Micro and Macro Crack Formation

Abstract

The formation of cleavage microcracks with a length of the order of one grain diameter is considered to be the initial step in fracture. It is assumed that the stress concentration required for cleavage is supplied by thick slip or twin bands, and the critical width of these yield bands is calculated. For example, in iron with a grain radius of 10−2 cm, the critical slip band width is 2 × 10−5 cm, and this value is compatible with observations in the vicinity of microcracks. The second stage of crack formation involves the semi-continuous propagation of microcracks to form unstable macroscopic cracks. We postulate that plane strain fractures occur under conditions where thick slip bands are formed in the yielded region in front of an advancing crack. Work required to extend the initial crack is used to calculate the crack extension force, GIc, which is required in linear fracture mechanics. In the case of iron, the microcrack extension force, Y, is calculated to be 5 × 103 dynes/cm, and the minimum value of GIc is calculated to be 2.5 × 106 dynes/cm. This approach emphasizes the three conditions required for fracture: 1) a combination of stress and yield band width sufficient to cause local cleavage; 2) sufficient mechanical energy in the system to propagate the crack; 3) the development of a critical value of the initiation stress in order to continue crack extension. These concepts are used to estimate the plane strain transition and the nominal stress for fracture, i.e. plate fracture stress, σn, is estimated from an elastic-plastic stress analysis to be σc/4, where σc is the yield stress at the tensile transition temperature. The tensile transition is chosen as the point at which the yield and fracture stress are about equal, and the plate transition temperature corresponds to the temperature, TC, at which the yield stress has a value of σc/4. We also estimate that crack arrest in steel plates corresponds to an energy absorption, GC = 22.5 × 103 × t/d, where GC is the crack extension force at the transition between plane strain and plane stress (dynes/cm), t is the plate thickness (cm), and d is the grain radius (cm). A reasonably good correlation for GIc and GC calculated and tested, is obtained. We also use tensile transition data to estimate a plate transition temperature and a critical tensile stress for crack propagation. These are combined with a suggested minimum value of the crack extension force, GC (arrest), to provide the basis for a fracture-safe design criterion.