On the statistical analysis of local fracture stresses in notched bars

Test results for critical local fracture stresses are analysed statistically for both “as-received” and “degraded” pressure-vessel weld metal. The values were determined from the fracture loads of blunt-notch four-point-bend specimens fractured over a range of low test temperatures, making use of results from a finite-element stress analysis of the stress-strain distributions ahead of the notch root. The “degraded” material tested in this work has been austenitized at a high temperature, followed by both prestraining and temper embrittlement. This has led to a situation in which the fracture stress for the “degraded” material is reduced significantly below that for the “as-received” material. The fracture mechanisms are different in that the “degraded” material shows evidence of intergranular fracture as well as cleavage fracture (in coarse grain size) whereas the “as-received” material shows only cleavage fracture (in fine grain size). The critical stress (σ_F) distributions plotted on normal probability paper show that the experimental cumulative distribution function (CDF) is linear for each condition with different mean values: for “as-received” material and for “degraded” material. The values of standard deviation are small and almost identical (33-). The decrease of the local fracture stress after degradation is related to the local fracture micro-mechanisms. Statistical analysis of the results for the two conditions supports the hypothesis that the values of σ_F are essentially single valued, within random experimental errors. A similar analysis of the data treating both conditions as a single population reveals some interesting points relating to statistical modelling and lower-bound estimation for mechanical properties. Comparisons are made with Weibull analysis of the data. A further conclusion is that it is extremely important to base any statistical model on inferences drawn from micro-mechanical modelling of processes, and that examination of “normal” CDFs can often provide good indications of when it is necessary to subject data to further statistical and physical analysis.