Analyzing statistical variability of fracture properties
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I.
INTRODUCTION
THEextreme scatter in impact-energy-absorption data for steel tested within the ductile/brittle transition region is well known. Figure 1 shows an unusual, but not rare example (see Reference 1). These four Charpy V-notch samples were taken from the same plate and impacted at the same temperature. Yet the absorbed energy varied by more than a factor of 20. Such a large difference cannot be explained by experimental errors; it reflects a true material variability that needs to be taken into account in specifying load and operating temperatures. The Weibull distribution is a natural choice for dealing with variability in fracture data, because it long has been applied to brittle materials (for a review see Reference 2) and because it is quite flexible. Mathematically, if Y is an observation taken at random from a two-parameter Weibull distribution, then for any value y the probability that Y ~ y is given by the function F(y) = Prob[Y ~ y] =
- e -~/~)~
y ~ 0
where a > 0 and/3 > 0. The probability function F(') is referred to as the cumulative-probability-distribution function (CDF) for the Weibull distribution with parameters a and/3. Figure 2 shows that the Weibull distribution provides an adequate description of the data from Figure 1. In the more usual case, the transition is spread out over a wide temperature range so that the scatter at any given temperature is less than that illustrated by Figure 1. However, the problem still remains of incorporating the scatter into a safety analysis. The present paper uses Charpy V-notch impact-test results to illustrate a new statistical approach to the analysis of fracture-toughness data for steels in the ductile/brittle transition region. In the cases shown below, a full energy/ temperature curve is available to specify the temperature above which the impact energy exceeds some given value. While the engineer's judgment is usually used to draw a curve through the data points in such cases, in some applications statistical procedures 3-6 are used. If there are a large number of points (typically on the order of 10 to 20) and little scatter, there is no problem in defining a transition temperature. On the other hand, often there are few data points and/or large scatter. In those cases, significant ambiguities can arise. T.A. BISHOP, Associate Section Manager, A.J. MARKWORTH, Senior Research Scientist, and A. R. ROSENFIELD, Research Leader, are all at Battelle-Columbus, 505 King Avenue, Columbus, OH 43201. Manuscript submitted August 31, 1982. METALLURGICALTRANSACTIONS A
Determination of a full curve is not always mandated by codes and standards. For example, Paragraph NB2331 of the ASME Boiler and Pressure Vessel Code requires that only three samples be tested and that all three exceed a given energy at the test temperature. Alternatively, ASTM A370 for steels requires both that the energies absorbed by three samples all exceed some given toughness and that their average also exceeds some given (higher) toughness. It is not clear how the transition tempe
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