Line-spring finite element for fully plastic crack growth-I. Formulation and one-dimensional results

line-spring finite element model is developed to resolve fully plastic, quasi-steady, through-thickness crack growth in plane strain single-edge-cracked (SEC) specimens and surfacecracked plate/shell structures. The plane strain sliding-off and cracking model of McClintock et al. (1995) is adopted to obtain the instantaneous crack-tip opening angle (CTOA) in terms of material parameters and the instantaneous slip-line angle and stress triaxiality at the crack-tip. The slip-line angle and crack-tip stress triaxiality are calculated approximately using the least upper bound method of Kim et al. (1996a). Utilizing these approaches, the generalized forces transmitted by the line-spring finite element provide the constraint-dependent CTOA. The increment of crack extension is then determined from the kinematic relation with incremental crack-tip opening displacement through CTOA. Detailed description of the model, as incorporated into the ABAQUS (1993) finite element code in the form of a user-defined element, is given in Part I. Parametric studies in plane strain SEC specimens are carried out to examine the effects of loading type, ductility and strain hardening on plane strain crack extension behavior, and the effects of elastic surroundings on structural stability. Applications of the line-spring model to problems of surface-cracked plate and pipe are presented in Part II (Lee and Parks, 1998). © 1998 Elsevier Science Ltd. All rights reserved