Fatigue behavior of aluminum alloys under biaxial loading

The biaxiality effect, especially the effect of non-singular stress cycling, on the fatigue behavior was studied, employing cruciform specimens of aluminum alloys 1100-H14 and 7075-T651. The specimens, containing a transverse or a 45^o inclined center notch, were subjected to in-phase (IP) or 100% out-of-phase (hereinafter referred to as “out-of-phase or OP”) loading of stress ratio 0.1 in air. The biaxiality ratio λ ranged from 0 to 1.5, and 3 levels of stress were applied. It was observed that: (1) at a given λ, a lower longitudinal stress induced a longer fatigue life under IP and OP loading, and the fatigue life was longer under IP loading, (2) the fatigue crack path profile was influenced by λ, phase angle (0^o or 180^o), and initial center notch (transverse or 45^o inclined); (3) the fatigue crack path profiles, predicted analytically and determined experimentally, had similar features for the specimens with a transverse center notch under IP loading; and (4) the fatigue crack growth rate was lower and the fatigue life longer for a greater λ under IP loading, whereas it changed little with change in λ under OP loading. These results demonstrate that non-singular stress cycling affects the biaxial fatigue behavior of aluminum alloys 1100-H14 and 7065-T651under IP and OP loading.     

Sequentially linear analysis of fracture under non-proportional loading

Sequentially linear analysis avoids convergence problems typical of non-linear finite element analysis by directly specifying a damage increment instead of a load or displacement increment. A series of linear analyses is used to model highly non-linear behavior without an iterative solution algorithm. The primary contribution herein is the extension of sequentially linear analysis to non-proportional loading, through an algorithm which selects the critical integration point to which a damage increment is applied. An orthotropic cracking model is presented which parallels the traditional fixed smeared crack concept. The non-proportional modeling framework is demonstrated through simulation of experimental results and settlement damage to a masonry façade.     

Modelling of fatigue lifetime under non-proportional multiaxial alternating loading

This paper presents two approaches to lifetime prediction under non‐proportional multiaxial alternating loading; a phenomenological approach using the Manson–Coffin relation and a microstructural approach. Both models have in common the use of a new multiaxiality factor. The data sets for the adaptation and validation of both models are taken from the authors' own experiments. In these tests, both the load paths and the phase shift are varied. The biaxial test apparatus allows for an application of fixed principal stress or strain directions even under non‐proportional loading. A fairly good agreement with our multiaxial lifetime results is obtained with both models. For an advanced assessment of the quality of the approaches used, the models are compared with several other well‐known models from the literature. An additive yardstick is used for the comparison of the different models.     

Damages to conic specimens of titanium and aluminum alloys under impact loading

We present the results of experimental determination of the character of damage to specimens having the shape of truncated cones made of titanium VT14 and aluminum AMg6 alloys under impact loading and perform a numerical analysis of longitudinal stresses at the sites of formation of rear cleavage cracks.     

Failure of AA 6061 and 2099 aluminum alloys under dynamic shock loading

Microstructural aspects of the deformation and failure of AA 6061 and AA 2099 aluminum alloys under dynamic impact loading are investigated and compared with their responses to quasi-static mechanical loading in compression. Cylindrical specimens of the alloys, heat-treated to T4, T6 and T8 tempers, were subjected to dynamic compressive loading at strain rates of between 2800 and 9200 s⁻¹ and quasi-static compressive loading at a strain rate of 0.0032 s⁻¹. Plastic deformation under the dynamic impact loading is dominated by thermal softening leading to formation of adiabatic shear bands. Both deformed and transformed shear bands were observed in the two alloys. The shear bands offer preferential crack initiation site and crack propagation path in the alloys during impact loading leading to ductile shear fracture. While cracks propagate along the central region of transformed bands in AA 6061 alloy, the AA 2099 alloy failed by cracks that propagate preferentially along the boundary region between the transformed shear bands and the bulk material. Whereas the AA 2099 alloy shows the greatest propensity for adiabatic shear banding and failure in the T8 temper condition, AA 6061 alloy is most susceptible to formation of adiabatic shear bands and failure in the T4 temper. Deformation under quasi-static loading is dominated by strain hardening in the two alloys. Rate of strain hardening is higher for naturally aged AA 6061 than the artificially aged alloy, while the strain hardening rate for the AA 2099 alloy is independent of the temper condition. The AA 2099 alloy shows a superior mechanical behaviour under quasi-static compressive loading whereas the AA 6061 shows a higher resistance to impact damage.     

Damages to conic specimens of titanium and aluminum alloys under impact loading

We present the results of experimental determination of the character of damage to specimens having the shape of truncated cones made of titanium VT14 and aluminum AMg6 alloys under impact loading and perform a numerical analysis of longitudinal stresses at the sites of formation of rear cleavage cracks. Translated from Problemy Prochnosti, No. 5, pp. 110–112, September–October, 1997.     

Multiaxial fatigue of a railway wheel steel under non-proportional loading

The results of an experimental investigation of the multiaxial fatigue behaviour of the R7T steel are presented. The R7T steel is currently employed in the production of solid high-speed railway wheels. Wheel failures due to rolling contact fatigue may occur and, on some occasions, fatigue cracks nucleate in the sub-surface region under the contact area between wheel and rail. Here, the stress field is multiaxial and the loading path is non-proportional. Specimens extracted from the rim of railway wheels were subjected to combined out-of-phase alternating torsion and pulsating compressive axial loads, a non-proportional stress state which is similar to that observed under the contact area in the wheel rim. The tests results are discussed in the light of some multiaxial fatigue theories, chosen among those based on the critical plane concept and those implementing an integral approach, with the aim of selecting a fatigue criterion suitable for the sub-surface fatigue assessment of railway wheels.     

A design procedure for assessing low cycle fatigue life under proportional and non-proportional loading

This paper discusses the design assessment for structural components subjected to proportional and non-proportional loading. Multiaxial low cycle fatigue lives are influenced by stress and strain multiaxiality, their non-proportionality and a material property that relates to the degree of additional hardening. Many low cycle fatigue studies under proportional and non-proportional loading were carried out in laboratories, but a little study discussed the application of the results obtained in laboratories to an actual design for structural components. This paper proposes a fatigue life assessment for structural components subjected to proportional and non-proportional low cycle fatigue loading. The assessment provides a simple method for evaluating principal strain range, strain multiaxiality and strain non-proportionality. This paper also discusses low cycle fatigue parameters suitable for the life assessment of structural components subjected to multiaxial loading.     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

Fatigue life prediction of vulcanized natural rubber under proportional and non-proportional loading

To investigate the multiaxial fatigue properties of vulcanized natural rubber (NR), a series of tests including both proportional and non-proportional loading paths on small specimens were performed. The existing fatigue life prediction approaches are evaluated with life data obtained in the tests. It is shown that the equivalent strain approach presents a good prediction of the fatigue life although it has a certain shortcoming. Compared with the strain energy density (SED) model, the cracking energy density (CED) model represents the portion of SED that is available to be released by virtue of crack growth on a given material plane, so it gives better results in the life prediction. Some of the approaches based on critical plane which are widely used for metal fatigue are also tested in this paper, and the results show that the Chen-Xu-Huang (CXH) model gives a better prediction, compared with the Smith-Watson-Topper (SWT) and Wang–Brown (WB) model. A modified Fatemi–Socie's model has also been introduced, and the results show that the modified model can be used to predict the fatigue life of rubber material well.     

Characteristics of fatigue-crack resistance of aluminum alloys in combined modes of failure under biaxial loading

The article contains a complex quantitative evaluation of the effect of the state of stress and of the angle of orientation of the initial crack on its growth rate for eight aluminum alloys subjected to combined modes of biaxial extension. A new dimensionless parameter of fatigue-crack resistance is introduced and substantiated. It is established that there exists a single dependence of the crack growth rate on the suggested parameter for all the investigated aluminum alloys with different mechanical properties.Translated from Problemy Prochnosti, No. 3, pp. 28–36, March, 1994.     

Evaluation of a phenomenological elastic‐plastic approach for magnesium alloys under multiaxial loading conditions

Magnesium alloys are greatly appreciated due to their high strength to weight ratio, stiffness, and low density; however, they can exhibit complex types of cyclic plasticity like twinning, de‐twinning, or Bauschinger effect. Recent studies indicate that these types of cyclic plastic deformations cannot be fully characterized using the typical tools used in cyclic characterization of steels and aluminium alloys; thus, it is required new approaches to fully capture their cyclic deformation and plasticity. This study aims to propose and evaluate a phenomenological cyclic elastic‐plastic approach designed to capture the cyclic deformation of magnesium alloys under multiaxial loading conditions. Series of experimental tests were performed to characterize the cyclic mechanical behaviour of the magnesium alloy AZ31BF considering proportional loadings with different strain amplitude ratios and a nonproportional loading with a 45° phase shift. The experimental results were modulated using polynomial functions in order to implement a cyclic plasticity model for the AZ311BF based on the phenomenological approach proposed. Results show good correlations between experiments and estimates.     

Prediction of die casting process parameters by using an artificial neural network model for zinc alloys

Pressure die casting is an important production process. In pressure die casting, the first setting of process parameters is established through guess work. Experts use their previous experience and knowledge to develop a solution for a new application. Due to rapid expansion in the die casting process to produce better quality products in a short period of time, there is ever increasing demand to replace the time-consuming and expert-reliant traditional trial and error methods of establishing process parameters. A neural network system is developed to generate the process parameters for the pressure die casting process. The system aims to replace the existing high-cost, time-consuming and expertdependent trial and error approach for determining the process parameters. The scope of this work includes analysing a physical model of the pressure die casting filling stage based on governing equations of die cavity filling and the collection of feasible casting data for the training of the network. The training data were generated by using ZN-DA3 material on a hot chamber die casting machine with a plunger diameter of 60 mm. The present network was developed using the MATLAB application toolbox. In this work, the neural network was developed by comparing three different training algorithms: i.e. error backpropagation algorithm; momentum and adaptive learning algorithm; and Levenberg-Marquardt approximation algorithm. It was found that the Levenberg-Marquardt approximation algorithm was the preferred method for this application as it reduced the sum-squared error to a small value. The accuracy of the developed network was tested by comparing the data generated from the network with those of an expert from a local die casting industry. It was established that by using this network the selection of process parameters becomes much easier, so that it can be used by a novice user without prior knowledge of the die casting process or optimization techniques.     

Prediction of elastic properties of precipitation-hardened aluminum cast alloys

A methodology is proposed for predicting the elastic properties of precipitation-hardened alloys by combining different modeling techniques: the CALPHAD method, first-principles calculation, and elasticity models. The proposed procedure was applied to conventional aluminum cast alloys to predict their elastic moduli. The predicted Young’s moduli are in reasonable agreement with values reported in the literature, which verifies the potential applicability of the methodology to the development of high-stiffness aluminum cast alloys.     

On low cycle fatigue life of nickel-based superalloy valve membranes under non-proportional cyclic loading

A numerical model for low cycle fatigue damage analysis of valve membranes is presented in this paper. The isotropic and non-linear kinematic hardening laws of Lemaître–Chaboche, which define both the cyclic hardening and the ratchetting phenomenon, are adopted. The model for prediction of the number of cycles to crack initiation is based on a combination between Manson–Coffin relationship and Jiang–Sehitoglu fatigue parameter. The applied cyclic loading consists in a load pressure imposed to the internal face of the membrane and a vertical displacement of its hub section. The experimental results and numerical simulation predictions in terms of number of cycles to failure turned out to be in good concordance. Thus, numerical predictions are confirmed by microscopic observations made on membranes failed during testing.