Evolution of anisotropy in the compliances of porous materials during plastic stretching or rolling - analysis and experiments

A consideration is given of the evolution of anisotropy in the overall comp liances (or moduli) of dilutely cavitated materials during large plastic de formation (sheet stretching or strip rolling). It is postulated that the so urce of the inplane anisotropy is the preferred orientation of the elliptic -like cavities (micro-pores, voids, etc.) which are elongated and rotated d uring the deformation process. The tendency of the larger axis of each pore to align itself along the rolling direction leads the macroscopic complian ces to evolve differently in orthogonal directions, as is evidenced herewit h by experiments with sheet rolling process. The evolution of the anisotrop y in the rolling process is formulated on a unit cell with a single ellipti cal pore and extended to dilute uniform porosity. The solution is based on an in-plane bi-axial stretch, but the outcome leads to the geometrical evol ution similar to that of rolling (featured by localized out-of plane compre ssion). The solution traces the geometrical evolution of a single pore duri ng a gradual increase of the load and computes the related average properti es (like stress, strain, porosity, compliance, etc.) by an incremental form of the deformation theory of plasticity. Several verifications are obtaine d from self made observations on rolling of thin strips with artificial por es and by comparing the analysis to data on stretched materials produced by Spitzig et al. (Spitzig, W.A., Smelser, R.E., Richmond, O., 1988. The evol ution of damage and fracture in iron compact with various initial porositie s, ACTA Metal 36 (5), 1201-1211). (C) 1999 Elsevier Science Ltd. All rights reserved.