Effective Stress Intensity Factor Range Research Articles

On the prediction of fatigue crack growth based on weight functions in residual stress fields induced by laser shock peening and laser heating

AbstractThis study deals with fatigue crack growth prediction for thin sheet AA2024 specimens with residual stresses introduced through laser shock peening and laser heating treatments. Different weight functions are used to calculate the stress intensity factor due to the presence of residual stresses. A superposition principle is used by calculating the total stress intensity factor considering the applied loads and residual stresses. The fatigue crack growth is predicted using the Paris' law based on the effective stress intensity factor range, in that the effect of residual stresses is considered by changing the total stress intensity factor ratio. It is concluded, that weight functions are a powerful tool to predict fatigue crack growth in AA2024 containing residual stress fields, as long as the gradient in the loading direction, as induced by laser shock peening and laser heating, is moderate.

3D predictions of the local effective stress intensity factor as the fatigue crack propagation driving force

The objective of this study is to develop a numerical tool using the commercial software, Abaqus and Python, to predict the fatigue crack front shape while taking into account the influence of plasticity induced crack closure on crack propagation in three Dimensional (3D) structures. In this aim, a 3D model of a compact tension specimen made out of stainless steel 304L, and subjected to a constant loading scheme, is proposed. The crack propagation is considered to be driven by the stress fields developed in the vicinity of the crack tip and thus by the stress intensity factor K. Two parallel simulations are used: an elastic simulation intends to calculate the local maximum stress intensity factor while the other, an elasto-plastic one, aims at obtaining the plastic wake and the resulting crack closure load. The results of both simulations are combined in order to constitute the effective stress intensity factor range, which is in turn used, along with Paris law, to calculate the crack propagation along the thickness. The local crack advancements obtained allow to construct the new crack front. Finally, a node release technique is used with geometry remeshing to issue new iterations with new boundary conditions that respond to the changes in the crack front. The procedure is repeated until the stabilization of the effective stress intensity factor values all along the specimen thickness is reached. The results obtained are compared with previously issued experimental results, showing very good results in small scale yielding and beyond that a large dependency on the plastic zone size developed in the neighborhood of the crack front.

Fatigue crack propagation behavior of polyether ether ketone under biaxial loading

AbstractPolyether ether ketone (PEEK) has become a promising material in total joint replacement. However, it still faces the risk of fatigue fracture during service. In this paper, the effects of biaxial stress ratio λ, cyclic stress ratio R, and load phase difference θ on fatigue crack propagation (FCG) behavior of PEEK are investigated. In the case of vertical cracks, results show that the FCG rate of PEEK increases with the R value, while decreases with the increase of λ value. Furthermore, the effective stress intensity factor range ΔKeff can uniformly describe the biaxial FCG behavior at different cyclic stress ratios. In the case of 45° slant cracks, compared with mode‐I intensity factor range ΔKI, the energy release rate range ΔG is more accurate for describing the FCG behavior under various load phase differences. In addition, the investigation on the 45° crack propagation path shows that a bifurcated Y‐shaped crack appears under 180° load phase difference, while no bifurcated crack appears under 90° load phase difference and uniaxial loading. Three different methods are used to predict the crack propagation path. The comparison results show that the maximum circumferential stress (MTS) criterion can well predict the crack propagation path under out‐of‐phase biaxial loading and uniaxial loading.

The Numerical Analysis of the In-Plane Constraint Influence on the Behavior of the Crack Subjected to Cyclic Loading.

The paper presents the influence of in-plane constraints defined by T-stress on the behavior of a crack subjected to cyclic loading. In the analysis, a modified boundary layer model approach was used in which the cohesive model was introduced. In the simulations, the constant maximum value of the stress intensity factor and four levels of T-stress were defined. The model was subjected to ten repeated stress cycles. Based on the results obtained, an analysis of the effect of the in-plane constraint on selected aspects of crack behavior was made. The strong influence of in-plane constraint applied in the model on the crack closure and the fatigue crack growth rate was proven. Since the in-plane constraint described the influence of geometry on the stress field surrounding the fatigue crack tip in real geometry, the results suggested that it is possible to create precise formulae connecting the level of the in-plane constraint with the effective stress intensity factor range and to incorporate the T-stress or Q-stress level in the Paris law.

Effects of rolling reduction and direction on fatigue crack propagation in commercially pure titanium with harmonic structure

Cold rolling followed by heat treatment was performed on commercially pure titanium with a bimodal harmonic structure, which is defined as a coarse-grained region (Core) surrounded by a network structure of fine grains (Shell), and fatigue crack propagation tests were conducted to clarify the effects of the rolling reduction, rolling direction, and force ratio. From the relationship between the crack propagation rate da/dN and the stress intensity factor range ΔK, da/dN for the L-T orientation was always higher than that for the T-L orientation, and da/dN was higher for a higher force ratio and a higher rolling reduction for either rolling reduction. Crack closure resulting from the roughness of the fracture surface can be partially explained by the above effects; however, the relationship between da/dN and the effective stress intensity factor range ΔKeff also depended on the same factors, while the effects were smaller than those for the da/dN–ΔK relationship. The crack opening stress intensity factor Kop,th and effective stress intensity factor range ΔKeff,th under the threshold condition linearly increased with the square root of the average grain size in the Shell region, which decreased with rolling reduction. Thus, the threshold condition of the harmonic structured material is considered to be determined by the average grain size in the Shell region.

Effects of Crack Closure on the Fatigue Crack Growth Rates of Ferritic Steels Subjected to Severe Reversing Loads

Abstract Low-alloy steels are extensively used in pressure boundary components of nuclear power plants. The structural integrity of the components made of low-alloy steels can be evaluated by the flaw evaluation procedure provided by Section XI of the ASME Boiler and Pressure Vessel Code. According to the Code, the stress intensity factor range ΔK can be used to determine the fatigue crack growth rates of the material. However, it has been reported that the fatigue crack growth rate under severe reversing loads is also strongly influenced by crack closure behavior. This paper discusses the relation between applied stresses and the fatigue crack growth rate for cracks in low-alloy steels exposed to air. Compressive-tensile cyclic loadings are applied to center-notched plates to obtain the fatigue crack growth curves. The test data demonstrate that effective stress intensity factor range predicted by our closure model described the crack growth property more accurately. A comparison among crack closure models indicates that our crack closure model is suitable to predict the crack growth rates when low constraint conditions are assumed at the crack tip due to severe reversing loads.

Fatigue crack propagation near the interface between Al and steel in dissimilar Al/steel friction stir welds

Fatigue crack propagation (FCP) tests were conducted using the dissimilar joints between Al alloy and steel fabricated by friction stir welding. CT specimens were sampled from the friction-stir-welded plates so that the initial notch was consistent with the interface. Crack closure during FCP was measured by a back-face strain gauge. The FCP rates of the welds were slower than those of Al parent metal. Crack opening points of the welds were higher than that of the parent metal. FCP rates were nearly the same among all the samples, when FCP rates were estimated by the effective stress intensity factor range.

Challenging the “ΔKeff is the driving force for fatigue crack growth” hypothesis

Tests are used to verify the hypothesis “the fatigue crack growth (FCG) driving force is the effective stress intensity factor range ΔKeff″. The tests are performed measuring FCG rates in steel and aluminum C(T) and DC(T) specimens under fixed {ΔK, Kmax} loading conditions and during FCG delays induced by single overloads. Crack-opening loads Pop are redundantly measured along the crack path in all tests, using independent near and far field strain-gages, as well as Digital Image Correlation (DIC) techniques. Finally, elastoplastic strain loops within the reverse plastic zone ahead of crack tips are measured using a stereo microscope DIC system.

Suitability of constraint and closure models for predicting crack growth in generic configurations

The effective stress intensity factor range ΔKeff is commonly considered to govern the fatigue crack growth and may be estimated through the crack opening stress Sop and the constraint factor α. In the literature closed-form expressions have been developed for estimating both variables in a center-cracked plate with elastic-perfectly plastic behavior subjected to remote uniform stresses. However, such expressions are frequently adopted regardless of geometry, material and loading and, moreover, α is often given a fixed value. The final objective is to assess the suitability of existing constraint and closure models for performing accurate crack-growth predictions in configurations that do not meet the original hypotheses. The region-II growth of a hole-edge crack is predicted in the 42CrMo4 steel by integrating crack growth laws calibrated with data from standard compact tension (CT) specimens. The results show overall better predictions by using the same constraint model for estimating α in both geometries, rather than by treating it as a fitting parameter in CT specimens. Unexpectedly, the predictions obtained at different stress ratios were, in general, more accurate by integrating a non-closure law based on ΔK and independent of Sop and α.

Fatigue Failure Characteristics of Single-Crystal Fe-3%Al Alloy

To obtain a better understanding of the mechanical properties and failure characteristics of the single-crystal Fe-3%Al alloy (SC), tensile and fatigue properties of the SC and polycrystalline Fe-3%Al alloy (PC) have been investigated. The tensile strength and fracture strain for the SC samples were different depending on the loading direction, i.e., 〈111〉, 〈110〉 and 〈100〉, which could be explained by the Schmid factor. Fatigue strength for the SC samples was basically correlated with their tensile strength. Different fatigue properties were obtained for the PC sample, e.g., the high fatigue strength was obtained in the early fatigue stage, and significant reduction in the fatigue strength was appeared in the later fatigue stage, e.g., low endurance limit at 107 cycles. The reason for this was caused by the material brittleness due to the accumulated dislocation at the grain boundaries. Because the high ductile SC samples made severe plastic deformation ahead of the crack tip, the crack growth rate did not enhance even if the high stress intensity factor range was applied in Region II (da/dN versus ΔK). The crack growth rate dropped just before the final fracture. Effective stress intensity factor range was estimated using the crack closure model, but the crack growth rate is found to be affected strongly by the slip system of SC sample.

How to get a correct estimate of the plastic zone size for shear-mode fatigue cracks?

It was found that standardly calculated sizes of plastic zones ahead of mode II and mode III cracks during fatigue experiments close to threshold loading were very large and the stresses in the specimen net cross section without stress concentration were close to the yield stress. This represents a theoretical contradiction, since at threshold loading the plastic zones should be very small. In order to clarify the situation, results from three approaches were compared: (i) linear-elastic fracture mechanics, (ii) nonlinear Hutchinson-Rice-Rosengren (HRR) stress field and (iii) elastic-plastic finite element analysis considering nonlinear material behaviour according to the cyclic stress-strain curve. It was explained that, unlike under mode I loading, the plastic zone size should not be calculated using the applied maximum stress intensity factor (SIF). Instead, the effective SIF range needs to be used for calculation of stress fields ahead of the crack tip and, consequently the plastic zone sizes. Using these values realistic plastic zone sizes were obtained (less than 50μm). It also implies that stress in the specimen net cross section should not be calculated directly. A large part of loading applied to the specimen in terms of force or torque is transferred by fracture surfaces.

High-temperature fatigue crack propagation study of superalloy GH4169 by single-lens 3D digital image correlation

The characterization of fatigue crack propagation behavior is crucial for performance and reliability evaluation of aerospace materials. In this study, high-temperature (maximum: 650°C) fatigue crack propagation experiments of Ni-based superalloy GH4169 were conducted. The bi-prism-based single-lens 3D digital image correlation (BSL 3D DIC) technique was used to in-situ measure the displacement and strain fields near fatigue crack tip. Based on the deformation information, the mode I stress intensity factor range ΔK and the crack opening displacement (COD) were determined for characterizing the crack closure effect. As the major fatigue crack growth model, the parameters of modified Paris’ law were obtained based on the effective stress intensity factor range ΔKeff and the fatigue crack propagation rate (FCPR). Additionally, two kinds of J integrals, JP (path integral method) and JK (stress intensity factor K method), were used to evaluate the small-scale yielding approximation.

Experimental and numerical investigation of residual stress effects on fatigue crack growth behaviour of S355 steel weldments

Fatigue crack growth tests have been conducted on S355 G10+M structural steel which is widely used in the fabrication of offshore structures. Fracture mechanics tests have been performed on compact tension specimens with the crack tip located in the heat affected zone. All tests were performed at room temperature in air and the obtained results are compared with the literature data available on a range of offshore structural steels and also the recommended BS7910 trends using the 2-stage law and simplified law. The specimen orientation, with respect to the location of the extraction within the welded plate, has also been examined and discussed in this work. Residual stress measurements have been performed prior to testing by using the neutron diffraction technique. Finally, a numerical model has been developed in order to calculate the effective stress intensity factor range in the presence of residual stresses. The results have shown that the residual stresses play a key role in the fatigue life of the welded structures, especially in the near threshold region.

Numerical analysis of central mixed-mode cracking in steel plates repaired with CFRP materials

Finite element method (FEM) was adopted to study the fatigue properties of steel plates with central mixed-mode (I/II) crack repaired with carbon fiber-reinforced polymer (CFRP) sheets. To simulate crack propagation in repaired and un-repaired specimens, a script was written in Python for automatic modelling. The numerical results were compared with the experimental results, and they fitted well in terms of crack growth trajectories and fatigue propagation lives. Thereafter, different parameters such as the number of CFRP layers, CFRP width, CFRP modulus, and load application angle were considered to investigate CFRP repairing efficiency. Results demonstrated that FEM effectively simulated the fatigue performance of steel plates with mixed-mode crack. CFRP sheets can reduce the effective stress intensity factor (SIF) range to prolong the fatigue life of the cracked steel plate. The aforementioned parameters significantly affected the fatigue performance.

Crack closure effects on fatigue damage ahead of crack tips

Elber’s assumed long ago that the effective stress intensity factor (SIF) range ΔKeff = Kmax − Kop is the actual driving force for fatigue crack growth (FCG), where Kop is the SIF that fully opens the crack, and his idea still is widely used to predict residual lives of cracked components. However, although crack closure can affect the FCG process, the ΔKeff idea cannot explain many of its peculiarities. To try to understand why this happens, the actual Kop role in FCG is questioned comparing ΔKeff–based predictions with similar predictions obtained using an alternate model that estimates crack increments assuming they are caused instead by the accumulated damage ahead of the crack tip. To be fair, this damage is calculated by the very same strip-yield mechanics used to calculate Kop and ΔKeff, i.e. the deformations predicted by the strip-yield model are used to describe the cyclic strain field ahead of the crack tip as well. Hence, the main goal of this exercise is to compare two different hypotheses for the actual FCG driving force using the same formulation basis. Both models are tested for different materials, constraint factors, and stress to yield strength ratios combinations, considering and neglecting the effect of crack closure. This exercise indicates that the effects of crack closure predicted by the critical damage model can be significantly lower than those predicted by the ΔKeff model.

A closure model for predicting crack growth under creep-fatigue loading

A strip-yield model was formulated to simulate creep-fatigue crack growth and to quantify the influence of hold time on plasticity-induced crack closure during creep-fatigue crack growth. Creep-fatigue experiments have shown that longer creep hold times result in faster crack growth rates in subsequent fatigue cycles. This model advances the idea that a decrease of plasticity-induced crack closure is experienced by the crack during fatigue loading when a longer hold time is applied each creep-fatigue cycle. Consequently, the crack tip experiences an increase in the effective stress intensity factor range causing faster growth rate during the fatigue loading. The weight function method was used to compute stress intensity factors and surface displacements for cracks embedded in a material experiencing elastic, plastic and creep deformations at elevated temperatures. It is shown that the longer the hold time, the larger the creep deformation and crack opening displacements in the near crack-tip region. In turn, this leads to a decrease in the crack-tip opening stress/load and faster crack growth rates during the subsequent fatigue cycle. The model was used to perform simulations of creep-fatigue crack growth at elevated temperatures in a nickel-base superalloy and AISI 316 austenitic steel.

Fatigue crack propagation under the condition where the superimposed stress history with different frequency components acts intermittently

ABSTRACT In this study, fatigue crack propagation under the condition where the superimposed stress history with different frequency components was given intermittently was investigated by numerical simulation and fatigue crack propagation test. The numerical simulation of fatigue crack propagation used in this study can consider the opening and closing behaviour of fatigue crack and implement stress history extraction algorithm that contributes to fatigue crack propagation under superimposed stress history with different frequency components. An advanced fracture mechanics approach based on the RPG (Re-tensile Plastic zone Generating) stress criterion to identify the effective stress intensity factor range was applied to estimate the fatigue crack propagation history. Fatigue crack propagation test under superimposed stress history containing different frequency component appearing intermittently was also conducted. Validity of our applied numerical simulation method was investigated by comparing numerical simulation results with experimental ones. As a result, the validity of our proposed numerical simulation procedure to estimate the fatigue crack propagation history under such a complicated applied stress history was confirmed.

Fatigue-crack growth in two aluminum alloys and crack-closure analyses under constant-amplitude and spectrum loading

Fatigue-crack-growth tests were conducted on compact, C(T), and middle-crack tension, M(T), specimens made of 7075-T6 and 7249-T76511 aluminum alloys. The 7075 tests were conducted on thin-sheet (2-mm thick) material; whereas, the 7249 tests were conducted on three thicknesses (2, 3.2 and 6.35-mm). The thin-sheet 7075 alloy did not have residual stresses, but the 7249 alloy (B = 2 mm) had low-level (<10 MPa) residual stresses from measurements. However, the other two 7249 alloy thicknesses were residual-stress free based on measurements. These tests were conducted to generate fatigue-crack-growth-rate data from threshold to near fracture at two load ratios (R = 0.1 and 0.7). Two methods were used to generate near threshold data on C(T) specimens: (1) compression pre-cracking constant-amplitude (CPCA) and (2) compression pre-cracking load-reduction (CPLR). Constant-amplitude tests were conducted on the M(T) specimens at the same two load ratios. Crack-closure measurements using a compliance method were made on some of the low R tests and a crack-closure model were used to develop an effective stress-intensity factor range against rate relation using a constant constraint factor (α = 1.85). The constraint factor accounts for three-dimensional stress-state effects on plastic yielding at crack tips and crack-closure behavior.Simulated aircraft wing spectrum tests were conducted on the M(T) specimens using two modified full-scale-fatigue-test (FSFT) spectra used on the P-3C aircraft. Tensile pre-cracking was used on all of the M(T) specimens, except one 3.2-mm thick 7249 specimen, before the spectra were applied. The same spectrum sequence was applied, but one had tension-compression loads, whereas, the other only tension-tension loads. The spectrum tests were used to calibrate the constraint-loss regime (plane-strain to plane-stress; α = 1.85–1.0) behavior for the FASTRAN strip-yield model. Comparisons were made between the spectrum tests and calculations made with the FASTRAN life-prediction code; and the calculated crack-growth lives were generally within ±20% of the test results.

Thermomechanical fatigue crack growth in a single crystal nickel base superalloy

Thermomechanical fatigue crack growth in a single crystal nickel base superalloy was studied. Tests were performed on single edge notched specimens, using in phase and out of phase thermomechanical fatigue cycling with temperature ranges of 100–750 °C and 100–850 °C and hold times at maximum temperature ranging from 10 s to 6 h. Isothermal testing at 100 °C, 750 °C and 850 °C was also performed using the same test setup. A compliance-based method is proposed to experimentally evaluate the crack opening stress and thereby estimate the effective stress intensity factor range ΔKeff for both isothermal and nonisothermal conditions. For in phase thermomechanical fatigue, the crack growth rate is increased if a hold time is applied at the maximum temperature. By using the compliance-based crack opening evaluation, this increase in crack growth rate was explained by an increase in the effective stress intensity factor range which accelerated the cycle dependent crack growth. No significant difference in crack growth rate vs ΔKeff was observed between in phase thermomechanical fatigue tests and isothermal tests at the maximum temperature. For out of phase thermomechanical fatigue, the crack growth rate was insensitive to the maximum temperature and also to the length of hold time at maximum temperature. The crack growth rate vs ΔKeff during out of phase thermomechanical fatigue was significantly higher than during isothermal fatigue at the minimum temperature, even though the advancement of the crack presumably occurs at the same temperature. Dissolution of γ′ precipitates and recrystallization at the crack tip during out of phase thermomechanical fatigue is suggested as a likely explanation for this difference in crack growth rate.

Fatigue design of weld part in non-combustible magnesium alloy based on fracture mechanics

Fatigue design of weld part in non-combustible magnesium alloy has been studied. Specimens for fatigue test were produced by TIG welding with different welding conditions. According to result of fatigue strength tests, all weld specimens tested in the present study were broken at the weld prat, and a weld defect was found as a fatigue fracture origin. Fatigue life was well arranged by effective stress intensity factor calculated with a size of weld defect played as a fracture origin and applied stress. Therefore, it is speculated that fatigue strength of weld part is depending on a size of weld defect and threshold stress intensity factor at the weld part. Size of weld defect and value of threshold stress intensity factor possibly changed by welding condition. Therefore, relationship between heat input during welding process and threshold stress intensity factor was studied by conducting fatigue crack growth test at the weld part. The value of threshold stress intensity factor range increased with increase in heat input of welding process. However, values for threshold stress intensity factor range almost coincided when the crack growth curves were arranged by effective stress intensity factor range. Difference in threshold stress intensity factor range due to difference in heat input of welding process was mainly induced by change in crack closure effect. It is proposed that effect of crack closure depending on mechanical property of weld part should be taken into account on fatigue design of weld part in non-combustible magnesium alloy.