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.     

Why do cracks avoid each other?

The experimentally known phenomenon that originally collinear mode I cracks seem to avoid each other before coalescence is studied by investigating the stability of straight crack paths. To this end a periodic array of approximately collinear but slightly curved cracks is considered. Stress intensity factors for modes I and II are derived and the growth of originally straight cracks under mode I conditions is studied after introduction of a disturbance that forces the cracks to deviate from a straight path. It is shown that the straight crack path is unstable, i.e. that tip to tip coalescence will not take place.     

FATIGUE CRACK GROWTH BEHAVIOUR OF SM45C STEEL UNDER CYCLIC MODE I WITH SUPERIMPOSED STATIC MODE II LOADINGS

Abstract— The practical applications of studies related to constant amplitude mode I loading are somewhat limited, since mode I crack growth is often influenced by mode II (sliding mode) or mode III (tearing mode) in industrial situations. For these cases, criteria, rules, and laws have to be worked out and verified by experiments. However, it is very difficult to evaluate mixed-mode fatigue cracking due to crack surface interference, crack closure, crack branching, etc. This paper, which defines the length of a branched crack as an effective slant crack with a length equal to the distance between the two crack tips, explains the influences of crack surface interference by introducing concepts of adhesive wear and scrutinizes some related researches on mixed-mode crack growth behaviour. Additionally an effective stress intensity factor range is described which considers crack closure and crack surface interference and is verified with crack growth tests under mode I fatigue loading and cyclic mode I with a superimposed static mode II loading.     

Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments

Whatever the external loading, a crack front in a solid tries to reach mode I loading conditions after propagation. In mode I + II, the crack kinks to annihilate mode II, kinking angle being well predicted by the principle of local symmetry (PLS) or by the maximum tangential stress criterion (MTS). In presence of mode III, the problem becomes three-dimensional and the proposed propagation criterion are not yet well proved and established. In particular in three point bending experiments (3PB) with an initially inclined crack, the crack twists around the direction of propagation to finally reach a situation of pure mode I. The aim of the paper is to compare the propagation paths predicted by two different criteria for 3PB fatigue experiments performed on PMMA. The first criterion developed by Schollmann et al. (Int J Fract 117(2):129–141, 2002), is a three-dimensional extension of the MTS criterion and predicts the local angles that annihilates mode II and III at each point of the front. The second one developed by Lazarus et al. (J Mech Phys Solids 49(7):1421–1443, 2001b), predicts an abrupt and then progressive twisting of the front to annihilate mode III. Due to presence of sign changing mode II and almost uniform mode III in the experiments, both criteria give good results. However, since mode III is predominant over mode II in the case under consideration, the global criterion gives better results. Nevertheless, the local type criterion seems to be of greater universality for practical engineering applications.     

On crack path stability in a layered material

Crack paths in an elastic layer on top of a substrate are considered. Crack growth is initiated from an edge crack in the layer. The plane of the initially straight crack forms an angle to the free surface. The load consists of a pair of forces applied at the crack mouth and parallel to the interface. Crack paths are calculated using a boundary element method. Crack growth is assumed to proceed along a path for which the mode II stress intensity factor vanishes. The inclination and the length of the initial crack are varied. The effect of two different substrates on the crack path evolution is demonstrated. A crack path initially leading perpendicularly to the interface is shown to be directionally unstable for a rigid substrate. Irrespective of its initial angle, the crack does not reach the interface, but reaches the free surface if the layer is infinitely long. At finite layer length the crack reaches the upper free surface if the initial crack inclination to the surface is small enough. For an inextendable flexible substrate, on the other hand, the crack reaches the interface if its initial inclination is large enough. For the flexible substrate an unstable path parallel with the sides of an infinitely long layer is identified. The results are compared with experimental results and discussed in view of characterisation of directionally unstable crack paths. The energy release rate for an inclined edge crack is determined analytically.     

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.     

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.     

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.     

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.     

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.     

A material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures

Crack growth under mode II cyclic loading was investigated in maraging steel, ferritic–pearlitic steel and TA6V. When ΔK_II exceeds a threshold value, cracks do not bifurcate but grow in mode II over a distance which increases with ΔK_II. Shear mode crack growth was much more extensive in maraging steel than in TA6V and ferritic–pearlitic steel. This result is discussed in relation with the cyclic behaviour of the materials and the importance of friction along the crack faces. The maximum growth rate criterion is shown to be suitable for the prediction of crack paths when shear mode crack growth is likely to occur.     

On the tearing of thin sheets

We perform an experimental study to investigate the propagation of one or two cracks in a thin elastic sheet of a brittle material torn in an out-of-plane shear mode. We observe that a single crack always follows a straight path, whereas two cracks propagating simultaneously follow curved paths and merge, forming a tongue-like shape. The present experimental setup allows the understanding of how the energy introduced at a large scale is focused at the crack tip. We find that the geometry of the sheet is determined by the direction of a large scale force, applied to the crack tip, which is perpendicular to cracked surfaces. While the material is deformed at large scales under mode III loading, the geometry of system in the vicinity of the crack tip adapts such that the material is locally broken under a pure mode I loading.     

FATIGUE AT NOTCHES SUBJECTED TO REVERSED TORSION AND STATIC AXIAL LOADS

Reversed torsion with and without a superimposed end load has been applied to 1% Cr-Mo-V steel specimens containing sharp notches. Crack propagation was monitored by a sensitive d.c. potential drop system that measured crack depths between 25 μm and 0.6 mm from the root of the notch. Stress intensity factors do not satisfactorily correlate all the crack growth data but a strain intensity factor which is a function of material properties and notch plastic zone size shows a significant improvement and provides a single upper bound solution for both ambient and elevated temperatures. This solution permits designers to make safe lifetime assessments. At room temperature cracks initially propagate by mode II along the surface, and mode III radially but at low stresses crack growth is continued by mode I propagation. At higher stresses a transition to mode I cracking is avoided. Elevated temperature causes a brittle layer to form and in this case cracks initially propagate by mode I which then translates to mode III cracking at high stresses. Mode III thresholds are significantly higher than mode I thresholds but a constrained shear strain zone, as found at the root of notches subjected to torsion, permits the initiation and generation of a mode III crack. The application of an axial load enhances the mode III crack propagation rate since this increases the effective crack tip intensification factor.     

Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading

The mixed mode I/II fracture initiation angle and the crack growth trajectory of a soft rock (Guiting limestone) were investigated experimentally and theoretically for two different shaped test specimens with various sizes. It was observed that for similar mode mixities in the two specimens, the fracture paths grew in two different trajectories. It is shown that the observed crack path and the fracture initiation angle can be predicted theoretically by using a generalized form of the maximum tangential stress criterion. The main difference in the fracture initiation angles was found to be related to the magnitude and sign of the T-stress.     

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.     

Observations on fatigue crack paths in the corners of cold-formed high-strength steel tubes

Fatigue crack propagation in cold-formed corners of high-strength structural steel plate-type structures has been investigated. Large- and small-scale test specimens having complex residual stress states and subject to multi-axial cyclic local stresses have been investigated using both laboratory tests and numerical simulations. The combinations of alternating bending stress, alternating shear stress and static mean stress producing complex multi-axial stress states have been found to influence the fatigue crack path behaviour. Straight, zig-zag and “S” shaped cracks were observed depending on the material strength, range of cyclic loading, residual stress field and multi-axiality of the local stresses. Numerical simulations of residual stresses and linear elastic fracture mechanics were used to help understand the alternate crack paths. Mode I cracks propagating into a static compressive stress field did not arrest, but, due to the multi-axial stresses, combinations of mixed mode I, II and III crack growth with distinct paths were observed. The crack paths depend on the type and range of cyclic loading, material properties and residual stress conditions of the specimens.     

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as a_o/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.     

Fracture analyses and experimental results of crack growth under general mixed mode loading conditions

In this paper detailed results of 3D finite element (FE) and mixed mode analyses of different fracture specimens are presented and discussed. Special interest is taken in 3D and mode coupling effects to be found in strain energy release rate (SERR) results along crack fronts, in particular adjacent to corners, where a crack front intersects a free surface of a specimen. It will be shown that these effects stay small if they are related to Poisson’s ratio but that they can also be considerably pronounced if they are related to the global deformation behaviour of the specimen. The computational fracture analysis is based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure integral (MVCCI)-method in order to calculate the local SERR-distributions along the crack front. Furthermore some qualitative experimental results will show the influence of these variable mixed mode I, II and III loading conditions along the crack front on crack initiation and on the further development of 3D crack growth in the specimens.     

Interlaminar fracture characterization for plain weave fabric composites

For the analysis of laminated composite plates under transverse loading and drilling of composites, all the elastic, strength and fracture properties of the composite plates are essential. Interlaminar critical strain energy release rate properties in mode I, mode II, mixed mode I/II and mode III have been evaluated for two types of plain weave fabric E-glass/epoxy laminates. The double cantilever beam test and the end notch flexure test have been used for mode I and mode II loading. The mixed mode bending test and split cantilever beam test have been used for mixed mode I/II and mode III loading. It is observed that the plain weave fabric composite with lesser strand width has higher interlaminar fracture properties compared to the plain weave fabric composite with more strand width. Further, crack length versus crack growth resistance plots have been presented for mode III loading. In general, it is observed that total fracture resistance is significantly higher than the critical strain energy release rate.     

Stability of a system of interacting cracks

In the absence of crack branching, a system of straight cracks may interact and their growth regime may become unstable in the sense that some cracks may grow faster at a certain critical state, or even snap into a longer length, while other cracks may stop growing, or even snap closed.When the crack extension involves Modes I, II, and III, and the fracture criterion is defined by a critical value for the total energy release rate, necessary and sufficient conditions are developed for both the stability of a given regime, and for unstable crack growth.