield strength and deformation mechanism in titanium single-crystal nanopillars orientated [0001] and [112̄0], Mater. Sci. Eng. A 615 (2014) 22–28. https://doi.org/10.1016/j.msea.2014.07.065

    work page doi:10.1016/j.msea.2014.07.065 2014

  25. [25]

    Y. Li, J. Li, B. Liu, Homogeneous shear-driven reversible α-to-α″ phase transformation and superelasticity of titanium investigated by molecular dynamics simulations, Acta Mater. 93 (2015) 105–113. https://doi.org/10.1016/j.actamat.2015.04.009

    work page doi:10.1016/j.actamat.2015.04.009 2015

  26. [26]

    Srinivasan, L

    P. Srinivasan, L. Nicola, A. Simone, Atomistic modeling of the orientation-dependent pseudoelasticity in NiTi: Tension, compression, and bending, Comput. Mater. Sci. 154 (2018) 25–36. https://doi.org/10.1016/j.commatsci.2018.07.028

    work page doi:10.1016/j.commatsci.2018.07.028 2018

  27. [27]

    Fazeli, M

    S. Fazeli, M. Izadifar, J.S. Dolado, A. Ramazani, S.K. Sadrnezhaad, Atomistic study of the effect of crystallographic orientation on the twinning and detwinning behavior of NiTi shape memory alloys, Comput. Mater. Sci. 203 (2022) 111080. https://doi.org/10.1016/j.commatsci.2021.111080

    work page doi:10.1016/j.commatsci.2021.111080 2022

  28. [28]

    Ma, X.-Z

    Z.-C. Ma, X.-Z. Tang, Y. Mao, Y.-F. Guo, The Plastic Deformation Mechanisms of hcp Single Crystals with Different Orientations: Molecular Dynamics Simulations, Materials 14 (2021) 733. https://doi.org/10.3390/ma14040733. 25

    work page doi:10.3390/ma14040733 2021

  29. [29]

    S. Chen, H. Wang, P. Yan, S. Li, H. Zhang, H. Zhan, Molecular Dynamics Simulation of Temperature and Ti Volume Fraction on Compressive Properties of Ti/Al Layered Composites, Metals (Basel) 14 (2024) 1182. https://doi.org/10.3390/met14101182

    work page doi:10.3390/met14101182 2024

  30. [30]

    Nelasov, A.I

    I.V. Nelasov, A.I. Kartamyshev, A.O. Boev, A.G. Lipnitskii, Y.R. Kolobov, T.K. Nguyen, Molecular dynamics simulation of the behavior of titanium under high-speed deformation, Model. Simul. Mater. Sci. Eng. 29 (2021) 065012. https://doi.org/10.1088/1361-651X/ac0c22

    work page doi:10.1088/1361-651x/ac0c22 2021

  31. [31]

    Rawat, N

    S. Rawat, N. Mitra, Molecular dynamics investigation of c-axis deformation of single crystal Ti under uniaxial stress conditions: Evolution of compression twinning and dislocations, Comput. Mater. Sci. 141 (2018) 19–29. https://doi.org/10.1016/j.commatsci.2017.09.015

    work page doi:10.1016/j.commatsci.2017.09.015 2018

  32. [32]

    Frenkel, Simulations: The dark side, Eur

    D. Frenkel, Simulations: The dark side, Eur. Phys. J. Plus 128 (2013) 10. https://doi.org/10.1140/epjp/i2013-13010-8

    work page doi:10.1140/epjp/i2013-13010-8 2013

  33. [33]

    Mahata, M

    A. Mahata, M. Asle Zaeem, Size effect in molecular dynamics simulation of nucleation process during solidification of pure metals: investigating modified embedded atom method interatomic potentials, Model. Simul. Mater. Sci. Eng. 27 (2019) 085015. https://doi.org/10.1088/1361-651X/ab4b36

    work page doi:10.1088/1361-651x/ab4b36 2019

  34. [34]

    Salacuse, A.R

    J.J. Salacuse, A.R. Denton, P.A. Egelstaff, Finite-size effects in molecular dynamics simulations: Static structure factor and compressibility. I. Theoretical method, Phys. Rev. E 53 (1996) 2382–2389. https://doi.org/10.1103/PhysRevE.53.2382

    work page doi:10.1103/physreve.53.2382 1996

  35. [35]

    Sainath, B.K

    G. Sainath, B.K. Choudhary, T. Jayakumar, Molecular dynamics simulation studies on the size dependent tensile deformation and fracture behaviour of body centred cubic iron nanowires, Comput. Mater. Sci. 104 (2015) 76–83. https://doi.org/10.1016/j.commatsci.2015.03.053

    work page doi:10.1016/j.commatsci.2015.03.053 2015

  36. [36]

    Hirel, Atomsk: A tool for manipulating and converting atomic data files.Comp

    P. Hirel, Atomsk: A tool for manipulating and converting atomic data files, Comput. Phys. Commun. 197 (2015) 212–219. https://doi.org/10.1016/j.cpc.2015.07.012

    work page doi:10.1016/j.cpc.2015.07.012 2015

  37. [37]

    Wood, The Lattice Constants of High Purity Alpha Titanium, Proc

    R.M. Wood, The Lattice Constants of High Purity Alpha Titanium, Proc. Phys. Soc. 80 (1962) 783–786. https://doi.org/10.1088/0370-1328/80/3/323

    work page doi:10.1088/0370-1328/80/3/323 1962

  38. [38]

    Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J

    S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys. 117 (1995) 1–19. https://doi.org/10.1006/jcph.1995.1039

    work page doi:10.1006/jcph.1995.1039 1995

  39. [39]

    Kim, B.-J

    Y.-M. Kim, B.-J. Lee, M.I. Baskes, Modified embedded-atom method interatomic potentials for Ti and Zr, Phys. Rev. B 74 (2006) 014101. https://doi.org/10.1103/PhysRevB.74.014101. 26

    work page doi:10.1103/physrevb.74.014101 2006

  40. [40]

    R.R. Zope, Y. Mishin, Interatomic potentials for atomistic simulations of the Ti-Al system, Phys. Rev. B 68 (2003) 024102. https://doi.org/10.1103/PhysRevB.68.024102

    work page doi:10.1103/physrevb.68.024102 2003

  41. [41]

    Sharifi, C.D

    H. Sharifi, C.D. Wick, Developing interatomic potentials for complex concentrated alloys of Cu, Ti, Ni, Cr, Co, Al, Fe, and Mn, Comput. Mater. Sci. 248 (2025) 113595. https://doi.org/10.1016/j.commatsci.2024.113595

    work page doi:10.1016/j.commatsci.2024.113595 2025

  42. [42]

    Nitol, D.E

    M.S. Nitol, D.E. Dickel, C.D. Barrett, Machine learning models for predictive materials science from fundamental physics: An application to titanium and zirconium, Acta Mater. 224 (2022) 117347. https://doi.org/10.1016/j.actamat.2021.117347

    work page doi:10.1016/j.actamat.2021.117347 2022

  43. [43]

    Hennig, T.J

    R.G. Hennig, T.J. Lenosky, D.R. Trinkle, S.P. Rudin, J.W. Wilkins, Classical potential describes martensitic phase transformations between the α, β, and ω titanium phases, Phys. Rev. B 78 (2008) 054121. https://doi.org/10.1103/PhysRevB.78.054121

    work page doi:10.1103/physrevb.78.054121 2008

  44. [44]

    Ackland, Theoretical study of titanium surfaces and defects with a new many-body potential, Philos

    G.J. Ackland, Theoretical study of titanium surfaces and defects with a new many-body potential, Philos. Mag. A 66 (1992) 917–932. https://doi.org/10.1080/01418619208247999

    work page doi:10.1080/01418619208247999 1992

  45. [45]

    Rawat, N

    S. Rawat, N. Mitra, Compression twinning and structural phase transformation of single crystal titanium under uniaxial compressive strain conditions: Comparison of inter- atomic potentials, Comput. Mater. Sci. 126 (2017) 228–237. https://doi.org/10.1016/j.commatsci.2016.09.034

    work page doi:10.1016/j.commatsci.2016.09.034 2017

  46. [46]

    Evans, B.L

    D.J. Evans, B.L. Holian, The Nose–Hoover thermostat, J. Chem. Phys. 83 (1985) 4069–

    1985

  47. [47]

    https://doi.org/10.1063/1.449071

    work page doi:10.1063/1.449071

  48. [48]

    Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Model

    A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Model. Simul. Mater. Sci. Eng. 18 (2010) 015012. https://doi.org/10.1088/0965-0393/18/1/015012

    work page doi:10.1088/0965-0393/18/1/015012 2010

  49. [49]

    Larsen, S

    P.M. Larsen, S. Schmidt, J. Schiøtz, Robust structural identification via polyhedral template matching, Model. Simul. Mater. Sci. Eng. 24 (2016) 055007. https://doi.org/10.1088/0965-0393/24/5/055007

    work page doi:10.1088/0965-0393/24/5/055007 2016

  50. [50]

    Stukowski, V.V

    A. Stukowski, V.V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces, Model. Simul. Mater. Sci. Eng. 20 (2012) 085007. https://doi.org/10.1088/0965-0393/20/8/085007

    work page doi:10.1088/0965-0393/20/8/085007 2012

  51. [51]

    Tadmor, R.E

    E.B. Tadmor, R.E. Miller, Modeling Materials, Cambridge University Press, 2011. https://doi.org/10.1017/CBO9781139003582. 27

    work page doi:10.1017/cbo9781139003582 2011

  52. [52]

    von Blanckenhagen, P

    B. von Blanckenhagen, P. Gumbsch, E. Arzt, Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation, Model. Simul. Mater. Sci. Eng. 9 (2001) 157–169. https://doi.org/10.1088/0965-0393/9/3/303

    work page doi:10.1088/0965-0393/9/3/303 2001

  53. [53]

    Hull, D.J

    D. Hull, D.J. Bacon, Defects in Crystals, in: Introduction to Dislocations, Butterworth- Heinemann, Oxford, 2011, pp. 1–20. https://doi.org/10.1016/B978-0-08-096672- 4.00001-3

    work page doi:10.1016/b978-0-08-096672- 2011

  54. [54]

    Nervo, A

    L. Nervo, A. King, A. Fitzner, W. Ludwig, M. Preuss, A study of deformation twinning in a titanium alloy by X-ray diffraction contrast tomography, Acta Mater. 105 (2016) 417–428. https://doi.org/10.1016/j.actamat.2015.12.032

    work page doi:10.1016/j.actamat.2015.12.032 2016

  55. [55]

    Clouet, D

    E. Clouet, D. Caillard, N. Chaari, F. Onimus, D. Rodney, Dislocation locking versus easy glide in titanium and zirconium, Nat. Mater. 14 (2015) 931–936. https://doi.org/10.1038/nmat4340

    work page doi:10.1038/nmat4340 2015

  56. [56]

    Rawat, N

    S. Rawat, N. Mitra, Twinning, phase transformation and dislocation evolution in single crystal titanium under uniaxial strain conditions: A molecular dynamics study, Comput. Mater. Sci. 172 (2020) 109325. https://doi.org/10.1016/j.commatsci.2019.109325

    work page doi:10.1016/j.commatsci.2019.109325 2020

  57. [57]

    Akhtar, Basal slip and twinning in α-titanium single crystals, Metall

    A. Akhtar, Basal slip and twinning in α-titanium single crystals, Metall. Trans. A 6 (1975) 1105–1113. https://doi.org/10.1007/BF02661366

    work page doi:10.1007/bf02661366 1975

  58. [58]

    Liu, X.K

    H. Liu, X.K. Shang, B.B. He, Z.Y. Liang, Strain rate dependence of strengthening mechanisms in ultrahigh strength lath martensite, Int. J. Plast. 161 (2023) 103495. https://doi.org/10.1016/j.ijplas.2022.103495

    work page doi:10.1016/j.ijplas.2022.103495 2023

  59. [59]

    Dowding, C.A

    I. Dowding, C.A. Schuh, Metals strengthen with increasing temperature at extreme strain rates, Nature 630 (2024) 91–95. https://doi.org/10.1038/s41586-024-07420-1

    work page doi:10.1038/s41586-024-07420-1 2024

  60. [60]

    Vedani, Plastic Deformation of Metals, in: Metal Science in Modern Manufacturing Technologies, Springer Nature Switzerland, 2025, pp

    M. Vedani, Plastic Deformation of Metals, in: Metal Science in Modern Manufacturing Technologies, Springer Nature Switzerland, 2025, pp. 35–56. https://doi.org/10.1007/978-3-031-97125-9_2. 28 Uniaxial compression of crystalline HCP titanium: an atomistic modelling study of size effects Fatemeh Safari a,*, Konstantinos Konstantinou a,* a Department of Mech...

    work page doi:10.1007/978-3-031-97125-9_2 2025