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Discrete-Continuous Model of Crystal Plasticity

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The Investigation of Plastic Behavior by Discrete Dislocation Dynamics for Single Crystal Pillar at Submicron Scale

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Abstract

Although the multi-scale discrete-continuous model (DCM) which couples discrete dislocation dynamics (DDD) and finite element method (FEM) to study crystal plasticity at submicron scale has been proposed for many years, some key issues are still not well addressed yet. First, a new regularization method with slip plane dependent regularization parameter is proposed to localize the discrete plastic strain to continuum material points and shows excellent accuracy compared with previous studies. Second, it is often thought of that DCM cannot accurately calculate the so called ‘image force’ acting on the dislocation near free surface. This study argues that the image force can be calculated accurately in the hybrid DCM in which the interpolated stress is used in the computation. The reproduction of deformed crystal configuration during finite deformation is another critical issue in DCM, especially for considering the rotation of slip system. The deformation field transfer between DDD and FEM, and the corresponding treatment of surface dislocations and slip system rotation are proposed to well capture the localized deformation. As an application, the dislocation behavior and stress field in heteroepitaxial films with thin/thick substrates are successfully investigated by the improved DCM.

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References

  1. Dunstan DJ, Bushby AJ (2013) The scaling exponent in the size effect of small scale plastic deformation. Int J Plast 40:152–162

    Article  Google Scholar 

  2. Uchic MD, Dimiduk DM, Florando JN, Nix WD (2004) Sample dimensions influence strength and crystal plasticity. Science 305:986–989

    Article  Google Scholar 

  3. Hu JQ, Liu ZL, Cui YN, Wang ZJ, Shan ZW, Zhuang Z (2014) Sensitive material behavior: theoretical model and experiment for compression collapse of gold particles at submicron scale. J Appl Mech 81(9):091007. doi:10.1115/1.4027916

    Article  Google Scholar 

  4. Zhou C, Beyerlein IJ, LeSar R (2011) Plastic deformation mechanisms of fcc single crystals at small scales. Acta Mater 59(20):7673–7682

    Article  Google Scholar 

  5. Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S (2007) Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318(5848):251

    Article  Google Scholar 

  6. Cui YN, Lin P, Liu ZL, Zhuang Z (2014) Theoretical and numerical investigations of single arm dislocation source controlled plastic flow in FCC micropillars. Int J Plast 55:279–292

    Article  Google Scholar 

  7. Zhou C, LeSar R (2012) Dislocation dynamics simulations of plasticity in polycrystalline thin films. Int J Plast 30:185–201

    Article  Google Scholar 

  8. Espinosa HD, Panico M, Berbenni S, Schwarz K (2006) Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films. Int J Plast 22(11):2091–2117

    Article  MATH  Google Scholar 

  9. Devincre B, Madec R, Monnet G, Queyreau S, Gatti R, Kubin L (2011) Modeling crystal plasticity with dislocation dynamics simulations: the ‘microMegas’ code. Mechanics of nano-objects. Presses de l’Ecole des Mines de Paris, Paris, pp 81–100

    Google Scholar 

  10. Gao Y, Zhuang Z, Liu ZL, Zhao XC, Zhang Z (2010) Characteristic sizes for exhaustion-hardening mechanism of compressed Cu single-crystal micropillars. Chin Phys Lett 27(8):086103

    Article  Google Scholar 

  11. Gao Y, Liu ZL, You XC, Zhuang Z (2010) A hybrid multiscale computational framework of crystal plasticity at submicron scales. Comput Mater Sci 49:672–681

    Article  Google Scholar 

  12. Liu ZL, Liu XM, Zhuang Z, You XC (2009) A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales. Int J Plast 25(8):1436–1455

    Article  MATH  Google Scholar 

  13. Gao Y (2011) Discrete Dislocation Mechanism on Submicro-crystal Plasticity, PhD thesis of Tsinghua University

    Google Scholar 

  14. Liu ZL (2009) The Investigation of Crystal Plasticity at Microscale by Discrete Dislocation and Nonlocal Theory. PhD thesis of Tsinghua University

    Google Scholar 

  15. Nadgornyi E (1998) Progress in materials science, dislocation dynamics and mechanical properties, vol 31. Pergamon Press, Oxiford

    Google Scholar 

  16. Hirth JP, Lothe J (1982) Theory of dislocations. Wiley, New York, p 857

    Google Scholar 

  17. Liu XH, Schwarz KW (2005) Modelling of dislocations intersecting a free surface. Modell Simul Mater Sci Eng 13:1233–1247

    Article  Google Scholar 

  18. Rhee M, Zbib HM, Hirth JP, Huang H, Rubia T (1998) Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals. Modell Simul Mater Sci Eng 6:467–492

    Article  Google Scholar 

  19. Bulatov VV, Cai W (2006) Computer simulations of dislocations. Oxford University Press, New York

    MATH  Google Scholar 

  20. Groh S, Zbib HM (2009) Advances in discrete dislocations dynamics and multiscale modeling. J Eng Mater Technol 131:041209

    Article  Google Scholar 

  21. Madec R, Devincre B, Kubin LP (2002) Simulation of dislocation patterns in multislip. Scr Mater 47(10):689–695

    Article  Google Scholar 

  22. Motz C, Weygand D, Senger J, Gumbsch P (2009) Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity. Acta Mater 57(6):1744–1754

    Article  Google Scholar 

  23. Rao SI, Dimiduk DM, Parthasarathy TA, El-Awady J, Woodward C, Uchic MD (2011) Calculations of intersection cross-slip activation energies in fcc metals using nudged elastic band method. Acta Mater 59(19):7135–7144

    Article  Google Scholar 

  24. Wang ZQ, Beyerlein IJ, LeSar R (2007) The importance of cross-slip in high-rate deformation. Modell Simul Mater Sci Eng 15:675–690

    Article  Google Scholar 

  25. Wei H, Wei Y (2012) Interaction between a screw dislocation and stacking faults in FCC metals. Mater Sci Eng A 541(15):38–44

    Article  Google Scholar 

  26. Püschl W (2002) Models for dislocation cross-slip in close-packed crystal structures: a critical review. Prog Mater Sci 47(4):415–461. doi:http://dx.doi.org/10.1016/S0079-6425(01)00003-2

  27. Cui YN, Liu ZL, Zhuang Z (2013) Dislocation multiplication by single cross slip for FCC at submicron scales. Chin Phys Lett 30(4):046103

    Article  Google Scholar 

  28. Devincre B (1996) Meso-scale simulation of the dislocation dynamics. NATO ASI Ser E Appl Sci-Adv Study Inst 308:309–324

    Google Scholar 

  29. Kubin LP, Canova G, Condat M, Devincre B, Pontikis V, Bréchet Y (1992) Dislocation microstructures and plastic flow: a 3D simulation. Solid State Phenom 23:455–472

    Article  Google Scholar 

  30. Groh S, Marin EB, Horstemeyer MF, Zbib HM (2009) Multiscale modeling of the plasticity in an aluminum single crystal. Int J Plast 25(8):1456–1473

    Article  MATH  Google Scholar 

  31. Zbib HM, de la Rubia TD, Bulatov V (2002) A multiscale model of plasticity based on discrete dislocation dynamics. J Eng Mater Technol 124(1):78–87

    Article  Google Scholar 

  32. Van der Giessen E, Needleman A (1995) Discrete dislocation plasticity: a simple planar model. Modell Simul Mater Sci Eng 3(5):689–735

    Article  Google Scholar 

  33. Po G, Mohamed MS, Crosby T, Erel C, El-Azab A, Ghoniem NM (2014) Recent progress in discrete dislocation dynamics and its applications to micro plasticity. JOM 66(10):2108–2120. doi:10.1007/s11837-014-1153-2

    Article  Google Scholar 

  34. Zhou C, Biner SB, LeSar R (2010) Discrete dislocation dynamics simulations of plasticity at small scales. Acta Mater 58(5):1565–1577

    Article  Google Scholar 

  35. El-Awady JA, Bulent Biner S, Ghoniem NM (2008) A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes. J Mech Phys Solids 56(5):2019–2035

    Google Scholar 

  36. Lemarchand C, Devincre B, Kubin LP (2001) Homogenization method for a discrete-continuum simulation of dislocation dynamics. J Mech Phys Solids 49(9):1969–1982

    Article  MATH  Google Scholar 

  37. Vattré A, Devincre B, Feyel F, Gatti R, Groh S, Jamond O, Roos A (2013) Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: the discrete-continuous model revisited. J Mech Phys Solids 63:491–505

    Article  MathSciNet  Google Scholar 

  38. Zbib HM, de la Rubia TD (2002) A multiscale model of plasticity. Int J Plast 18(9):1133–1163

    Article  MATH  Google Scholar 

  39. Chen Q, Biner B (2006) Evolution and interaction of dislocations in intermetallics: fully anisotropic discrete dislocation dynamics simulations. MRS online proceedings library 980, null-null (2006). doi:10.1557/PROC-980-0980-II05-16

  40. O’day MP, Curtin WA (2005) Bimaterial interface fracture: a discrete dislocation model. J Mech Phys Solids 53(2):359–382

    Google Scholar 

  41. Cui YN, Liu ZL, Zhuang Z (2015) Quantitative investigations on dislocation based discrete-continuous model of crystal plasticity at submicron scale. Int J Plast 69:54–72

    Article  Google Scholar 

  42. Weinberger CR, Cai W (2007) Computing image stress in an elastic cylinder. J Mech Phys Solids 55(10):2027–2054

    Article  MathSciNet  MATH  Google Scholar 

  43. Uchic MD, Shade PA, Dimiduk DM (2009) Plasticity of micrometer-scale single crystals in compression. Annu Rev Mater Res 39:361–386

    Article  Google Scholar 

  44. Dimiduk DM, Uchic MD, Parthasarathy TA (2005) Size-affected single-slip behavior of pure nickel microcrystals. Acta Mater 53(15):4065–4077

    Article  Google Scholar 

  45. Deshpande VS, Needleman A, Van der Giessen E (2003) Finite strain discrete dislocation plasticity. J Mech Phys Solids 51(11–12):2057–2083. doi:10.1016/j.jmps.2003.09.012

    Article  MathSciNet  MATH  Google Scholar 

  46. Akarapu S, Zbib HM, Bahr DF (2010) Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression. Int J Plast 26(2):239–257

    Article  MATH  Google Scholar 

  47. Mura T (1987) Micromechanics of defects in solids, vol 3. Springer, Berlin

    Google Scholar 

  48. Cai W, Arsenlis A, Weinberger C, Bulatov V (2006) A non-singular continuum theory of dislocations. J Mech Phys Solids 54(3):561–587

    Article  MathSciNet  MATH  Google Scholar 

  49. Tang M, Cai W, Xu G, Bulatov VV (2006) A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics. Modell Simul Mater Sci Eng 14:1139

    Article  Google Scholar 

  50. Yoffe EH (1961) A dislocation at a free surface. Phil Mag 6(69):1147–1155

    Article  MathSciNet  MATH  Google Scholar 

  51. Li JCM (1964) Stress field of a dislocation segment. Phil Mag 10(108):1097–1098

    Article  Google Scholar 

  52. Crone JC, Chung PW, Leiter KW, Knap J, Aubry S, Hommes G, Arsenlis A (2014) A multiply parallel implementation of finite element-based discrete dislocation dynamics for arbitrary geometries. Modell Simul Mater Sci Eng 22(3):035014. doi:035014/0965-0393/22/3/035014

    Google Scholar 

  53. Asaro RJ, Rice J (1977) Strain localization in ductile single crystals. J Mech Phys Solids 25(5):309–338

    Article  MATH  Google Scholar 

  54. Rao SI, Dimiduk DM, Tang M, Uchic MD, Parthasarathy TA, Woodward C (2007) Estimating the strength of single-ended dislocation sources in micron-sized single crystals. Philos Mag 87(30):4777–4794

    Article  Google Scholar 

  55. Wang YU, Jin YM, Khachaturyan AG (2003) Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films. Acta Mater 51(14):4209–4223. doi:10.1016/s1359-6454(03)00238-6

    Article  Google Scholar 

  56. Shen YL (2008) Externally constrained plastic flow in miniaturized metallic structures: a continuum-based approach to thin films, lines, and joints. Prog Mater Sci 53(5):838–891. doi:10.1016/j.pmatsci.2008.03.001

    Article  Google Scholar 

  57. Newberger M (ed) (1971) Handbook of electronic materials group IV semiconducting materials. IFI/Plenum, New York

    Google Scholar 

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Authors and Affiliations

  1. Tsinghua University, Beijing, China

    Yinan Cui

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  1. Yinan Cui
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Correspondence to Yinan Cui .

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Cui, Y. (2017). Discrete-Continuous Model of Crystal Plasticity. In: The Investigation of Plastic Behavior by Discrete Dislocation Dynamics for Single Crystal Pillar at Submicron Scale. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-3032-1_2

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  • DOI: https://doi.org/10.1007/978-981-10-3032-1_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3031-4

  • Online ISBN: 978-981-10-3032-1

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