Maximum uniform deformation in tension

Abstract

An equation is derived for the hyperbola which touches the true stress curve S =f(ψ), where ψ is the contraction of the specimen at the point ψ_p (uniform contraction), S_B (true ultimate strength). With a flat maximum of the tensile force, this hyperbola coincides with the true stress curve at a part corresponding to extension by the maximum force. The use of the tangent hyperbola for determining ψ_p and S_B is demonstrated.

It is found that for those metals and alloys which are at present known to have a convex true stress curve in the uniform plasticity range, the uniform contraction ψ_p cannot exceed 0.5, corresponding to a uniform elongation σ_p ≤ 1, while the true (logarithmic) uniform elongation λ_p ≤ 0.693. The limiting values of the hardening modulus and of the ratio S_B/σ_B are also found.