Elastic-plastic orthotropic multilayered pipe deformation under external load and internal pressure

Abstract

Elastic-plastic deformation of a thin-walled pipe, composed of layers with material orthotropic in the elastic and plastic domains, is analyzed. The first material direction for each layer is inclined for an angle (+a and -a successively) with respect to the pipe axis. The yield condition of the material represents a generalization of Hill's criterion to include material hardening. The pipe is loaded by internal pressure and other external loads, and it is supposed that the pipe cross section is free to expand or contract. The derived incremental relations for stress integration, which take into account the stress-strain conditions in the pipe wall, are based on the governing parameter method, developed by the first author, where the problem of implicit integration of inelastic constitutive relations within a tune (load) step is reduced to solution of one governing nonlinear equation. Also, the expressions for the tangent elastic-plastic constitutive matrix are derived. One solved simple numerical example demonstrates the main characteristics of the developed algorithm, especially suited for a general elastic-plastic analysis of composite pipes (within the displacement-based finite element method). B, N C e, ein p S Nomenclature = material constants = tangent constitutive matrix = total and inelastic strains = governing parameter = deviatoric stress = internal variable = increment of plastic strain = stress