Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Mechanical Engineering


A precise determination of the influence of plastic yielding on the deformation and failure at a crack tip is needed for accurate predictions of the behavior of cracked bodies under static load large enough to cause fracture, and subcritical repetitive loads which cause fatigue. The catastrophic growth of cracks in plates under monotonically increasing load depends on a number of factors. A general view concerning the behavior of material at the leading edge of a crack is that plastic flow and subsequent fracture of the material is influenced by factors such as strain hardening, strain rate, the state of stress, and temperature. Therefore, for a proper understanding of fracture mechanism it is essential to determine appropriate inelastic solutions describing the behavior of plastic zone as a function of loads and mechanical properties. The elastic-plastic problem has been considered by Rosenfield et al. and Swedlow. Rosenfield has described experiments revealing the shapes and extent of the plastic zone in front of notches and cracks. While these analyses have produced information to indicate the role of plasticity in notched or cracked plates, they have yet to produce a criterion for fracture useful to the designer. Dugdale model for static yielding at the tip of the crack has been considered by Newman and extended to include the. influence of stress-strain curve on the plastic zone size and subsequently on the fracture strength of the plate. A fracture toughness equation which accounts for non-perfect plasticity has been derived by him for the uniformly loaded plate. Elastic-plastic crack problems in plane strain and plane stress have been discussed by Rice through the use of deformation and incremental plasticity theories. Nevertheless, his treatment provides an insight to the inelastic fracture. In the present work, Dugdale model for static yielding at the crack tip has been used and then modified to include the effect of strain-hardening on the plastic zone size and crack tip displacement. An attempt has been made to determine the plastic energy dissipation for the strain hardening material. These properties of material are influenced by factors such as the state of stress, strain rate, and the test temperature. In the present work, only the case of plane stress at room temperature for rate-insensitive material is considered. Many attempts have been made in recent years to establish a satisfactory relationship between engineering design parameters and cyclic crack growth rates. Generally, these proposed relationships indicate that the fatigue crack growth rate is dependent upon the alternating stress level and the current crack length. The main objective of the present work was to modify the Dugdale model to include the influence of strain hardening on the plastic zone size and crack tip displacement. For a given stress level, both plastic zone size and tip displacement decrease with increasing strain hardening. For the non-hardening case, the modified Dugdale model coverages very well to the original Dugdale model.

Library of Congress Subject Headings

Fracture mechanics
Strains and stresses



Number of Pages



South Dakota State University