On the statistical analysis of local fracture stresses in notched bars

Su Wu, John Knott

Research output: Contribution to journalArticle

22 Citations (Scopus)


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 (sigma(F)) distributions plotted on normal probability paper show that the experimental cumulative distribution function (CDF) is linear for each condition with different mean values: 1560 MPa for "as-received" material and 1400 MPa for "degraded" material. The values of standard deviation are small and almost identical (33-35 MPa). 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 CF 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 proper-ties. 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. (C) 2003 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)907-924
Number of pages18
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - 1 Jan 2004


Dive into the research topics of 'On the statistical analysis of local fracture stresses in notched bars'. Together they form a unique fingerprint.

Cite this