Estimation of fracture strain of ductile round bar specimen, having a given initial volume fraction of voids, was tried using the previously reported equation for the ductile fracture condition. As the equation involves four variables i.e. volume fraction of voids,
v, relative radial stress, σ
r⁄
Y, relative work hardening ratio, \dfrac
dσ⁄
dεσ, and specimen size, changes of these variables with strain were investigated.
σ
r⁄
Y at the center of the neck of specimens was expressed in terms of the curvature radius of the neck,
R, and a radius of the section of specimen,
r, using Bridgman’s equation. It was shown that
r⁄
R could be uniquely related to strain, ε, irrespective of examined materials. Next, densities of the necked region of tensile specimens of several materials (low carbon steel, stainless steel, aluminium, etc.) were measured. Using these results, experimental equations for the change in volume fraction of voids with the effect of work hardening and the difference in materials were obtained. Applying these equations, the
v-ε curve of a specimen having a given volume fraction,
v0, could be drawn.
Using
r⁄
R-ε, and
v-ε curves and the equation for the fracture condition, the relation between fracture strain ε
f and initial volume fraction of voids
v0 could be obtained graphically in each case of three different
n-values \left(σ=
Cε
n,\dfrac
dσ⁄
dεσ=\dfrac
nε\
ight) and three different specimen sizes, which agreed well with the experimental results (Edelson, et al., present work). The theoretical expectation that fracture strain increases with
n-value and decreases with specimen size, agreed quantitatively with the experimental results described in this paper.
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