An investigation of the mechanical fatigue behavior of low thermal expansion lattice structures

A study of the mechanical fatigue behavior of a Ti–6Al–4V lattice structure designed to exhibit controlled thermal expansion has been performed. Comparison of S–N curves generated under both zero-tension and fully reversed cyclic loading has determined that the fatigue resistance of the lattice is substantially poorer than that of the constituent Ti–6Al–4V material for the same remote applied (macroscopic) stress. In addition, the effect of beta annealing the as-received mill-annealed alloy was also to reduce fatigue life in both the lattices and parent material. This effect is due to significant microstructural changes that occurred during heat treatment. Increasing the stress ratio (σ_min/σ_max) of the cyclic waveform from −1 to 0 had a similar effect. An analytical model has been developed to predict the fatigue life of the lattice structures from the S–N curves of the parent material, by determining the relationship between the macroscopic stresses acting on the lattice structure and the local stresses. The local stresses were then used in a multiaxial fatigue model to determine the fatigue life. The analytical model is able to predict the fatigue life with reasonable accuracy and minimal cost. The Findley multiaxial fatigue parameter for the parent material and lattice structures can be fitted with a power law equation and appears to fall onto a single curve, suggesting the local behavior within the lattice material is similar to the parent material. The analytical tools developed in this study can be hugely beneficial to the design of these lattice structures in the aerospace and communications industries.     

Reprint of “Multiaxial fatigue property of Ti–6Al–4V using hollow cylinder specimen under push-pull and cyclic inner pressure loading”

This paper studies a multiaxial fatigue crack mode and a fatigue life of Ti–6Al–4V. Load controlled fatigue tests at room temperature were carried out using a hollow cylinder specimen under multiaxial loading with principal stress ratio λ equal to 0, 0.4, 0.5 and 1.0 and loading ratio R kept constant and equal to 0. λ is defined as λ = σ₂/σ₁, where σ₁ and σ₂ are maximum and intermediate/minimum principal stresses, respectively. Here, the test at λ = 0 is a uniaxial loading test and that at λ = 1.0 an equi-biaxial loading test. A testing machine employed was a newly developed multiaxial fatigue testing machine which can apply push-pull and reversed torsion loading with inner pressure into the hollow cylinder specimen. Based on the obtained results in this study, multiaxial fatigue properties are examined, where the fatigue life evaluation and the crack mode are discussed. The fatigue life is reduced with an increase of λ, due to cyclic ratcheting and crack mode in multiaxial loading. The crack mode is also affected by the surface condition resulting from cut-machining.     

Multiaxial fatigue property of Ti–6Al–4V using hollow cylinder specimen under push-pull and cyclic inner pressure loading

This paper studies a multiaxial fatigue crack mode and a fatigue life of Ti–6Al–4V. Load controlled fatigue tests at room temperature were carried out using a hollow cylinder specimen under multiaxial loading with principal stress ratio λ equal to 0, 0.4, 0.5 and 1.0 and loading ratio R kept constant and equal to 0. λ is defined as λ = σ₂/σ₁, where σ₁ and σ₂ are maximum and intermediate/minimum principal stresses, respectively. Here, the test at λ = 0 is a uniaxial loading test and that at λ = 1.0 an equi-biaxial loading test. A testing machine employed was a newly developed multiaxial fatigue testing machine which can apply push-pull and reversed torsion loading with inner pressure into the hollow cylinder specimen. Based on the obtained results in this study, multiaxial fatigue properties are examined, where the fatigue life evaluation and the crack mode are discussed. The fatigue life is reduced with an increase of λ, due to cyclic ratcheting and crack mode in multiaxial loading. The crack mode is also affected by the surface condition resulting from cut-machining.     

Multiaxial fatigue assessment of welded joints – Recommendations for design codes

In the assessment of welded joints submitted to multiaxial loading the calculations method applied, independently of the concept (nominal, structural, hot-spot or local), must consider primarily the materials ductility. While proportional loading can be assessed by von Mises, the principal stress hypothesis, the Findley method or the Gough–Pollard relationship, using any of the mentioned concepts, difficulties occur when the loading is non-proportional, i.e. the principal stress (strain) direction changes. This causes a significant fatigue life reduction for ductile steel welds, but an indifferent behaviour for semi-ductile aluminium welds. This different response to non-proportional loading can be assessed when ductility related mechanisms of fatigue failures, i.e. the mean value of plane oriented shear stresses for ductile materials and a combination of shear and normal stresses for semi-ductile materials, are properly considered.However, as these methods require a good expertise in multiaxial fatigue, for design codes used by non-fatigue experts, simpler but sound calculation methodologies are required. The evaluation of known fatigue data obtained with multiaxial constant and variable amplitude (spectrum) loading in the range N > 10⁴ cycles suggests the application of the modified interaction algorithm of Gough–Pollard. In the case of variable amplitude loading, constant normal and shear stresses are replaced by modified reference normal and shear stresses of the particular spectrum. The modification of the reference stresses is based on the consideration of the real Palmgren–Miner damage sum of D_PM = 0.5 (for spectra with constant mean loads) and the modification of the Gough–Pollard algorithm by consideration of the multiaxial damage parameter D_MA = 1.0 or 0.5, which is dependent on the material’s ductility and on whether the multiaxial loading is proportional or non-proportional. This method is already part of the IIW-recommendations for the fatigue design of welded joints and can also be applied by using hot-spot or local stresses.     

Transverse crack growth behavior considering free-edge effect in quasi-isotropic CFRP laminates under high-cycle fatigue loading

The high-cycle fatigue characteristics focused on the behavior of the transverse crack growth up to 10⁸ cycles were investigated using quasi-isotropic carbon fiber reinforced plastic (CFRP) laminates whose stacking sequence was [−45/0/45/90]_s. To assess the fatigue behavior in the high-cycle region, fatigue tests were conducted at a frequency of 100 Hz in addition to 5 Hz. In this study, to evaluate quantitative characteristics of the transverse crack growth in the high-cycle region, the energy release rate considering the free-edge effect was calculated. Transverse crack growth behavior was evaluated based on a modified Paris law approach. The results revealed that transverse crack growth was delayed under the test conditions of the applied stress level of σ_max/σ_b = 0.2.     

Effect of stress ratios on tension–tension fatigue behavior and micro-damage evolution of basalt fiber-reinforced epoxy polymer composites

The tension–tension fatigue behavior and damage mechanism of basalt fiber-reinforced epoxy polymer (BFRP) composites at different stress ratios are studied in this paper. The fatigue experiments were performed under stress ratios, R?=?σ_min/σ_max of 0.1 and 0.5, while the lifetime and the stiffness degradation were monitored and analyzed to investigate the effect of stress ratios. The damage propagation during fatigue loading was periodically monitored by using an in situ scanning electron microscope (SEM). The results show that the fatigue life decreases and the fatigue life degradation rate increases with the decrease of stress ratio for examined BFRP composites. The stiffness degradation is also sensitive to different stress ratios, showing a greater stiffness loss before failure at lower stress ratio. From the SEM images, it is indicated that the micro-damage mode shifts from interface debonding and matrix cracking into fiber breaking with decreasing stress ratios.     

Influence of load ratio on the biaxial fatigue behaviour and damage evolution in glass/epoxy tubes under tension–torsion loading

An extensive experimental campaign was carried out to understand the influence of the multiaxial stress state and load ratio on the matrix-dominated damage initiation and evolution in composite laminates under fatigue. Tubular glass/epoxy specimens were tested under combined tension–torsion loadings with different values of the load ratio and biaxiality ratio (shear to transverse stress ratio). Results are reported in terms of S–N curves for the first crack initiation and Paris-like diagrams for crack propagation, showing a strong influence of both parameters. Fracture surfaces were also analysed to identify the damage mechanisms at the microscopic scale responsible for the initiation and propagation of transverse cracks. Eventually, a crack initiation criterion presented by the authors in a previous work is applied to the experimental data showing a good agreement.     

Influence of casting defect and SDAS on the multiaxial fatigue behaviour of A356-T6 alloy including mean stress effect

The effect of mean stress on the multiaxial High Cycle Fatigue (HCF) behaviour of cast A356-T6 alloy containing natural and artificial defects with varying Secondary Dendrite Arming Spacing (SDAS) has been investigated experimentally. Tension, torsion and combined tension–torsion fatigue tests have been performed for two loading ratios: R_σ = 0 and R_σ = −1. A Scanning Electron Microscopy (SEM) was used to perform fractographic analysis of the fracture surfaces to characterise the defect causing failure. In order to gauge the effect of mean stress and defects, the results are reported with standard Kitagawa and Haigh diagrams. A surface response method has been employed to characterise the influence of defect size and SDAS on the fatigue limit. Relationships and correlations describing the observed behaviour have been incorporated in the Defect Stress Gradient (DSG) criterion with the goal of determining the influence of defects on the fatigue limit through a stress gradient approach.Results clearly show that: (i) the mean stress has a detrimental effect on the fatigue limit. This effect is a function of the loading, which is most pronounced under tension, less under combined tension–torsion, and least pronounced under torsion conditions; (ii) in the absence of defects, the SDAS controls the fatigue limit of cast A356, this effect is much more important under torsion loading; (iii) the DSG criterion is improved by the mean of a parameter describing the microstructure effect through the SDAS.     

The Modified Wöhler Curve Method applied along with the Theory of Critical Distances to estimate finite life of notched components subjected to complex multiaxial loading paths

This paper is concerned with the use of the Modified Wöhler Curve Method (MWCM) applied in conjunction with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of mechanical components subjected to multiaxial cyclic loading and experiencing stress concentration phenomena. In more detail, our engineering approach takes as its starting point the idea that accurate estimates can be obtained by simply assuming that the value of the critical length, L_M, to be used to evaluate fatigue damage in the medium–cycle multiaxial fatigue regime is a function of the number of cycles to failure, N_f. In other words, the MWCM, which is a bi‐parametrical critical plane approach, is suggested here to be applied by directly post‐processing the linear‐elastic stress state damaging a material point whose distance from the notch tip increases as N_f decreases. According to the main feature of the TCD, the above L_M versus N_f relationship is assumed to be a material property to be determined experimentally: such an hypothesis results in a great simplification of the fatigue assessment problem because, for a given material, the same critical length can be used to estimate fatigue damage independent of the considered geometrical feature. The accuracy of the devised approach was checked by analysing about 150 experimental results we generated by testing V‐notched cylindrical samples made of a commercial cold‐rolled low‐carbon steel. The above specimens were tested under in‐phase and out‐of‐phase combined tension and torsion, considering the damaging effect of superimposed static stresses as well. Moreover, in order to better check its accuracy in assessing notched components subjected to complex loading paths, our method was also applied to several data sets taken from the literature. This extensive validation exercise allowed us to prove that the MWCM applied along with the TCD is successful in estimating medium‐cycle multiaxial fatigue damage (N_f values in the range 10⁴–10⁶), resulting in predictions falling within the widest scatter band between the two used to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that the proposed approach predicts multiaxial fatigue lifetime by post‐processing the linear elastic stress fields in the fatigue process zone: this makes our method suitable for being used to assess real components by performing the stress analysis through simple linear‐elastic FE models.     

Flexural fatigue failures and lives of Eco-Core sandwich beams

Eco-Core is a class of syntactic foam made from small volume of high char yield binder and large volume of a class of flyash for fire resistance application. Very little or no flexural fatigue data of this class of core material is reported in the open literature. This paper presents a flexural fatigue response of Eco-Core in a glass/vinyl ester composite face sheet sandwich beam. A four-point loaded flexural test specimen was designed and tested in static and fatigue loadings to cause tension failure in the core. The fatigue test was conducted at maximum cyclic stress (σ_max) ranged from 0.7σ_ct to 0.9σ_ct, where σ_ct is the static flexural strength of the core. The sinusoidal loading frequency of 2 Hz with the stress ratio of 0.1 was used. Flexural fatigue failure modes of Eco-Core sandwich beam were classified: damage onset (single tension crack), damage progression (multiple tension cracks) and ultimate failure (a combination of tension and shear). These failures were characterized by 1%, 5% and 7% changes in compliance that corresponds to N_1%, N_5% and N_7% lives. The fatigue stress-life (S–N) relationship was found to follow the well-known power law equation, σ_max/σ_ct = A_oN^α. The constants A_o and α were established for all three types of failures. The endurance limit was established based on 1 million cycles limit and it was found to be 0.65σ_ct, 0.70σ_ct and 0.71σ_ct, respectively for the three modes of failure. Flexural fatigue and static failure modes of Eco-Core sandwich beams were similar.     

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

Abstract

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σ_ref/σ_y) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σ_ref/σ_y<<1.     

Multiaxial fatigue behaviour of AA6068 and AA2017A aluminium alloys under in‐phase bending with torsion loading condition

This paper presents an analysis of the multiaxial fatigue properties of two selected aluminium alloys. Several experimental results were used to perform the analysis e.g. the latest experimental results done in Opole University of Technology on PA6 (2017 A), PA4 (6068) under bending, torsion, and combined bending with torsion. Analyses of the results were done to find similarities of the multiaxial fatigue behaviour of selected aluminium alloys. Based on the (σ_a – τ_a) curves, prepared for a fixed number of cycles, it was possible to show some tendencies of the multiaxial fatigue behaviour of selected material group. This is an important indicator while selecting proper multiaxial fatigue failure criterion suitable to perform fatigue life assessment of aluminium alloys.     

Fatigue strength of the Cu/Si interface in nano-components

The fracture behavior of the Cu/Si interface in a nano-cantilever specimen with a 200 nm-thick Cu film (Specimen-200), which possesses a nanometer-scale strain-concentrated region, is examined under a cyclic bending load. The fatigue strength is around GPa level owing to the high yield stress of the Cu nano-film and the deformation constraint associated with the neighboring hard materials. The S-N curve shows clear dependence of fatigue life on the applied stress in the high-stress range, Δσ. Specimens with a 20 nm-thick Cu film (Specimen-20) are also investigated for comparison. The stress range in the fatigue fracture of Specimen-20 is higher than that of Specimen-200 for the same fatigue life. However, there is good coincidence in the Δσ/σ_s (σ_s: strength in monotonic load) vs. N_f (number of cycles to fracture) at high Δσ. The S-N curves suggest the existence of a fatigue threshold (Δσ_w) at low Δσ. The ratio of fatigue limit to the fracture stress in a monotonic loading, Δσ_w/σ_s, is large compared with the magnitude of bulk metal, which suggests the brittle behavior of the interface. Moreover, the fatigue limits have good coincidence with their yield stresses.     

Fatigue failure modes of rib-to-deck joints under the multiaxial stress states caused by various wheel loading characteristics

Orthotropic steel bridge decks (OSBDs) are characterized by overall structural asymmetries and severe local stress concentrations; meanwhile, complicated service loadings always cause relevant rib-to-3deck (RD) welded joints in multiaxial stress states. Under such circumstances, a full-scale OSBD model was established. Six loading cases were applied, and the multiaxial fatigue deviation was calculated to represent the multiaxial stress state of the bridge deck. Based on the effective traction structural stress method, the most unfavorable loading case for the failure mode of the RD joint under a multiaxial stress state was analyzed, and the failure mode transition in the process of wheel load movement was discussed. The results indicated that the fatigue failure mode of the RD joint was determined by the transverse loading locations. In-between-rib loading can cause the initiation of toe-rib cracks. Cracks are prone to occur under over-rib loading and riding-rib loading, and the arrangement of diaphragms can increase the risk that the fatigue crack originates from the weld root.     

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

In engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter Γ_T is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.     

Fatigue life estimation under multiaxial random loading by means of the equivalent Lemaitre stress and multiaxial S–N curve methods

In this paper, the frequency domain formula of equivalent Lemaitre stress taking into account the hydrostatic stress effect is first introduced, and the corresponding method for estimating fatigue life under multiaxial random loading is developed based on multiaxial S–N curve. The proposed method is systematically validated with the random bending-torsion fatigue tests and numerical simulations. It has been shown that the hydrostatic stress has a significant influence on multiaxial fatigue life; the results predicted by the proposed method agree well with the experiment, and are more accurate than those obtained for the equivalent von Mises stress method.     

A notch multiaxial-fatigue approach based on damage mechanics

The fatigue assessment of structural components under complex multiaxial stresses (cyclic or random stress histories) can be conveniently tackled by means of damage mechanics concepts. In the present paper, a model for notch fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which quantifies the damage accumulation in the material up to the final failure. The material collapse can be assumed to occur when the damage is complete, that is, when the parameter D reaches the unity. In the case of notched structural components, such a damage parameter D must be evaluated by taking into account the stress value as well as the gradient effect at the notch root. The proposed model, which also employs the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, is calibrated through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some uniaxial or complex stress histories. The model presents the advantages to be mechanically based and to not require any evaluation of a critical plane and any loading cycle counting algorithm to determine the fatigue life.     

Thermomechanical fatigue of titanium aluminides

This paper reviews the thermomechanical fatigue (TMF) studies performed on various titanium aluminide (TiAl) alloys during the last decade in the research group of one of the authors (H.-J. Christ). The investigated alloys are Ti–47Al–2Mn–2Nb (XD), Ti–46Al–4(Cr, Nb, Ta, B) (γ-MET), Ti–45Al–5Nb–0.2C–0.2B (TNB-V5) and Ti–45Al–8Nb–0.2C (TNB-V2). An interesting result of this comparison is that the materials, though different in chemical compositions, yield comparable TMF behaviour. It can be demonstrated that both out-of-phase (OP) and in-phase (IP) TMF life depend on mean stress σ_m, which is primarily determined by the temperature-strain phasing, but also strongly affected by total strain amplitude Δε/2, maximum temperature T_max and temperature interval ΔT – highest mean stresses (i.e. compressive σ_m in the case of IP-TMF, tensile σ_m for OP-TMF) resulted in lowest TMF lives. Furthermore, the investigation reveals that the ratio between IP and OP fatigue lives under corresponding conditions can be expressed as a function of the temperature range ΔT. At low values of ΔT the ratio is rather small because the material’s fatigue behaviour approaches isothermal conditions. Higher strain and temperature amplitudes result in very high ratios between IP and OP lives. The influence of cyclic hardening at low temperature during IP-TMF applying a very large ΔT seems to reduce the fatigue life ratio again, because of the rather high stress amplitude established.     

Fatigue life assessment under a complex multiaxial load history: an approach based on damage mechanics

In order to assess the fatigue behaviour of structural components under a complex (cyclic or random) multiaxial stress history, methods based on damage mechanics concepts can be employed. In this paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which allows us to determine the damage accumulation up to the final failure of the material. By introducing an evolution equation for the endurance function, the final collapse can be assumed to occur when the damage D is complete, that is when D reaches the unity. The parameters of this model, which adopts the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, are determined through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some complex stress histories. With respect to traditional approaches to multiaxial fatigue assessment, the proposed model presents the following advantages: (1) the evaluation of a critical plane is not necessary; (2) no cycle counting algorithm to determine the fatigue life is required, because it considers the progressive damage process during the fatigue load history; (3) the model can be applied to any kind of stress history (uniaxial cyclic loading, multiaxial in‐phase or out‐of‐phase cyclic loading, uniaxial or multiaxial random loading).     

High temperature fatigue deformation behaviors of thermally sprayed steel measured with electronic speckle pattern interferometry method

High temperature fatigue (R=0) damage and deformation behaviors of SUS304 steel thermally sprayed with Al₂O₃/NiCr coating were investigated using an electronic speckle pattern interferometry (ESPI) method. Surface cracks and delamination occurred after 1×10⁵ cycles test when σ_max was 202 MPa at 873 K. The lengths and number of cracks and delamination largely decreased when σ_max or temperature decreased to 115 MPa or 573 K, respectively. Strain values along cracks measured with the ESPI method were much larger than other areas due to crack opening under the tensile load. The positions of strain concentration zones on strain distribution figures by ESPI method were well corresponded to those of cracks on sprayed coatings. Strain values decreased largely where local delamination occurred.