Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.

[1]  N. Hansen,et al.  Grain orientation dependence of microstructure in aluminium deformed in tension , 1997 .

[2]  B. Peeters,et al.  Modelling of the evolution of dislocation sheets during strain-path changes and their influence on the Bauschinger effect of B.C.C. polycrystals , 2001 .

[3]  R. E. Abdi,et al.  A non-linear kinematic hardening model for a steel under complex loadings , 2000 .

[4]  N. Park,et al.  The development of the deformed microstructure in commercially pure nickel , 1989 .

[5]  H. Maier,et al.  Long-range internal stresses in cell and subgrain structures of copper during deformation at constant stress , 1996 .

[6]  M. Hecker,et al.  Stress fields of tilted dislocation walls , 1998 .

[7]  G. Winther.  Slip patterns and preferred dislocation boundary planes , 2003 .

[8]  S. Karashima,et al.  Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium , 1975 .

[9]  R. Sedláček.  Internal stresses in dislocation wall structures , 1995 .

[10]  N. Hansen,et al.  Large strain deformation structures in aluminium crystals with rolling texture orientations , 1994 .

[11]  W. Blum,et al.  Internal stresses in dislocation subgrain structures , 1998 .

[12]  S. Forest,et al.  Non‐Local Plasticity at Microscale: A Dislocation‐Based and a Cosserat Model , 2000 .

[13]  D. Kuhlmann-wilsdorf,et al.  Microstructural evolution in rolled aluminium , 1992 .

[14]  Tamás Ungár,et al.  Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-oriented copper single crystals: The correction of an erratum , 1991 .

[15]  J. K. Lee,et al.  Modeling the Bauschinger effect for sheet metals, part I: theory , 2002 .

[16]  H. Mughrabi.  Self-consistent experimental determination of the dislocation line tension and long-range internal stresses in deformed copper crystals by analysis of dislocation curvatures , 2001 .

[17]  M. Zehetbauer,et al.  Stage IV work hardening in cell forming materials, part I: Features of the dislocation structure determined by X-ray line broadening , 1996 .

[18]  N. Hansen,et al.  Crystallographic and macroscopic orientation of planar dislocation boundaries—correlation with grain orientation , 2000 .

[19]  W. Blum,et al.  Microstructure-based constitutive law of plastic deformation , 2002 .

[20]  H. Mughrabi.  A two-parameter description of heterogeneous dislocation distributions in deformed metal crystals , 1987 .

[21]  Daryl C. Chrzan,et al.  Scaling of microstructural parameters: Misorientations of deformation induced boundaries , 1996 .

[22]  Paul Steinmann,et al.  Views on multiplicative elastoplasticity and the continuum theory of dislocations , 1996 .

[23]  F. Mollica.  The inelastic behavior of metals subject to loading reversal , 2001 .

[24]  J. Nye.  Some geometrical relations in dislocated crystals , 1953 .

[25]  J. F. Besseling,et al.  Mathematical Modelling of Inelastic Deformation , 1994 .

[26]  Q. Liu,et al.  Dislocation boundaries and active slip systems , 1995 .

[27]  D. Parks,et al.  Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density , 1999 .

[28]  S. R. MacEwen,et al.  Effect of stress reversals on the work hardening behaviour of polycrystalline copper , 1986 .

[29]  Bart Peeters,et al.  Work-hardening/softening behaviour of B.C.C. polycrystals during changing strain paths: II. TEM observations of dislocation sheets in an if steel during two-stage strain paths and their representation in terms of dislocation densities , 2001 .

[30]  van der Erik Giessen,et al.  SIMULATION OF MATERIALS PROCESSING: THEORY, METHODS AND APPLICATIONS , 1998 .

[31]  N. Hansen,et al.  Microstructural evolution and hardening parameters , 2001 .

[32]  H. Maier,et al.  Long-range internal stresses in steady-state subgrain structures , 1993 .

[33]  H. Mughrabi,et al.  Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals , 1983 .

[34]  W. T. Roberts,et al.  Effects of changes in strain path on work-hardening in CP aluminium and an AlCuMg alloy , 1990 .

[35]  J. Gracio,et al.  Plastic behaviour of copper sheets during sequential tension tests , 1991 .

[36]  N. Hansen,et al.  The development of deformation substructures in face-centred cubic metals☆ , 1989 .

[37]  N. Hansen,et al.  Geometrically necessary boundaries and incidental dislocation boundaries formed during cold deformation , 1995 .

[38]  L. Menezes,et al.  A modified swift law for prestrained materials , 1998 .

[39]  B. Peeters,et al.  A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase B.C.C. polycrystals , 2002 .

[40]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[41]  G. Gottstein,et al.  A microstructural work hardening model based on three internal state variables , 2001 .

[42]  Tamás Ungár,et al.  Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-orientated copper single crystals , 1986 .

[43]  P. Haasen,et al.  A new mechanism of work hardening in the late stages of large strain plastic flow in F.C.C. and diamond cubic crystals , 1993 .

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

[45]  J. Harder,et al.  A crystallographic model for the study of local deformation processes in polycrystals , 1999 .

[46]  M. Hecker,et al.  Investigation of the tensor character of mesoscopic internal stresses in tensile-deformed nickel single crystals by X-ray diffraction , 2002 .

[47]  E. Viatkina.  Micromechanical modelling of strain path dependency in FCC metals , 2005 .

[48]  L. Murr,et al.  Large strain plastic deformation of commercially pure nickel , 1983 .

[49]  W. Brekelmans,et al.  Modelling the evolution of dislocation structures upon stress reversal , 2007 .

[50]  N. Hansen,et al.  Slip pattern, microstructure and local crystallography in an aluminium single crystal of copper orientation {112}〈111〉 , 1998 .

[51]  C. T. Young,et al.  Dislocation substructures formed during the flow stress recovery of high purity aluminum , 1986 .

[52]  Frédéric Barlat,et al.  Plastic flow for non-monotonic loading conditions of an aluminum alloy sheet sample , 2003 .

[53]  R. Mccabe,et al.  Experimentally determined content of a geometrically necessary dislocation boundary in copper , 2004 .

[54]  E. Aernoudt,et al.  Dislocation arrangement and residual long-range internal stresses in copper single crystals at large deformations , 1997 .

[55]  Q. Liu,et al.  Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminium , 1998 .

[56]  Bart Peeters,et al.  Work-hardening/softening behaviour of b.c.c. polycrystals during changing strain paths: I. An integrated model based on substructure and texture evolution, and its prediction of the stress–strain behaviour of an IF steel during two-stage strain paths , 2001 .

[57]  H. Mughrabi,et al.  X-ray line-broadening study of the dislocation cell structure in deformed [001]-orientated copper single crystals , 1984 .