Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size () (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

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The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range ( K _RP) corresponding to the period in which the re-tensile plastic zone appears, in place of K _eff proposed by Elber [1], for a fatigue crack propagation parameter.We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover K _th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of K _RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on K _eff based on the crack opening load and K _eff ^cl based on the crack closing load. Moreover K _RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

Analysis of crack propagation using ΔK and Kmax

In this investigation a general relationship between fatigue crack growth rate, da/dN, and a two-parameter ΔK and K_max driving force is derived using fundamental fatigue (ε–N curve) properties. A power-law relationship between ΔK and K_max is obtained by relating the crack growth rate to the fatigue life of the ‘process zone’. Theoretically, there are four different regions on a log–log plot depending on the particular combinations of ΔK and K_max. The actual analysis of experimental data indicates only two different regions namely, ΔK and K_max dominated, corresponding to high and low load ratios, respectively. A new way of representing the da/dN data in terms of ΔK and K_max by means of the crack propagation (CP) table is proposed. Finally, the application of the CP table for predicting crack growth rate under constant amplitude loading is explained and discussed.     

Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy

The micromechanisms of fatigue crack propagation in a forged, polycrystalline IN 718 nickel-based superalloy are evaluated. Fracture modes under cyclic loading were established by scanning electron microscopy analysis. The results of the fractographic analysis are presented on a fracture mechanism map that shows the dependence of fracture modes on the maximum stress intensity factor, K_max, and the stress intensity factor range, ΔK. Plastic deformation associated with fatigue crack growth was studied using transmission electron microscopy. The effects of ΔK and K_max on the mechanisms of fatigue crack growth in this alloy are discussed within the context of a two-parameter crack growth law. Possible extensions to the Paris law are also proposed for crack growth in the near-threshold and high ΔK regimes.     

Generation and analysis of FCG data using a single specimen and Kmax–ΔK testing matrix

A custom method to generate fatigue crack growth (FCG) data requires testing of multiple specimens at different load ratios, R, and the application of a load shedding procedure from pre-cracking level to threshold. In this paper, a novel method of testing has been investigated which utilizing a single specimen and a testing matrix in terms of K_max and ΔK values corresponding to predetermined R-ratios for which FCG data are recorded. Automatic K-controlled tests on 2324-T39 Al alloy were conducted using both increasing and decreasing ΔK procedures while K_max was kept constant. Results show that the increasing ΔK procedure gives less scatter than decreasing ΔK procedure. Also, fatigue crack growth curves near the threshold region obtained from increasing ΔK are above the curves obtained from decreasing ΔK procedure. These differences are explained by means of interaction between cyclic plastic zones and their effect on fatigue damage. The procedure with increasing ΔK demonstrated minimal interaction effects and hence it is recommended for efficient FCG data generation. The proposed procedure reduces testing time, the overall scatter associated with multiple samples and eliminates possible uncertainty linked to the load shedding procedure and its effects on threshold.     

Internal stress behavior of the short ceramic fiber reinforced aluminum alloy under tensile deformation

The in situ measurement of phase stress under tensile deformation on an A6061 alloy reinforced with SiC whiskers (Al/SiCw MMC: Metal Matrix Composite) was performed using the X-ray diffraction technique. In order to raise a preciseness of measurements, we applied a profile fitting technique to separate the nearby located diffraction peak. Tensile deformation on elastic to plastic range was applied by four points bending device and discussed internal stress behavior in the short ceramic fiber reinforced MMC. Phase stress in Al matrix was increased linearly up to 2800×10⁻⁶ in strain and then saturated immediately. On the other hand phase stress in SiC whiskers shows an unstable stress behavior. It was decreased at first because of the Poisson's effect from Al matrix but reversed over 500×10⁻⁶ applied strain. The measured phase stress behavior in elastic region agreed with the calculations using micromechanics based on Eshelby/Mori–Tanaka model except for this unstable internal stress region. The macro stress behavior in plastic region was extremely small than that of the tensile test results. It supposed that the mechanism of strength is not so much the fiber reinforcing as the dispersion strengthening like the Orowan mechanism. Regarding the fatigue property, ΔK_th of the Al/SiC MMC, this was lower than that of the A6061 alloy. On the Al/SiCw MMC specimen, many micro void formations were observed around the fatigue crack tip even under the ΔK_th of A6061. It was considered that these were caused by the high gradient of residual stress on composite process and the unstable stress behavior in low ΔK region.     

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.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth 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-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using 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 was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.     

Classification of environmentally assisted fatigue crack growth behavior

Fatigue crack growth is represented using fracture mechanics parameters, ΔK and K_max. Environmental effects that depend on time and stress affect the fatigue behavior predominantly through K_max parameter. The superimposed effects of environment and stress are seemingly complex. We have developed a methodology for classifying and separating the effects of environment on fatigue crack growth. A “crack growth trajectory map” is constructed from the behavior of ΔK versus K_max for various constant crack growth rate curves. A “pure fatigue” behavior is defined, in terms of environment-free behavior, such as in high vacuum. Deviation from this “pure fatigue” reference of the trajectory map is associated with either monotonic mode of fracture or to the superimposed environmental effects on crack growth. Using such an approach, called “Unified Damage Approach”, we classify the environmental effects in almost all materials into only five types. Each of these types shows the combination of time and stress affecting the crack tip driving force, and thus ΔK and K_max. The trajectory map depicts the changing material resistance due to the changing crack growth mechanisms with increasing crack growth rate, as reflected in terms of the applied stress intensities, ΔK and K_max. Thus the trajectory map provides a useful tool to separate the contributions from pure fatigue and superimposed monotonic modes and the governing crack growth mechanisms as a function of load-ratio, crack growth rate and environment. Understanding and quantification of the governing mechanisms would help in developing a more fundamental and reliable life prediction method.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Effects of various environments on fatigue crack growth in Laser formed and IM Ti–6Al–4V alloys

The fatigue crack growth behaviors of Laser formed and ingot metallurgy (IM) Ti–6Al–4V alloys were studied in three environments: vacuum, air and 3.5% NaCl solution. Taking the Unified Fatigue Damage Approach, the fatigue crack growth data were analyzed with two intrinsic parameters, stress intensity amplitude ΔK and maximum stress intensity K_max, and their limiting values ΔK^* and . Fatigue crack growth rates da/dN were found increase with stress ratio R, highest in 3.5% NaCl solution, somewhat less in air and lowest in vacuum, and higher in IM alloy than in Laser formed one. In 3.5% NaCl solution, stress corrosion cracking (SCC) was superimposed on fatigue at R=0.9 for where K_max>K_ISCC, the threshold stress intensity for SCC. This and environment-assisted fatigue crack growth were evidenced by the deviation in fatigue crack growth trajectory (ΔK^* vs. curve) from the pure fatigue line where . Furthermore, the fractographic features, identified along the trajectory path, reflected the fatigue crack growth behaviors of both alloys in a given environment.     

FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR THROUGH A COMPRESSIVE RESIDUAL STRESS FIELD

Behaviour of fatigue crack growth and closure through a compressive residual stress field is investigated by performing fatigue crack growth tests on welded SEN specimens of a structural steel (JIS SM50A). Depending on the type of the initial residual stress in the region of crack growth, the growth and closure of the crack show different behaviour. In particular, in the transition region from a compressive residual stress field to a tensile residual stress field, the fatigue crack growth rates cannot be described by the effective stress intensity factor range ΔK_eff, based on the measured crack opening stress intensity factor K_op. Also it is found that the R'-method using the data of da/dN vs ΔK for residual stress-free specimens, with the effective stress ratio R'[=(K_max+K_r)/(K_min+K_r)], gives non-conservative predictions of the growth rates in the transition region. Observations of crack closure behaviour in this study indicates that partial opening of the crack occurs and this plays an important role in crack growth through a compressive residual stress field. Based on the concept of a partial opening point (defined and measured in this work), fatigue crack growth behaviour can be better explained.     

Effect of sudden load decrease on the fatigue crack growth in cold drawn prestressing steel

This paper analyzes the overload retardation effect (ORE) on the fatigue crack growth (FCG) of cold drawn prestressing steel when different loading sequences are used. The ORE is more intense for elevated load decrease or for low initial stress intensity factor (SIF) range ΔK₀. A transient stage can be observed in the Paris curve (da/dN–ΔK) when the K_maxΔK value suddenly decreases, associated with the ORE and with the evolution of the plastic zone and compressive residual stresses near the crack tip. In tests with K_max decrease, a small zone appears related to FCG initiation, with a fatigue fractography resembling the tearing topography surface (TTS) mode, and associated with a decrease of crack tip opening displacement (CTOD).     

Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Fatigue thresholds and fatigue crack growth (FCG) rates in corner notched specimens of a forged Ti–6Al–4V aero-engine disk material were investigated at room temperature and 350 °C. The threshold stress intensity range, ΔK_th, was determined by a method involving a step change in stress ratio (the ‘jump in’ method). It was found that for three high stress ratios (R=0.7–0.9), where crack closure effects are widely accepted to be negligible, there were similar ΔK_th values at room temperature and 350 °C under the same R. For a given temperature, ΔK_th was observed to decrease from 3.1 to 2.1 MPam with R increasing from 0.7 to 0.9. The fatigue crack growth rate was influenced by increasing temperature. For high stress ratios, FCG rate at 350 °C was higher than that at room temperature under the same ΔK. For a low stress ratio (R=0.01), higher temperature led to higher FCG rates in the near-threshold regime, but showed almost no effect at higher ΔK. The influence of stress ratio and temperature on threshold and FCG rates was analysed in terms of a K_max effect and the implication of this effect, or related mechanisms, are discussed. In light of this, an equation incorporating the effects of the K_max and fatigue threshold, is proposed to describe FCG rates in the near-threshold and Paris regimes for both temperatures. The predictions compare favourably with experimental data.     

A genetic algorithm for unified approach-based predictive modeling of fatigue crack growth

This paper presents a framework to derive models of fatigue crack growth in real-life applications based on the unified approach.The unified approach enunciates that two parameters-namely, the stress intensity amplitude ΔK and the peak stress intensity K_max-drive fatigue crack growth. It captures and explicates the various fatigue phenomena coherently. However, its application for damage prediction is still in its infancy. Mathematical models that are consistent with the approach and the various observed characteristics under various environments are imperative for fatigue damage life prediction. These models will reduce cumbersome experimentation that is usually needed for the fatigue crack growth analysis. The framework presented in this paper consists of using the unified approach to design the structure of a model that relates fatigue crack growth with the specified microstructure, applied stress and environmental conditions. The fatigue growth model is derived by parametrizing, using a genetic algorithm, these structural relationships from the known experimental data. This model can quantitatively estimate crack growth rate under the given combination of microstructure, applied stress and environmental conditions. The initial research on modeling fatigue crack growth dynamics in Al-5052 under vacuum and air has revealed that the models resulting from the framework can capture the actual crack growth pattern to within 12% accuracy, and that an automatic rendering of ΔK^* vs. trajectories is possible for a given material and environmental conditions.