A general method for estimation of fracture surface roughness: Part I. Theoretical aspects
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Rs = RL" where Rs is the fracture surface roughness parameter and ~b is the profile structure factor, which is completely determined by the profile orientation distribution function, f(a). RL" ~ is the expected value of the product RL" ~ on a set of sectioning planes normal to the average topographic plane of the fracture surface; measurement of RL and ~ on few such sectioning planes can give a reliable estimate of the fracture surface roughness, Rs. The result is geometrically general, and it is applicable to fracture surfaces of any arbitrary complexity and anisotropy.
I.
INTRODUCTION
THE deformation and
fracture processes generate fracture surface. The geometric attributes of fracture surface and the associated microstructural features may contain quantitative information concerning the processes that lead to fracture. It is essential to establish such correlations by using the characterization techniques which are assumption-free and unbiased. An important geometric characteristic of fracture surface is the quantitative measure of its roughness. It is the purpose of this paper to develop an assumption-free and unbiased method for the estimation of the fracture surface roughness from the measurements performed on the fracture profiles observed in the metallographic sections through fracture Surface.
The quantitative descriptor of the surface roughness is the fracture surface roughness parameter, Rs, defined as follows:[ ~1 S
Rs = -
A
[11
where S is the true fracture surface area and A is the
apparent projected area on a plane parallel to the mean or average topographic plane of the fracture surface (Figure 1(a)). The overlapped segments of the projected area are not added for calculating the apparent projected area, A. The surface roughness parameter, Rs, is equal to the true average area of a fracture surface segment having unit apparent projected area. For a flat surface, Rs is equal to one. The rougher the fracture surface, the higher is the value of Rs. In general, Rs can have any value ranging from one to infinity, t2,31 A fracture profile is a line generated by the intersection of fracture surface and a metallographic section-
A.M. GOKHALE, Associate Professor, and E.E. UNDERWOOD, Professor Emeritus, are with the School of Materials Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245. Manuscript submitted August 28, 1989. METALLURGICAL TRANSACTIONS A
ing plane (Figure l(b)). In general, a fracture profile is an irregular line of complex nature, and it may contain overlaps. In practice, it is convenient to generate fracture profiles on sectioning planes which are perpendicular to the average topographic plane of fracture surface, t2,3,41 Analogous to the surface roughness parameter, the profile roughness parameter, RL, is defined as follows t1'4] (Figure l(b)): Ao RL = - L
[2]
where A0 is the true length of fracture profile and L is its apparent projected length on the mean or average topographic direction of the profile. The overlapped segments of projected length are not add
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