Evaluation of Stress-Intensity Factors Using General Finite-Element Models

Abstract

Finite-element methods are commonly used to evaluate cracked solids. Post-processing methods are used to extract Mode I stress-intensity factor values from finite-element analyses. These methods include the Crack-Opening-Displacement (COD) method, the Force method, the Virtual Crack Closure Technique (VCCT) and the Equivalent Domain Integral (EDI) method. The COD method, Force method and the VCCT appear to require that the finite-element mesh intersect the crack front in an orthogonal manner in order to obtain accurate stress-intensity factor values. The EDI does not appear to require this orthogonality with the crack front to obtain accurate stress intensity factor values. The objectives of this study are to determine if accurate stress intensity factor values can be obtained from finite-element models that lack orthogonality with the crack front and, if accurate values cannot be obtained, to modify the extraction methods so that accurate stress-intensity factor values can be obtained from models without orthogonality at the crack front. Models of a through-the-thickness crack in plane strain, an embedded elliptic crack, and a semi-elliptic surface crack were created with and without orthogonality at the crack front. The models with orthogonality at the crack front were termed orthogonal models while the models without orthogonality the crack front were termed general models. Stress-intensity factors were evaluated for both the orthogonal and general models using the COD method, Force method, VCCT, and EDI method. The stress-intensity factor values obtained from these models were compared to accepted reference solutions to determine their accuracy. The COD method, Force method, and VCCT were not able to extract accurate stress-intensity factor values from general models. The EDI method was not affected by the lack of orthogonality at the crack front. The COD method, Force method, and VCCT were modified for application to general models. These new formulations do not require the finite-element mesh to be orthogonal to the crack front. The values of the stress-intensity factors obtained from the general models using the new formulations of the extraction methods are of the same accuracy as those obtained from the models with orthogonality at the crack front.