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.     

Fatigue crack growth testing at negative stress ratios: discussion on the comparability of testing results

It is an accepted fact in fatigue community that compressive loads contribute to fatigue crack growth. Evidences range from fatigue crack growth under fully compressive loads to effects of compressive underloads to negative stress ratio loading. Because the crack closes under compression and the crack flanks transmit compressive stresses, the loading situation is completely different to those of tensile loading. The present paper addresses the comparability of crack growth testing procedures at negative stress ratios. It reveals that compressive loading at the crack tip differs in different specimens for an equal maximum stress intensity factor K_max and negative stress ratio R. Furthermore, the crack length can significantly influence the loading conditions at the crack tip for tension–compression loading. Depending on the specimen type and crack length, a negative force ratio may lead to a change of algebraic sign of the stresses at the crack tip or not. As a consequence, the comparability of available literature results for R ≤ 0 tests is not ensured. Proposals to improve the comparability of tension–compression crack growth testing will be given.     

Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains

It is generally accepted that the fatigue crack growth (FCG) depends mainly on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). The two parameters are usually combined into one expression called often as the driving force and many various driving forces have been proposed up to date. The driving force can be successful as long as the stress intensity factors are appropriately correlated with the actual elasto-plastic crack tip stress-strain field. However, the correlation between the stress intensity factors and the crack tip stress-strain field is often influenced by residual stresses induced in due course.A two-parameter (ΔK_tot, K_max,tot) driving force based on the elasto-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified to the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of the local crack tip stresses and strains on fatigue crack growth. The FCG was predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region. The model was developed to predict the effect of the mean and residual stresses induced by the cyclic loading. The effect of variable amplitude loadings on FCG can be also quantified on the basis of the proposed model. A two-parameter driving force in the form of: was derived based on the local stresses and strains at the crack tip and the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The effect of the internal (residual) stress induced by the reversed cyclic plasticity manifested itself in the change of the resultant (total) stress intensity factors controlling the fatigue crack growth.The model was verified using experimental fatigue crack growth data for aluminum alloy 7075-T6 obtained under constant amplitude loading and a single overload.     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Fatigue crack closure study based on whole-field displacements

This study is concerned with crack tip strain field fluctuations at loads below the point of crack closure in fatigue cycling. Moiré interferometry was used to investigate crack tip fields in compact tension specimens, cracked under constant stress intensity range and fixed R-ratio conditions. An elastic-plastic finite element model of simulated closure was developed to provide a theoretical cross-reference for the moiré studies. The ‘stretched zone’, which is believed to be the most significant source of closure effects, was simulated by inserting a constant thickness strip of elements into the crack before unloading from the maximum load point. Analysis of the crack tip fields in the experimental and theoretical cases was made in terms of crack face opening profiles, compliance changes and elastic stress intensity parameters. The latter were inferred through stress and displacement measurements made along circular and radial paths relative to the crack tip. Closure on the stretched zone was found to generate non-proportional loading in the crack tip field, so that the resulting stress changes were not well characterized by the asymptotic elastic equations. It is concluded firstly, that significant strain fluctuations occur below the point of closure load and that these should not be ignored in crack propagation studies. Secondly, the effective stress intensity range in fatigue cycling is not simply related to the open-crack stress intensity range and the need therefore remains for R-ratio and geometry effects to be treated as variables in crack propagation data collection programmes.     

Effect of strain rate on stepwise fatigue and creep slow crack growth in high density polyethylene

The effects of frequency and R-ratio (the ratio of minimum to maximum stress in the fatigue loading cycle) on the kinetics of step-wise crack propagation in fatigue and creep of high density polyethylene (HDPE) was characterized. Stepwise crack growth was observed over the entire range of frequency and R-ratio examined. A model relating crack growth rate to stress intensity factor parameters and applied strain rate was proposed by considering the total crack growth rate to consist of contributions from creep and fatigue loading components. The creep contribution in a fatigue test was calculated from the sinusoidal loading curve and the known dependence of creep crack growth on stress intensity factor in polyethylene. At a very low frequency of 0.01 Hz, fatigue crack growth rate was found to be completely controlled by creep processes. Comparison of the frequency and R-ratio tests revealed that the fatigue loading component depended on strain rate. Therefore, crack growth rate could be modeled with a creep contribution that depended only on the stress intensity factor parameters and a fatigue contribution that depended on strain rate.     

Analytical and computational investigation into the influence of the compressive stress cycles on crack growth under variable amplitude loading using CTOD

Fatigue crack growth rate of 6061 T651 aluminum alloy centre‐cracked plates, subject to a variable amplitude loading (VAL), is established using a coupled analytical/computational approach. The method utilises the generalised Willenborg retardation model in conjunction with the Walker model, with several of the models parameters obtained through nonlinear finite element analyses. A two‐parameter approach is also used in this study to explore the influence of compressive stress cycles in a VAL scenario on the crack tip opening displacement, and in turn, on the resulting fatigue crack growth rate of the material. The work includes the evaluation of the crack tip opening displacement and residual stresses in the vicinity of a crack by nonlinear finite element analysis, and application of the Generalised Willenborg model to evaluate the fatigue crack growth; particularly, under the influence of the compressive stress cycles, tensile overloads and underloads have been investigated. The finite element analysis results are compared with the experimental results reported in earlier studies by the authors. The results further demonstrate two important phenomena, that is, (i) the influence of FCG retardation effects due to the tensile overloads and (ii) the acceleration effect due to the applied compressive underloads of a VAL stress–time history.     

Analysis of temperature distribution near the crack tip under constant amplitude loading

An analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two‐dimensional conduction heat transfer equation, in moving co‐ordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power–law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

Compressive maximum shear crack initiation and propagation

A maximum shear crack γ (a Mode II shear crack along the maximum shear direction associated with the crack tip shear displacement) was produced successfully in a so-called compressive maximum shear (CMS) specimen. This specimen was specificially designed to produce a compressive maximum shear failure which is one of two mechanisms widely believed to be responsible for limiting bearing fatigue life in rolling contact. The fracture initiation stress (or crack nucleation stress) σ_c and the upward crack propagation rate (toward the loading surface) $\text{dli}\text{dσi}$ per unit cyclic compressive stress increment were determined for the 52100 steel. These parameters were measured at two cleanness levels (DE and CEVM) [DE: basic electric arc furnace melted plus vacuum degassed. CEVM: Consumable electrode vacuum melted] and two tempered hardness levels, RC61 and 51. The possibility of determining K₁₁ for ith cycle was also elucidated. The formation of tail cracks and parallel multiple cracks as fine structure of CMS cracks can be well expounded by the concept of restoring tensile stresses and the residual shear stress relaxation at the CMS crack tip. The fracture mechanism advanced here can explain the formation of similar tail cracks and parallel multiple cracks frequently observed along the inclined shear cracks existing in the subsurface regions of rolling     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

High-temperature crack growth in low-cycle fatigue

The rates of low-cycle fatigue crack propagation in 1 Cr-1 Mo-0·25 V low alloy steel were determined under several types of loading at 1000 F. It was found that crack growth rates correlate well with the nominal crack tip stress. This method was also applied with good results to some published data where the fracture mechanics stress intensity factor had given only limited correlation. Several questions are thus raised regarding the relative importance of crack tip stress and crack length during crack growth in actual components.     

Measuring stress intensity factors during fatigue crack growth using thermoelasticity

Thermoelastic stress analysis has been developed in recent years as a direct method of investigating the crack tip stresses in a structure under cyclic loading. This is a consequence of the fact that stress intensity factors obtained from thermoelastic experiments are determined from the cyclic stress field ahead of a fatigue crack, rather than inferred from measurement of the crack length and load range. In the present paper the results of fatigue crack growth tests performed on welded ferritic steel plates are reported. From the results it can be observed that the technique is sensitive to the effects of crack closure and the presence of tensile and compressive residual stresses due to welding.     

Study of fatigue crack growth retardation due to overloads in polymethylmethacrylate

Retardation of the fatigue crack growth after overloading was investigated in conjunction with the craze deformation at the fatigue crack tip in polymethylmethacrylate. The craze deformation was measured by optical interference and analysed numerically with reference to a previously proposed craze model. In the base line loading, the craze stress concentrates at the crack tip with the applied load and, hence, the non-uniform stress distribution is attained at the maximum load. The overload alters this stress distribution. Just after overloading, the crack tip stress does not reach the previous level, even at the same maximum load. The reduced crack tip stress correlates well with the retarded duration after the overload. It is concluded, therefore, that the craze stress reduction at the crack tip is the cause of crack growth retardation.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

A diffusion-based approach for modelling crack tip behaviour under fatigue-oxidation conditions

Modelling of crack tip behaviour was carried out for a nickel-based superalloy subjected to high temperature fatigue in a vacuum and air. In a vacuum, crack growth was entirely due to mechanical deformation and thus it was sufficient to use accumulated plastic strain as a criterion. To study the strong effect of oxidation in air, a diffusion-based approach was applied to investigate the full interaction between fatigue and oxygen penetration at a crack tip. Penetration of oxygen into the crack tip induced a local compressive stress due to dilatation effect. An increase in stress intensity factor range or dwell times imposed at peak loads resulted in enhanced accumulation of oxygen at the crack tip. A crack growth criterion based on accumulated levels of oxygen and plastic strain at the crack tip was subsequently developed to predict the crack growth rate under fatigue-oxidation conditions. The predicted crack-growth behaviour compared well with experimental results.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.     

An experimental investigation of fatigue crack growth of stainless steel 304L

A series of fatigue crack growth experiments were conducted using round compact tension specimens of AISI 304L stainless steel under Mode I loading. The influences of the R-ratio (the ratio of the minimum load to the maximum applied load in a cycle), notch size, the tensile and compressive overloads, and the loading sequence on crack growth were studied. The results show that the material displays sensitivity to the R-ratio. The application of a tensile overload results in a short period of acceleration in the crack growth rate followed by a significant retardation in the crack growth rate. A compressive overload (underload) produces a short period of acceleration in crack growth and the magnitude of such an acceleration depends on the value of the loading amplitude of the constant-amplitude loading. Results from the two-step high-low loading sequence reveal a period of crack growth retardation at the beginning of the lower amplitude step, an effect similar to that of a single overload. Two existing crack growth models which are based on the stress intensity factor concept are evaluated using the experimental results. A two-parameter crack driving force approach together with a modified Wheeler’s model is found to correlate well the crack growth experiments.