Incompatibility and crystal plasticity
- Univ. of Pennsylvania, Philadelphia, PA (United States)
During deformation processing of ductile materials, plastic deformation often concentrates within narrow bands. Upon further straining, the deformation may become diffuse again or it may continue to concentrate leading to fracture in the vicinity of the bands. These phenomena may produce failure during the processing itself, for example, under sheet rolling and sheet bending conditions, respectively, thus causing a type of forming limit which is known to be a strong function of mean stress state. Or they may lead to inferior products, because of aesthetically unacceptable strain markings or in the reduction in ductility arising from inhomogeneous microstructures. Based upon a new understanding and theory of single crystal hardening it can be shown that fine secondary slips play an important role in the nucleation and saturation of such localized modes of deformation. At finite strain, a relation between incompatibility of the intermediate configuration and the presence of geometrically necessary dislocations can be established using a non-Riemannian geometry. The incompatibility and hence the density of geometrically necessary dislocations is characterized by a certain skew symmetry property of the gradient of the inverse of the elastic deformation gradient field, on the current configuration. This measure of the geometrically necessary dislocation density introduces a material length scale in the constitutive description of single crystals as a natural consequence. A frame indifferent measure of this density is then deduced, and compatibility with thermodynamics in the absence of higher-order-stresses is shown to reduce to a material description in which the free energy, stress and the entropy response are independent of any higher-order-gradients of deformation (as in the conventional case), but the yield response and the flow rules for the relevant internal variables are dependent on them.
- OSTI ID:
- 175391
- Report Number(s):
- CONF-950686-; TRN: 95:006111-0362
- Resource Relation:
- Conference: Joint applied mechanics and materials summer meeting, Los Angeles, CA (United States), 28-30 Jun 1995; Other Information: PBD: 1995; Related Information: Is Part Of AMD - MD `95: Summer conference; PB: 520 p.
- Country of Publication:
- United States
- Language:
- English
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