R.B. Pęcherski

Inelastic Flow and Failure of Metallic Solids. Material Effort: Study Across Scales

The multiscale physical foundations of the concept of material effort in isotropic solid body are studied, in particular for solids revealing the strength differential effect. Various yield criteria result from this hypothesis: ellipsoid, paraboloid or hyperpoloid ones. The examples are discussed and visualized in the principal axes of stress or in the plane defined by coordinates: equivalent stress and mean stress. The numerical implementation of paraboloid yield surface forming plastic potential in an associated flow law is presented and an example of the identification of the strength differential effect ratio is discussed. Finally, some problems related with an account for the third invariant of stress deviator in failure criteria for isotropic solids and energy-based failure criteria for anisotropic solids are shortly discussed. Also the possibility for an account of two basic mechanisms responsible for inelastic flow: crystallographic slip and shear banding in modelling the inelastic flow law is outlined.

Physical and Theoretical Aspects of Large Plastic Deformations Involving Shear Banding

Shear banding is related with large plastic deformations produced by mechanisms of crystallographic slip and/or twinning and micro—shear. Plane deformations of elastoplastic material accounting for micro—shear bands are considered. Micro—shear bands produce the non—coaxiality between principal directions of the tensors of stress and rate of plastic deformations. Relations to known vertex—type plasticity models are discussed.

Constitutive Description and Numerical Approach in Modelling for Metal Forming Processes

Modelling for metal forming, strain localization and ductile fracture produces an increasing demand for the adequate constitutive description of inelastic material behaviour and the efficient numerical strategies. The constitutive equations for small elastic and finite plastic deformations with combined isotropic-kinematic hardening have been implemented in finite element programs (cf. e.g.[l]). In[2–4] the Ziegler model of kinematic hardening with the Zaremba-Jaumann rate was applied for the numerical analysis of the effect of yield surface curvature on localization in porous plastic solids. The effect of deformation induced anisotropy in plasticity of damaged solids was also studied in [5].