Non-self-similar crack growth in elastic-plastic finite thickness plate

Abstract

Abstract This work is concerned with non-self-similar crack growth in medium strength metal plates while the loading step, plate thickness and material properties are altered. The three-dimensional elastic-plastic finite element stress analysis is combined with the strain energy density criterion for modeling the material damage process from crack initiation to final global instability including the intervening stage of slow crack growth. Both inelastic deformation and crack growth are accounted for each increment of loading such that the redistribution of stresses and strains are made for each new crack profile. Numerical results are obtained for the center cracked plate configuration under uniform extension with twenty-seven (27) different combinations of specimen thickness, loading step and material type. The fracture toughness S c being related to K 1c for three different materials are predicted analytically from the corresponding uniaxial tensile test data. Effective strain energy density factor S and half crack length a are defined so that the results can be compared with their two-dimensional counterparts. Crack growth resistance curves ( R- curves ) are constructed by plotting S as a function of a . The condition d S / d a = const. is found to prevail during slow crack growth. Translation and/or rotation of the S − a lines can yield results other than those calculated and serve a useful purpose for scaling component size and test time. The minimum thickness requirement for the ASTM valid K 1c test is also discussed in connection with predictions based on the strain energy density criterion. The corresponding K 1c for smaller specimens that exhibit moderate ductility and nonlinearity can also be obtained analytically. In such cases, the influence of loading step can be significant and should not be neglected. Notwithstanding the shortcomings of the theory of plasticity, the qualitative features of non-self-similar crack growth are predicted by the strain energy density criterion. Any refinements on the analytical modeling of the material damage process would only affect the results qualitatively, a subject that is left for future investigation.