History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

Three-dimensional mixed-mode fatigue crack growth in a functionally graded titanium alloy

The implementation of unitized structure in the aerospace industry has resulted in complex geometries and load paths. Hence, structural failure due to three-dimensional mixed-mode fatigue crack growth is a mounting concern. In addition, the development of functionally graded materials has further complicated structural integrity issues by intentionally introducing material variability to create desirable mechanical behavior. Ti-6Al-4V β-STOA (solution treated over-aged) titanium is a functionally graded metallic alloy that has been tailored for superior fatigue crack growth and fracture response compared with traditional titanium alloys. Specifically, the near-surface material of Ti β-STOA is resistant to fatigue crack incubation and the interior is more resistant to fatigue crack growth and fracture. Therefore, Ti β-STOA is well suited for applications where surface cracking is a known failure mode. Advances in experimental testing have shown that complex loading conditions and multi-faceted materials can be tested reliably. In this paper, the authors will experimentally generate three-dimensional mixed-mode surface crack data in functionally graded Ti-6Al-4V β-STOA and comment on the effect of the material tailoring.     

The mixed-mode investigation of the fatigue crack in CTS metallic specimen

The experiments of a fatigue crack under mixed-mode loading are performed with CTS (Compact-Tension-Shear) specimens associated to a mixed mode loading device. The effect of loading angle on crack growth rate and on crack bifurcation angle is analyzed. Also, the welded specimens are introduced in the experiments in order to investigate the influence of the filled weld. In the fatigue tests, three loading angles, two loading levels and two materials are selected in the experiments. Furthermore, on the basis of the experimental data, a mixed-mode crack growth model is proposed in order to evaluate numerically a fatigue crack growth rate, in which the effects of the loading mode and of the residual stresses due to weld are considered. The validation of the model is carried out on CTS specimens under mixed mode loading.     

Very-high-cycle fatigue crack initiation and propagation behaviours of magnesium alloy ZK60

The aim of this paper is to assess the very-high-cycle fatigue (VHCF) behaviour of a magnesium alloy (ZK60). Results indicate that the fatigue crack initiates from an area consisting of many distributed facets, while the region of early crack propagation is characterised by parallel traces, based on a fractographic analysis. The significant differences in morphology around the crack initiation area result from the interaction between the deformation twinning and the plastic zone at the crack tip. In addition, the fatigue crack propagation rate around the crack initiation site is also estimated based on a modified Murakami model. It is found that the formation stage for the fatigue crack is of great importance to the fatigue failure mechanism in the VHCF regime.     

Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads

It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the retardation of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history. However, studies of the combined effect of mixed-mode I+II constant amplitude fatigue loadings and a mixed-mode I+II single overload on fatigue behavior are still scant. In this study, fatigue tests were conducted under mixed-mode I+II constant amplitude loadings with a mixed-mode I+II single overload, with reference to the variation of fatigue crack retardation. The formation of the overload plastic zone (OPZ) ahead of the crack tip under a mixed-mode I+II single overload is studied experimentally by the measurement of the shape and size of the OPZ. The behavior of fatigue crack propagation under mixed-mode loading conditions is examined by changing the loading mode of a single overload, and the relationship between the mixed-mode I+II single overload and the behavior of fatigue crack propagation in terms of the characteristics of the OPZ is evaluated. The empirical modeling of the fatigue life under mixed-mode I+II constant amplitude loadings is proposed by considering the characteristics of both the OPZ and the combination of the mode-mixity of mixed-mode I+II constant amplitude loadings and a mixed-mode I+II single overload.     

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.     

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.     

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.     

Computational analysis of mixed-mode fatigue crack growth in quasi-brittle materials using extended finite element methods

In the present paper an extended finite element method (XFEM) containing strong discontinuity within elements is introduced and implemented in the commercial general purpose software ABAQUS. The algorithm allows introducing a new crack surface at arbitrary locations and directions in elements. To consider fatigue crack nucleation and propagation in quasi-brittle materials the XFEM is combined with a cyclic cohesive model. Accumulative material damage is described by separate evolution equations. The crack path is completely independent of the mesh structure but determined by the mixed-mode loading cases. Numerical simulations illustrate the ability of this method to simulate fracture with unstructured meshes. The computational results agree with known fracture experiment data. Known fatigue observations can be predicted using the present model.     

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.     

Discussions of three-dimensional models for mixed-mode fatigue crack growth

This technical note discusses several three-dimensional models for mixed-mode fatigue crack growth that were developed recently by Bian and coauthors [1], [2], [3], [4] and [5]. However, these models are found being formulated from a generally incorrect three-dimensional crack-front stress field for embedded elastic elliptical cracks. The corresponding correct crack-front stress field for the elliptical cracks is thus presented, and then the three-dimensional fatigue crack growth models are corrected and expressed in much simpler functions.     

A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

The crack growth behavior after overloading on rotating bending fatigue

Most of the crack propagation behavior relating to the variable amplitude load is conducted in flat specimens such as centered-crack specimens or compact test specimens with various thicknesses. For that reason, it is also important to understand the crack growth behavior relating to the overload on other geometry which differs from the previous investigation. In the present study, the crack growth behavior after being overloaded was investigated on a solid round bar. It was found that the size of diameter influences the crack growth behavior. The retardation or acceleration depends on the residual stress state in front of the crack tip. If the residual stress state developing was compressive, retardation was observed, and if the tensile residual stress state developed, the acceleration of the crack occurred after overloading. In addition, the shape of the component has to be taken into consideration for evaluating fatigue life in association with the crack growth.     

Using fatigue crack propagation mechanism maps to predict changes in propagation mechanisms

The conditions determining the fatigue fracture mechanism in quenched and tempered steel are discussed with reference to fatigue crack propagation mechanism (FCPM) maps. Criteria for the change from one fatigue mechanism to another are presented.     

Elastic–plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low‐alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one‐sided sharp notch were used. The tests were performed under the stress ratios R=?1, ?0.5 and 0. The test results were described by the ΔJ‐integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ‐integral range.     

Effect of impact damage on fatigue performance of structures reinforced with GLARE bonded crack retarders

Fibre-Metal Laminates (FML) such as GLARE are of interest as bonded crack retarders (BCR) to improve the fatigue performance of aircraft structures. The degradation of the performance of the crack retarder in service if subjected to damage is a critical factor in designing with this concept. Bonded assemblies of an aluminium alloy substrate reinforced with a GLARE strap were prepared, and were subjected to low velocity impact damage onto the GLARE, with impact energies ranging from 10 to 60 J. The thermal residual stresses developed during the bonding process of the GLARE to the aluminium were determined using neutron diffraction, and the change in the thermal residual stresses owing to impact damage onto the GLARE was evaluated. Pre- and post-impact fatigue performance of the BCR assemblies has been investigated. The results show that the BCR provides an improvement in fatigue life, but the reduction is impaired following impact damage. The results show that monitoring of impact damage will be critical in the damage tolerance assurance for aerospace structures containing bonded crack retarders.     

Some comments on the Arcan mixed-mode (I/II) test specimen

Although the Arcan specimen has been used frequently for mixed-mode crack growth testing using single-axis servohydraulic test equipment, the specimen and its commonly-used fixturing have features and behaviors that have implications to the proper understanding of results garnered from their use. These implications extend to hardware issues as well, as the Arcan specimen (when mounted at off-axis angles) can generate significant and even potentially damaging side loads on the load frame actuator. This paper discusses a number of the issues associated with the Arcan specimen and Arcan testing.