A Probabilistic Treatment of Microstructural Effects on Fatigue Crack Growth of Large Cracks

Abstract

A probabilistic model has been developed for treating the effects of microstructural variation on the fatigue crack growth response of large cracks in structural alloys. The proposed methodology is based on a microstructure-based fatigue crack growth law that relates the crack growth rate, da/dN, to the dislocation barrier spacing, yield stress, fatigue ductility coefficient, Young’s modulus, and the dislocation cell size or crack jump distance. Probabilistic treatment of these microstructure-dependent variables has led to a fatigue crack growth law that includes explicitly the randomness of the yield stress, fatigue ductility coefficient, and the dislocation barrier spacing in the response equation. Applications of the probabilistic crack growth model to structural reliability analyses for steels and Ti-alloys are illustrated, and the probabilistic sensitivities of individual random variables are evaluated.

A microstructure-based fatigue-crack-initiation model

“…At a large crack length (i.e., 1000 m), the calculated S-N i curve approaches that which can be rearranged to yield of the smooth specimen. It occurs when the condition Thompson et al [13,42] single phase Usami [40] (gb) slipband Smith [42] Fe-3 pct Si Tanaka et al [43] single phase 1.4 ϫ 10 6 Taira et al [32] 3. Kunio and Yamada [44] ferrite 4320 steels Bhat et al [53] precipitates Ti-6Al-4V bi-modal 6 primary alpha 15 SEM 720 680 --Peters et al [46] Ti-6Al-4V bi-modal Chan and Shih [34] Ti-8.6Al [48,49,50] slipbands 50 to 70 Wei et al [30] PM LC Jiang et al [38] Fig.…”

“…of PSBs or extrusions reported in the literature. [6,[15][16][17]81] 6. Capabilities of the crack-size-based initiation model For lifing of components, it is a common practice to include computations of the stress-initiation life curves, compute a crack-initiation life based on low-cycle-fatigue fatigue-crack growth curve for just-initiated cracks, data generated by testing smooth specimens and a crackcrack-length vs fatigue-cycle curve for crack sizes below growth life based on fatigue-crack-growth data obtained the current crack-detection limit, and the variability of from large-crack fracture-mechanics specimens.…”

“…[5] Applications of the fatigue-crack-growth The current life-prediction systems may be improved by model in a probabilistic life-prediction framework have also development of better crack-initiation-life models, probabibeen demonstrated for steels and a Ti alloy. [6] Microstructurelistic treatment of the variability of crack-initiation life, and based fatigue-crack-initiation models have been developed enhanced local notch analysis capability. [3] One of the limitaby Tanaka and Mura on the basis of the accumulation of tions of current crack-initiation-life models is that they are dislocation dipoles generated by irreversible slip on slipincapable of predicting the crack size at fatigue-crack initiabands.…”

Probabilistic micromechanical modeling of fatigue-life variability in an α+β Ti alloy

“…If N i is taken to be zero, then N f ϭ N p , leading to [13] where a i and a f are the initial and final crack length, respectively, and a f is defined as the crack length when K Ն K c . The FCG life is most sensitive to the initial crack size (a i ), [27] but also depends on microstructure. Effects of microstructure on N f arise mainly through its influence on the and U i parameters.…”

Effects of Microstructure Variability on Intrinsic Fatigue Resistance of Nickel-base Superalloys – A Computational Micromechanics Approach

“…Chan (2003) and Chan and Enright (2002) modified the Tanaka-Mura formulation to include initiation crack length and other microstructural parameters in the prediction of initiation life. For crack propagation they adopted the formulation of Chan and Torng (1996) that gave an explicit relationship between fatigue resistance and material parameters such as dislocation cell size, dislocation barrier spacing, yield stress, fatigue ductility and Young's modulus. This model treats propagation as a result of a LCF process within the crack tip process zone.…”