This paper presents a method for estimating high-cycle fatigue strength under multiaxial loading conditions. The physical interpretation of the fatigue damage is based on the theory of cyclic deformation in single crystals. Such a theory is also used to single out those stress components which can be considered significant for crack nucleation and growth in the so-called Stage I regime. Fatigue life estimates are carried out by means of a modified Wohler curve which can be applied to both smooth and blunt notched components, subjected to either in-phase or out-of-phase loads. The modified Wohler curve plots the fatigue strength in terms of the maximum macroscopic shear stress amplitudes, the reference plane - where such amplitudes have to be evaluated - being thought of as coincident with the fatigue microcrack initiation plane. The position of the fatigue strength curve also depends on the stress component normal to such a plane and the phase angle as well. About 450 experimental data taken from the literature are used to check the accuracy of the method under multiaxial fatigue conditions.

A bi-parametric Wöhler curve for high cycle multiaxial fatigue assessment

An incremental fatigue damage model is proposed. The model incorporates the critical plane concept in multiaxial fatigue, plastic strain energy and material memory in cyclic plasticity. With an incremental form the model does not require a cycle counting method for variable amplitude loading. The model is designed to consider mean stress and loading sequence effects. Features of the new model are discussed and the determination of material constants is detailed. Verification of the model is achieved by comparing the predictions obtained by using the new model and experimental data of four materials under different loading conditions.

A fatigue criterion for general multiaxial loading

A computational study is conducted to determine the influence of microstructure attributes and properties on driving forces for fatigue crack formation and microstructurally small crack growth in a polycrystalline Ni-base superalloy, IN100, a turbine disk alloy. A principal objective is to obtain quantitative estimates of the effect of variability of microstructure features on scatter in fatigue life or fatigue strength for a given life. Understanding is sought regarding sensitivity of driving forces to various microstructure attributes that may guide selection of the process route to tailor microstructure to achieve fatigue resistance. A microstructure-sensitive crystal plasticity model is used to explicitly model individual grains and polycrystals, which is then used to explore effects of: (a) grain size distribution and (b) secondary and tertiary coherent γ′ precipitate size distributions and volume fractions on the cyclic inelastic strain distribution. Multiple statistical volume elements (SVEs) are subjected to random periodic boundary conditions to build up statistically significant measures of distributions of cyclic microplasticity. Multiaxial fatigue criteria with critical plane approaches are used to estimate the crack initiation life. Methods are developed for assessing crack formation and microstructurally small crack growth as a function of microstructure attributes.

Estimating fatigue sensitivity to polycrystalline Ni‐base superalloy microstructures using a computational approach

Viscoplastic behavior of metallic materials is manifested by collective behavior of lattice defects at multiple length scales. The full gamut of length scales, from atomic to macroscopic, is considered in terms of both concurrent and hierarchical multiscale modeling of plasticity of metals. Particular challenges are identified in the realm between atomistic simulations and the scale of dislocation substructure formation in establishing next generation constitutive models. Bottom–up modeling is useful in applications such as fracture or dislocation mediation by interfaces. This is differentiated from top–down modeling that supports design of a material as a hierarchy of sub-systems. Examples of hierarchical microstructure-sensitive models are presented for both Ni-base superalloys and α–β Ti alloys, with emphasis on cyclic deformation behavior. Future directions to advance both discrete dislocation and crystal plasticity theories are discussed, emphasizing the need for additional focus on dislocation sources and dislocation line curvature in modeling scale dependent behavior. Difficulties with low order approximations of the dislocation density distribution, such as second-order gradient theories, are discussed in terms of predictive capability and transferability among geometric configurations. The multiscale nature of the decomposition of the deformation gradient into elastic and plastic parts is discussed in light of sources of incompatibility at each scale considered, with interpretation offered at different scales of Burgers circuits that highlight dislocation substructures and polycrystals, respectively. Recent atomistic studies of dislocation nucleation at grain boundaries are outlined and some thoughts are offered towards potentially fruitful directions to incorporate this understanding into statistical continuum models that account for the role of grain boundary structure as an element of the evolving incompatibility field.

Viscoplasticity of heterogeneous metallic materials

A model for rolling contact failure

Bulk deformation fatigue damage models assume that the stresses and strains at the critical location of the component or structure govern the fatigue life. They allow engineering estimates of fatigue life to be made without explicitly modeling the detailed mechanisms of the fatigue process. To be successful, however, these models must reflect the physical process. Observations of fatigue cracking behavior show that fatigue damage is dependent upon the loading mode, the strain amplitude and the type of material. The cracking behaviors of AISI stainless steel 304, SAE 1045 steel and Inconel 718, tested in tension and torsion, are used to identify the development of damage in these materials for various strain levels. Damage develops either on planes of maximum shear strain or on planes of maximum tensile strain. Identification of the damage in these materials then allows estimates of the lifespan to be made for complex multiaxial loading using an appropriate bulk deformation model. Multiaxial fatigue tests results, including mean stress effects, are presented and successfully correlated with the model that incorporates the dominant or controlling damage parameter.

Julie Bannantine

Papers

Bulk deformation fatigue damage models