Non-proportional Fatigue Loading Research Articles

Topology optimization for fatigue reserve factors

This paper describes a topology optimization approach that applies the common fatigue analysis practices of rainflow cycle counting and critical plane searches to cover both proportional and non-proportional fatigue loading conditions of metals. The existing literature on topology optimization has so far mainly considered fatigue damage under proportional loading conditions and typically uses continuous damage models to avoid the discontinuous nature of fatigue rainflow cycle counting and critical plane searches. Furthermore, previous publications often introduced heuristic schemes to scale the fatigue damage and set the move limits for the design variables rather low to avoid oscillations in the design variables and damage responses during the optimization iterations, because fatigue damage is typically highly localized. Therefore, these approaches cause many optimization iterations. Contrarily, our present approach applies the fatigue reserve factor (FRF) directly in the optimization formulation instead of the fatigue damage where FRF is a fatigue reserve factor for infinite fatigue life. The inverse FRF scales nearly linearly with the stresses. Therefore, the present approach needs no heuristic scaling for the fatigue topology optimization. The numerical implementation applies the semi-analytic adjoint sensitivity method for multiple load cases. Numerically, FRF shows more stable optimization convergence using less optimization iterations. Different FRF topology-optimized designs for a variety of fatigue damage types are validated and compared. Additionally, the optimized FRF designs are compared to both strictly stiffness optimized designs and stress strength optimized designs.

Path-dependent multiaxial fatigue behavior of A319 aluminum alloy under non-proportional loading conditions

Abstract In the multiaxial low fatigue test study, four multiaxial non-proportional fatigue loading paths were used including rectangular, square, rhombic and circular. The effect of loading condition changes on the fatigue behavior and cyclic damage characteristics of A319 aluminum alloy was investigated by means of stress response curves, stress–strain hysteresis lines, fatigue fracture morphology, and dislocation substructure morphology in combination with material microstructure. The non-proportional hardening behavior exhibits strong loading path dependence, and the fatigue plastic deformation in the torsional direction is greater in the circular and rhombic paths, and the fatigue damage is more severe, resulting in a shorter fatigue life of A319 aluminum alloy. The axial directions under non-proportional multiaxial loading all have tensile and compressive asymmetric behavior. The differences in loading paths result in different fatigue crack expansion modes. The non-proportional additional hardening behavior under different loading paths is closely related to the dislocation substructure. In the rhombic and circular paths, the alloys have higher dislocation density and strong interaction between dislocations and precipitation phases, which is macroscopically expressed as stronger non-proportional hardening ability in the rhombic and circular loading paths.

Fatigue Life Assessment of Metals under Multiaxial Asynchronous Loading by Means of the Refined Equivalent Deformation Criterion

As is well-known, non-proportional fatigue loading, such as asynchronous one, can have significant detrimental effects on the fatigue behavior of metallic materials by reducing the fatigue strength/fatigue limit and by leading to a fatigue damage accumulation increased with respect to that under proportional loading. In the present paper, the novel refined equivalent deformation (RED) criterion is applied for the first time to estimate the fatigue lifetime of materials, sensitive to non-proportionality, subjected to asynchronous loading under low-cycle fatigue regime. The present criterion is complete since it considers: (i) the strain path orientation, (ii) the degree of non-proportionality, and (iii) the changing of material cyclic properties under non-proportional loading. To evaluate its accuracy, this criterion is applied to examine two different metals (a 304 stainless steel and a 355 structural steel) whose experimental data under multiaxial asynchronous loading are available in the literature. More precisely, the parameters of the criterion are firstly determined by using experimental strain paths, and then the computed refined equivalent deformation amplitude is used to represent the experimental data with a satisfactory accuracy. Finally, a comparison with the results obtained through two other criteria available in the literature is performed, highlighting the good prediction of the present RED criterion.

A survey on fatigue life analysis approaches for metallic notched components under multi-axial loading

In this paper, several fatigue failure approaches of metallic notched components under multi-axial loading in recent decades are reviewed in detail. They are classified into three categories according to their different fatigue physical mechanisms and hypotheses: nominal stress approach, local stress–strain approach and the theory of critical distance. The accuracy, applicable range and computing complexity of these three different fatigue failure theories of metallic notched specimen under multi-axial fatigue loading are given. It is concluded that theory of critical distance accords with experimental results under multi-axial fatigue loading and it gives unambiguous explanation for physical mechanism of fatigue damage. However, the computing process is complex, especially under non-proportional fatigue loading, and the key parameter of theory of critical distance is difficult to calculate especially in engineering. These difficulties limit the application of theory of critical distance.

Sharp three-dimensional notches under combined nominal normal and shear fatigue loading

Many engineering structures are exposed to non-proportional fatigue loading. However, at the critical location of crack initiation, often only one of the load sequences dominates – the individual load cases result in different crack initiation sites. Based on engineering judgment a simplified local uniaxial or proportional loading situation may be assessed. In general, the critical location must be identified by calculating fatigue lives for a variety of locations. The position of the critical location depends on the hypothesis applied for life calculation – besides loading, geometry, material and many other influence factors. For sharp three-dimensional notches the region for the search of the critical location may be restricted considerably. Weld start and stop points are an industrial example for such sharp notches. They are the object of the present investigation. They are exposed to nominal normal and shear loading. The individual hot spots for crack initiation lie necessarily close together. A strong interaction of the loading cases for both proportional and non-proportional loading was experimentally observed. In the numerical investigation notch stresses were calculated using an idealised weld end model. Based on the critical plane approach according to Findley, numerical interaction lines were produced.

An Energy-Critical Plane Based Fatigue Damage Approach for the Life Prediction of Metal Alloys

This paper presents a new energy-critical plane based fatigue damage approach for the assessment of the fatigue life under uniaxial and multiaxial proportional and non-proportional fatigue loading. The proposed approximate method, based on Farahani's multiaxial fatigue damage model, takes into account the critical plane orientations during a loading cycle and the values of the respective damage parameters on them. The uniqueness of the proposed method lies on the fact that it considers a weighted contribution of each critical plane orientation to the material damage. The relative weighting factors depend on the declination of each critical plane with respect to the critical plane, where the damage parameters exhibit their maximum values during a fatigue loading cycle. Herein, several low, mid and high-cycle fatigue loading cases are being investigated. The induced elastic-plastic stress-strain states are approximated by means of respective finite element analyses (FEA). Several experimental fatigue data derived from uniaxial and multiaxial fatigue tests on StE460 steel alloy thin-walled hourglass-type specimens have been used to verify the model's calculation accuracy. Comparison of experimental and calculated fatigue lives confirm remarkable fatigue life calculation accuracy in all cases examined.

Ratcheting-based microstructure-sensitive modeling of the cyclic hardening response of case-hardened bearing steels subject to Rolling Contact Fatigue

Rolling Contact Fatigue (RCF) is a commonly observed phenomenon in bearings that imposes a highly localized subsurface volume to a complex triaxial and non-proportional fatigue loading. Case-hardened M50-NiL steel, a widely used aerospace bearing material, when subjected to RCF loading shows a definite increase in hardness within the localized RCF-affected zone as a function of cycles. To simulate such cyclic hardening material response during RCF using finite element (FE) modeling, knowledge of localized cyclic hardening properties of bearing steels is required. However, these properties are not available for through-hardened and case hardened steels nor are they readily measurable from the conventional bulk specimen testing methods used in high cycle fatigue. To overcome this challenge, an alternative method to evaluate the material-specific localized cyclic hardening properties as a function of case-layer depth is presented. This method uses the experimentally measured increase in micro-hardness within the RCF-affected zone, in conjunction with elastic–plastic FE simulation of RCF cyclic hardening, to extract localized cyclic constitutive properties, and investigate the underlying physics associated with the local hardness increase. Case hardened bearing steels are complex composites having a heterogeneous graded microstructure with carbide precipitates ranging from nanometer to micrometer length scales that are largely responsible for the material hardening. Micro-plastic strain accumulation via ratcheting at the scale of the carbide microstructure is proposed to be the underlying mechanism for cyclic hardening. This manuscript presents for the first time a procedure to estimate microstructure-sensitive isotropic and kinematic cyclic hardening parameters, from a judicious combination of numerical and experimental methods. Methods presented are applicable to both through-hardened and case hardened bearing steels.

The Influence of Fatigue Loading on the Microstructure of an Austenitic Stainless Steel

Abstract The rotation of principal stress/strain axes, which takes place under conditions of non-proportional fatigue loading, may significantly worsen the fatigue life. An explanation of this phenomenon can be found through microstructure examination. In this paper, we present the results of a microstructure examination of a X5CrNi18-10 steel subjected to fatigue loading, both, proportional and non-proportional. The variability of the positions of the principal stress axes was controlled by a fatigue loading program that consisted of alternatively realised blocks of torsion and tension-compression. The microscopic investigations were carried out by X-ray structural analysis and the micro-hardness of the material was examined. The results revealed that the application of cyclic loading caused a plasticity-induced martensitic transformation. Comparative analysis showed that the transformation depended on intensity and the kind of applied loading.

A new non-local criterion in high-cycle multiaxial fatigue for non-proportional loadings

The objective of the present paper consists in evaluating the fatigue reliability of a railway wheel subject to multiaxial non-proportional fatigue loading. For this purpose, a combined traction/torsion loading has been considered and the endurance curve has been reported in terms of both load factor and von Mises maximum stress as a function of the number of cycles to failure. Based on fracture surface observations, a new non-local approach, using the effective normal stress and the effective shear stress, is proposed. Finally, a comparison between experimental results and theoretical prediction demonstrates that the proposed criterion gives us satisfactory results.

Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading

A new mixed-mode threshold stress intensity factor is developed using a critical plane-based multiaxial fatigue theory and the Kitagawa diagram. The proposed method is a nominal approach since the fatigue damage is evaluated using remote stresses acting on a cracked component rather than stresses near the crack tip. An equivalent stress intensity factor defined on the critical plane is proposed to predict the fatigue crack growth rate under mixed-mode loading. A major advantage is the applicability of the proposed model to many different materials, which experience either shear or tensile dominated crack growth. The proposed model is also capable to nonproportional fatigue loading since the critical plane explicitly considers the influence of the load path. The predictions of the proposed fatigue crack growth model under constant amplitude loading are compared with a wide range of fatigue results in the literature. Excellent agreements between experimental data and model predictions are observed.

Elastic–plastic FE analysis of a notched cylinder under multiaxial nonproportional fatigue loading with variable amplitudes

This paper presents an elastic–plastic finite element (FE) analysis of an axisymmetric circular cylinder with a circumferential notch subject to multiaxial nonproportional fatigue loading with variable amplitudes. The von Mises yield criterion and the linear kinematic hardening rule of Prager–Ziegler are applied to describe the elastic–plastic material behavior. Two different loading combinations are considered: (1) constant tension with variable amplitude torsion; (2) variable amplitude tension with variable amplitude torsion. Numerical results for the local stress–strain curves at the notch-root are presented and discussed.