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Localization and macroscopic instability in nanoporous metals

纳米多孔金属的应变局域化和宏观失稳

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Abstract

Ductile fracture generally relates to microscopic voiding and to strain localization in metallic materials. When the void size is reduced to the nanoscale, size effects often lead to a different macroscopic plastic behavior from that established for the same material with larger voids. For example, irradiation of metallic materials can generate a large number of voids at the nanoscale, leading to complex deformation behaviors. The present work advances the understanding of strain localization in nanoporous metallic materials, connecting both the microscopic (nano-) and macroscopic scales. To explore the physical mechanisms at the nanoscale, molecular dynamics (MD) simulations were here carried out, capturing multiple nanovoids explicitly. Then, a homogenized continuum theory based in Gurson’s constitutive framework is proposed, which enables us to explore how localized behavior at the macroscopic scale evolves. The homogenized model incorporates the surface tension associated with nanosized void. The importance of this surface tension is illustrated by several parametric studies on the conditions of localization, when a specimen is subjected to uniaxial tension. Our parametric studies show that for smaller nanovoid sizes, and for a hardening matrix material, shear localization onset is delayed. Our proposed homogenization model was then used to predict localization behavior captured by our MD simulation. The yield stress and the localization strain predicted by our continuum model are in general agreement with the trends obtained by MD simulation. Moreover, based on our present study, experimental results of shear failure strain vs. dose of irradiation for several metals could be qualitatively explained rather successfully. Our model can therefore help shed light on prolonging the operation limits and the lifetime of irradiated metallic materials under complex loading conditions.

摘要

韧性断裂通常与金属材料中的微观孔洞和应变局域化有关. 当孔洞尺寸减小到纳米级时, 尺寸效应通常会导致与具有较大孔洞的同种材料建立的宏观塑性行为不同. 例如, 金属材料在辐照下会产生大量纳米级的孔洞, 导致复杂的变形行为. 目前的工作促进了对纳米多孔金属材料中应变局域化的理解, 将微观(纳米)和宏观尺度联系起来. 为了探索纳米尺度下的物理机制, 本工作运用分子动力学(MD)模拟了多个纳米孔洞. 然后提出基于Gurson本构框架的均匀化连续统理论探索宏观尺度上的局域化行为如何演变. 均匀化模型结合了与纳米级孔洞相关的表面张力. 当样品受到单轴张力时, 对失稳条件的多项参数研究说明了这种表面张力的重要性. 我们的参数研究表明, 对于较小的纳米孔洞尺寸和加工硬化基体材料, 剪切局域化会延迟. 然后, 我们提出的均匀化模型预测了MD模拟的局域化行为. 本文提出的连续体模型预测的屈服应力和失稳应变与MD模拟获得的趋势基本一致. 此外, 我们目前的研究对几种金属的剪切破坏应变与辐照剂量的实验结果进行了定性解释. 因此, 我们的模型可以帮助阐明在复杂负载条件下延长辐照金属材料的使用寿命.

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References

  1. A. Weck, and D. S. Wilkinson, Experimental investigation of void coalescence in metallic sheets containing laser drilled holes, Acta Mater. 56, 1774 (2008).

    Article  Google Scholar 

  2. M. J. Nemcko, H. Qiao, P. Wu, and D. S. Wilkinson, Effects of void fraction on void growth and linkage in commercially pure magnesium, Acta Mater. 113, 68 (2016).

    Article  Google Scholar 

  3. O. Furukimi, C. Kiattisaksri, Y. Takeda, M. Aramaki, S. Oue, S. Munetoh, and M. Tanaka, Void nucleation behavior of single-crystal high-purity iron specimens subjected to tensile deformation, Mater. Sci. Eng.-A 701, 221 (2017).

    Article  Google Scholar 

  4. T. Luo, and X. Gao, On the prediction of ductile fracture by void coalescence and strain localization, J. Mech. Phys. Solids 113, 82 (2018).

    Article  MathSciNet  Google Scholar 

  5. O. T. Bruhns, Large deformation plasticity, Acta Mech. Sin. 36, 472 (2020).

    Article  MathSciNet  Google Scholar 

  6. H. Dang, P. Liu, Y. Zhang, Z. Zhao, L. Tong, C. Zhang, and Y. Li, Theoretical prediction for effective properties and progressive failure of textile composites: a generalized multi-scale approach, Acta Mech. Sin. 37, 1222 (2021).

    Article  MathSciNet  Google Scholar 

  7. Q. Huang, and Z. Zhong, Cavitation-induced damage model of soft materials in exposure to high-intensity focused ultrasound, Acta Mech. Sin. 36, 1058 (2020).

    Article  MathSciNet  Google Scholar 

  8. R. Liu, S. Pathak, W. M. Mook, J. K. Baldwin, N. Mara, and A. Antoniou, In situ frustum indentation of nanoporous copper thin films, Int. J. Plast. 98, 139 (2017).

    Article  Google Scholar 

  9. N. R. Kang, E. J. Gwak, H. Jeon, E. Song, and J. Y. Kim, Microstructural effect on time-dependent plasticity of nanoporous gold, Int. J. Plast. 109, 108 (2018).

    Article  Google Scholar 

  10. S. Babaee, J. Shim, J. C. Weaver, E. R. Chen, N. Patel, and K. Bertoldi, 3D soft metamaterials with negative Poisson’s ratio, Adv. Mater. 25, 5044 (2013).

    Article  Google Scholar 

  11. M. Taylor, L. Francesconi, M. Gerendás, A. Shanian, C. Carson, and K. Bertoldi, Low porosity metallic periodic structures with negative Poisson’s ratio, Adv. Mater. 26, 2365 (2014).

    Article  Google Scholar 

  12. T. Zhang, X. Li, and H. Gao, Defects controlled wrinkling and topological design in graphene, J. Mech. Phys. Solids 67, 2 (2014).

    Article  MathSciNet  Google Scholar 

  13. X. Xiao, D. Terentyev, H. Chu, and H. Duan, Theoretical models for irradiation hardening and embrittlement in nuclear structural materials: a review and perspective, Acta Mech. Sin. 36, 397 (2020).

    Article  Google Scholar 

  14. N. Li, M. Nastasi, and A. Misra, Defect structures and hardening mechanisms in high dose helium ion implanted Cu and Cu/Nb multilayer thin films, Int. J. Plast. 32–33, 1 (2012).

    Article  Google Scholar 

  15. W. Han, E. G. Fu, M. J. Demkowicz, Y. Wang, and A. Misra, Irradiation damage of single crystal, coarse-grained, and nanograined copper under helium bombardment at 450°C, J. Mater. Res. 28, 2763 (2013).

    Article  Google Scholar 

  16. Y. Chen, K. Y. Yu, Y. Liu, S. Shao, H. Wang, M. A. Kirk, J. Wang, and X. Zhang, Damage-tolerant nanotwinned metals with nanovoids under radiation environments, Nat. Commun. 6, 7036 (2015).

    Article  Google Scholar 

  17. Y. Chen, X. Zhang, and J. Wang, Radiation enhanced absorption of Frank loops by nanovoids in Cu, JOM 68, 235 (2016).

    Article  Google Scholar 

  18. J. Wen, Y. Huang, K. C. Hwang, C. Liu, and M. Li, The modified Gurson model accounting for the void size effect, Int. J. Plast. 21, 381 (2005).

    Article  MATH  Google Scholar 

  19. U. Borg, C. F. Niordson, and J. W. Kysar, Size effects on void growth in single crystals with distributed voids, Int. J. Plast. 24, 688 (2008).

    Article  MATH  Google Scholar 

  20. W. X. Zhang, T. J. Wang, and X. Chen, Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites, Int. J. Plast. 26, 957 (2010).

    Article  MATH  Google Scholar 

  21. Y. Wang, Y. Yao, Z. Long, and L. Keer, Energy variation in diffusive void nucleation induced by electromigration, Acta Mech. Sin. 36, 866 (2020).

    Article  MathSciNet  Google Scholar 

  22. X. Rong, J. Rong, S. Zhao, F. Li, J. Yi, and L. Peng, New method for controlling minimum length scales of real and void phase materials in topology optimization, Acta Mech. Sin. 36, 805 (2020).

    Article  MathSciNet  Google Scholar 

  23. B. N. Singh, T. Leffers, and A. Horsewell, Dislocation and void segregation in copper during neutron irradiation, Philos. Mag. A 53, 233 (1986).

    Article  Google Scholar 

  24. D. Pons, and J. C. Bourgoin, Irradiation-induced defects in GaAs, J. Phys. C-Solid State Phys. 18, 3839 (1985).

    Article  Google Scholar 

  25. M. Victoria, N. Baluc, C. Bailat, Y. Dai, M. I. Luppo, R. Schäublin, and B. N. Singh, The microstructure and associated tensile properties of irradiated fcc and bcc metals, J. Nucl. Mater. 276, 114 (2000).

    Article  Google Scholar 

  26. B. Skocze, and A. Ustrzycka, Kinetics of evolution of radiation induced micro-damage in ductile materials subjected to time-dependent stresses, Int. J. Plast. 80, 86 (2016).

    Article  Google Scholar 

  27. E. T. Seppälä, J. Belak, and R. E. Rudd, Onset of void coalescence during dynamic fracture of ductile metals, Phys. Rev. Lett. 93, 245503 (2004), arXiv: cond-mat/0410613.

    Article  Google Scholar 

  28. G. P. Potirniche, M. F. Horstemeyer, G. J. Wagner, and P. M. Gullett, A molecular dynamics study of void growth and coalescence in single crystal nickel, Int. J. Plast. 22, 257 (2006).

    Article  Google Scholar 

  29. S. Traiviratana, E. M. Bringa, D. J. Benson, and M. A. Meyers, Void growth in metals: Atomistic calculations, Acta Mater. 56, 3874 (2008).

    Article  Google Scholar 

  30. V. A. Lubarda, Emission of dislocations from nanovoids under combined loading, Int. J. Plast. 27, 181 (2011).

    Article  Google Scholar 

  31. P. Jing, L. Yuan, R. Shivpuri, C. Xu, Y. Zhang, D. Shan, and B. Guo, Evolution of spherical nanovoids within copper polycrystals during plastic straining: Atomistic investigation, Int. J. Plast. 100, 122 (2018).

    Article  Google Scholar 

  32. F. D. Fischer, and T. Antretter, Deformation, stress state and thermodynamic force for a growing void in an elastic-plastic material, Int. J. Plast. 25, 1819 (2009).

    Article  Google Scholar 

  33. J. W. Wilkerson, and K. T. Ramesh, A dynamic void growth model governed by dislocation kinetics, J. Mech. Phys. Solids 70, 262 (2014).

    Article  MathSciNet  Google Scholar 

  34. V. S. Krasnikov, and A. E. Mayer, Plasticity driven growth of nanovoids and strength of aluminum at high rate tension: Molecular dynamics simulations and continuum modeling, Int. J. Plast. 74, 75 (2015).

    Article  Google Scholar 

  35. F. Meng, T. Ma, and X. Xu, Experimental and theoretical investigation of the failure behavior of a reinforced concrete target under high-energy penetration, Acta Mech. Sin. 36, 116 (2020).

    Article  MathSciNet  Google Scholar 

  36. M. P. Santisi d’Avila, N. Triantafyllidis, and G. Wen, Localization of deformation and loss of macroscopic ellipticity in microstructured solids, J. Mech. Phys. Solids 97, 275 (2016).

    Article  MathSciNet  Google Scholar 

  37. X. Lu, Y. Hou, Y. Tie, C. Li, and C. Zhang, Crack nucleation and propagation simulation in brittle two-phase perforated/particulate composites by a phase field model, Acta Mech. Sin. 36, 493 (2020).

    Article  MathSciNet  Google Scholar 

  38. D. E. S. Rodrigues, J. Belinha, L. M. J. S. Dinis, and R. M. Natal Jorge, Analysis of antisymmetric cross-ply laminates using highorder shear deformation theories: a meshless approach, Acta Mech. Sin. 36, 1078 (2020).

    Article  MathSciNet  Google Scholar 

  39. Z. Song, and S. Cai, Cavitation dynamics in a vitrimer, Acta Mech. Sin. 37, 767 (2021).

    Article  MathSciNet  Google Scholar 

  40. R. Hill, Acceleration waves in solids, J. Mech. Phys. Solids 10, 1 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  41. J. Mandel, Conditions de Stabilité et Postulat de Drucker, in: Rheology and Soil Mechanics (Springer, Berlin, Heidelberg, 1966), pp. 58–68.

    Google Scholar 

  42. J. R. Rice, The localization of plastic deformation, Theor. Appl. Mech. 207 (1977).

  43. M. Saje, J. Pan, and A. Needleman, Void nucleation effects on shear localization in porous plastic solids, Int. J. Fract. 19, 163 (1982).

    Article  Google Scholar 

  44. J. Pan, M. Saje, and A. Needleman, Localization of deformation in rate sensitive porous plastic solids, Int. J. Fract. 21, 261 (1983).

    Article  Google Scholar 

  45. M. E. Mear, and J. W. Hutchinson, Influence of yield surface curvature on flow localization in dilatant plasticity, Mech. Mater. 4, 395 (1985).

    Article  Google Scholar 

  46. N. Triantafyllidis, and M. W. Schraad, Onset of failure in aluminum honeycombs under general in-plane loading, J. Mech. Phys. Solids 46, 1089 (1998).

    Article  MATH  Google Scholar 

  47. K. Nahshon, and J. W. Hutchinson, Modification of the Gurson Model for shear failure, Eur. J. Mech.-A Solids 27, 1 (2008).

    Article  MATH  Google Scholar 

  48. F. López Jiménez, and N. Triantafyllidis, Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear, Int. J. Solids Struct. 50, 3934 (2013).

    Article  Google Scholar 

  49. L. Gong, S. Kyriakides, and N. Triantafyllidis, On the stability of Kelvin cell foams under compressive loads, J. Mech. Phys. Solids 53, 771 (2015).

    Article  MATH  Google Scholar 

  50. Y. Chen, M. Q. Jiang, and L. H. Dai, Collective evolution dynamics of multiple shear bands in bulk metallic glasses, Int. J. Plast. 50, 18 (2013).

    Article  Google Scholar 

  51. G. G. Ye, S. F. Xue, M. Q. Jiang, X. H. Tong, and L. H. Dai, Modeling periodic adiabatic shear band evolution during high speed machining Ti-6Al-4V alloy, Int. J. Plast. 40, 39 (2013).

    Article  Google Scholar 

  52. C. Zhu, V. Livescu, T. Harrington, O. Dippo, G. T. Gray Iii, and K. S. Vecchio, Investigation of the shear response and geometrically necessary dislocation densities in shear localization in high-purity titanium, Int. J. Plast. 92, 148 (2017).

    Article  Google Scholar 

  53. C. K. C. Lieou, and C. A. Bronkhorst, Dynamic recrystallization in adiabatic shear banding: Effective-temperature model and comparison to experiments in ultrafine-grained titanium, Int. J. Plast. 111, 107 (2018).

    Article  Google Scholar 

  54. A. Chatterjee, A. Ghosh, A. Moitra, A. K. Bhaduri, R. Mitra, and D. Chakrabarti, Role of hierarchical martensitic microstructure on localized deformation and fracture of 9Cr-1Mo steel under impact loading at different temperatures, Int. J. Plast. 104, 104 (2018).

    Article  Google Scholar 

  55. C. C. Roth, T. F. Morgeneyer, Y. Cheng, L. Helfen, and D. Mohr, Ductile damage mechanism under shear-dominated loading: In-situ tomography experiments on dual phase steel and localization analysis, Int. J. Plast. 109, 169 (2018).

    Article  Google Scholar 

  56. Z. H. Cao, Y. P. Cai, C. Sun, Y. J. Ma, M. Z. Wei, Q. Li, H. M. Lu, H. Wang, X. Zhang, and X. K. Meng, Tailoring strength and plasticity of Ag/Nb nanolaminates via intrinsic microstructure and extrinsic dimension, Int. J. Plast. 113, 145 (2019).

    Article  Google Scholar 

  57. R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids 15, 79 (1967).

    Article  Google Scholar 

  58. J. R. Rice, and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields, J. Mech. Phys. Solids 17, 201 (1969).

    Article  Google Scholar 

  59. A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Tech. 99, 2 (1977).

    Article  Google Scholar 

  60. A. A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture: Part I: Experiments, Acta Mater. 52, 4623 (2004).

    Article  Google Scholar 

  61. A. A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture, Part II: Theory, Acta Mater. 52, 4639 (2004).

    Article  Google Scholar 

  62. T. F. Guo, J. Faleskog, and C. F. Shih, Continuum modeling of a porous solid with pressure-sensitive dilatant matrix, J. Mech. Phys. Solids 56, 2188 (2008).

    Article  MATH  Google Scholar 

  63. V. Tvergaard, Material failure by void growth to coalescence, Adv. Appl. Mech. 27, 83 (1989).

    Article  MATH  Google Scholar 

  64. V. Tvergaard, and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, Acta Metall. 32, 157 (1984).

    Article  Google Scholar 

  65. T. F. Guo, and L. Cheng, Thermal and vapor pressure effects on cavitation and void growth, J. Mater. Sci. 36, 5871 (2001).

    Article  Google Scholar 

  66. T. F. Guo, and L. Cheng, Modeling vapor pressure effects on void rupture and crack growth resistance, Acta Mater. 50, 3487 (2002).

    Article  Google Scholar 

  67. X. Gao, T. Zhang, M. Hayden, and C. Roe, Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy, Int. J. Plast. 25, 2366 (2009).

    Article  Google Scholar 

  68. S. M. Keralavarma, and S. Chockalingam, A criterion for void coalescence in anisotropic ductile materials, Int. J. Plast. 82, 159 (2016).

    Article  Google Scholar 

  69. M. I. El Ghezal, and I. Doghri, Porous plasticity: Predictive second moment homogenization models coupled with Gurson’s single cavity stress-strain solution, Int. J. Plast. 108, 201 (2018).

    Article  Google Scholar 

  70. L. Dormieux, and D. Kondo, An extension of Gurson model incorporating interface stresses effects, Int. J. Eng. Sci. 48, 575 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  71. F. Fritzen, S. Forest, T. Böhlke, D. Kondo, and T. Kanit, Computational homogenization of elasto-plastic porous metals, Int. J. Plast. 29, 102 (2012).

    Article  Google Scholar 

  72. V. Monchiet, and D. Kondo, Semi-analytical investigation of stress interfacial effects in ductile media with nanosized spheroidal cavities, Procedia IUTAM 3, 228 (2012).

    Article  Google Scholar 

  73. L. Dormieux, and D. Kondo, Non linear homogenization approach of strength of nanoporous materials with interface effects, Int. J. Eng. Sci. 71, 102 (2013).

    Article  MATH  Google Scholar 

  74. J. Paux, L. Morin, R. Brenner, and D. Kondo, An approximate yield criterion for porous single crystals, Eur. J. Mech.-A Solids 51, 1 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  75. L. Morin, D. Kondo, and J. B. Leblond, Numerical assessment, implementation and application of an extended Gurson model accounting for void size effects, Eur. J. Mech.-A Solids 51, 183 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  76. S. Brach, K. Anoukou, D. Kondo, and G. Vairo, Limit analysis and homogenization of nanoporous materials with a general isotropic plastic matrix, Int. J. Plast. 105, 24 (2018).

    Article  Google Scholar 

  77. S. Brach, L. Dormieux, D. Kondo, and G. Vairo, A computational insight into void-size effects on strength properties of nanoporous materials, Mech. Mater. 101, 102 (2016).

    Article  Google Scholar 

  78. S. Brach, L. Dormieux, D. Kondo, and G. Vairo, Nanoporous materials with a general isotropic plastic matrix: Exact limit state under isotropic loadings, Int. J. Plast. 89, 1 (2017).

    Article  Google Scholar 

  79. S. Brach, K. Anoukou, F. Pastor, P. Dufrenoy, and D. Kondo, Limit analysis and homogenization of nanoporous materials with a general isotropic plastic matrix. Part I: Theoretical formulation, J. Mech. Phys. Solids 91, 145 (2016).

    MathSciNet  MATH  Google Scholar 

  80. V. Gallican, and J. Hure, Anisotropic coalescence criterion for nanoporous materials, J. Mech. Phys. Solids 108, 30 (2017), arXiv: 1709.05556.

    Article  MathSciNet  Google Scholar 

  81. J. M. Scherer, J. Besson, S. Forest, J. Hure, and B. Tanguy, Strain gradient crystal plasticity with evolving length scale: Application to voided irradiated materials, Eur. J. Mech.-A Solids 77, 103768 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  82. L. Xue, Constitutive modeling of void shearing effect in ductile fracture of porous materials, Eng. Fract. Mech. 75, 3343 (2008).

    Article  Google Scholar 

  83. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117, 1 (1995).

    Article  MATH  Google Scholar 

  84. J. Cai, and Y. Y. Ye, Simple analytical embedded-atom-potential model including a long-range force for fcc metals and their alloys, Phys. Rev. B 54, 8398 (1996).

    Article  Google Scholar 

  85. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—the Open Visualization Tool, Model. Simul. Mater. Sci. Eng. 18, 015012 (2010).

    Article  Google Scholar 

  86. C. Mi, D. A. Buttry, P. Sharma, and D. A. Kouris, Atomistic insights into dislocation-based mechanisms of void growth and coalescence, J. Mech. Phys. Solids 59, 1858 (2011).

    Article  MATH  Google Scholar 

  87. B. Li, B. Y. Cao, K. T. Ramesh, and E. Ma, A nucleation mechanism of deformation twins in pure aluminum, Acta Mater. 57, 4500 (2009).

    Article  Google Scholar 

  88. B. Q. Li, M. L. Sui, B. Li, E. Ma, and S. X. Mao, Reversible twinning in pure aluminum, Phys. Rev. Lett. 102, 205504 (2009).

    Article  Google Scholar 

  89. V. Yamakov, D. Wolf, S. R. Phillpot, and H. Gleiter, Deformation twinning in nanocrystalline Al by molecular-dynamics simulation, Acta Mater. 50, 5005 (2002).

    Article  Google Scholar 

  90. Y. T. Zhu, X. Z. Liao, and X. L. Wu, Deformation twinning in nanocrystalline materials, Prog. Mater. Sci. 57, 1 (2012).

    Article  Google Scholar 

  91. T. F. Guo, and L. Cheng, Vapor pressure and void size effects on failure of a constrained ductile film, J. Mech. Phys. Solids 51, 993 (2003).

    Article  MATH  Google Scholar 

  92. V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fract. 17, 389 (1981).

    Article  Google Scholar 

  93. V. Tvergaard, On localization in ductile materials containing spherical voids, Int. J. Fract. 18, 237 (1982).

    Article  Google Scholar 

  94. S. Tang, A. M. Kopacz, S. Chan O’Keeffe, G. B. Olson, and W. K. Liu, Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography, J. Mech. Phys. Solids 61, 2108 (2013).

    Article  Google Scholar 

  95. S. C. O’Keeffe, S. Tang, A. M. Kopacz, J. Smith, D. J. Rowenhorst, G. Spanos, W. K. Liu, and G. B. Olson, Multiscale ductile fracture integrating tomographic characterization and 3-D simulation, Acta Mater. 82, 503 (2015).

    Article  Google Scholar 

  96. Y. Zhu, J. Wang, Y. Xiang, and X. Guo, A three-scale homogenisation approach to the prediction of long-time absorption of radiation induced interstitials by nanovoids at interfaces, J. Mech. Phys. Solids 105, 1 (2017).

    Article  MathSciNet  Google Scholar 

  97. L. Vitos, A. V. Ruban, H. L. Skriver, and J. Kollár, The surface energy of metals, Surf. Sci. 411, 186 (1998).

    Article  Google Scholar 

  98. L. Xue, Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading, Int. J. Solids Struct. 44, 5163 (2007).

    Article  MATH  Google Scholar 

  99. L. Xue, Ductile Fracture Modeling: Theory, Experimental Investigation and Numerical Verification, Dissertation for Doctoral Degree (Massachusetts Institute of Technology, Cambridge, 2007).

    Google Scholar 

  100. C. Tekoğlu, J. W. Hutchinson, and T. Pardoen, On localization and void coalescence as a precursor to ductile fracture, Phil. Trans. R. Soc. A. 373, 20140121 (2015).

    Article  Google Scholar 

  101. S. Tang, M. Steven Greene, and W. K. Liu, Two-scale mechanism-based theory of nonlinear viscoelasticity, J. Mech. Phys. Solids 60, 199 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  102. J. F. Rodriguez-Nieva, C. J. Ruestes, Y. Tang, and E. M. Bringa, Atomistic simulation of the mechanical properties of nanoporous gold, Acta Mater. 80, 67 (2014).

    Article  Google Scholar 

  103. C. J. Ruestes, E. M. Bringa, A. Stukowski, J. F. Rodríguez Nieva, Y. Tang, and M. A. Meyers, Plastic deformation of a porous bcc metal containing nanometer sized voids, Comput. Mater. Sci. 88, 92 (2014).

    Article  Google Scholar 

  104. P. O. Barrioz, J. Hure, and B. Tanguy, Void growth and coalescence in irradiated copper under deformation, J. Nucl. Mater. 502, 123 (2018), arXiv: 1803.03983.

    Article  Google Scholar 

  105. P. O. Barrioz, J. Hure, and B. Tanguy, Effect of dislocation channeling on void growth to coalescence in FCC crystals, Mater. Sci. Eng.-A 749, 255 (2019).

    Article  Google Scholar 

  106. Z. Z. He, Y. B. Zhu, and H. A. Wu, Multiscale mechanics of non-covalent interface in graphene oxide layered nanocomposites, Theor. Appl. Mech. Lett. 12, 100304 (2022).

    Article  Google Scholar 

  107. J. Huang, M. Chen, and J. Sun, Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method, Theor. Appl. Mech. Lett. 4, 041001 (2014).

    Article  Google Scholar 

  108. M. Ren, L. Wang, T. Li, and B. Wei, Molecular investigation on the compatibility of epoxy resin with liquid oxygen, Theor. Appl. Mech. Lett. 10, 38 (2020).

    Article  Google Scholar 

  109. S. Wang, D. Marmysh, and S. Ji, Construction of irregular particles with superquadric equation in DEM, Theor. Appl. Mech. Lett. 10, 68 (2020).

    Article  Google Scholar 

  110. Z. Zheng, S. Lü, and M. Long, Simulation and prediction of membrane fusion dynamics, Theor. Appl. Mech. Lett. 12, 100321 (2022).

    Article  Google Scholar 

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Acknowledgements

Shan Tang appreciates the support from National Natural Science Foundation of China (Grant No. 11872139). Nian Zhou appreciates the support from Guizhou Provincial Department of Education (Grant No. KY[2021]255).

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Authors and Affiliations

  1. School of Earth Sciences and Resources, China University of Geosciences (Beijing), Beijing, 100083, China

    Zhangtao Sun  (孙张涛)

  2. Institute of High Performance Computing, A*STAR, Singapore, 138632, Singapore

    Tianfu Guo  (郭田福)

  3. Department of Mechanical Engineering, The American University in Cairo, New Cairo, 11835, Egypt

    Khalil I. Elkhodary

  4. Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116081, China

    Hang Yang  (杨航) & Shan Tang  (唐山)

  5. School of Materials and Energy Engineering, Guizhou Institute of Technology, Guiyang, 550003, China

    Nian Zhou  (周念)

Authors
  1. Zhangtao Sun  (孙张涛)
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  2. Tianfu Guo  (郭田福)
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  3. Khalil I. Elkhodary
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  4. Hang Yang  (杨航)
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  5. Nian Zhou  (周念)
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  6. Shan Tang  (唐山)
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Contributions

Author contributions Shan Tang designed the research. Zhangtao Sun and Nian Zhou wrote the first draft of the manuscript. Zhangtao Sun, Nian Zhou and Hang Yang set up the simulation set-up and processed the simulation data. Tianfu Guo helped organize the manuscript. Khalil I. Elkhodary and Shan Tang reviewed the manuscript. Zhangtao Sun, Shan Tang and Khalil I. Elkhodary revised and edited the final version.

Corresponding authors

Correspondence to Nian Zhou  (周念) or Shan Tang  (唐山).

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Sun, Z., Guo, T., Elkhodary, K.I. et al. Localization and macroscopic instability in nanoporous metals. Acta Mech. Sin. 38, 121538 (2022). https://doi.org/10.1007/s10409-022-21538-x

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  • DOI: https://doi.org/10.1007/s10409-022-21538-x

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