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Two models are presented for the long life (107 cycles) axial fatigue strength of four ferrous powder metal (PM) material series: sintered and heat-treated iron-carbon steel, iron-copper and copper steel, iron-nickel and nickel steel, and pre-alloyed steel. The materials are defined at ranges of carbon content and densities using the broad data available in the Metal Powder Industries Federation (MPIF) Standard 35 for PM structural parts. The first model evaluates 107 cycles axial fatigue strength as a function of ultimate strength and the second model as a function of hardness. For all 118 studied materials, both models are found to have a good correlation between calculated and 107 cycles axial fatigue strength with a high Pearson correlation coefficient of 0.97. The article provides details on the model development and the reasoning for selecting the ultimate strength and hardness as the best predictors for 107 cycles axial fatigue strength.

Recent developments in time-dependent reliability have introduced the concept of a composite limit state. The composite limit state method can be used to calculate the time-dependent probability of failure for dynamic systems with limit-state functions of input random variables, input random processes and explicit in time. The probability of failure can be calculated exactly using the composite limit state if the instantaneous limit states are linear, forming an open or close polytope, and are functions of only two random variables. In this work, the restriction on the number of random variables is lifted. The proposed algorithm is accurate and efficient for linear instantaneous limit state functions of any number of random variables. An example on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates the accuracy of the proposed general composite limit state approach.