Effect Of Prior Tensile Strain On Fracture

THE object of this study is to investigate the effect of prior tensile strain on the fracture stress of a metal. This is done in a theoretical manner starting from the point of view developed by the author in his thermodynamic theory of the fracture of metals. The results are compared with experimental findings and a rational interpretation is given to work that shows the variation of fracture stress with prior tensile strain. THEORY OF FRACTURE In the thermodynamic theory of the fracture of metals developed earlier,1 it was shown that a critical strain energy per unit volume exists. This is characteristic of the material and may be calculated from basic thermodynamic data. When the area under the flow curve reaches this characteristic value, fracture occurs. The general criterion for fracture is expressed in the form u ± uo = JLm?AV/V [1] where Lm, is the latent heat of melting of the unit volume, ?V/V is the ratio of the change in volume of the unit volume to the original unit volume on passing from the solid to the liquid state, [uo] is an initial energy density, and J is a conversion factor, which changes energy from heat to mechanical units. As a first approximation, it will be assumed that the stress-strain curve is the straight line that extends from the point of maximum load onward, extrapolated back to the axis of zero strain, for example, line AC of Fig. 1. If the point of intersection of the straight line with the axis of zero strain is represented by so, and the slope of the straight line is p, the analytic form of the flow curve is [s = s + pd [2]] and the strain energy per unit volume evaluated from [JvdS] becomes (vsod + pd2/ 2). When this latter term reaches the critical value JLm?V/V (designated hereafter by M), it is assumed that fracture occurs. This leads to the following expression for the fracture stress: [s1 = \/C r.2 + 2Mp [31] The strain at fracture may be calculated from Eqs 2 and 3. It is assumed in this paper that the initial energy density is either zero or that it may be neglected. Furthermore, the complicated states of stress and of strain existing in the necked region of the tensile specimen after "necking" has occurred will also be neglected for the present, so that average conditions will be assumed to prevail. FLOW AND FRACTURE CURVES Ludwig2 attributed to materials two fundamental properties: (I) a resistance to flow and (2) a resistance to fracture. He reasoned that at each instant the