Unloading Behavior of Elastic-power-law Strain Hardening Materials Indented by Elastic Indenter

Both strain hardening and indenter elastic deformation usually cannot be neglected in engineering contacts. By the finite element (FE) method, this paper investigates the unloading behavior of elastic-power-law strain-hardening half-space frictionlessly indented by elastic sphere for systematic materials. The effects of strain hardening and indenter elasticity on the unloading curve, cavity profile during unloading and residual indentation are analyzed. The unloading curve is observed to follow a power-law relationship, whose exponent is sensitive to strain hardening but independent upon indenter elastic deformation. Based on the power-law relationship of the unloading curve and the expression of the residual indentation fitted from the FE data, an explicit theoretical unloading law is developed. Its suitability is validated numerically and experimentally by strain hardening materials contacted by elastic indenter or rigid flat.

Influence of Distributed Dislocations on Stability of Hollow Nonlinearly Elastic Sphere

The phenomenon of stability loss of a hollow elastic sphere containing distributed dislocations and loaded with external hydrostatic pressure is studied. The study was carried out in the framework of the nonlinear elasticity theory and the continuum theory of continuously distributed dislocations. An exact statement and solution of the stability problem for a three-dimensional elastic body with distributed dislocations are given. The static problem of nonlinear elasticity theory for a body with distributed dislocations is reduced to a system of equations consisting of equilibrium equations, incompatibility equations with a given dislocation density tensor, and constitutive equations of the material. The unperturbed state is caused by external pressure and a spherically symmet-ric distribution of dislocations. For distributed edge dislocations in the framework of a harmonic (semi-linear) mate-rial model, the unperturbed state is defined as an exact spherically symmetric solution to a nonlinear boundary value problem. This solution is valid for any function that characterizes the density of edge dislocations. The perturbed equilibrium state is described by a boundary value problem linearized in the neighborhood of the equilibrium. The analysis of the axisymmetric buckling of the sphere was performed using the bifurcation method. It consists in determining the equilibrium positions of an elastic body, which differ little from the unperturbed state. By solving the linearized problem, the value of the external pressure at which the sphere first loses stability is found. The effect of dislocations on the buckling of thin and thick spherical shells is analyzed.