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A probabilistic distribution function roughly consists of two parts: the middle part and the tails. The fatigue life distribution at a stress/load level is often described with two-parameter lognormal or Weibull distribution functions, which are more suitable for modeling the mean (middle) behaviors. The domains of the conventional probabilistic distribution functions are often unbounded, either infinite small (0 for the two-parameter Weibull) or infinite large or both. For most materials in low- and medium-cycle fatigue regimes, the domains of fatigue lives are usually bounded, and the inclusion of the bounds in a probabilistic model is often critical in some applications, such as product validation and life management. In this paper, four- and five-parameter Weibull distribution functions for the probabilistic distributions with bounds are developed. Finally, the applications of these new models in fatigue data analysis and damage assessment are provided and discussed.

Life testing or test-to-failure method and binomial testing method are the two most commonly used methods in product validation and reliability demonstration. The two-parameter Weibull distribution function is often used in the life testing and almost exclusively used in the extended time testing, which can be considered as an accelerated testing method by appropriately extending the testing time but with significantly reduced testing samples. However, the fatigue data from a wide variety of sources indicate that the three-parameter Weibull distribution function with a threshold parameter at the left tail is more appropriate for fatigue life data with large sample sizes. The uncertainties introduced from the assumptions about the underlying probabilistic distribution would significantly affect the interpretation of the test data and the assessment of the performance of the accelerated binomial testing methods, therefore, the selection of a probabilistic model is critically important.

In this study fatigue tests of GMAW (Gas Metal Arc Welding) welded joints were conducted on both 1.6mm body sheet (DQSK-GA, DP590-GA, DP780-GI, and TRIP 780-GI) and 3.4mm frame materials (SAE1008 HR 240MPa, HSLA420 HR, DP600 HR, and uncoated Boron). Further, mixed thickness joints were tested which combined 3.4mm SAE1008 HR with each of the 1.6mm separately – with the exception of DQSK. A number of different joint configurations were tested including single and double lap-shear, start-stop lap shear, butt weld, and perch mount. Great care was taken in this study to ensure that the geometry of the welds was consistent, not only within a given material lay-up, but between all of the specimens of a given type – this effort was made in order to substantially reduce life scatter and provide a better understanding of the role base material plays in the fatigue life of GMAW joints.