Structural model of mechanical twinning and its application for modeling of the severe plastic deformation of copper rods in Taylor impact tests

Abstract We propose a new structural model of the mechanical twinning applicable for description of severe plastic deformation in 2D formulation. The twinning model together with the dislocation plasticity model is applied to modeling of the dynamical axis-symmetric Taylor tests with copper samples. Contributions of the dislocation plasticity and twinning in the formation of the shape of the compacted rod are revealed; modification of the defect structure behind the propagating shock wave is considered. The dislocation plasticity gives the main contribution in the case of low impact velocities (about or less than 100 m/s), while the twinning predominates at high impact velocities (about 500 m/s). Substantial influence of both mechanisms of plasticity takes place at moderate impact velocities, which results in formation of an area of the intensively twinned material near the colliding base of the rod and an adjoined area with a high density of dislocations; all this reflects on the profile of the lateral surface of the deformed rod.

[1]  G. Kanel,et al.  Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point , 2001 .

[2]  J. Knap,et al.  A phase field model of deformation twinning: Nonlinear theory and numerical simulations , 2011 .

[3]  Naresh N. Thadhani,et al.  Instrumented anvil-on-rod tests for constitutive model validation and determination of strain-rate sensitivity of ultrafine-grained copper , 2007 .

[4]  U. F. Kocks,et al.  Physics and phenomenology of strain hardening: the FCC case , 2003 .

[5]  Localization of plastic flow at dynamic channel angular pressing , 2013 .

[6]  Laszlo S. Toth,et al.  A dislocation-based model for all hardening stages in large strain deformation , 1998 .

[7]  I. Beyerlein,et al.  Pure-Shuffle Nucleation of Deformation Twins in Hexagonal-Close-Packed Metals , 2013 .

[8]  E. Zaretsky,et al.  Effect of temperature, strain, and strain rate on the flow stress of aluminum under shock-wave compression , 2012 .

[9]  Jens Lothe John Price Hirth,et al.  Theory of Dislocations , 1968 .

[10]  B. Bacroix,et al.  Evolution of microstructure and texture during planar simple shear of magnesium alloy , 2012 .

[11]  N. Thadhani,et al.  Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states , 2006 .

[12]  M. Abolbashari,et al.  General analytical solution for elastic radial wave propagation and dynamic analysis of functionally graded thick hollow cylinders subjected to impact loading , 2010 .

[13]  Shin Takeuchi,et al.  Dislocation dynamics and plasticity , 1991 .

[14]  I. Lapczyk,et al.  Deformation twinning during impact – numerical calculations using a constitutive theory based on multiple natural configurations , 1998 .

[15]  K. Rajagopal,et al.  A phenomenological model of twinning based on dual reference structures , 1998 .

[16]  William G. Proud,et al.  Symmetrical Taylor impact studies of copper , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  David L. McDowell,et al.  Simulation of shock wave propagation in single crystal and polycrystalline aluminum , 2014 .

[18]  A. Rosakis,et al.  A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals , 2000 .

[19]  Arun R. Srinivasa,et al.  On the inelastic behavior of solids — Part 1: Twinning , 1995 .

[20]  M. Wilkins Calculation of Elastic-Plastic Flow , 1963 .

[21]  R. H. Wagoner,et al.  An efficient constitutive model for room-temperature, low-rate plasticity of annealed Mg AZ31B sheet , 2010 .

[22]  A. Mayer,et al.  Yield strength of nanocrystalline materials under high-rate plastic deformation , 2012 .

[23]  Y. Estrin,et al.  Dislocation density-based modeling of deformation behavior of aluminium under equal channel angular pressing , 2003 .

[24]  Yonggang Huang,et al.  A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials , 2010 .

[25]  N. Saintier,et al.  Elastic-plastic transition in iron: Structural and thermodynamic features , 2009 .

[26]  R. Armstrong,et al.  Dislocation-mechanics-based constitutive relations for material dynamics calculations , 1987 .

[27]  K. Chawla,et al.  Mechanical Behavior of Materials , 1998 .

[28]  J. D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[29]  A. Yalovets Calculation of flows of a medium induced by high-power beams of charged particles , 1997 .

[30]  David J. Benson,et al.  Constitutive description of dynamic deformation: physically-based mechanisms , 2002 .

[31]  Arun R. Srinivasa,et al.  Inelastic behavior of materials. Part II. Energetics associated with discontinuous deformation twinning , 1997 .

[32]  Jian Wang,et al.  A constitutive model of twinning and detwinning for hexagonal close packed polycrystals , 2012 .

[33]  A. Mayer,et al.  Modeling of plastic localization in aluminum and Al-Cu alloys under shock loading , 2014 .

[34]  Jian Wang,et al.  A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms , 2013 .

[35]  R. G. Chembarisova Elastoplastic behavior of copper upon high-strain-rate deformation , 2015, The Physics of Metals and Metallography.

[36]  Bjørn Clausen,et al.  Reorientation and stress relaxation due to twinning: Modeling and experimental characterization for Mg , 2008 .

[37]  I. Beyerlein,et al.  Twinning dislocations on {1¯011} and {1¯013} planes in hexagonal close-packed crystals , 2011 .

[38]  V. Stegailov,et al.  Molecular-dynamics simulation of edge-dislocation dynamics in aluminum , 2008 .

[39]  Ronald W. Armstrong,et al.  High strain rate properties of metals and alloys , 2008 .

[40]  D. Steinberg,et al.  Pressure and temperature derivatives of the isotropic polycrystalline shear modulus for 65 elements , 1974 .

[41]  L. Capolungo,et al.  Prediction of internal stresses during growth of first- and second-generation twins in Mg and Mg alloys , 2012 .

[42]  E. Zaretsky,et al.  Response of copper to shock-wave loading at temperatures up to the melting point , 2013 .

[43]  Distribution of dislocations and twins in copper and 18Cr-10Ni-Ti steel under shock-wave loading , 2014 .

[44]  A. Mayer,et al.  Numerical investigation of the change of dislocation density and microhardness in surface layer of iron targets under the high power ion- and electron-beam treatment , 2012 .

[45]  M. Boyce,et al.  Mechanics of Taylor impact testing of polycarbonate , 2007 .

[46]  Mark L. Wilkins,et al.  Impact of cylinders on a rigid boundary , 1973 .

[47]  Huamiao Wang,et al.  Modeling inelastic behavior of magnesium alloys during cyclic loading–unloading , 2013 .

[48]  A. Rosakis,et al.  Dynamically propagating shear bands in impact-loaded prenotched plates—II. Numerical simulations , 1996 .

[49]  J. Duffy,et al.  On critical conditions for shear band formation at high strain rates , 1984 .

[50]  M. Cherkaoui,et al.  On the elastic–viscoplastic behavior of nanocrystalline materials , 2007 .

[51]  P. Levashov,et al.  Modeling of plasticity and fracture of metals at shock loading , 2013 .

[52]  G. Taylor,et al.  The Emission of the Latent Energy due to Previous Cold Working When a Metal is Heated , 1937 .

[53]  Somnath Ghosh,et al.  A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys , 2015 .

[54]  Lallit Anand,et al.  A constitutive model for hcp materials deforming by slip and twinning: application to magnesium alloy AZ31B , 2003 .

[55]  A. Mayer,et al.  Dislocation based high-rate plasticity model and its application to plate-impact and ultra short electron irradiation simulations , 2011 .

[56]  P. N. Mayer,et al.  Numerical modelling of physical processes and structural changes in metals under intensive irradiation with use of CRS code: dislocations, twinning, evaporation and stress waves , 2014 .

[57]  Y. Petrov,et al.  Maximum yield strength under quasi-static and high-rate plastic deformation of metals , 2014 .

[58]  R. Lebensohn,et al.  Numerical study of the stress state of a deformation twin in magnesium , 2015 .

[59]  E. M. Lifshitz,et al.  Course in Theoretical Physics , 2013 .

[60]  O. Bouaziz,et al.  A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel , 2004 .

[61]  Jianmin Qu,et al.  Homogenization Method for Strength and Inelastic Behavior of Nanocrystalline Materials , 2004 .

[62]  A. Kuksin,et al.  Dynamics and kinetics of dislocations in Al and Al–Cu alloy under dynamic loading , 2014 .

[63]  A. Romanov,et al.  Between dislocation and disclination models for twins , 1994 .

[64]  Sia Nemat-Nasser,et al.  Determination of temperature rise during high strain rate deformation , 1998 .

[65]  D. Radford,et al.  Shock induced void nucleation during Taylor impact , 2005 .

[66]  Jian Wang,et al.  (1¯012) Twinning nucleation mechanisms in hexagonal-close-packed crystals , 2009 .

[67]  Bingqing Cheng,et al.  A new dislocation-density-function dynamics scheme for computational crystal plasticity by explicit consideration of dislocation elastic interactions , 2015 .

[68]  G. A. Malygin Dislocation self-organization processes and crystal plasticity , 1999 .

[69]  I. Beyerlein,et al.  A multi-scale statistical study of twinning in magnesium , 2011 .

[70]  Naresh N. Thadhani,et al.  Instrumented anvil-on-rod impact experiments for validating constitutive strength model for simulating transient dynamic deformation response of metals , 2008 .

[71]  G. M. Zhang,et al.  Modified Smoothed Particle Hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test , 2008, J. Comput. Phys..

[72]  M. Meyers Dynamic Behavior of Materials , 1994 .

[73]  I. Beyerlein,et al.  Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study , 2011 .

[74]  C. Kittel Introduction to solid state physics , 1954 .

[75]  R. Armstrong Wedge Dislocation as the Elastic Counterpart of a Crystal Deformation Twin , 1968, Science.

[76]  Geoffrey Ingram Taylor,et al.  The use of flat-ended projectiles for determining dynamic yield stress I. Theoretical considerations , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[77]  G. Cailletaud,et al.  Cyclic behavior of extruded magnesium: Experimental, microstructural and numerical approach , 2011 .

[78]  A. Kuksin,et al.  Plastic deformation under high-rate loading: The multiscale approach , 2010 .