Using Probabilistic Microstructural Methods to Predict the Fatigue Response of a Simple Laboratory Specimen

Abstract

For the purpose of this chapter, fatigue is defined as the entire range of damage-accumulation sequences, from crack nucleation of the initially unflawed bar to final fast fracture. Background Various Stages of FatigueCurrent fatigue-life prediction methods in metallic components consider three stages: crack initiation, long-crack propagation, and final fracture. Long-crack propagation and final fracture are the stages of damage accumulation that are well characterized using linear elastic or elastic-plastic fracture mechanics. Crack initiation is the early stage of damage accumulation where small cracks (cracks with depths less than several grain diameters) have been observed to deviate significantly from predicted long-crack fracture mechanics behavior [1]. The deviation is attributed to the heterogeneous media in which small cracks evolve [2].The crack-initiation stage can be broken down into two phases: crack nucleation and small-crack growth. Crack nucleation is the locally complex process of crack formation on the microstructural scale. Crack nucleation is characterized by smooth fracture surfaces at angles inclined to the loading direction. This type of failure is indicative of shear stress Mode II (sliding mode) fracture. Although loading has been shown to affect the nucleation size [3,4], experimental evidence suggest that the nucleation size is on the order of the grain size [5][6][7].Small-crack growth is characterized by fracture-surface striations perpendicular to the loading direction. This type of failure is indicative of tensile stress Mode I (opening mode) fracture. The behavior of small cracks tends to transition to linear or elastic-plastic fracture mechanics behavior when the crack depth reaches about ten mean grain diameters [8]. Crack nucleation and small-crack growth must be modeled separately because different mechanisms control each phase. The relative importance of the crack-nucleation stage on overall fatigue life depends on several factors. Materials that exhibit a strong preference for planar slip show a strong correlation between the crack causing final fracture and the earliest nucleated cracks [9]. Materials that prefer cross slip showed almost no correlation between the crack causing final fracture and the earliest nucleated cracks [9]. The relative importance of the crack nucleation may also depend on the loading condition. If the loading is relatively low (high-cycle fatigue), the majority of life will be spent in the nucleation of a crack. If the loading is high (low-cycle fatigue), cracks may nucleate early and spend the remainder of the fatigue life in the crack-growth stages. However, high-strength materials have been shown to spend the majority of fatigue life in the crack-nucleation stage, even during low-cycle fatigue [10]. Scatter in Fatigue LifeThe coefficient of variation (COV) of fatigue-life tests range widely, depending on the material alloy and load level. Even for well-controlled laboratory tests of annealed smooth specimens at room temperature, the COV varies fro...

Science-Based Multiscale Modeling of Fatigue Damage for Structural Prognosis

“…The VEXTEC VPS-MICRO model includes a probabilistic fatigue life prediction algorithm that explicitly models fatigue crack initiation and growth starting at the microstructural scale. 11 The overall fatigue damage model uses Monte Carlo simulation to proceed through three different levels of fatigue damage accumulation that are commonly observed in the process of fatigue, each with its separate modeling regimes: (1) crack nucleation, (2) short crack growth and (3) long crack growth. The probabilistic micromechanics model is based on dislocation theory, crystal plasticity and fracture mechanics.…”