Symposium on Computation & Probabilistic Fracture Mechanics 10th International Congress on Fracture, Honolulu, HI, Dec 2-7, 2001 Figure 1. Recommended Damage Locations The first step in the assessment of the structural strength was to examine the point estimate of the probability of failure. To do this we examine the calculated maximum principal strain calculated in the base case analysis and compare it to the (assumed) Weibull distribution for the strength. Thus, the maximum principal strain of 8.97 x 10-5 is compared to the TPS allowable strain distribution with a shape factor, β, equal to 2 and 4. When the value of 4 is used the maximum principal strain calculated by the FE code falls at a point in the strength distribution that states the strength would be less than this point value is equal to a probability of 4.5 x 10-7. This is encouraging but we must recall that the Weibull distribution has very long. We know look at the estimated failure probability for the C-C composite shell for all eight of the response surface calculations. These are shown in Table I. The estimated failure probabilities rang from 9 x 10-8 to 1.3 x 10-5. However, we must remember that these probabilities are conditional probabilities, i.e. they are dependent on the inputs to the finite element model. Since these are not equally weighted we cannot simply take the arithmetic average of the numbers to determine the overall failure probability. Rather we must perform the FPI analysis of the fitted response surface to obtain our final result. C-C RESPONSE SURFACE ANALYSES The FE code analyses were performed using ABAQUS. The results of the FE analyses are reported as the maximum principal strain within the C-C shell structure. These results are given in Table I. Here we take these eight values and calculate the coefficients of the response surface equation.* A cursory examination of the values in Table I shows that the maximum principal strain changes by a factor of 2.2 from the highest to lowest value ratio. Table I indicates that the failure probability can * Recall that since the temperature is no longer a variable all columns in Table VI involving the factor 4 must be removed from the analysis. - 4 -
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