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

Abstract

Several well-known equations for estimating the crack length in the SE(B) specimens from the normalized CMOD compliance are evaluated based on two- and three-dimensional finite element analyses. Two-dimensional analyses are carried out first to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Three-dimensional analyses are then carried out to estimate the errors of prediction of the equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plain-sided and side-grooved models are included in the three-dimensional analyses 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, crack length, presence of side grooves, and use of the plane stress- and plane strain-normalized CMOD compliance. Based on the errors of prediction, the relevance of the plane strain and plane stress conditions to the actual state of stress in the ligament of the SE(B) specimens is inferred. Knowledge of the relevance of the plane stress and plane strain conditions can be used to select either plane stress- or plane strain-based CMOD compliance in the crack length-CMOD equations and improve the accuracy of the prediction.