A CDM analysis of stochastic ductile damage growth and reliability

The accumulation of damage within a structure due to service loading or environmental conditions is a random phenomenon. Continuum damage mechanics (CDM) enables macroscopic manifestations of damage to be related to microscopic defects and discontinuities present within a material. This permits margins of safety to be assessed prior to the time at which damage becomes visible or detectable. Under fairly general thermodynamic conditions, equations of damage growth can be formulated in terms of the Helmholtz free energy. Spatial and temporal fluctuations in the state variables, caused first by the intrinsic variations in the material microstructure and second to environmental and loading conditions, are modeled by treating the Helmholtz free energy as a random process. This leads to a stochastic differential equation (SDE) of random damage growth, the solution of which describes the evolution of time-dependent random ductile damage and residual strength. Available experimental results are used to validate the CDM formulation.