Microstructure-sensitive modeling of high cycle fatigue
Introduction
While much previous work in modeling fatigue processes in metallic components has focused on component life estimation, there is increasing interest in designing microstructures with tailored fatigue resistance or components with microstructures that vary spatially in composition and/or heat treatment to achieve enhanced performance. Furthermore, there is great financial and time pressure to compress overall material development and product design cycles, albeit retaining appropriate characterization of fatigue variability for purposes of design for low probability of failure in the High Cycle Fatigue (HCF) regime. Moreover, there is a need to better understand minimum fatigue life behavior of materials to address expensive, overly conservative early retirement of components.
This push towards reducing insertion time for new or modified materials has brought the notion of microstructure-sensitive fatigue analysis to the forefront. There are practical limitations to modeling and simulation, of course. Incomplete understanding of failure mechanisms, dominance of each failure mode, and uncertainty in associated models highlight the continuing importance of experiments in guiding modeling and simulation. Key advances can be realized by populating the probability density of failure modes with a combination of experiments and results from properly calibrated modeling and simulation that considers microstructure effects.
In the HCF regime, microstructure plays a key role. The distribution of cyclic slip is quite heterogeneous in this regime, as is the development and growth of small cracks that interact with local microstructure. The reader is referred to several reviews regarding microstructural fatigue mechanisms [1], [2]. Fatigue at the microstructure scale is a complex, evolutionary process with stages of formation and growth that depend on a hierarchy of microstructure features. Undue focus on any one scale from an academic perspective is sometimes misleading, as the ratio of total fatigue life associated with each stage of crack formation and growth depends on microstructure, loading conditions, and stress state [3], [4], [5], [6], [7], [8].
It is noted that fatigue is a cascade of processes of crack formation and growth that depends on the hierarchical morphology of phases or grains, as well as the presence of nonmetallic inclusions in cast or wrought alloys. For example, cracks may form at matrix–inclusion interfaces, assisted by matrix strain localization associated with interfacial debonding or particle fracture. Moreover, cracks can form via impingement of slip bands on grain or phase boundaries, as in certain dual phase alloys or for ostensibly single phase, solid-solution strengthened alloys with second phase particles near grain boundaries. In practical alloy systems, the nucleation regime is often either bypassed or coupled with debonding or fracture of interfaces between inclusions and matrix or at grain boundaries, or crack formation at existing surface scratches, machining marks, or at near-surface pores or inclusions. The problem then focuses on the formation of small cracks at micronotches that subsequently propagate as microstructurally small cracks. Eventually, these cracks either arrest (fatigue limit) or grow until they are sufficiently long compared to microstructure scales to facilitate the assumption of propagation in a homogeneous material; for many alloy systems under low amplitude HCF conditions, such cracks must typically be several hundred micrometers long.
The distribution of localized cyclic plastic deformation in the microstructure (cyclic microplasticity) plays a key role in modeling fatigue resistance. Unlike effective properties such as elastic stiffness, fatigue is manifested by extremal microstructure features that promote slip intensification. Under HCF conditions, the cyclic plastic deformation is highly heterogeneous within the microstructure; a strategy for computational HCF modeling of components that must last millions of cycles, such as shafts, bearings, and gears, for example, should focus on extreme statistics of potential sites for microplastic strain localization and fracture that drive crack formation. Moreover, the issue of arrest of small cracks that form at isolated sites of cyclic plastic strain intensification is pertinent to the estimation of the fatigue limit. The crack propagation life beyond the candidate point of initial arrest is often inconsequential as a fraction of the component fatigue life. Complicating features of such components include gradient strain fields, sub-surface inclusions, residual stresses due to thermo-mechanical processing, environmental effects, and characterization of potential mechanisms/sites for crack formation.
On the other hand, for finite life design (for example hundreds of thousands of cycles) the distribution of slip processes is less heterogeneous, and in fact may no longer occur in isolated regions. As the applied strain amplitude increases, slip heterogeneity decreases [6]. Still, microstructure plays a role in establishing “connectivity” of slip within the microstructure that provides enhancement of driving force for small crack formation and growth. Accordingly, concepts of percolation limits for microplastic deformation may be introduced, along with the notion of a microstructurally small crack growth regime in which the crack driving force couples strongly with microstructure barriers [1], [9], [10]. For such cases, both crack formation and small crack propagation can play a key role in life prediction. Moreover, in the small crack regime, the crack tip plasticity is often large scale such that the cyclic plastic zone is not small compared to crack length and also does not conform to isotropic continuum plasticity assumptions.
These kinds of issues are perhaps most fruitfully explored with computational fatigue analyses to develop understanding in view of the difficulty of obtaining statistically significant fatigue crack formation and propagation data from experiments.
Section snippets
Computational methods in fatigue modeling
Experiments are typically used to characterize both mean fatigue resistance and scatter in fatigue as a function of microstructure to facilitate tailoring of microstructure to improve component level fatigue resistance. Recently, there has been an emphasis on applying computational micromechanics [8], [11] to hierarchical microstructures (phases, grains, inclusions, etc.) to characterize multiaxial cyclic plasticity and driving forces [12] for fatigue crack formation and early stages of growth
HCF crack formation in carburized and shot peened martensitic gear steel
High strength martensitic gear steel is a viable candidate material for high performance, reliable transmission systems in aerospace and automotive applications. Microstructure at different length scales (inclusions, precipitates, and composition gradients) affects fatigue crack nucleation and growth in martensitic steels [32], [33], [34], [35], [36]; however, efforts to develop computational models that correlate these attributes to variability in fatigue crack formation and microstructurally
Extreme value statistics of fatigue crack formation in Ni-base superalloys
Ni-base superalloys are extensively used in aircraft gas turbine engines due to their high strength and creep resistance at high temperatures, conferred by coherent γ’ Ni3Al precipitates. Commonly, fatigue crack formation and early growth in these superalloys has been linked to the existence of process-induced defects such as pores or nonmetallic inclusions [64], [65], [66]. As processing techniques improve, cleaner Ni-base superalloys are being developed with fewer defects, increasing the
Fatigue failure mode transition: surface versus bulk inclusions
Primary inclusions are often dominant sites of fatigue crack formation and early growth in high strength steels, powder metallurgy alloys, and casting alloys. Transition from surface-dominated fatigue processes to subsurface failure initiation is often observed in these systems in the transition from HCF (106 cycles) to the VHCF regimes (109 cycles and beyond) [87], [88]. Competition between near-surface and bulk inclusions is key to this failure mode transition. Cashman [89] studied competing
Conclusions
Certain underdeveloped elements of microstructure-sensitive computational methods are outlined and discussed for estimating effects of process route and microstructure on variability of crack formation and early growth in the HCF regime for a wide range of alloy systems. The concept of microplasticity within individual grains is introduced as a key driving force parameter for HCF resistance and variability of response, and associated Fatigue Indicator Parameters (FIPs) are introduced that
Acknowledgments
The authors acknowledge support for the work on martensitic gear steel by the ONR/DARPA D3D tools consortia (J. Christodoulou, monitor, contract # N00014-05-C-024), administered through a subcontract through QuesTek LLC in Evanston, IL (contract monitors H. Jou and G.B. Olson). We are also grateful for the support of the NSF Center for Computational Materials Design, a joint Penn State-Georgia Tech I/UCRC, for development of extreme value HCF and VHCF statistical methods informed by
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