A microstructure based fatigue life prediction framework and its validation
Fatigue crack initiation in polycrystalline materials can be attributed to various mechanistic and microstructural features acting in concert like the elastic stress anisotropy, plastic strain accumulation, resolved shear stress, normal stress, slip-system length, and grain boundary character. In nickel-base superalloys, fatigue cracks tend to initiate near twin boundaries. The factors causing fatigue crack initiation depend on the material’s microstructure, the variability of which results in the scatter observed in the fatigue life. In this work, a robust microstructure based fatigue framework is developed, which takes into account i) the statistical variability of the material's microstructure, ii) the continuum scale complex heterogeneous 3D stress and strain states within the microstructure, and iii) the atomistic mechanisms such as slip-grain boundary (GB) interactions, extrusion formations, and shearing of the matrix and precipitates due to slip. The quantitative information from crystal plasticity simulations and molecular dynamics is applied to define the energy of persistent slip bands (PSB). The energy of a critical PSB and its associated stability with respect to the dislocation motion is used as the failure criterion for crack initiation. This unified framework helps us gain insights on why fatigue cracks tend to initiate at twin boundaries. In addition to that, the computational framework links variability in material’s microstructure to the scatter observed in fatigue life. ^ The microstructure based fatigue model is used to study the role played by various microstructural attributes (like grain size, γ′ volume fraction, GB character) in limiting fatigue life. Additionally, the role played by local microstructural response (plastic strain accumulation, elastic stress anisotropy developed at the GBs, extrusion height at intersection of persistent slip bands and GBs) in triggering crack initiation is also studied. We show that the aforementioned attributes have varying degree of influence over fatigue life, which in turn gives rise to a wide spectrum of opportunities (in the bulk of the material) with varying degree of severity where fatigue cracks can potentially initiate, thereby contributing to the scatter observed in fatigue life. ^ The fatigue model is validated using an uncertainty quantification and propagation framework. First, global sensitivity analysis (GSA) is used to identify the set of the most influential parameters in the life prediction model. Following GSA, the posterior distributions of all influential model parameters are calculated using a Bayesian inference framework, which is built based on a Markov chain Monte Carlo algorithm. The quantified uncertainties thus obtained, are propagated through the model using Monte Carlo sampling technique to make robust predictions of fatigue life. The model is validated by comparing the predictions to experimental fatigue life data. ^
Michael D. Sangid, Purdue University.
Aerospace engineering|Materials science