On the Sensitivity of J Estimation to Materials' Stress-Strain Curves in Fracture Toughness Testing Using the Finite Element Method

The present paper reports the accuracy of the J estimation equations for three typical homogeneous fracture toughness testing specimens: M(T), C(T), and SE(B) specimens, based on systematic 2D FE analyses. A wide range of crack lengths is considered, except for C(T) specimens where only deep cracks are considered, a/W = 0.45 to 0.7. By carefully selecting the properties of the materials in the analysis, particular emphasis is placed on the sensitivity of such equations to the strain hardening as well as the type of stress strain curve, such as continuously hardening materials or materials with Lüders strain. Two different J estimation schemes are considered, one based on load-load line displacement records and the other on load-crack mouth opening displacement (CMOD) records. For all cases considered, the J estimation based on load-CMOD records gives more accurate results, compared to those based on load-load line displacement records. Moreover, the J estimation is not sensitive to the material's strain hardening and to the type of the stress-strain curve, except for shallow-cracked M(T) specimens with a/W < 0.2. For shallow-cracked M(T) specimens with a/W < 0.2, the J estimation equation is not sensitive to the material, for materials with Lüders strain, but is sensitive for continuously hardening materials. The error increases with the hardening, i.e., a higher hardening material gives a larger error in J.