A Numerical Study on CMOD Compliance for Single Edge Notched Bending Specimens

Abstract

Several wellknown equations for estimating the crack length in the singleedge notched bending (SE(B)) specimens from the normalized crack mouth opening displacement (CMOD) compliance are evaluated based on twodimensional (2D) and threedimensional (3D) finite element analyses (FEAs). Twodimensional FEAs are first carried out to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Threedimensional FEAs are then carried out to estimate the errors of prediction of equations that evaluate the crack length from the plane stressand plane strainbased CMOD compliances. Both planesided and sidegrooved models are included in 3D FEAs and have seven different thicknesstowidth ratios. The error of prediction of a given equation is largely impacted by the thicknesstowidth ratio, the crack length, the presence of side grooves, and the use of the plane stressor plane strainnormalized CMOD compliance. Based on the errors of prediction, the relevance of the actual state of stress in the ligament of the SE(B) specimens to the plane strain condition or the plane stress condition is inferred. Knowledge of the relevance of the plane stress condition or the plane strain condition can be used to select the corresponding CMOD compliance in crack lengthCMOD equations, and, therefore, the corresponding predictive accuracy can be improved.