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.     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Measurement of fatigue crack growth in large compact tension specimens using an AC magnetic field method

Fatigue crack growth rate data are required in order to carry out a numerical analysis of the fatigue performance of complex structural components. These data are obtained by measuring crack growth in standard fracture mechanics specimens. A new method for measuring fatigue crack growth in compact tension specimens has been developed. The technique is based on the measurement of the surface magnetic fields produced when passing a high-frequency alternating current through the specimen. Fatigue crack growth data recorded using this method indicated an accuracy of ±0.02 mm when compared with optical measurements. The technique is suitable for computer-controlled operation and could easily be applied to other standard specimen geometries.     

Mixed-mode crack opening displacement measurements for small fatigue cracks growing in Astroloy at 20 °C

Crack opening displacements were measured for small fatigue cracks in Astroloy being grown with uniaxial stress application under high-cycle fatigue conditions. Four cracks were investigated including one that grew from 27 to 74 μm in three increments. Most of the cracks grew at an angle to the loading axis and all opened bimodally. Crack opening scaled with distance from the crack tip similar to an elastic crack, which allowed the calculation of a local stress intensity factor for both mode I and mode II. The proportion of mode II stress intensity factor was relatively large, varying as 0.06 < Δ K _II /Δ K _I < 0.42, with an average of ~0.3. Thus, uniaxial loading remote to the cracks resulted in a bimodal opening response on the scale of the cracks.     

Creep crack growth in power plant materials

Economic considerations have made it desirable to extend the 30 to 40 year operating life of power plants by another 10 to 20 years. Crack growth at elevated temperatures is an important consideration in estimating the remaining life, determining operating conditions and deciding inspection criteria and intervals for power plant materials. This paper presents an overview of high-temperature crack growth phenomenon in such materials. The focus is on various techniques used for characterizing creep crack growth (CCG) and creep-fatigue crack growth (CFCG) in high-temperature materials. The collection of data, their analysis and the interpretation of results is discussed in detail, especially for CFCG laboratory testing. The discussion is primarily focussed on creep-ductile materials such as those used in power plant applications. Special considerations for elevated temperature crack growth in weldments are also presented. Finally, the application of these concepts to the life prediction of power plant components is also discussed.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

An experimental investigation of mixed-mode creep crack growth in Jethete M152 at 550°C

Creep crack growth tests have been made on Jethete M152 at 550°C under initially mixed-mode (i.e. K_I/K_II ≈ 1.6) and mode-II crack tip conditions using compact mixed-mode (CMM) specimens. The results of these tests have been compared with mode-I data obtained from compact tension (CT) tests, using a C* approach. The correlation between the mode-I, mode-II and mixed-mode data is reasonably good. However, the scatter band is greater than that obtained from the mode-I results only. The results indicate that the C* approach, which has been used successfully in mode-I situations, may also be useful for predicting creep crack growth in more general situations.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Fatigue crack growth in Haynes 230 single crystals: an analysis with digital image correlation

Fatigue crack growth was investigated in Haynes 230, a nickel‐based superalloy. Anisotropic stress intensity factors were calculated with a least squares algorithm using the displacements obtained from digital image correlation. Crack opening/sliding levels were measured by analysing the relative displacement of crack flanks. Reversed crack tip plastic zones were calculated adopting an anisotropic yield criterion. The strains measured in the reversed plastic zone by digital image correlation showed a dependence on crystallographic orientation. Finally, a finite element model was adopted to examine plasticity around the crack tip. Results were compared with the experimentally observed strains.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Mixed-mode I/II fracture behaviour of a high strength steel

Mixed mode fracture in a certain high strength steel has been investigated through physical experiments and numerical calculations. The main objective has been to investigate the implications of local crack tip processes on the macroscopic mixed mode fracture behaviour. A scrutiny of the fractured specimens revealed evidence of crack branching in all cases where β_{_eq} < 40° ( β_{_eq =} atan ( K_{_I} /K_{_II} ) ). The appearance of branching was found to be accompanied to a rather abrupt increase in the macroscopic mixed mode fracture toughness. In the numerical calculations the effective plastic strain criterion suggested by Hallbäck and Nilsson (1994) was applied to the present material. Crack tip branching was from the analysis predicted to occur at β_{_eq =} 60°. Besides the presence of branching, it was however questionable whether the analysis corroborated the experimentally observed behaviour.     

Micromechanisms of fatigue crack growth in aluminium alloys

The fatigue crack growth characteristics of high-strength aluminium alloys are discussed in terms of behaviour during mechanical testing and fracture surface appearance. For a wide range of crack growth rates, the crack extends both by the formation of ductile striations and by the coalescence of micro-voids. Dimples are observed at stress intensities very much less than the plane strain fracture toughness, and this is explained in terms of the probability of inclusions lying close to the crack tip. The striation formation process is described as a combination of environmentally-enhanced cleavage processes and plastic blunting of the crack tip.     

Investigation of small fatigue crack initiation and growth behaviour of nickel base superalloy GH4169

Surface replication method was utilized to monitor the small fatigue crack initiation and growth process of single‐edge‐notch tension specimens fabricated by nickel base superalloy GH4169. Three different stress levels were selected. Results showed that small fatigue cracks of nickel base superalloy GH4169 initiated from grain boundaries or surface inclusions. The small fatigue crack initiation and growth stages took up about 80–90% of the total fatigue life. Multiple major cracks were observed in the notch root, and specimen with more major cracks seemed to have smaller fatigue life under the same test conditions. At the early growth stage, small crack behaviour might be strongly influenced by microstructures; thus, the crack growth rates had high fluctuations. However, the stress level effect on the small fatigue crack growth rates was not distinguishable for the three different stress levels. And no clear differences were found among the crack initiation lives by using replication technique.     

Shear mode fatigue crack growth in 1050 aluminium

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

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fatigue crack growth, physical understanding and practical application

The paper presents a discussion on two problems associated with fatigue crack growth in aluminium alloys. First, the application of the similarity approach to crack growth prediction in specimens and structures of aluminium alloys is discussed. The significance of similarity conditions is emphasized and the K-dominated zone is briefly addressed. Secondly, the significance of water vapour for fatigue crack growth in aluminium alloy is reported with a case history of subsurface crack initiation and crack growth in vacuum. Some comments are presented on physical understanding and practical applications.     

Small crack growth in combined bending–torsion fatigue of A533B steel

Crack growth rate data from bending, torsional and in-plane and 90° out-of-phase combined bending–torsional fatigue tests of A533B steel are presented. Crack growth was monitored from initial sizes generally in the range of 50–300  μm to final sizes of several millimetres. Crack growth rate was found to vary linearly with crack size. Two approaches for correlating the A533B crack growth rate were evaluated, an effective strain-based intensity factor range and a method based on total cyclic strain energy density. The approaches were also evaluated using small crack growth data from the literature for SAE 1045 steel and Inconel 718 specimens tested under axial–torsional loadings. Predicted crack growth lives using both approaches were found to agree within a factor of two of observed lives for nearly all of the data examined.     

Elastic–plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading

The paper presents the results of fatigue crack growth on low‐alloy 18G2A steel under proportional bending with torsion loading. Specimens with square sections and a stress concentration in the form of external one‐sided sharp notch were used. The tests were performed under the stress ratios R=?1, ?0.5 and 0. The test results were described by the ΔJ‐integral range and compared with the ΔK stress intensity factor range. It has been found that there is a good agreement between the test results and the model of crack growth rate, which includes the ΔJ‐integral range.     

A comparison of fatigue crack growth performance of two aerospace grade aluminium alloys reinforced with bonded crack retarders

To improve the fail‐safety performance of integral metallic structures, the bonded crack retarder concept has been developed in recent years. This paper presents an experimental investigation on the effectiveness of bonded crack retarder on fatigue crack growth life in two aerospace aluminium alloys: 2624‐T351 and 7085‐T7651. M(T) specimens bonded with a pair of straps made of GLARE fibre‐metal laminate were tested under the constant amplitude load. Although the bonded crack retarders increased the crack growth life in both alloys, the magnitude of life improvement is very different between them. Compared to unreinforced specimens, application of crack retarders has resulted in 90% increase in fatigue life in AA7085, but only 27% increase in AA2624. The significant difference in fatigue life improvement is owing to the material's intrinsic fatigue crack growth rate property, ie, the Paris law constants C and n. Value of n for AA7085 is 1.8 times higher than that for AA2624. Therefore, AA7085 is much more sensitive to reductions in the effective stress intensity factor brought by the crack retarders, hence better life improvement.