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

Abstract

In ASTM standard E1820, the crack size, a, may be evaluated during J-integral or crack-tip opening displacement (CTOD) resistance testing using the measured crack-mouth 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 plane-strain modulus E/(1 − υ2) where υ is Poisson's ratio. However, the three-dimensional (3-D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither plane-stress nor plane-strain condition, especially for B×B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of plain- and side-grooved B×B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using plane-stress and plane-strain assumptions with the CMOD compliance calculated from FEA for the 3-D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using plane-strain or plane-stress assumptions can be as high as 5–10%, respectively, especially for shallow-cracked specimens. In the present study, an effective modulus with value between plane-stress and plane-strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plain-sided and side-grooved 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.