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.     

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.     

A study of fatigue crack growth with changing loading direction

Round compact specimens made of 1070 steel were experimentally tested under cyclic loading for crack growth. The specimen was first subjected to Mode I loading. After the crack reached a certain length, the external loading direction was changed 50° from the original loading direction. Right after the change of the loading direction, the specimen experienced the combined Mode I/II loading condition. Following a short transient period, the fatigue crack was found to grow in the direction approximately perpendicular to the external loading direction, indicating the recovery of Mode I cracking. A recently developed approach was used to predict the cracking behavior of the specimens. Detailed elastic-plastic stress analysis was conducted using the finite element (FE) method. Both crack growth rate and cracking direction were predicted by employing a critical plane multiaxial fatigue criterion based on the stress-strain response outputted from the FE analysis. The predictions made by using the approach were in excellent agreement with the experimental observations in terms of both crack growth rate and cracking direction. The material constants used in the approach were obtained from testing smooth specimens for crack initiation.     

Fatigue cracks emanating from sharp notches in high-strength aluminium alloys: The effect of loading direction, kinking, notch geometry and microstructure

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches was investigated. To this purpose, an experimental campaign has been conducted on Al-7075–T651 specimens carrying notches with aperture angles of 45°, 90°, and 135°. In order to investigate the role of microstructure texture, specimens were extracted from the plates with the main axis either in the longitudinal rolling direction (L-samples) or in the transversal direction (T-samples), or 45° inclined with respect to both directions (LT-samples). The effect of stress amplitude was investigated by performing tests at two load levels. Three loading directions θ = 0°, 45° and 90° were considered. Some specimens experienced pure Mode I loading condition, whereas the remaining ones were subjected to combined Mode I and Mode II loading condition. The crack deflection induced by the variation in loading direction was determined by measuring the kinking angle. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors (SIF) of straight cracks were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. On the contrary, a finite element model has been built up to derive the SIFs at the tip of the kinked cracks. The influence of K_II on the crack propagation was discussed on the basis of theoretical and semi-empirical models. It has been found that (i) the crack initiation at the notch root occurred in mixed mode conditions, (ii) a decreasing Mode II component with growing crack length was observed under initial loading direction θ₀ = 45° and θ₀ = 90°, (iii) a crack deflection was observed after 45° rotation of the initial loading direction; a good prediction of the kinking angle was obtained using the maximum tangential stress criterion, and (iv) a fairly good rationalization of all the collected crack growth rate data is obtained if the driving force for crack propagation is expressed in terms of K_I.     

Sustained Mode I and Mode II fatigue crack growth in flat plates

This study was conducted to contribute to the understanding of fatigue crack growth under mixed mode loading. This was accomplished by developing and analyzing a flat plate specimen capable of maintaining crack growth on a plane oblique to the direction of the applied load. Several specimens were built and exposed to controlled fatigue loading in the laboratory. These specimens were then modeled using finite elements to determine the stress intensity factors (SIF). For the “Mode I/Mode II” specimens developed, the crack was forced to grow in a direction other than perpendicular to the load. The resulting crack front did not remain straight and flat, but stabilized into a curved or warped shape. Based on finite element analyses of these curved specimen cracks, it is concluded that the SIR were predominantly Mode I, with the Mode II and III SIR being negligible.     

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.     

Influence of overloads and block loading sequences on Mode III fatigue crack propagation in A469 rotor steel

A study has been made of the influence of variable amplitude loading on Mode III (anti-plane shear) fatigue crack propagation in circumferentially-notched cylindrical specimens of ASTM A469 rotor steel (yield strength 621 MN/m²), subjected to cyclic torsional loading. Specifically, transient crack growth behavior has been examined following spike and fully-reversed single overloads and for low-high and high-low block loading sequences, and the results compared to equivalent tests for Mode I (tensile opening) fatigue crack growth. It is found that the transient growth rate response following such loading histories is markedly different for the Mode III and Mode I cracks. Whereas Mode I cracks show a pronounced transient retardation following single overloads (in excess of 50% of the baseline stress intensity), Mode III cracks show a corresponding acceleration. Furthermore, following high-low block loading sequences, the transient velocity of Mode I cracks is found to be less than the steady-state velocity corresponding to the lower (current) load level, whereas for Mode III cracks this transient velocity is higher. Such differences are attributed to the fact that during variable amplitude loading histories. Mode III cracks are not subjected to mechanisms such as crack tip blunting/branching and fatigue crack closure, which markedly influence the behavior of Mode I cracks. The effect of arbitrary loading sequences on anti-plane shear crack extension can thus be analyzed simply in terms of the damage accumulated within the reversed plastic zones for each individual load reversal. Based on a micro-mechanical model for cyclic Mode III crack advance, where the crack is considered to propagate via a mechanism of Mode II shear (along the main crack front) of voids initiated at inclusion close to the crack tip, models relying on Coffin-Manson damage accumulation are developed which permit estimation of the cumulative damage, and hence the crack growth rates, for arbitrary loading histories. Such models are found to closely predict the experimental post-overload behavior of Mode III cracks, provided that the damage is confined to the immediate vicinity of the crack tip, a notion which is consistent with fractographic analysis of Mode III fracture surfaces.     

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.     

Non-propagating cracks and high-cycle fatigue failures in sharply notched specimens under in-phase Mode I and II loading

Sharply notched specimens were tested under in-phase Mode I and II loading to study the non-propagating crack behaviour in the presence of complex stress states. The material employed in the present investigation was a commercial low carbon steel. Non-propagating cracks were generated under different ratios between Mode I and Mode II stress components. The direct inspection of the cracked samples showed that the early stage of the crack propagation was mixed Mode governed (Stage 1-like process), whereas the subsequent propagation was seen to be mainly Mode I dominated (Stage 2-like process). Moreover, it was observed that non-propagating crack length tended to increase as the Mode II contribution to fatigue damage increased. In any case, independently of the degree of multiaxiality, their average length was of the order of 2L, where L was the material characteristic length calculated according to the theory of critical distances. Finally, the detected crack paths were used to form some hypotheses on the reason why two methods previously formulated by the authors are successful in predicting the multiaxial high-cycle fatigue strength, even though they make quite different assumptions on the physical mechanisms damaging metallic materials in the high-cycle fatigue regime.     

Stress analysis of a kinked crack initiating from a rigid line inclusion. Part II: Direction of propagation

The propagation direction of a kinked crack initiating from a rigid line inclusion is investigated. The criteria of maximum energy release rate, maximum Mode I stress intensity factor, and zero Mode II stress intensity factor are used as predictors for the kinked crack direction. Uniform farfield tension and pure shear loading conditions are used for illustration.     

Mechanisms of mixed mode fatigue crack propagation at rail butt-welds

In the present paper, the fatigue crack propagation of longitudinal flaws starting in butt-welded joints of rails is analysed. Firstly Finite Element simulations are carried out, in order to determine the actual stress intensity factor histories caused by the passage of the wheel over the rail. Simulations show that fatigue crack growth is dominated by an out-of-phase Mode I–Mode II mechanism with an overlapping of about 180 degrees. Then, mixed-mode fatigue test experiments have been designed in order to reproduce in-service conditions at laboratory test level. For this purpose, tubular specimens have been subjected to mixed-mode loading (reversal torsion combined with axial tension/compression). The crack growth propagation dominated by the shear has been confirmed. At the end of the paper, the conditions to obtain the shear mode crack propagation are discussed and the kinetics data are presented.     

ELASTIC-PLASTIC FINITE ELEMENT ANALYSES OF CRACKED NOTCHES IN PLATES UNDER MIXED-MODE LOADING

Plates containing inclined elliptical notches with and without cracks are analysed for five different major axis inclinations, namely, θ equal to 0, 11.25, 22.5, 33.75 and 45?. Short cracks emanating from the roots of such inclined circular and elliptical notches are analysed. Under various mixed-mode loading conditions, when cracks are present, a simple method is described for the evaluation of the Mode I and Mode II stress intensity factors, for the elastic state. Values of the J integral along three different contours are also evaluated in the elastic and elastic-plastic states, as well as the Mode I and Mode II components of the crack tip opening displacenient (CTOD), the maximum principal stresses, the maximum average equivalent plastic strains and the location of the elements in which they occur. Comparisons of the different loading conditions are presented and the implications of the effects of mixed-mode loading on fracture and fatigue crack propagation are discussed.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

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.     

Crack growth rate under cyclic bending in the explosively welded steel/titanium bimetals

The paper presents the results of the tests on fatigue crack growth in a steel/titanium composite under oscillatory bending. Two kinds of specimens of rectangular cross sections were tested. In the tested specimens, the ratio of heights of basic and overlaid materials was h₁:h₂ = 2.5:1 and 1:1. In the specimens, the fatigue crack growth was parallel to the applied loading and its direction changed at the interface line. Next, the crack growth along the interface line or the crack growth passing through the interface line were observed. When the crack growth passed along the interface line, decrease of the crack growth rate took place. The specimens have the uniform crack growth at both sides of lateral surfaces. At the composite fractures in the steel and titanium, transcrystalline cracks are dominating.     

Simulation of Fatigue Crack Propagation in Ductile Metals by Blunting and Re-sharpening

Laird and Smith [(1962). Philosophical Magazine 8, 847–857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Laird’s plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J₂ hypo-elasto-plasticity model with Armstrong–Frederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletaud’s model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Laird’s mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 1155–1165] on pure copper single crystals.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.     

The effect of steady torsion on fatigue crack growth in shafts

Most of catastrophic mechanical failures in power rotor shafts occur under cyclic bending combined with steady torsion: Mode I (ΔK_I) combined with Mode III (K_III). An analysis of the influence of steady torsion loading on fatigue crack growth rates in shafts is presented for short as well as long cracks. Long cracks growth tests have been carried out on cylindrical specimens in DIN Ck45k steel for two types of testing: rotary or alternating bending combined with steady torsion in order to simulate real conditions on power rotor shafts. The growth and shape evolution of semi-elliptical surface cracks, starting from the cylindrical specimen surface, has been measured for several loading conditions and both testing types. Short crack growth tests have been carried out on specimens of the same material DIN Ck45k, under alternating bending combined with steady torsion. The short crack growth rates obtained are compared with long crack growth rates. Results have shown a significant reduction of the crack growth rates when a steady torsion Mode III is superimposed to cyclic Mode I. A 3D Finite Element analysis has also shown that Stress Intensity Factor values at the corner crack surface depend on the steady torsion value and the direction of the applied torque.     

CRACK PROPAGATION UNDER MIXED MODE (I + III) LOADING

Abstract— In this paper are presented the results of fatigue crack propagation tests on angled-slit, three point bend mixed-mode (I + III) specimens manufactured from a low pressure steam turbine rotor forging. The path of crack propagation has been studied for two mixed mode (I + III) loading conditions. It has been observed that crack growth occurs by a mode I mechanism and a model has been developed to correlate crack growth rates in mixed mode (I + III) specimens with data from pure mode I fatigue tests.     

Effects of loading frequency and environment on delamination fatigue crack growth of CFRP

The delamination fatigue crack growth was investigated with two kinds of unidirectional CF/epoxy laminates. In the T300/3601 laminate, Mode I crack growths in air were cycle dependent, while it was time dependent in water, and the growth rate in water was lower than that in air. Mode II crack propagation rate either in air or in water was also constant with crack extension, and the crack growth was time-dependent. The crack propagation rate in water was faster than that in air, and it increased with prior-immersion period in water. In the M40J/2500 laminate either in air or in water, Mode I delamination fatigue crack growth was cycle-dependent, and the growth rate in water was lower than that in air. Mode II crack propagation rate either in air or in water was almost constant with crack extension, and the crack growth was cycle-dependent. The crack propagation rate in air was almost identical to that in water.