Fatigue crack propagation under non-proportional mixed mode loading

Under non-proportional mixed I+II loading, two kinds of stable crack propagation may be distinguished. An existing precrack will either kink, mode I controlled (tensile mode), or will propagate, coplanarly mode II controlled (shear mode). Shear mode growth will occur if the effective mode II range exceeds the material-specific threshold ΔK_{II th sm} and in addition to that, the ΔK_II-value on the starter crack is larger than the ΔK¹_I (Δϕ)-range on the infinitesimally short additional crack. Examination under the scanning electron microscope showed that flaws are not the reason for the mode II controlled crack propagation and support the criteria introduced. If the crack opening is large enough, the crack propagation rate is higher for shear-stress controlled crack growth than for normal-stress controlled crack extension, the deviation angle of which is well predictable via the MTS criterion due to Erdogan and Sih [On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963;85:519–25].     

Mixed-mode fatigue crack growth behaviour in aluminium alloy

Fatigue crack propagation tests in compact mixed-mode specimens were carried out for several stress intensity ratios of mode I and mode II, K_I/K_II, in AlMgSi1-T6 aluminium alloy with 3 mm thickness. The tests were performed in a standard servo-hydraulic machine. A linkage system was developed in order to permit the variation of the K_I/K_II ratio by changing the loading angle. Crack closure loads were obtained through the compliance technique. A finite element analysis was also done in order to obtain the K_I and K_II values for the different loading angles. Crack closure increases under mixed-mode loading conditions in comparison to mode-I loading due the friction between the crack tip surfaces. Moreover, the crack closure level increases with the K_I/K_II ratio decrease. Correlations of the equivalent values of the effective stress intensity factor with the crack growth rates are also performed. Finally, an elastic–plastic finite element analysis was performed to obtain the plastic zones sizes and shapes and model the effect of mixed-mode loading on crack closure.     

Fatigue crack growth under non-proportional mixed-mode loading in ferritic-pearlitic steel

Mode II fatigue crack growth tests as well as tests in sequential mode I and then mode II were performed on ferritic‐pearlitic steel. For ΔK_II ranging from 7 to , bifurcation occurs after 12–450 μm of coplanar growth at a decreasing speed. By contrast, hundreds of micrometres of constant speed coplanar growth were obtained under sequential mode I and then mode II loading, for and ΔK_I ranging from 0.25 to 1.0 ΔK_II . The crack growth rate is a simple sum of the contributions of each mode for ΔK_I= 0.25 ΔK_II but above this value a synergetic effect is found. The mechanism of this fast‐propagation mode is discussed in the light of strain range maps ahead of the crack tip obtained by digital SEM image correlation and elastic–plastic finite element calculations. The stability of the crack path according to the maximum growth rate criterion is demonstrated.     

A fracture mechanics analysis on the fatigue behaviour of cruciform joints of duplex stainless steel

The paper presents the results of an experimental and numerical study on the fatigue behaviour of cruciform load carrying joints made from the duplex stainless steel and failing from the weld root through the weld metal. Fatigue crack growth (FCG) data, obtained in specimens of the weld metal, are presented, as well as threshold data, both obtained for R= 0 and 0.5. The influence of stress ratio is discussed, and the FCGR results are compared with data for low carbon structural steels. S–N data were obtained in the joints, both for R= 0.05 and 0.5, and the fatigue cracking mechanisms were analysed in detail with the SEM. It was found that the cracks propagated very early in the lifetime of the joints, under mixed mode conditions (I + II), but the mode I component was found to be predominant over mode II. The geometries of the cracks were defined in detail from measurements taken in the fracture surfaces. A 2D FE analysis was carried out for the mixed mode inclined cracks obtained at the weld root, and the J‐integral formulations were obtained as a function of crack length and crack propagation angle. The values of the crack propagation angle, θ_i, were obtained for the J_max conditions, and it was found that, in the fatigue tests, the cracks propagated in directions very close to the predicted directions of maximum J. K_I and K_II formulations were obtained, and the K_I data were compared with the formulations given in the PD6493 (BS7910) document, and some differences were found. A more general formulation for K under mixed mode conditions was derived. The derived K solutions were applied to predict the fatigue lives of the joints under crack propagation, and an extremely good agreement was found with the experimental results obtained in the fatigue tests.     

FATIGUE CRACK GROWTH UNDER MODE II LOADING

Abstract— The behavior of fatigue crack growth for low and medium carbon steels, an austenitic stainless steel and an aluminum alloy under pure Mode II loading was investigated experimentally, using cruciform specimens. The results show that under pure Mode II loading, fatigue crack propagation has three possibilities, namely, bifurcation into two branches, propagation along the original Mode II direction, and the mixture of these two situations, depending on the material. The growth rate da/dN vs. ΔK_II relation for Mode II propagation is similar to a Pans type law for Mode I growth. Fractographic observations by optical microscopy and SEM were made also on all specimens tested. When a crack branched, striations parallel to the crack front which were often associated with Mode I fatigue crack growth were observed and long marks parallel to the crack propagation direction were also found for slanted fracture surfaces. When a crack propagated along the original Mode II direction, many frictional marks parallel to the crack propagation direction were observed.     

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.     

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.     

Fatigue crack growth rates under sequential mixed-mode I and II loading cycles

One common mode of failure that occurs in rolling bodies such as gears, bearings and rails is due to the fatigue process. Several research workers suggest that rolling contact fatigue cracks are subjected to mixed mode I and II loading cycles. It is believed that the correct modelling of loading cycles can help us to study the mechanics of crack growth because fatigue comprises a major safety consideration in the design process. Experiments have been performed under nonproportional mixed-mode I and II loading cycles with fixed degrees of overlap, so that coplanar cracks were produced. Three empirical crack propagation laws have been established which are related to both mode I and mode II effective stress intensity factor ranges.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

Mixed mode crack tip parameters for different wheel positions relative to a vertical crack at the rail foot

Finite element method is used to analyze a rail with a vertical bottom up crack at its foot, under the axle load and surface traction of a wheel. The possibility of crack formation at the foot of the rail in the neighborhood of a welding connection is discussed. A brief review on the importance of T‐stress in brittle fracture is presented. Seven cases with different locations of the crack relative to rail's sleeper contact region are considered. Numerous positions of the wheel are considered, and in each case, 3 crack parameters K_I, K_II, and T‐stress are calculated. Then, the biaxiality ratio and the mixity parameter for each loading and crack condition are calculated. It is shown that the location of crack and wheel can create mixed mode loading in the cracked rail and that the magnitude of crack tip parameters are strongly dependent on these geometric variables. In particular, the magnitudes of T‐stress and biaxiality ratio are significant in some cases. The effect of friction between the crack faces in the presence of compressive mode I loading on the mode II stress intensity factor is studied. Under mixed mode loading, due to the axle load and surface traction, the most critical condition is the formation of vertical cracks near the sleeper contact region.     

A two-dimensional in situ fatigue cohesive zone model for crack propagation in composites under cyclic loading

In this paper a two-dimensional fatigue cohesive zone model (CZM) for crack propagation in composites under cyclic loading has been formulated and validated through successful predictions of fatigue crack growth under pure and mixed mode conditions for several different composites. The proposed fatigue CZM assumes simple power-law functions for fatigue damage accumulation of which the damage parameters can be calibrated from simple fatigue tests under pure mode I and mode II conditions. The model relies solely on the in situ cohesive responses for fatigue damage rate calculation, enabling the differentiation of the local elemental load history from the global load history. An effective cycle jump strategy for high-cycle fatigue has also been proposed. It has been demonstrated that once calibrated, the fatigue CZM can predict the Paris laws for the pure modes. Furthermore, it can predict the Paris laws of any mixed-mode conditions without the need of additional empirical parameters. This is of significant practical importance because it leads to greatly reduced experimental needs for mixed mode crack propagation widely observed in composites under cyclic loads.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Computer simulation of fatigue crack propagation under random loading conditions

The aim of this study is to simulate fatigue crack propagation under random loading conditions using a simple algorithm based on the Wheeler model [Wheeler O. Spectrum loading and crack growth. J Basic Eng D 1972;94:181–86]. To create the computer simulation, a model based on the mechanical properties of the material has been used. These properties include the yield stress (σ_y) and Paris’s constants C and m. The loading conditions (baseline loading ratio R, baseline stress intensity factor range ΔK and overload stress intensity factor K_ol, R_ol) are also required. The present model is validated with fatigue crack growth test data conducted on 12NC6 steel samples with four different heat treatments in order to have different types of mechanical behavior. The computer simulation and experimental results for crack propagation for different overload distributions (a single overload, a repeated overload, different overload magnitudes, random overload) are in good agreement.     

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.     

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.     

Fatigue crack growth resistance of ECAPed ultrafine-grained copper

This work presents the experimental results of fatigue crack growth resistance of ultrafine-grained (UFG) copper. The UFG copper has a commercial purity level (99.90%) and an average grain size of 300 nm obtained by a 8-passes route Bc ECAP process. The fatigue propagation tests are conducted in air, at load ratios R = K_min/K_max varying from 0.1 to 0.7, on small Disk Shaped CT specimens. Both stage I and stage II regime of growth rate are explored. Results are partially in contrast with the few experimental data available in the technical literature, that are by the way about high purity UFG copper. In fact, the present material shows a relatively high fatigue crack resistance with respect to the unprocessed coarse-grained alloy, especially at high values of applied stress intensity factor ΔK. At higher R-ratio a smaller threshold intensity factor is found, together with a lower stage II fatigue crack growth rate. The explanation of such crack growth retardation is based on a diffuse branching mechanism observed especially at higher average ΔK.     

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.     

Mixed mode fatigue and fracture in planar geometries: Observations on Keq and crack path modelling

The mixed mode I‐II fatigue and fracture is briefly reviewed, addressing experimental and numerical modelling aspects, and focusing on planar specimens. One major challenge concerns the determination of equivalent stress intensity factor (K_eq) in mixed mode situations. Several approaches were compared through the determination of K_eq/K_I over a wide range of values of K_I/K_II or K_II/K_I. Whereas all different approaches converge to the same value as K_I/K_II increases, the same does not happen for large K_II/K_I, where differences between values of K_eq persist. In the regions of 0 < K_I/K_II < 2 and 0 < K_II/K_I < 2, no stable trend of results can be defined. Experimental fatigue crack growth results are presented for Al alloy AA6082‐T6. Compact tension specimens, modified with holes, and four‐point bending specimens under asymmetrical loading promoting mixed mode situations, were subjected to fatigue crack growth tests, where crack path and crack growth rate were measured. The presentation of the fatigue crack growth data was made using a Paris law based upon K_eq. Differences in the Paris law constants were found for the different K_eq criteria. Recent developments in numerical techniques, as the implementation of the extended finite element method (XFEM) in finite element software packages allows to determine accurately crack paths in mixed mode fracture. This article highlights concepts for mixed‐mode fatigue and fracture and supporting data, identifying challenges still to be overcome.     

Near‐threshold behaviour of shear‐mode fatigue cracks in metallic materials

This review paper presents a brief state‐of‐the art of the research on long fatigue shear‐mode cracks and describes some recent results on effective crack growth thresholds and mode I branching conditions achieved by the authors for ARMCO iron, titanium with two different microstructures, nickel and stainless steel. A special technique for preparation of fatigue precracks enabled us to substantially suppress the crack closure (friction) effects at the beginning of the experiment, and the measured threshold values could be considered to be very close to the effective ones. In all investigated materials, the effective thresholds under the remote mode II loading were found to be about 1.7 times lower than those under the remote mode III loading. Effective thresholds under mode II loading of investigated materials were found to follow a simple formula assembled by the shear modulus G, the magnitude of Burgers vector b and a goniometrical function n_α of the mean deflection angle that depends on the number of available crystallographic slip systems. These quantities determine the intrinsic material resistance to mode II crack propagation at the threshold. A simple criterion for mode I branching in terms of effective threshold values well reflects a transition from the shear‐mode to the opening‐mode controlled crack propagation at the threshold. The associated transition deflection angle of 40° is a material independent constant.     

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.