GD3: generalized discrete defect dynamics
Tóm tắt
A mesoscale model is introduced to study the dynamics of material defects lying at interface junctions. The proposed framework couples the dynamics of discrete dislocation and disclination lines. Disclinations are expected to be natural defects at interface junctions; their presence serving the purpose of accommodating discontinuities in rotation fields at material interface junctions. Crystallography-based rules are proposed to describe the kinematics of disclination motion. A discrete-continuous couple-stress framework, in which discrete defect lines are introduced as plastic eigenstrains and eigencurvatures, is proposed to explicitly follow the dynamics of interfacial defects. The framework is then applied to study
$\left (10\bar {1}2\right)$
twin transverse propagation and thickening in magnesium. Focusing first on the case of a twin domain, It is shown that a disclination based representation of twin domains allows for an appropriate mechanistic description of the kinematics of shear transformations. In what concerns twin thickening, the stability of defects at twin interfaces is further studied. To this end, a 3D crater lying on a twin interface is described as a dipole of disclination loops. Upon self-relaxation, it is found that out of plane motion of disclinations followed by the nucleation of twinning dislocations can be activated; thereby showing that conservative non-planar motion of disclinations can be thermodynamically favorable; mechanism that had been postulated some 50 years ago.
Tài liệu tham khảo
A. Acharya, A model of crystal plasticity based on the theory of continuously distributed dislocations. J. Mech. Phys. Solids. 49:, 761 (2001).
N. Ahmed, A. Hartmaier, Mechanisms of grain boundary softening and strain-rate sensitivity in deformation of ultrafine-grained metals at high temperatures. Acta Mater. 59:, 4323–4334 (2011).
A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G Pierce, V. V. Bulatiov, Enabling strain hardening simulations with dislocation dynamics. Modelling Simul. Mater. Sci. Eng. 15:, 553–95 (2007).
C. D. Barrett, H. El Kadiri, The roles of grain boundary dislocations and disclinations in the nucleation of 10\(\bar {1}\)2 twinning. Acta Mater. 63:, 1–15 (2014).
E. Bayerschen, A. T McBride, B. D. Reddy, T. Böhlke, Review on slip transmission criteria in experiments and crystal plasticity models. J. Mater. Sci.51:, 2243–2258 (2016).
B. Beausir, C. Fressengeas, Disclination densities from EBSD orientation mapping. Int. J. Solids. Structures. 50:, 137 (2013).
S. Berbenni, V. Taupin, K. S. Djaka, C. Fressengeas, A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics. Int. J. Solids Structures. 51:, 4157 (2014).
N. Bertin, C. N. Tomé, I. J. Beyerlein, M. R. Barnett, L. Capolungo, On the strength of dislocation interactions and their effect on latent hardening in pure magnesium. Int. J. Plasticity. 62:, 72–92 (2014).
N. Bertin, M. V. Upadhyay, C. Pradalier, L. Capolungo, A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics. Modelling Simul. Mater. Sci. Eng. 23:, 065009 (2015).
B. A. Bilby, in Bristol Conference Report on Defects in Crystalline Solids. Types of dislocation source (The Physical SocietyLondon, 1955), p. 124.
E. Bitzek, P. Gumbsch, Atomistic study of drag, surface and inertial effects on edge dislocations in face-centered cubic metals. Mater. Sci. Eng., A. 387-389:, 11–15 (2004).
W. Bollmann, Crystal defects and crystalline interfaces (Springer-Verlag, Berlin Heidelberg GmbH, 1970).
S. I. Bozhko, V. Taupin, M. Lebyodkin, C. Fressengeas, E. A. Levchenko, K. Radikan, O. Lübben, V. N. Semenov, I. V. Shvets, Disclinations in molecular layers on WO2/W(110) surfaces. Phys. Rev. B. 90:, 214106 (2014).
V. Bulatov, F. Abraham, F. Kubin, B. Devincre, S. Yip, Connecting atomistic and mesoscale simulations of crystal plasticity. Nature. 391:, 669–72 (1998).
V. V. Bulatov, L. L. Hsiung, M. Tang, A. Arsenlis, M. C. Bartelt, W. Cai, J. N. Florando, M. Hiratani, M. Rhee, G. Hommes, T. G. Pierce, T. Diaz de la Rubia, Dislocation multi-junctions and strain hardening. Nature. 440:, 1174–8 (2006).
N. B. Burbery, G. Po, R. Das, N. Ghoniem, W. G. Ferguson, J. Micromech, Dislocation dynamics in polycrystals with atomistic-informed mechanisms of dislocation-grain boundary interactions. Mol. Phys. 02:, 1750003 (2017).
L. Capolungo, D. E. Spearot, M. Cherkaoui, D. L. McDowell, J. Qu, K. I. Jacob, Dislocation nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation. J. Mech. Phys. Solids. 55:, 2300–2327 (2007).
L. Capolungo, I. J. Beyerlein, Z. Qwang, The role of elastic anisotropy on plasticity in hcp metals: a three-dimensional dislocation dynamics study. Modelling Simul. Mater. Sci. Eng. 18:, 085002 (2010).
J. Cho, J. -F. Molinari, G. Anciaux, Mobility law of dislocations with several character angles and temperatures in FCC aluminum. Int. J. Plast. 90:, 66–75 (2017).
P. Cordier, S. Demouchy, B. Beausir, V. Taupin, F. Barou, C. Fressengeas, Disclinations provide the missing mechanism for deforming olivine-rich rocks in the mantle. Nature. 507:, 51 (2014).
E. Cosserat, F. Cosserat, Théorie des corps déformables (Hermann, Paris, 1909).
M. de Koning, R. Miller, V. V. Bulatov, F. F. Abraham, Modelling grain-boundary resistance in intergranular dislocation slip transmission. Philos Mag A Physics of Condensed Matter Structure Defects and Mechanical Properties. 82:, 2511–2527 (2002).
M. de Koning, R. J. Kurtz, V. V. Bulatov, C. H. Henager, R. G. Hoagland, W. Cai, M. Nomura, Modeling of dislocation-grain boundary interactions in FCC metals. J. Nucl. Mater. 323:, 281–289 (2003).
B. Devincre, L. P. Kubin, Mesoscopic simulations of dislocations and plasticity. Mater. Sci. Eng. Struct. Mater. Prop. Microstruct. Process. 234:, 8–14 (1997).
B. Devincre, Dislocation dynamics simulations of slip systems interactions and forest strengthening in ice crystals. Phil. Mag. 93:, 235–46 (2013).
R. deWit, in Fundamental aspects of dislocation theory, ed. by J. A. Simmons, R. deWit, and R. Bullough. Linear theory of static disclinations. Nat. Bur. Stand. (US), Spec. Publ. 317, Vol. I, (1970), pp. 651–673.
R. deWit, Theory of disclinations: IV. Straight disclinations. J Res Natl Bur Stand-A Phys Chem. 77A:, 607 (1973).
D. J. Eyre, G. W. Milton, A fast numerical scheme for computing the response of composites using grid refinement. Eur Phys J Appl Phys. 6:, 41–47 (1999).
H. Fan, S. Aubry, A. Arsenlis, J. A. El-Awady, Orientation influence on grain size effects in ultrafine-grained magnesium. Scripta Mater. 97:, 25–28 (2015).
Fan, H., S. Aubry, A. Arsenlis, J. A. El-Awady, Grain size effects on dislocation and twinning mediated plasticity in magnesium. Scripta Mater. 112:, 50–53 (2016).
M. C. Fivel, G. R. Canova, Developing rigorous boundary conditions to simulations of discrete dislocation dynamics. Modelling Simul. Mater. Sci. Eng. 7:, 753–68 (1999).
P. Franciosi, M. Berveiller, A. Zaoui, Latent hardening in copper and aluminium single crystals. Acta Metall. 28:, 273–283 (1980).
F. C. Frank, in Symposium on The Plastic Deformation of Crystalline Solids. The resultant content of dislocations in an arbitrary intercrystalline boundary (Mellon InstitutePittsburgh, 1950), pp. (NAVEXOS-P-834), 150.
C. Fressengeas, V. Taupin, L. Capolungo, An elasto-plastic theory of dislocation and disclination fields. Int. J. Solids Structures. 48:, 3499–3509 (2011).
S. Gao, M. Fivel, A. Ma, A. Hartmaier, Influence of misfit stresses on dislocation glide in single crystal superalloys: A three-dimensional discrete dislocation dynamics study. J. Mech. Phys. Solids. 76:, 276–290 (2015).
N. M. Ghoniem, S. H. Tong, L. Z. Sun, Parametric dislocation dynamics: A thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys. Rev. B. 61:, 913–27 (2000).
J. P. Hirth, R. C. Pond, Steps, dislocations and disconnections as interface defects relating to structure and phase transformations. Acta Mater. 44:, 4749 (1996).
J. P. Hirth, R. C. Pond, J. Lothe, Disconnections in tilt walls. Acta Mater. 54:, 4237 (2006).
J. P. Hirth, J. Wang, C. N. Tomé, Disconnections and other defects associated with twin interfaces. Progr. Mater. Sc. 83:, 417–471 (2016).
R. G. Hoagland, T. E. Mitchell, J. P. Hirth, H. Kung, On the strengthening effects of interfaces in multilayer fee metallic composites. Philos. Mag. a-Phys. Condens. Matter Struct. Defects Mech. Prop. 82:, 643–664 (2002).
C. Hou, Z. Li, M. Huang, C. Ouyang, Cyclic Hardening Behavior of Polycrystals with Penetrable Grain Boundaries: Two-Dimensional Discrete Dislocation Dynamics Simulation. Acta Mechanica Solida Sinica. 22:, 295 (2009).
H. A. Khater, A. Serra, R. C. Pond, J. P. Hirth, The disconnection mechanism of coupled migration and shear at grain boundaries. Acta Mater. 60:, 2007 (2012).
A. L. Kolesnikova, M. Y. Gutkin, A. V. Proskura, N. F. Morozov, A. E. Romanov, Elastic fields of straight wedge disclinations axially piercing bodies with spherical free surfaces. Int. J. Solids Structures. 99:, 82–96 (2016).
L. Kubin, B. Devincre, T. Hoc, Modeling dislocation storage rates and mean free paths in face-centered cubic crystals. Acta Mater. 56:, 6040–6049 (2008).
C. Lemarchand, B. Devincre, L. P. Kubin, Homogenization method for a discrete-continuum simulation of dislocation dynamics. J. Mech. Phys. Solids. 49:, 1969–82 (2001).
Z. Li, C. Hou, M. Huang, C. Ouyang, Strengthening mechanism in micro-polycrystals with penetrable grain boundaries by discrete dislocation dynamics simulation and Hall-Petch effect. Comput. Mater. Sci. 46:, 1124–1134 (2009).
A. T. Lim, M. Haataja, W. Cai, D. J. Srolovitz, Stress-driven migration of simple low-angle mixed grain boundaries. Acta Mater. 60:, 1395–1407 (2012).
B. Liu, D. Raabe, P. Eisenlohr, F. Roters, A. Arsenlis, G. Hommes, Dislocation interactions and low-angle grain boundary strengthening. Acta Mater. 59:, 7125–7134 (2011).
B. Liu, P. Eisenlohr, F. Roters, D. Raabe, Simulation of dislocation penetration through a general low-angle grain boundary. Acta Mater. 60:, 5380–5390 (2012).
Y. Liu, N. Li, S. Shao, M. Gong, J. Wang, R. J. McCabe, Y. Jiang, C. N. Tomé, Characterizing the boundary lateral to the shear direction of deformation twins in magnesium. Nat. Commun. 7:, 11577 (2016).
R. Madec, B. Devincre, L. Kubin, T. Hoc, D. Rodney, The role of collinear interaction in dislocation-induced hardening. Science. 301:, 1879–1882 (2003).
J. C. Michel, H. Moulinec, P. Suquet, A computational scheme for linear and non-linear composites with arbitrary phase contrast. Internat. J. Numer. Methods Engrg. 52:, 139–160 (2001).
F. Mompiou, D. Caillard, M. Legros, Grain boundary shear-migration coupling–I. In situ TEM straining experiments in Al polycrystals. Acta Materialia. 57:, 2198 (2009).
B. Muntifering, L. Kovarik, N. D. Browning, R. C. Pond, W. B. Knowlton, P. Müllner, Stress-assisted removal of conjugation boundaries in non-modulated Ni-Mn-Ga by coordinated secondary twinning. J. Mater. Sci. 51:, 457–466 (2016).
T. Mura, Micromechanics of Defects in Solids (Kluwer Academic Publishers, Dordrecht, 1987).
M. Murayama, J. M. Howe, H. Hidaka, S. Takaki, Atomic-level observation of disclination dipoles in mechanically milled, nanocrystalline Fe. Science. 295:, 2433 (2002).
P. G. Partridge, The crystallography and deformation modes of hexagonal close-packed metals. Metall. Rev. 12:, 169–194 (1967).
G. Po, M. Lazar, D. Seif, N. Ghoniem, Singularity-free dislocation dynamics with strain gradient elasticity. J. Mech. Phys. Solids. 68:, 161–178 (2014).
L Priester, Grain boundaries, from theory to engineering. Springer Ser. Mater. Sci. 172: (2013).
S. S. Quek, Z. Wu, Y. W. Zhang, D. J. Srolovitz, Polycrystal deformation in a discrete dislocation dynamics framework. Acta Mater. 75:, 92–105 (2014).
S. S. Quek, Z. H. Chooi, Z. Wu, Y. W. Zhang, D. J. Srolovitz, The inverse hall-petch relation in nanocrystalline metals: A discrete dislocation dynamics analysis. J. Mech. Phys. Solids. 88:, 252–266 (2016).
S. Queyreau, G. Monnet, B. Devincre, Slip systems interactions in α-iron determined by dislocation dynamics simulations. Int. J. Plasticity. 25:, 361–77 (2009).
A. Rajabzadeh, M. Legros, N. Combe, F. Mompiou, D. A. Molodov, Evidence of grain boundary dislocation step motion associated to shear-coupled grain boundary migration. Phil. Mag. 93:, 1299 (2013).
B. Reinholz, S. Brinckmann, A. Hartmaier, B. Muntifering, W. B. Knowlton, P. Müllner, Influence of the twin microstructure on the mechanical properties in magnetic shape memory alloys. Acta Mater. 108:, 197–206 (2016).
A. E. Romanov, A. L. Kolesnikova, Application of disclination concept to solid structures. Prog. Mat. Sci. 54:, 740 (2009).
H. Rösner, C. Kübel, Y. Ivanisenko, L. Kurmanaeva, S. V. Divinski, M. Peterlechner, G. Wilde, Strain mapping of a triple junction in nanocrystalline Pd. Acta Mater. 59:, 7380 (2011).
D. Seif, G. Po, M. Mrovec, M. Lazar, C. Elsässer, P. Gumbsch, Atomistically enabled nonsingular anisotropic elastic representation of near-core dislocation stress fields in α-iron. Phys. Rev. B. 91:, 184102 (2015).
C. Sobie, L. Capolungo, D. L. McDowell, E. Martinez, Thermal activation of dislocations in large scale obstacle bypass. J. Mech. Phys. Solids. 105:, 150–160 (2017a).
C. Sobie, L. Capolungo, D. L. McDowell, E. Martinez, Scale transition using dislocation dynamics and the nudged elastic band method. J. Mech. Phys. Solids. 105:, 161–178 (2017b).
D. E. Spearot, M. D. Sangid, Insights on slip transmission at grain boundaries from atomistic simulations. Curr. Opinion Solid State Mater. Sci. 18:, 188–195 (2014).
X. -Y. Sun, V. Taupin, C. Fressengeas, P. Cordier, Continuous description of the atomic structure of grain boundaries using dislocation and generalized-disclination density fields. Int. J. Plast. 77:, 75 (2016).
A. P. Sutton, R. W. Baluffi, Interfaces in crystalline materials (Clarendon Press, Oxford, 1995).
V. Taupin, L. Capolungo, C. Fressengeas, A. Das, M. Upadhyay, Grain boundary modeling using an elasto-plastic theory of dislocation and disclination fields. J. Mech. Phys. Solids. 61:, 370 (2013).
V. Taupin, L. Capolungo, C. Fressengeas, Disclination mediated plasticity in shear-coupled boundary migration. Int. J. Plast. 53:, 179–192 (2014).
V. Taupin, K. Gbemou, C. Fressengeas, L. Capolungo, Nonlocal elasticity tensors in dislocation and disclination cores. J. Mech. Phys. Solids. 100:, 62–84 (2017).
M. Upadhyay, L. Capolungo, V. Taupin, C. Fressengeas, Elastic constitutive laws for incompatible crystalline media: the contributions of dislocations, disclinations and G-disclinations. Phil. Mag. 93:, 794 (2013).
A. J. Vattré, M. J. Demkowicz, Determining the Burgers vectors and elastic strain energies of interface dislocation arrays using anisotropic elasticity theory. Acta Mater. 61:, 5172 (2013).
A. J. Vattré, B Devincre, F Feyel, R Gatti, S Groh, O Jamond, A Roos, Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: the discrete-continuous model revisited. J. Mech. Phys. Solids. 63:, 491–505 (2014a).
A. J. Vattré, N. Abdolrahim, K. Kolluri, M. J. Demkowicz, Computational design of patterned interfaces using reduced order models. Nature Sci. Reports. 4:, 1 (2014b).
A. J. Vattré, M. J. Demkowicz, Partitioning of elastic distortions at a semicoherent heterophase interface between anisotropic crystals. Acta Mater. 82:, 234 (2015).
A. J Vattré, Elastic strain relaxation in interfacial dislocation patterns: I. A parametric energy-based framework. J. Mech. Phys. Solids. 105:, 254–282 (2017a).
A. J. Vattré, Elastic strain relaxation in interfacial dislocation patterns: II. From long- and short-range interactions to local reactions. J. Mech. Phys. Solids. 105:, 283–305 (2017b).
Y. U. Wang, Y. M. Jin, A. M. Cutino, A. G. Khachaturyan, Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations. Acta Mater. 49:, 1847–1857 (2001).
Y. M. Wang, E. Ma, Strain hardening, strain rate sensitivity, and ductility of nanostructured metals. Mat. Sci. Eng. A. 375–377:, 46–52 (2004).
J. Wang, C. Zhou, I. J. Beyerlein, S. Shao, Modeling interface-dominated mechanical behavior of nanolayered crystalline composites. J. Applied Mech. 66:, 102–113 (2014).
B. Xu, L. Capolungo, D. Rodney, On the importance of prismatic/basal interface in the growth of (1012) twins in hexagonal close packed crystals. Scripta Mater. 68:, 901–904 (2013).
K. Yashiro, F. Kurose, Y. Nakashima, K. Kubo, Y. Tomita, H. M. Zbib, Discrete dislocation dynamics simulation of cutting of γ precipitate and interfacial dislocation network in Ni-based superalloys. Int. J. Plasticity. 22:, 713–723 (2006).
H. M. Zbib, M. Rhee, J. P. Hirth, On plastic deformation and the dynamics of 3D dislocations. Int. J. Mech. Sci. 40:, 113–27 (1998).
Z. Zheng, D. S. Balint, F. P. E. Dunne, Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue. Acta Mater. 127:, 43–53 (2017).
C. Zhou, R. LeSar, Dislocation dynamics simulations of plasticity in polycrystalline thin films. Int. J. Plasticity. 30-31:, 185–201 (2012).