Intermittency in Crystal Plasticity Informed by Lattice Symmetry

详细信息    查看全文

• 作者：Paolo Biscari ; Marco Fabrizio Urbano ; Anna Zanzottera…
• 关键词：Crystal plasticity ; Intermittency ; Dislocations ; Finite strain ; Phase field modeling ; 74C15 ; 74E15 ; 74N30
• 刊名：Journal of Elasticity
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：123
• 期：1
• 页码：85-96
• 全文大小：1,917 KB
• 参考文献：1. Acharya, A.: Jump condition on GND evolution as a constraint on slip transmission at grain boundaries. Philos. Mag. 87, 1349–1359 (2007) CrossRef ADS
  2. Alava, M.J., Laurson, L., Zapperi, S.: Review: Crackling noise in plasticity. Eur. Phys. J. Spec. Top. 223, 2353–2367 (2014) CrossRef
  3. Ariza, M.P., Ortiz, M.: Discrete crystal elasticity and discrete dislocations in crystals. Arch. Ration. Mech. Anal. 178, 149–226 (2005) CrossRef MathSciNet MATH
  4. Asaro, R.J.: Crystal plasticity. J. Appl. Mech. 50, 921–934 (1983) CrossRef ADS MATH
  5. Balandraud, X., Barrera, N., Biscari, P., Grédiac, M., Zanzotto, G.: Strain intermittency in shape-memory alloys. Phys. Rev. B 91, 174111 (2015) CrossRef ADS
  6. Bhattacharya, K., Conti, S., Zanzotto, G., Zimmer, J.: Crystal symmetry and the reversibility of martensitic transformations. Nature 428, 55–59 (2004) CrossRef ADS
  7. Bilby, B.A., Bullough, R., de Grinberg, D.K.: General theory of surface dislocations. Discuss. Faraday Soc. 38, 61–68 (1964) CrossRef
  8. Bortoloni, L., Cermelli, P.: Dislocation patterns and work-hardening in crystalline plasticity. J. Elast. 76, 113–138 (2004) CrossRef MathSciNet MATH
  9. Brinckmann, S., Kim, J.-Y., Greer, J.R.: Fundamental differences in mechanical behavior between two types of crystals at the nanoscale. Phys. Rev. Lett. 100, 155502 (2008) CrossRef ADS
  10. Cermelli, C., Gurtin, M.E.: The dynamics of solid-solid phase transitions 2. Incoherent interfaces. Arch. Ration. Mech. Anal. 127, 41–99 (1994) CrossRef MathSciNet MATH
  11. Cermelli, P., Gurtin, M.E.: On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids 49, 1539–1568 (2001) CrossRef ADS MATH
  12. Chaari, N., Clouet, E., Rodney, D.: First-principles study of secondary slip in zirconium. Phys. Rev. Lett. 112, 075504 (2014) CrossRef ADS
  13. Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009) CrossRef ADS MathSciNet MATH
  14. Conti, S., Zanzotto, G.: A variational model for reconstructive phase transformations in crystals, and their relation to dislocations and plasticity. Arch. Ration. Mech. Anal. 173, 69–88 (2004) CrossRef MathSciNet MATH
  15. Cottrell, A.H., Bilby, B.A.: Dislocation theory of yielding and strain ageing of iron. Proc. Phys. Soc. A 62, 49–62 (1949) CrossRef ADS
  16. Csikor, F.F., Motz, C., Weygand, D., Zaiser, M., Zapperi, S.: Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318, 251–254 (2007) CrossRef ADS
  17. Dahmen, K.A., Ben-Zion, Y., Uhl, J.T.: Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Phys. Rev. Lett. 102, 175501 (2009) CrossRef ADS
  18. Denoual, C., Caucci, A.M., Soulard, L., Pellegrini, Y.-P.: Phase-field reaction-pathway kinetics of martensitic transformations in a model \(\mathrm{Fe}_{3}\) Ni alloy. Phys. Rev. Lett. 105, 035703 (2010) CrossRef ADS
  19. Devincre, B., Hoc, T., Kubin, L.: Dislocation mean free paths and strain hardening of crystals. Science 320, 1745–1748 (2008) CrossRef ADS
  20. Dezerald, L., Ventelon, L., Clouet, E., Denoual, C., Rodney, D., Willaime, F.: Ab initio modeling of the two-dimensional energy landscape of screw dislocations in bcc transition metals. Phys. Rev. B 89, 024104 (2014) CrossRef ADS
  21. Dimiduk, D.M., Woodward, C., LeSar, R., Uchic, M.D.: Scale-free intermittent flow in crystal plasticity. Science 312, 1188–1190 (2006) CrossRef ADS
  22. Ding, X., Zhao, Z., Lookman, T., Saxena, A., Salje, E.K.H.: High junction and twin boundary densities in driven dynamical systems. Adv. Mater. 24, 5385–5389 (2012) CrossRef
  23. Ericksen, J.L.: Some phase transitions in crystals. Arch. Ration. Mech. Anal. 73, 99–124 (1980) CrossRef MathSciNet MATH
  24. Fedelich, B., Zanzotto, G.: Hysteresis in discrete systems of possibly interacting elements with a double-well energy. J. Nonlinear Sci. 2, 319–342 (1992) CrossRef ADS MathSciNet MATH
  25. Fressengeas, C., Beaudoin, A.J., Entemeyer, D., Lebedkina, T., Lebyodkin, M., Taupin, V.: Dislocation transport and intermittency in the plasticity of crystalline solids. Phys. Rev. B 79, 014108 (2009) CrossRef ADS
  26. Gu, R., Ngan, A.H.W.: Dislocation arrangement in small crystal volumes determines power-law size dependence of yield strength. J. Mech. Phys. Solids 61, 1531–1542 (2013) CrossRef ADS MathSciNet
  27. Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, Cambridge (2010) CrossRef
  28. Hirth, J., Lothe, J.: Theory of Dislocations. Wiley, New York (1982)
  29. Ispanovity, P.D., Laurson, L., Zaiser, M., Groma, I., Zapperi, S., Alava, M.J.: Avalanches in 2D dislocation systems: Plastic yielding is not depinning. Phys. Rev. Lett. 112, 235501 (2014) CrossRef ADS
  30. Koslowski, M., Ortiz, M.: A multi-phase field model of planar dislocation networks. Model. Simul. Mater. Sci. Eng. 12, 1087–1097 (2004) CrossRef ADS
  31. Koslowski, M., LeSar, R., Thomson, R.: Dislocation structures and the deformation of materials. Phys. Rev. Lett. 93, 265503 (2004) CrossRef ADS
  32. Levitas, V.I.: Thermodynamically consistent phase field approach to phase transformations with interface stresses. Acta Mater. 61, 4305–4319 (2013) CrossRef
  33. Levitas, V.I.: Phase-field theory for martensitic phase transformations at large strains. Int. J. Plast. 49, 85–118 (2013) CrossRef
  34. Levitas, V.I.: Phase field approach to martensitic phase transformations with large strains and interface stresses. J. Mech. Phys. Solids 70, 154–189 (2014) CrossRef ADS MathSciNet
  35. Levitas, V.I., Javanbakht, M.: Advanced phase-field approach to dislocation evolution. Phys. Rev. B 86, 140101(R) (2012) CrossRef ADS
  36. Mamivand, M., Asle Zaeem, M., El Kadiri, H.: Shape memory effect and pseudoelasticity behavior in tetragonal zirconia polycrystals: A phase field study. Int. J. Plast. 60, 71–86 (2014) CrossRef
  37. Miguel, M.-C., Vespignani, A., Zaiser, M., Zapperi, S.: Dislocation jamming and Andrade creep. Phys. Rev. Lett. 89, 165501 (2002) CrossRef ADS
  38. Miller, R.E., Rodney, D.: On the nonlocal nature of dislocation nucleation during nanoindentation. J. Mech. Phys. Solids 56, 1203–1223 (2008) CrossRef ADS MATH
  39. Moretti, P., Miguel, M.-C., Zaiser, M., Zapperi, S.: Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries. Phys. Rev. B 69, 214103 (2004) CrossRef ADS
  40. Niemann, R., Baró, J., Heczko, O., Schultz, L., Fähler, S., Vives, E., Mañosa, Ll., Planes, A.: Tuning avalanche criticality: Acoustic emission during the martensitic transformation of a compressed Ni-Mn-Ga single crystal. Phys. Rev. B 86, 214101 (2012) CrossRef ADS
  41. Niemann, R., Kopecek, J., Heczko, O., Romberg, J., Schultz, L., Fähler, S., Vives, E., Mañosa, Ll., Planes, A.: Localizing sources of acoustic emission during the martensitic transformation. Phys. Rev. B 89, 214118 (2014) CrossRef ADS
  42. Perez-Reche, F.-J., Truskinovsky, L., Zanzotto, G.: Training-induced criticality in martensites. Phys. Rev. Lett. 99, 075501 (2007) CrossRef ADS
  43. Pitteri, M., Zanzotto, G.: Continuum Models for Phase Transitions and Twinning in Crystals. Chapman & Hall, London (2002) CrossRef
  44. Planes, A., Mañosa, Ll., Vives, E.: Acoustic emission in martensitic transformations. J. Alloys Compd. 577, S699–S704 (2013) CrossRef
  45. Reina, C., Conti, S.: Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of \(\mathbf {F}=\mathbf{F}_{\mathrm{r}} \mathbf{F}_{\mathrm{p}}\) . J. Mech. Phys. Solids 67, 40–61 (2014) CrossRef ADS MathSciNet
  46. Rodney, D.: Activation enthalpy for kink-pair nucleation on dislocations: Comparison between static and dynamic atomic-scale simulations. Phys. Rev. B 76, 144108 (2007) CrossRef ADS
  47. Rodney, D., Proville, D.: Stress-dependent Peierls potential: Influence on kink-pair activation. Phys. Rev. B 79, 094108 (2009) CrossRef ADS
  48. Rodney, D., Le Bouar, Y., Finel, A.: Phase field methods and dislocations. Acta Mater. 51, 17–30 (2003) CrossRef
  49. Salman, O.U., Truskinovsky, L.: Minimal integer automaton behind crystal plasticity. Phys. Rev. Lett. 106, 175503 (2011) CrossRef ADS
  50. Salman, O.U., Truskinovsky, L.: On the critical nature of plastic flow: One and two dimensional models. Int. J. Eng. Sci. 59, 219–254 (2012) CrossRef
  51. Shen, C., Wang, Y.: Incorporation of \(\gamma\) -surface to phase field model of dislocations: Simulating dislocation dissociation in fcc crystals. Acta Mater. 52, 683–691 (2004) CrossRef
  52. Song, Y., Chen, X., Dabade, V., Shield, T.W., James, R.D.: Enhanced reversibility and unusual microstructure of a phase-transforming material. Nature 502, 85–88 (2013) CrossRef ADS
  53. Steinbach, I., Pezzolla, F., Nestler, B., Seeßelberg, M., Prieler, R., Schmitz, G.J., Rezende, J.L.L.: A phase field concept for multiphase systems. Physica D 94, 135–147 (1996) CrossRef ADS MATH
  54. Toth, L.Z., Szabo, S., Daroczi, L., Beke, D.L.: Calorimetric and acoustic emission study of martensitic transformation in single-crystalline \(\mathrm{Ni}_{2}\) MnGa alloys. Phys. Rev. B 90, 224103 (2014) CrossRef ADS
  55. Truskinovsky, L., Vainchtein, A.: The origin of nucleation peak in transformational plasticity. J. Mech. Phys. Solids 52, 1421–1446 (2004) CrossRef ADS MathSciNet MATH
  56. Tsekenis, G., Uhl, J.T., Goldenfeld, N., Dahmen, K.A.: Determination of the universality class of crystal plasticity. Europhys. Lett. 101, 36003 (2013) CrossRef ADS
  57. Uchic, M.D., Shade, P.A., Dimiduk, D.M.: Plasticity of micrometer-scale single crystals in compression. Annu. Rev. Mater. Res. 39, 361–386 (2009) CrossRef ADS
  58. Wang, Y., Li, J.: Phase field modeling of defects and deformation. Acta Mater. 58, 1212–1235 (2010) CrossRef
  59. Wang, Y.U., Jin, Y.M., Cuitiño, A.M., Khachaturyan, A.G.: Nanoscale phase field microelasticity theory of dislocations: Model and 3D simulations. Acta Mater. 49, 1847–1857 (2001) CrossRef
  60. Wang, Y.U., Jin, Y.M., Khachaturyan, A.G.: Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin. Acta Mater. 51, 4209–4223 (2003) CrossRef
  61. Weiss, J., Ben Rhouma, W., Richeton, T., Dechanel, S., Louchet, F., Truskinovsky, L.: From mild to wild fluctuations in crystal plasticity. Phys. Rev. Lett. 114, 105504 (2015) CrossRef ADS
  62. Zaiser, M.: Scale invariance in plastic flow of crystalline solids. Adv. Phys. 55, 185–245 (2006) CrossRef ADS
  63. Zhang, X., Pan, B., Shang, F.: Scale-free behavior of displacement bursts: Lower limit and scaling exponent. Europhys. Lett. 100, 16005 (2012) CrossRef
  
• 作者单位：Paolo Biscari (1)
  Marco Fabrizio Urbano (2)
  Anna Zanzottera (1)
  Giovanni Zanzotto (3)
  
  1. Department of Physics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy
  2. SAES Getters, Viale Italia 77, 20020, Lainate, Italy
  3. DPG, Università di Padova, Via Venezia 8, 35131, Padova, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-2681

文摘

We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group \(G\) of the underlying periodic lattice. This generates a complex energy landscape with countably-many \(G\)-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a \(G\)-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears. Keywords Crystal plasticity Intermittency Dislocations Finite strain Phase field modeling