CMOD Compliance of B×B Single Edge Bend Specimens

Abstract

In ASTM standard E1820, the single edge bend (SE(B)) geometry is one of those recommended for fracture toughness testing. The width to thickness (W/B) ratio recommended in E1820 for this specimen is 2. However, in certain cases, it is desirable to use specimens having alternative W/B ratios; the range of W/B suggested in E1820 is 1 to 4. In E1820, the crack size a may be evaluated during J-integral or CTOD resistance testing using the crack mouth opening displacement (CMOD) elastic unloading compliance C. The equation given to relate a to C using a dimensionless compliance BCE incorporates Young’s modulus E. For the three-dimensional (3-D) SE(B) specimens that are in neither plane stress nor plane strain condition, this parameter E may be considered as a normalizing parameter varying between extremes E (plane stress) and E/(1−ν2) (plane strain) depending on crack depth (a/W) and specimen W/B ratio. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of B×B SE(B) specimens with shallow and deep cracks and compared with that from Tada’s plane stress equation. Crack sizes evaluated using plane stress and plane strain assumptions with the 3-D CMOD compliance obtained from FEA were compared with the actual crack size of the specimens used in FEA. It was found that the errors in crack size using plane strain or plane stress assumptions can be larger than 5%, especially for shallow-cracked specimens. In the present study, an effective modulus with values between plane stress and plane strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens. The values were fitted to a polynomial equation as a function of u = 1/(√(BCE)+1) for use in estimating the dimensionless compliance for crack size evaluation for B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be significantly reduced using this effective modulus.