Determination of the Optimum Fitting Probabilistic Distribution for Fracture Toughness in Small Sample Size

Abstract

Plane strain fracture toughness is an important mechanical performance index for damage tolerance design, so how to obtain this value through test deserves consideration. In this paper, the ductile fracture toughness test was performed. It was difficult for the specimen with big dimensions in the case of plane strain to be carried out through ordinary testing machine with lower capacity because of the higher fracture toughness value of the material, that it was attained indirectly for plane strain fracture toughness value by the way of ductile fracture toughness test and pertinent formula calculation if proper specimen selected. The fracture property tests according to the corresponding standard were conducted. The compact tension specimens were obtained from the main rotor butt of a helicopter in service. Based on the single specimen measuring ductile fracture toughness method, the experiments of measuring the ductile fracture toughness were carried out. A method was given to determine the optimum fitting probabilistic distribution function of fracture toughness in the small sample size. The statistic results show that the optimum probabilistic distribution function of ductile fracture toughness is the Extreme Maximum. Value distribution. The following factors were taken into account, the linear relative coefficient, total fit effect probability relative coefficient, consistency with the relevant fatigue physics and tail most importantly, safety of design evaluation. The shape parameter, scale parameter, and location parameter are -1.1231, 860.53, 6036.4, respectively. The statistical variation coefficient is 11.22%. The result shows that there is a large risk probability for a definite value to fracture toughness only with one or two pieces of samples according to the test.