Internal variable theory of plasticity based on dislocation mechanics
Using the internal variable theory of material behavior, a theory of plasticity for polycrystalline solids has been developed. Assuming that the motion of a dislocation flux is the primary cause of plastic flow, the average mobile and immobile dislocation density tensors and the dislocation velocity vector are chosen as the internal variables. By decomposing the deformation gradient into its elastic and plastic components, the dislocation density tensor is expressed in terms of the plastic deformation gradient. Similarly, the rate of plastic deformation tensor is expressed as a function of the mobile dislocation density tensor and the dislocation velocity vector. For isotropic materials, a representation theorem is used to express the dislocation velocity vector in terms of the dislocation density and the macroscopic state of stress. It is shown that under the condition of plastic incompressibility, the octahedral shear planes of the stress tensor are the glide planes for dislocation motion. Thus the total rate of plastic deformation is obtained by summing the dislocation motion over the eight octahedral shear planes of the stress tensor. In addition, the internal variables are reduced to the scalar dislocation density and mobile fraction which enter the rate of plastic deformation tensor. Each of these scalar internal variables is, in turn, governed by a rate equation which reflects the history of motion. As a special case the rate of plastic deformation tensor reduces to the Prandtl-Reuss flow rule. The resulting theory yields an elastic-viscoplastic material behavior and is incorporated as a constitutive subroutine in a finite element code. Several problems, including a uniaxial tensile specimen, a thick-walled cylinder, and plane strain wave propagation, are solved which demonstrate the range of material behavior.
- Research Organization:
- California Univ., Livermore (USA). Lawrence Livermore Lab.
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 7363575
- Report Number(s):
- UCRL-52062
- Country of Publication:
- United States
- Language:
- English
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