Crack path evaluation on HC and BCC microstructures under multiaxial cyclic loading

In this paper the multiaxial loading path effect on the fatigue crack initiation, fatigue life and fracture surface topology are evaluated for two different crystallographic microstructures (bcc and hc): high strength low-alloy 42CrMo4 steel and the extruded Mg alloy AZ31B-F, respectively.A series of multiaxial loading paths were carried out in load control, smooth specimens were used. Experimental fatigue life and fractographic results were analyzed to depict the mechanical behavior regarding the different microstructures.A theoretical analysis was performed with various critical plane models such as the Fatemi–Socie, SWT and Liu in order to correlate the theoretical estimations with the experimental data. A new approach based on maximum stress concentration factors is proposed to estimate the crack initiation plane, estimations from this new approach were compared with the measured ones with acceptable results. To implement this new approach a virtual micro-notch was considered using FEM. Moreover, the multiaxial loading path effect on stress concentration factors is also studied. The obtained results clearly show the effect of the applied load conditions on local microstructures response.     

Experimental and numerical study on crack initiation under fretting fatigue loading

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.     

Long life fatigue under multiaxial loading

A life prediction model in the field of high-cycle (i.e. long-life) fatigue is presented in this paper. The proposed model applies in the case of constant amplitude multiaxial proportional and non-proportional loading. The problems of the fatigue limit criterion and of the fatigue life prediction are both addressed and comparisons with experimental data are shown. Some limited discussion of the stress gradient effect is also offered. Although the particular model developed here is better suited for ferritic steels, it is explained in the paper that the methodology used to obtain this model can be adequately adapted to derive mathematically consistent models for other classes of metallic materials.     

Short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading

A short crack model originally proposed for multiaxial constant amplitude loading is extended and applied to multiaxial variable amplitude loading. Load sequences have a significant influence on variable amplitude life; they are taken into account using algorithms originally proposed only for uniaxial loading. The estimated fatigue lives of unnotched tubular specimens and notched shafts under different in- and out-of-phase multiaxial constant and variable amplitude load histories are compared with the experimental results. The comparison reveals that the proposed short crack approach enables sufficiently accurate estimation. Moreover, the estimated critical planes, i.e., the planes of maximum crack growth rate or minimum life, are in good agreement with the experimental observations.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 10⁷ cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.     

Extension of the Tanaka-Mura model for fatigue crack initiation in thermally cut martensitic steels

A multi scale numerical approach for evaluation of crack initiation and propagation in thermally cut structural elements made of martensitic steel is presented. A numerical simulation of micro-crack initiation is based on the Tanaka-Mura micro-crack nucleation model, where individual grains of synthetic microstructure are simulated using the Voronoi tessellation. Three improvements are added to this model (multiple slip bands, micro-crack coalescence and segmented micro-crack generation). Crack propagation is then solved on a macro scale model using linear elastic fracture mechanics approach. Some experimental tests have also been performed to check the accuracy of the numerical model. The results of the proposed computational model show a reasonable correlation with the experimental results.     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

Comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials

Fatigue damage prediction under a general multiaxial service loading consists of three main steps: multiaxial cycle counting, damage evaluation for an identified cycle (or reversal), and damage accumulations. The accuracy of fatigue life predictions depends on all the above steps. This paper reviews the evolutions of various multiaxial fatigue damage models, a comparative study is conducted about the physical basis, the computational efficiency, and the application range of the approaches. Based on the comparative studies, a new procedure is proposed to evaluate fatigue damage under general multiaxial random loading, which uses the Wang and Brown´s multiaxial cycle counting method for identifying cycles (or reversals), the modified procedure of the minimum circumscribed ellipse (MCE) approach for fatigue damage evaluation for an identified cycle (or reversal), and the Miner´s linear damage law for fatigue damage accumulations. By comparisons of the predicted life results with experimental results and with other approaches, it is shown that the proposed procedure is very efficient and suitable for computer aided structural optimization against fatigue.     

Crack initiation in VHCF regime on forged titanium alloy under tensile and torsion loading modes

This paper is focused on the VHCF behavior of aeronautical titanium alloy under tensile and torsion fatigue loadings. Tensile tests were carried out with two different stress ratios: R = −1 and R = 0.1. Both surface and subsurface crack initiations were observed. In the case of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R = 0.1, have shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation mechanism in presence of positive mean stress. Like for the tensile results, surface and subsurface crack initiations were observed under ultrasonic torsion in spite of the maximum shear stress location on the specimen surface. But the real reason for the subsurface crack initiation under torsion was not found.     

Remarks on multiaxial fatigue limit criteria based on prismatic hulls and ellipsoids

This paper focuses on a class of multiaxial fatigue limit criteria where the equivalent shear stress amplitude is calculated by means of a scalar measure associated with a hypersurface enclosing the deviatoric stress history at a material point. We consider two hypersurfaces proposed by the authors, namely the maximum prismatic hull and the minimum Frobenius norm ellipsoid. Previous results obtained with elliptic and non-elliptic stress paths strongly suggested that such measures might always be the same. In this work we consider two counter-examples which show that these approaches are distinct. Fatigue limit criteria based on the linear combination of these measures with the maximum hydrostatic stress were applied to experimental data including: axial–torsional, biaxial tension and plane stress tests performed under harmonic and non-harmonic, synchronous and asynchronous waveforms. The predictions for both criteria fell within a 15% scatter band.     

Numerical modelling of fatigue crack initiation and growth of martensitic steels

This paper presents a numerical simulation of micro‐crack initiation that is based on Tanaka‐Mura micro‐crack nucleation model. Three improvements were added to this model. First, multiple slip bands where micro‐cracks may occur are used in each grain. Second improvement deals with micro‐crack coalescence by extending existing micro‐cracks along grain boundaries and connecting them into a macro‐crack. The third improvement handles segmented micro‐crack generation, where a micro‐crack is not nucleated in one step like in Tanaka‐Mura model, but is instead generated in multiple steps. High cycle fatigue testing was also performed and showed reasonably good correlation of proposed model to experimental results. Because numerical model was directed at simulating fatigue properties of thermally cut steel, edge properties of test specimens were additionally inspected in terms of surface roughness and micro‐structural properties.     

FML full scale aeronautic panel under multiaxial fatigue: Experimental test and DBEM Simulation

This paper concerns the numerical and experimental characterization of the static and fatigue strength of a flat stiffened panel, designed as a Fibre Metal Laminate (FML) and made of aluminium alloy and Fibre Glass FRP. The panel is full scale and was tested under both static and fatigue bi-axial loads, applied by means of an in house designed and built multiaxial fatigue machine. The strain gauge outcomes from a preliminary static test are compared with the corresponding numerical results, getting a satisfactory correlation. A crack propagation in the FML is simulated by a two dimensional original approach based on the Dual Boundary Element Method (DBEM). To overcome the lack of experimental information on the size of delamination area an “inverse” procedure is applied: the delamination introduced in the DBEM model is calibrated in such a way to minimise the numerical and experimental growth rate differences.This approach aims at providing a general purpose evaluation tool for a better understanding of the fatigue resistance of FML panels, providing a deeper insight into the role of fibre stiffness and of delamination extension on the Stress Intensity Factors. The experimental test was realized in the context of a European research project (DIALFAST).     

A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading

There is increasing demand for analytical methods that estimate the fatigue life of engineering components and structures with a high degree of accuracy. The fatigue life is determined by the stress–strain sequences at the critical locations. Therefore, these sequences have be calculated with sufficient accuracy for arbitrary nonproportional cyclic loading. Based on the experience with a variety of material models following macroscale continuum mechanics approaches, an improved set of constitutive equations is proposed. The stress–strain behaviour of a commercial structural steel has been investigated experimentally. Firstly, the results of this experimental study serve to identify the material parameters comprised in the model. Secondly, the predicted stress–strain paths are compared to their experimentally determined counterparts as well as to paths predicted by other models. The overall accuracy of the proposed model is quite satisfying, especially as far as calculated amplitudes are concerned.     

Crack initiation and propagation in torsional fatigue of circumferentially notched steel bars

Circumferentially notched bars of austenitic stainless steel, SUS316L, and carbon steel, SGV410, with three different notch-tip radii were fatigued under cyclic torsion without and with static tension. The torsional fatigue life of SUS316L was found to increase with increasing stress concentration under the same nominal shear stress amplitude. Electrical potential monitoring revealed that the crack initiation life decreased with increasing stress concentration, while the crack propagation life increased. This anomalous notch-strengthening effect was ascribed to the larger retardation of fatigue crack propagation by sliding contacts of fracture surfaces. The superposition of static tension on cyclic torsion causes notch weakening. The notch-strengthening effect in torsional fatigue was not found in carbon steels, SGV410. The difference in the crack path of small cracks near notch root between stainless steel and carbon steel gives rise to the difference in the notch effect in torsional fatigue. The factory-roof shape observed on fracture surfaces of SUS316L became finer with higher stress amplitude and for sharper notches. The superposition of static tension makes the factory-roof shape less evident. Under higher stresses, the fracture surface was smeared to be flat. The fracture surfaces of SGV410 became smoother with increasing stress amplitude and notch acuity. The three-dimensional feature of fracture surfaces clearly showed the difference of the topography of fracture surfaces. The topographic feature was closely related to the amount of retardation of crack propagation due to the sliding contact of fracture surfaces.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.