CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

SHEAR FATIGUE CRACK GROWTH: A LITERATURE SURVEY

A fatigue crack is often initiated by a localized cyclic plastic deformation in a crystal where the active slip plane coincides with the plane of maximum shear stress. Once a crack is initiated, the crack will propagate on the maximum shear plane for a while and, in the majority of the cases, will eventually change to the plane of the applied tensile stress. The “shear” and “tensile” modes of fatigue crack propagation are termed stage I and stage II fatigue crack growth. They are also known as mode II and mode I fatigue crack growth. However, the mechanism of the tensile mode fatigue crack propagation is shear in nature. Considerable progress has been made recently in the understanding of mode II fatigue crack growth. This paper reviews the various test methods and related data analyses. The combined mode I and mode II elastic crack tip stress field is reviewed. The development and the design of the compact shear specimen are described and the results of fatigue crack growth tests using the compact shear specimens are reviewed. The fatigue crack growth tests and the results of inclined cracks in tensile panels, center cracks in plates under biaxial loading, cracked beam specimens with combined bending and shear loading, center cracked panels and the double edge cracked plates under cyclic shear loading are reviewed and analyzed in detail.     

Crack initiation and growth path under multiaxial fatigue loading in structural steels

In real engineering components and structures many accidental failures occur due to unexpected or additional loadings, such as additional bending or torsion. There are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path. It is widely believed that fatigue crack nucleation and early crack growth are caused by cyclic plasticity. This paper studies the effects of multiaxial loading paths on the cyclic deformation behaviour, crack initiation and crack path. Three types of structural steels are studied: Ck45, medium carbon steel, 42CrMo4, low alloy steel and the AISI 303 stainless steel. Four biaxial loading paths were applied in the tests to observe the effects of multiaxial loading paths on the additional hardening, fatigue crack initiation and crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It is shown that these materials have different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were conducted using the critical plane approaches, either based on stress analysis or strain analysis (Findley, Smith–Watson–Topper, Fatemi–Socie, Wang–Brown–Miller, etc). Comparisons of the predicted crack orientation based on the critical plane approaches with the experimental observations for the wide range of loading paths and the three structural materials are shown and discussed. Results show the applicability of the critical plane approaches to predict the fatigue life and crack initial orientation in structural steels.     

Estimating the orientation of Stage I crack paths through the direction of maximum variance of the resolved shear stress

Our formalisation of the Shear Stress-Maximum Variance Method takes as a starting point the hypothesis that, in ductile materials subjected to fatigue loading, the crack initiation planes, i.e. the so-called Stage I planes, are those containing the direction experiencing the maximum variance of the resolved shear stress. From a computational point of view, the most remarkable implication of the above assumption is that, as soon as the variance and covariance terms characterising the considered load history are known, the effective time needed to estimate the orientation of the critical plane does not depend on the length of the load history itself. Further, such a computational efficiency is seen to be associated with an high-level of accuracy in estimating fatigue lifetime of both plain and notched engineering components, this holding true under constant as well as under variable amplitude uniaxial/multiaxial fatigue loading. In this scenario, by assuming that the orientation of Stage I planes can directly be determined through the orientation of Stage II crack paths, the present paper investigates whether, independently from the degree of multiaxiality and non-proportionality of the applied loading history, the direction of maximum variance of the resolved shear stress is also capable of accurately estimating the orientation of Stage I crack paths.     

Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression

An extensive experimental program has been conducted on pre-cracked specimens of a rock-model material to investigate crack propagation and coalescence from frictional discontinuities. Prismatic gypsum specimens have been prepared with three pre-existing closed cracks (flaws). The flaws all have a constant length of 12.7 mm and are parallel to each other. Different geometries are obtained by changing the angle of the flaws with respect to the direction of loading, the spacing, and the continuity of the flaws. In the experiments, three different types of cracks have been observed: wing cracks, coplanar shear, and oblique shear cracks. These are the same types of cracks observed with open flaws. Crack initiation occurs simultaneously at all the tips of the flaws for wing and shear cracks. Mean crack initiation stress is higher for secondary cracks than for wing cracks. The differences however decrease as the flaws are oriented at smaller angles with the direction of loading. The types of coalescence (i.e. the type of cracks and crack pattern that link two flaws) from closed flaws are similar to those from open flaws. However, the type of coalescence observed in a specimen with open flaws is not necessarily produced when using the same geometry but with closed flaws. The most important conclusion reached in this research is that the fracturing processes in open and closed flaws are similar. Friction along the flaws increases the initiation and coalescence stress and favors linkage through shear cracks.     

A shear stress-based parameter for fretting fatigue crack initiation

The purpose of this study was to investigate the fretting fatigue crack initiation behaviour of titanium alloy, Ti–6Al–4V. Fretting contact conditions were varied by using different geometries of the fretting pad. Applied forces were also varied to obtain fretting fatigue crack initiation lives in both the low- and high-cycle fatigue regimes. Fretting fatigue specimens were examined to determine the crack location and the crack angle orientation along the contact surface. Salient features of fretting fatigue experiments were modelled and analysed with finite element analysis. Computed results of the finite element analyses were used to formulate a shear stress-based parameter to predict the fretting fatigue crack initiation life, location and orientation. Comparison of the analytical and experimental results showed that fretting fatigue crack initiation was governed by the maximum shear stress, and therefore a parameter involving the maximum shear stress range on the critical plane with the correction factor for the local mean stress or stress ratio effect was found to be effective in characterizing the fretting fatigue crack initiation behaviour in titanium alloy, Ti–6Al–4V.     

Fatigue and creep crack growth behaviour of Inconel MA 6000

Crack growth in MA 6000 under cyclic loading was studied at 24, 760, and 1000°C and under static loading at 1000°C in two matenal onentatwns. Correlatwns of fattgue crack growth rate with parameters ?K and ?J were examined. Also comparisons were made of experimental and predicted growth rates.

The rate of growth was influenced by temperature and onentatwn m addttwn to the loading mode. Fatigue crack growth rate generally increased with temperature. However in the L-T orientation at 1000°C secondary cracks developed perpendtcular to the primary crack and significantly altered its behaviour. Creep crack growth at 1000°C was strongly orientation dependent, mainly due to secondary crackmg m the L-T oriented specimen in the direction perpendicular to the main crack.

Fracture surfaces were examined by scanning electron microscopy. Also, comparisons were made between crack growth behaviour of MA 6000, MA 754 and MA 956.     

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

The paper presents a review of multiaxial fatigue failure criteria based on the critical plane concept. The criteria have been divided into three groups, according to the fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the critical plane orientation. Multiaxial fatigue criteria based on the critical plane concept usually apply different loading parameters in the critical plane whose orientation is determined by (a) only shear loading parameters (crack Mode II or III), (b) only normal loading parameters (crack Mode I) or sometimes (c) mixed loading parameters (mixed crack Mode). There are also criteria based on few critical plane orientations and criteria based on critical plane orientations determined by a weighted averaging process of rotating principal stress axes.     

Fracture statistics of brittle materials with surface cracks

Several different statistical fracture theories are developed for materials with cracks confined to the surface. All assume that crack planes are normal to the surface, but are otherwise randomly oriented. The simplest theory assumes that only the component of stress normal to the crack plane contributes to fracture. This theory is in fair agreement with biaxial fracture data on Pyrex glass obtained by Oh. When the contribution of shear is included in the analysis, the crack shape has to be considered. Several shapes are examined and the corresponding fracture statistics are derived. Two failure criteria are employed. In one the fracture occurs when the maximum tensile stress on some part of the crack surface reaches the intrinsic strength of the material. The other is based on a critical strain energy release rate. The assumption of shear-sensitive cracks leads to improved agreement with experiment, but really good agreement appears to require the assumption that the cracks have a preferred orientation.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

Fretting fatigue crack initiation mechanism in Ti–6Al–4V

Fretting fatigue crack initiation in titanium alloy, Ti?6Al?4V, was investigated experimentally and analytically by using finite element analysis (FEA). Various types of fretting pads were used in order to determine the effects of contact geometries. Crack initiation location and crack angle orientation along the contact surface were determined by using microscopy. Finite element analysis was used in order to obtain stress state for the experimental conditions used during fretting fatigue tests. These were then used in order to investigate several critical plane based multiaxial fatigue parameters. These parameters were evaluated based on their ability to predict crack initiation location, crack orientation angle along the contact surface and the number of cycles to fretting fatigue crack initiation independent of geometry of fretting pad. These predictions were compared with their experimental counterparts in order to characterize the role of normal and shear stresses on fretting fatigue crack initiation. From these comparisons, fretting fatigue crack initiation mechanism in the tested titanium alloy appears to be governed by shear stress on the critical plane. However, normal stress on the critical plane also seems to play a role in fretting fatigue life. At present, the individual contributions/importance of shear and normal stresses in the crack initiation appears to be unclear; however, it is clear that any critical plane describing fretting fatigue crack initiation behaviour independent of geometry needs to include components of both shear and normal stresses.     

Transient analysis of multiple parallel cracks under anti-plane dynamic loading

The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave.     

The green's function for a slant edge crack

The Green's functions are determined for plane edge cracks which meet the free surface at an arbitrary angle. Modes I and II stress intensification factors are found for both normal and shear loading of the crack, since coupling is found to occur between each type of loading and the two possible modes of crack-tip response.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Analysis of compressive fracture of three different concretes by means of 3D-digital image correlation and vacuum impregnation

Fracture of three different concretes under uniaxial compression was investigated. The three different materials were normal concrete, high strength concrete and foamed cement, with uniaxial strength varying between 8 and 92 MPa. The prismatic specimens were loaded between two different types of loading platens, providing maximum boundary restraint (rigid steel platens) or almost zero boundary restraint (Teflon (PTFE) sandwich inserts). Fracture propagation was measured using 3D-digital image correlation where emphasis was placed on measuring crack development just before and at peak stress. The stress at first cracking is dependent on the resolution of the digital image correlation technique, and as such not very well defined. The frictional restraint of the loading platens is recognized in the failure modes, in particular in the direction and structure of the main cracks. Also, the results for normal and high strength concrete underscore previous results: high friction results in a higher uniaxial compressive strength. This finding was not confirmed for foamed cement, where both loading systems gave approximately the same compressive strength. Likely the Teflon inserts do not function properly on the highly porous surfaces of the foamed cement specimens. The direction of the main cracks at peak is defined before the softening regime is entered: cracks have a vertical orientation when loading is applied through Teflon inserts, whereas ‘en-echelon’ tensile cracks forming inclined shear bands are observed for rigid loading platens. The results from 3D-digital image correlation were confirmed by results from vacuum impregnation with fluorescent epoxy after test termination. Although digital image correlation is capable of showing cracks at relatively early stages of loading, the vacuum impregnation technique shows all the fine detail and crack branches, but this can, unfortunately, only be done once for each specimen. Therefore, combining the two different techniques is more appropriate.     

Mikrorissentstehung und Mikrorisswachstum in Aluminiumlegierungen bei zyklischer Beanspruchung – Werkstoffliche Untersuchung und Simulation

Microcrack Initiation and Microcrack Growth in Aluminium Alloys Subjected to Cyclic Loading – Material Analysis and Simulation In this paper a model designed to simulate the growth of microcracks under the influence of cyclic loading is presented. Considering fatigue crack growth microstructural barriers as well as the state of stress play an essential role. The polycristalline metal was modelled as an aggregate of hexagonal grains with each of the grains showing a different crystallographic orientation. The crack growth is initially dominated by shear stresses leading to microstructurally short cracks (stage I). As the tip of the microcrack approaches a grain boundary the crack growth rate decreases. The transition from stage I to stage II crack growth is also considered in the model as the crack reaches a specific length and continues to grow under the influence of normal stresses (physically short cracks). The model is applied to tubular specimens of the aluminum alloy AlMgSi1 which are subjected to tension and torsion as well as to combined tension‐torsion loading cycles. In terms of the microcrack distribution as a function of their orientation the simulated crack growth behaviour reveals a close match with the experimental results.     

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.     

MIXED MODE SMALL CRACK GROWTH

Abstract— The fatigue crack growth behavior of small part-through cracks in 1045 steel and Inconel 718 subjected to biaxial loading has been investigated. Experiments were performed on thin-wall tubular specimens loaded in tension, torsion and combined tension torsion. Crack sizes analyzed ranged from 20 μm to 1 mm and growth rates ranged from 10^-7 to 10^-4 mm/cycle for 1045 steel and from 10^-5 to 10^-2 mm/cycle for Inconel. Nucleation and the early growth of cracks occurs on planes of maximum shear strain amplitude for both of these materials even in tensile loading. An equivalent strain based intensity factor was employed to correlate the crack growth rate under mixed mode loading conditions In loading conditions other than torsion, a transition from mode II to mode I was observed for 1045 steel. Principal strains were used to analyze mode I cracks. Cracks in Inconel 718 grow in mode II for the majority of the fatigue life. The maximum shear strain amplitude and the tensile strain normal to the maximum shear strain amplitude plane were used to calculate the strain based intensity factor for mixed mode loading.     

CLOSURE AND GROWTH OF MODE I CRACKS IN BIAXIAL FATIGUE

Abstract— —The closure behavior of mode I fatigue cracks under biaxial loading is studied with an elastic-plastic plane stress finite element model. Biaxial stresses are shown to have a significant impact on crack closure behavior at higher maximum stresses. In general, normalized crack opening stresses are highest for equibiaxial loading and lowest for pure shear loading. The differences are apparently negligible for maximum applied stresses less than about 0.4 σ₀. Experimental crack growth data are quantitatively consistent with these trends. Correlations of the experimental data with a simple Δ K _eff were successful as first-order engineering estimates. Changes in forward and reversed plastic zone sizes with biaxiality are not entirely consistent with trends in crack growth rates.     

Transformation zones, crack shielding, and crack-growth resistance of Ce-TZP/alumina composite in mode II and combined mode II and mode I loading

Crack-tip transformation zones, crack shielding and crack-growth-resistance (R-curve) behaviors of a transformation-toughened ceria-partially stabilized zirconia–alumina (Ce-TZP/alumina) composite were studied in mode II and combined mode I and mode II loading using compact-tension-shear (CTS) specimens. The mode II and mode I stress intensities for both the initial straight cracks and the subsequent kinked cracks were assessed by the method of caustics using geometrically equivalent specimens of polymethyl methacrylate (PMMA). The angle of formation of the transformation zones as well as of extension of the cracks increased systematically with increasing ratio of the mode II and the mode I stress intensities and approached a value of θ^*=−72° in pure mode II loading. This angle was close to the angle for maximum hoop tension in the stress field of a mode II crack (θ^*=−70.5°). A crack-initiation toughness envelope was constructed on a K_I–K_II diagram using the critical loads for incremental crack extension. The crack-initiation toughness in pure mode II loading was less than the corresponding toughness in mode I loading. This result was consistent with calculations that indicated no shielding from the asymmetric and elongated zones developed in mode II loading. The fracture toughness measured for the kinked cracks at long kink lengths approached the maximum fracture toughness measured for a mode I crack.