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

Several well-known equations for estimating the crack length in the single-edge notched bending (SE(B)) specimens from the normalized crack mouth opening displacement (CMOD) compliance are evaluated based on two-dimensional (2D) and three-dimensional (3D) finite element analyses (FEAs). Two-dimensional 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. Three-dimensional FEAs are then carried out to estimate the errors of prediction of equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plane-sided and side-grooved models are included in 3D FEAs and have seven different thickness-to-width ratios. The error of prediction of a given equation is largely impacted by the thickness-to-width ratio, the crack length, the presence of side grooves, and the use of the plane stress- or plane strain-normalized 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 length-CMOD equations, and, therefore, the corresponding predictive accuracy can be improved.