Plastic deformation in brittle and ductile fracture

An effort is made to cover the full elastic-plastic range from the very troublesome fractures which initiate and propagate at nominal or net stress well down in the elastic range to the common yet more easily understandable and preventable fractures at fully plastic or limit load conditions. Similarities and differences of behavior between steels which are highly rate-sensitive and aluminum alloys or other rather insensitive materials are examined. The very marked distinctions between the very special extremes of plane stress and plane strain are brought out along with their relevance to the failure of complex structures and elements. In contrast, the need to consider bending in most shell structures is emphasized. A demonstration is given of the likelihood in the laboratory, but even more so in the field, of confusing limit load fractures with low stress fractures. Crack extension under plane strain conditions is studied in some detail, and the important role of progressive blunting is indicated both in limiting maximum achievable stresses and providing a small region of intense strain in which ductile fracture mechanisms are operative. Comparison with appropriate microstructural dimensions leads to a rationale for minimum thickness dimensions for plane strain fracture. Plane stress yield patterns in cracked sheets are shown to be greatly sensitive to the yield criterion. The line plastic zone Dugdale model provides a correct solution for a non-hardening Tresca material, but diffuse zones result for a Mises material. The important role of thickness direction anisotropy is indicated. Stable extension under increasing load appears as a possible consequence of crack advance into previously deformed material. Conditions for stable vs. abrupt growth, the appropriateness of energy balance approaches, and plastic limit load calculations are also studied. An attempt is made to place all in perspective.