The temperature dependence of the fracture stress of metals

Abstract

A “Griffith” criterion σ _f ∝ c_f ^−1/2, relating the length of micro-cracks and the tensile fracture stress σ _f , when coupled with the work-hardening law σ²=χ(T). ϵ and the relation representing the crack growth rate c=c ₀(1 + α ϵ^1+α), where a and α are positive constants, is shown to imply a temperature dependence of σ _f of ductile metals at relatively low temperatures given by σ_f ∝ χ^m, 1/4 < m < 1/2. This agrees with experimental values for polycrystalline cobalt (m=0·30) and copper (m=0·40) deformed in the range 77–360°K, but an anomalously high value of m=0·70 is found with α-brasses containing 10–35% of zinc, fractured in tension in the same temperature interval. This is explained on the assumption, suggested by evidence obtained by microscopy, that heterogeneous glide, characteristic of α-brasses, tends to diminish micro-cracks by transverse shears at large strains.