A benchmark fracture mechanics solution for a two-dimensional eigenstrain problem considering residual stress, the stress intensity factor, and superposition

Eigenstrain is a distributed strain field considered in mechanics that is particularly helpful in evaluating residual stress fields in the finite element method, and estimating the stress intensity factor due to residual stress in cracked components. The objective of this paper is to provide a solution for a simple eigenstrain problem in a two-dimensional rectangular domain that can serve as a benchmark for validation of fracture mechanics analysis methods. The solution provides residual stress fields and the stress intensity factor for a single edge crack as a function of crack size. Documenting the benchmark provides opportunities to demonstrate the correlation of different means to determine the stress intensity factor and to highlight details in implementing stress intensity factor calculations.