Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

Significance of morphology changes at a propagating crack edge

During dynamic crack propagation, several distinct changes in the morphology of the dissipative region near the crack edge occur, and they have a pronounced influence on the main propagation mechanism. There are also distinct morphological differences between mode I and mode II. For mode I crack expansion, four successive generations of localization may be observed: micro-separations coalescing with the main crack, protruding clusters of micro-separations, micro-branches, and finally (macro-)branches. The region of localizations is increasing laterally from the main crack plane with crack growth and velocity, as it appears, because of high normal stresses in planes normal to the crack direction. If sufficient space is available, an expanding mode I crack accelerates to a constant velocity, which appears to prevail even after branching and multiple-branching. This indicates an amazing self-similarity over the four generations of localization. The morphology changes during crack propagation depend both on the magnitude of the applied load and on the travelled length of the crack edge. For mode II, the energy dissipation seems generally to be much more concentrated to the crack plane than for mode I. A main reason appears to be that normal stresses in planes normal to the crack direction are comparatively small in front of the crack. Therefore, strong micro-separation localizations seem to appear mainly in shear planes parallel with the crack plane. The appearance of such localizations may be analogous to the remarkable flow velocity gradient discontinuity discovered in turbulent shear flow near a wall.As a consequence of the apparently stronger concentration of the dissipative region to the crack plane, a mode II crack can reach higher velocities than a mode I crack, and it may even reach intersonic velocities.     

Evaluation of fatigue crack propagation by mode I and mixed mode in 1050 aluminium

The mechanism of mixed‐mode fatigue crack propagation was investigated in pure aluminum. Push‐pull fatigue tests were performed using two types of specimens. One was a round bar specimen having a blind hole, one was a plate specimen having a slit. The slit direction cut in the specimen was perpendicular or inclined 45 degrees relative to the centre of the specimen axis. In both cases, cracks propagated by mode I or by the mixed mode combining mode I and shear mode, depending on the testing conditions. In these cases the crack propagation rate was evaluated with a modified effective stress intensity factor range. Crack propagation retardation was observed in some specimens. However, it was found that the crack propagation rate could also be evaluated by the effective stress intensity factor range independent of the crack propagation mode.     

A REVIEW OF FATIGUE CRACK GROWTH IN STEELS UNDER MIXED MODE I AND II LOADING

The majority of methods for predicting the direction of propagation of mixed mode cracks have assumed that they branch to grow as mode I cracks. However, under some circumstances mode II crack growth occurs. Rolling contact fatigue cracks are one example of an industrial problem where cracks appear to grow under predominantly mode II loading without branching. This paper reviews the available models and the experimental studies in the literature on mixed mode I and II loading, and discusses the parameters that affect the mode of crack growth.     

Experimental study of I + III mixed mode fatigue crack transformation propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the mode transformation process. It is found that with the crack growth, I + III mixed mode changes to Mode I. Crack mode transformation is governed by the Mode III component and the transformation rate is a function of the relative magnitude of the Mode III stress intensity factor. However, even in the process of the crack mode transformation the fatigue crack propagation is controlled by the Mode I deformation.     

An examination of small fatigue crack morphology

Test results for the growth of a small corner crack under cyclic loading are presented. The number of grains that are crossed by the crack front ranges from about three to ten during the crack advance. Crack path profile measurements on the adjacent corner faces are presented. Also, a microscopic examination of the crack path morphology of a polished and etched surface that is adjacent to the corner reveals the presence of complex branching mechanisms, and localized regions of intensive damage. Examination of sub-surfaces reveals that though branching and localized damage are present, they diminish with increasing depth of the subsurface. It is concluded that during early growth, the crack surface deviates substantially from an idealized planar surface model, and that Modes I, II, and III are all operative.     

Characteristics of fatigue crack propagation behaviour as identified by hysteresis loop at the crack tip

Fatigue crack propagation tests have been carried out under various load conditions. Hysteresis loops denoting the relationship between load and strain at the crack tip are obtained by using local compliance measurement. Crack growth acceleration, delayed retardation and non‐propagation phenomena are investigated by considering the variation of hysteresis loop expansion and hysteresis loop tail. Based on the physical meaning of hysteresis loops, two types of crack closure are ascertained and the effect of crack closure on fatigue crack propagation is studied. Results show that change of the effective amplitude of the stress intensity factor at the crack tip is the reason that crack propagation rates vary.     

Path prediction of I + III mixed mode fatigue crack propagation

In this paper, compact tension specimens with tilted cracks under monotonic fatigue loading were tested to investigate I + III mixed mode fatigue crack propagation in the material of No. 45 steel with the emphasis on the propagation rate expression and the path prediction. It is found that during the mode transformation process, the crack propagation rate is still controlled by the mode I stress intensity factor; and Paris equation also holds for the relationship between and ΔK_I . Crack propagation path can be predicted only when both the crack mode transformation rate and propagation rate are available.     

Prediction of the crack extension under fretting wear loading conditions

Fretting is associated with small amplitude oscillatory movements between two surfaces in contact. One possible consequence of fretting is the formation and subsequent growth of cracks at the edges of the contact. This paper presents an experimental investigation of the cracking behaviour under fretting loading of two different aluminium alloys: 2024-T351 and 7075-T651. Systematic and controlled experiments with a cylinder-flat contact under partial slip fretting conditions were carried out. A model which combines both crack nucleation and propagation processes is used to predict the crack extension throughout the life of the component. The direction of crack propagation experimentally observed was taken into account by the model. Furthermore, an analytical prediction of crack nucleation based on the process volume approach is made. The predictions of both crack extension and nucleation are compared with the experimental results, and show good agreement.     

On crack paths

Crack paths are discussed from several different points of view. The remarkable reproducibility of crack paths, especially the frequent occurrence of straight cracks, is considered. The general dominance of mode I growth at mixed mode loading (via kinking or tilting of the crack edge) is examined, and it is shown that mode I growth can be suppressed by superposition of a high pressure. Mode I growth is scarcely combineable with mode II or III, because of different micromechanisms, whereas a mixture of modes II and III growth appears to be possible. Directional stability of straight crack paths is also analysed with special reference to the importance of a meaningful definition of the concept itself. Finally crack branching is briefly discussed.     

Shear mode fatigue crack growth in 1050 aluminium

The shear mode crack growth mechanism in 1050 aluminium was investigated using pre‐cracked specimens. A small blind hole was drilled in the centre section of the specimens in order to predetermine the crack initiation position, and a push–pull fatigue test was used to make a pre‐crack. Crack propagation tests were carried out using both push–pull and cyclic torsion with a static axial load. With push–pull testing, the main crack grew by a mixed mode. It is thus apparent that shear deformation affects the fatigue crack growth in pure aluminium. In tests using cyclic torsion, the fatigue crack grew by a shear mode. The micro‐cracks initiated perpendicular and parallel to the main crack's growth direction during the cyclic torsion tests. However, the growth direction of the main crack was not changed by the coalescence of the main crack and the micro‐cracks. Shear mode crack growth tends to occur in aluminium. The crack growth behaviour is related to a material's slip systems. The number of slip planes in aluminium is smaller than that of steel and the friction stress during edge dislocation motion of aluminium is lower than many other materials. Correlation between the crack propagation rate and the stress intensity factor range was almost the same in both push–pull and cyclic torsion with tension in this study.     

Mixed mode fatigue crack propagation in a ferritic–perlitic cold drawn tube

Previous work by the authors has shown that torsional fatigue tests on cold drawn tube specimens with a longitudinal micronotch present both Mode III ahead of the crack tip (throughout the tube thickness) and Mode I at the defect edges. The co-planar Mode III propagation was prevalent and is followed by Mode II crack propagation along the cold drawn direction.In this work, this behaviour is further investigated by a new series of experimental tests together with a finite element analysis. The mechanisms behind this competition between Mode I and Mode III cracks are analysed and some fractographies were performed on run-outs, broken and interrupted tests.Indeed, pure Mode I and pure Mode II crack propagation rates along with mixed mode crack propagation rates are analysed. Finally, the conditions in order to get Mode I crack growth or shear driven propagation are discussed.     

Simulation of dynamic crack curving and branching under biaxial loading by a time domain boundary integral equation method

Bifurcation and trifurcation of a fast running crack under various biaxial loading conditions is investigated numerically. The solution procedure for the 2D model in the framework of linear elastodynamics employs a time-domain boundary element method and allows for arbitrary curvilinear crack propagation. Branching events are controlled by the criterion of a critical mode I stress intensity factor while the propagation direction and growth rate of each branch are determined from the criterion of maximum circumferential stress. Numerical results are compared with experimental findings and are discussed with respect to macroscopic and microscopic aspects of dynamic fracture.     

Can pure mode III fatigue loading contribute to crack propagation in metallic materials?

The possibility of pure mode III crack growth is analysed on the background of theoretical and experimental results obtained in the last 20 years. Unlike for modes I and II, there is no plausible micromechanistic model explaining a pure mode III crack growth in ductile metals. In order to realize 'plain' mode III fracture surface, we propose the propagation of a series of pure mode II cracks along the crack front. Fractographical observations on crack initiation and propagation in a low alloy steel under cyclic torsion support such a model. The authors have not seen any clear indication of a pure mode III crack growth micromechanism in metals until now.     

Interface crack in periodically layered bimaterial composite

A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K _I is vanishing. Hence the mode II stress intensity factor K _II remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k ₂ at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor K _II of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k ₂. Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y=cx , where the exponent is equal to 3/2. In that case, when =3/2, predicts the analytical model a propagation path that is self-similar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor K _II at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed.     

Experimental investigation of crack growth direction in multiple cracks

In this paper, the interaction between multiple cracks in crack growth direction is studied in an aluminium alloy under static and fatigue loading. Self similar as well as non‐self‐similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the criterion for crack coalescence and crack growth direction are expressed in terms of the crack positions defined by crack offset and crack tip distances. The criterion presented in this study can be used to determine the limiting value of crack tip and crack offset distance and to determine the mode in which cracks coalesce during their growth process. Experimental results and crack interaction criterion presented under various crack positions and size conditions could be used to derive a new evaluation method of crack growth in multiple crack geometry.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage 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.