Dimensionless Compliance With Effective Modulus in Crack Length Evaluation for B أ— B Single Edge Bend Specimens

Abstract

In ASTM standard E1820, the crack size, a, may be evaluated during Jintegral or cracktip opening displacement (CTOD) resistance testing using the measured crackmouth opening displacement (CMOD) elastic unloading compliance C (UC). The equation given to relate a to dimensionless compliance BCE (the product of thickness B, the compliance C and the modulus of elasticity E) in E1820 incorporates Young's modulus E rather than the planestrain modulus E/(1 − د…2) where د… is Poisson's ratio. However, the threedimensional (3D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither planestress nor planestrain condition, especially for Bأ—B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3D finite element analysis (FEA) was used to evaluate the CMOD compliance of plainand sidegrooved Bأ—B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using planestress and planestrain assumptions with the CMOD compliance calculated from FEA for the 3D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using planestrain or planestress assumptions can be as high as 5–10%, respectively, especially for shallowcracked specimens. In the present study, an effective modulus with value between planestress and planestrain is proposed and evaluated by FEA for the 3D Bأ—B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of Bأ—B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plainsided and sidegrooved specimens, respectively, using this effective modulus. The effect of material removal to accommodate integral knife edges on the CMOD compliance was studied and taken into account in the crack length evaluations in the present study. Elastic unloading tests were conducted to measure the compliance of SE(B) specimens with two widths W and notch depths a/W from 0.1 to 0.5. Notch depths of the specimens evaluated by using the measured compliance and assumptions of plane stress, plane strain, and effective moduli were compared with the notch depths of the specimens used in the tests. It was found that best agreement of notch depth was achieved using the effective modulus.