The Structure of Stress-Strain Relations in Finite Elasto-Plasticity

103 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.The stress-strain behavior of time-independent elastic-plastic material is investigated for finite strain taking the stable range of response of thin-walled tubes as the starting point.Brief considerations at the microstructural and atomic scale show the difficulty of choosing physically helpful variables in constitutive relations.Most of the present study deals with the mathematical structure of stress-strain relations that can be inferred under the constraint that thin-walled tubes are stable in Drucker's sense for all load cycles starting inside the elastic domain and involving infinitesimal plastic straining. Both work-hardening and work-softening behavior are included. The work of Hill and Rice concerning normality of the plastic strain rate is reexamined in connection with symmetric, objective stress measures with non-integrable work-associated strain rates and with non-symmetric stresses of the Piola type. It is shown that the yield surface must be convex when the rate of change of the tensor of elastic compliances with plastic deformation is positive semi-definite. The degree to which convexity carries over from one system of stress to another is investigated.The plastic strain rate is defined here from the additive decomposition of strain rates into current elastic and plastic components. The difference when the rate of residual strain in the unloaded or stressfree state is labelled as plastic is evaluated explicitly. Normality is derived for Lee's isotropic model and the residual strain rate interpreted in the present context. With a change to anisotropy, or in another system of stress and strain, normality of the residual strain rate is seen not to hold in general.The magnitude of the change of elastic constants of metals and alloys with plastic deformation is investigated from data based on the unloaded configuration.The definition of hardening is examined both at a regular and at a singular point on the yield surface. At a regular point, the criterion in stress or in strain space for additional plastic deformation is discussed for a linear incremental stress-strain relation of a classical form.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD