Jand CTOD Estimation Equations for Shallow Cracks in Single Edge Notch Bend Specimens

Abstract

AbstractFracture toughness values determined using shallow cracked single edge notch bend. SE(B), specimens of structural thickness are useful for structural integrity assessments. However, testing standards have not yet incorporated formulas that permit evaluation of J and CTOD for shallow cracks from experimentally measured quantities (i.e., load, crack mouth opening displacement (CMOD), and load line displacement (LLD)). Results from two-dimensional plane strain finite element analyses are used to develop J and CTOD estimation strategies appropriate for application to both shallow and deep crack SE(B) specimens. Crack depth to specimen width (a/W) ratios between 0.05 and 0.70 are modeled using Ramberg-Osgood strain hardening exponents (n) between 4 and 50. The estimation formulas divide J and CTOD into small scale yielding (SSY) and large scale yielding (LSY) components. For each case, the SSY component is determined by the linear elastic stress intensity factor. Kf. The formulas differ in evaluation of the LSY component. The techniques considered include: estimating J or CTOD from plastic work based on load line displacement (Apl∣CMOD), from the area under a load versus plastic crack mouth opening displacement diagram (Apl∣CMOD), and from the plastic component of crack mouth opening displacement (CMODpl). Apl∣CMOD provides the most accurate J estimation possible. The finite element results for all conditions investigated fall within 9% of the following formula. J=K2(1−v2)F+ηJ−CBbApl∣CMOD whereηJ−C=3.785−3.101aW+2.018(aW)2 The insensitivity of ηJ−C to strain hardening permits J estimation for any material with equal accuracy. Further, estimating J from CMOD rather than LLD eliminates the need to measure LLD, thus simphfying the test procedure. Alternate estimates of J and CTOD from measured plastic areas have equivalent accuracy to this formula; however, the η coefficients in these equations depend on the strain hardening coefficient. CTOD estimates based on scalar proportionality of CTODlsy, and CMODpl, such as that used in ASTM E 1290, Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement, are highly inaccurate especially for materials with considerable strain hardening.