Quantitative fractography: A modern perspective
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INTRODUCTION
QUANTITATIVE fractography is an analytical tool which provides true estimates of the feature characteristics and topography of fracture surfaces. Since the inception of the scanning electron microscope (SEM), researchers in the fracture of metals have attempted quantitative measurements on SEM fractographs in one way or another. The SEM fractograph depicts the topography, appearance, and specific feature characteristics of fracture surfaces. These attributes are manifestations of the various microfracture mechanisms in materials. The motivation to quantify fracture surfaces is to understand the precise role the microstructure plays in the fracture process. The objective of quantitative fractography is to determine the true three-dimensional characteristics of quantities in the fracture surface. It will then be possible to apply the procedures in any general situation and permit comparisons on a quantitative, objective basis. In recent years, several major contributions to the quantitative analysis of fracture surfaces t~-51 have focused on various aspects of the problem. Although more work needs to be done, a consistent formalized approach has emerged. The ultimate objective is to transform measurements made on flat two-dimensional SEM images to the true quantities as they exist in the fracture surface in three dimensions. Central to this objective is the need to determine the true area of the fracture surface with respect to its projected area in the SEM photomicrograph. Earlier attempts in the metallurgical literature to quantify fracture surfaces did not
K. BANERJI is Research Associate, School of Materials Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245. This paper is based on a presentation made at the symposium "Stochastic Aspects of Fracture" held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee. METALLURGICAL TRANSACTIONS A
take into account the true three-dimensional nature of the fracture surface. The implicit assumption was that the fracture surface was flat as it appeared in the SEM image. In some recent publications, t6,7,8] it has been demonstrated that the errors induced by this unrealistic assumption can exceed 100 percent! In order to arrive at unbiased estimates of the true fractions, lengths, areas, etc., of specific features in the fracture surface, we wish to use the capabilities of classical stereologyIg.m] to the utmost. However, some practical problems based on adequate sampling of the fracture surface must be borne in mind when selecting an experimental procedure. Relationships of classical stereology are founded on the premise of random sampling of the Structure. The inherent preferential orientation of fracture surface elements renders the angular randomness of sampling via SEM imaging rather prohibitive. Since unbiased sampling is not feasible by SEM, the dimensions apparent on such images will always be statistically biased in some sense. [m In order to extract m
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