Stress Intensity Factor Range Research Articles

Fatigue Crack Propagation in 5754 Aluminum Alloy under Four-Point Bending

The aluminum 5754 alloy is one of the widely used engineering materials in shipping, rivet making, tread plates and automotive industries. These engineering structures envisage variable loading conditions during their service. In addition to it, it is also experiencing seismic vibrations. Hence, the engineering components made from such aluminum alloy are susceptible to fatigue fracture. In the current study, the prediction of fatigue crack growth (FCG) in 5754 aluminum alloy was made using the exponential function. The beam specimen comes up with a cross-section of 25X25 mm2, a span length of 300 mm with a mechanical notch length of 2.70 mm at the centre was subjected to four-point bending (FPB) employing hydraulic INSTRON 8800 tensile testing apparatus. The periodic loading condition deformed the material up to large plastic deformation. The applied load was further down the elasticity of the material. The experimental data provided the relation between crack length (a) to the number of cycles (N) to failure. The response surface methodology (RSM) and modified exponential equation were used to predict the FCG. In RSM, when “stress intensity factor (K)” and “number of the cycle (N)" were considered independent variables, the response (a) was optimum (maximum) as compared to when “stress intensity factor range (del K)” and “fatigue crack growth rate (da/dN)” were considered independent variables. Hence, for designing the aluminum 5754 alloys as engineering structures, it was the number of cycles which provides a safe design as compared to da/dN. The modified exponential equation using an exponential function predicted the FCG for aluminum 5754 alloy in the form of a beam specimen. The anticipated results agreed with experimental data as the prediction ratio was 1.20 and the % deviation was 3.7.

Numerical prediction of fretting fatigue crack growth in scaled railway axles considering fretting wear evolution

To predict the fretting fatigue crack growth (FFCG) life of railway axles, a series of interrupted fatigue experiments were conducted on scaled railway axles. Subsequently, the evolutions of fretting wear and fatigue cracks in the press-fitted region were analyzed. Based on the test results, finite element models incorporating fretting wear evolution were established, and the FFCG was investigated using the maximum tangential stress criterion, cyclic resistance curve, and the modified NASGRO equation. The analysis revealed that the fretting wear evolution leads to stress redistribution at the press-fitted region, thereby promoting FFCG. When considering fretting wear evolution, the equivalent stress intensity factor (SIF) range of the crack remains above the threshold value throughout the short crack stage. However, neglecting fretting wear evolution results in the SIF range being below the threshold value for cracks shallower than 0.30 mm. This implies that considering fretting wear evolution enables life prediction throughout the short crack stage. As the crack length increases, the influence of fretting wear evolution on crack growth gradually diminishes. By accounting for fretting wear, a more accurate stress distribution in the press-fitted region can be obtained, leading to a more precise and conservative prediction of crack growth life.

Crack growth behaviour of P91 steel under trapezoidal loading at high temperature

The increased incentives to utilize renewable energy sources so as to supplement the energy requirements of the present civilization pose a challenge to the power plants running on fossil fuels, as they are required to operate in a ‘flexible’ manner instead of operating at a constant load as intended during their design and inception. This flexible mode of operation at elevated temperature causes a combined creep and fatigue type of loads to be applied on the components. This allows for a comprehensive and effective understanding of synergistic creep-fatigue crack growth behaviour to assess long term failure of components and accessories in plant. The use of P91 steel has been widely prevalent in power plant components owing to its high creep resistance, superior mechanical properties and excellent thermal conductivity, cost-effectiveness, and minimal coefficient of thermal expansion when compared to austenitic steels and Ni-based alloys. The American Society for Testing and Materials (ASTM) has proposed a standard for experimentally evaluating creep-fatigue crack growth, E 2760-19, wherein compact specimens, C(T) are tested under load-controlled conditions. The creep-fatigue crack growth regime and mode of fracture undergone by P91 steel at 600 °C were studied using C(T) specimens at two different force ratio 0.1 and 0.5 and with two different hold time 10 and 600 sec. The Creep fatigue crack growth behaviour has been characterized using stress intensity factor range parameter ∆K and (Ct)avg parameter to study the effect of hold time and force ratio.

Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures

In the shipbuilding, construction, automotive, and aerospace industries, welding is still a crucial manufacturing process because it can be utilized to create massive, intricate structures with exact dimensional specifications. These kinds of structures are essential for urbanization considering they are used in applications such as tanks, ships, and bridges. However, one of the most important types of structural damage in welding continues to be fatigue. Therefore, it is necessary to take this phenomenon into account when designing and to assess it while a structure is in use. Although traditional methodologies including strain life, linear elastic fracture mechanics, and stress-based procedures are useful for diagnosing fatigue failures, these techniques are typically geometry restricted, require a lot of computing time, are not self-improving, and have limited automation capabilities. Meanwhile, following the conception of machine learning, which can swiftly discover failure trends, cut costs, and time while also paving the way for automation, many damage problems have shown promise in receiving exceptional solutions. This study seeks to provide a thorough overview of how algorithms of machine learning are utilized to forecast the life span of structures joined with welding. It will also go through their drawbacks and advantages. Specifically, the perspectives examined are from the views of the material type, application, welding method, input parameters, and output parameters. It is seen that input parameters such as arc voltage, welding speed, stress intensity factor range, crack growth parameters, stress histories, thickness, and nugget size influence output parameters in the manner of residual stress, number of cycles to failure, impact strength, and stress concentration factors, amongst others. Steel (including high strength steel and stainless steel) accounted for the highest frequency of material usage, while bridges were the most desired area of application. Meanwhile, the predominant taxonomy of machine learning was the random/hybrid-based type. Thus, the selection of the most appropriate and reliable algorithm for any requisite matter in this area could ultimately be determined, opening new research and development opportunities for automation, testing, structural integrity, structural health monitoring, and damage-tolerant design of welded structures.

A hybrid modeling method of fatigue crack growth for gas turbine blades under combined high and low cycle fatigue loadings

Fatigue crack is one of the major faults of the gas turbine blades. Previous modeling studies on fatigue crack growth of blades mainly focus on a single numerical or analytical approach considering different sizes of cracks under various fatigue loadings. However, the actual crack propagation process is time-varying. The iteration and update of the model are necessary to evaluate the fatigue life of blades precisely. This paper proposes a hybrid modeling method to study blade crack growth under combined high and low cycle fatigue (CCF) loadings. The method emphasizes the combination and interaction between the finite element (FE) numerical simulation and the analytical calculation based on the fracture mechanics model. The current crack propagation length of the blade FE model is calculated from the crack growth rate obtained by the stress intensity factor (SIF) range according to Paris law. Then, a new SIF range is resolved from the FE model with the updated crack length. The proposed method is verified by the first-stage compressor blade from an in-service gas turbine. Results show that the crack growth is faster using the proposed hybrid modeling method than the traditional method. The update of the SIF range under CCF loadings cannot be ignored when predicting the fatigue life of the blade. Also, a sensitivity analysis is carried out. Suggestions are given on how to set the crack extension length at each stage during modeling, especially when the blade approaches failure.

Experimental Data-Driven approach for the evaluation of crack tip opening loads under variable amplitude loading

In this paper, we present a new data-driven approach for the evaluation of crack tip opening load (Pop) values under variable amplitude loading. These values are analysed for CT specimens manufactured from common aircraft grade aluminium alloys and subjected to several load sequences, all of which have a relatively high R-ratio content without significant overloads and underloads. Direct experimental measurements and outcomes of numerical simulations indicate that the Pop change abruptly from cycle to cycle. For this type of fatigue loading (including a military transport aircraft load spectrum with more than 400,000 turning points) and materials, it was found that Pop is well described by a linear function of the preceding minimum and maximum values of the applied loading. This finding provides a new simple way to evaluate the effective stress intensity factor range, which is often considered as a fatigue crack driving force. It is also verified via the use of machine learning that the proposed approach is capable of predicting the mean stress (R-ratio) effect on Pop for block loading. Therefore, the developed data-driven approach is a promising alternative to the computational methods, which currently dominate advanced fatigue life assessment procedures.

Influence of solution heating rate on grain structures and fatigue crack propagation behaviors of an aviation Al-Li alloy sheet

In this study, the effects of grain structure on the fatigue crack propagation (FCP) behaviors in the aviation Al-Li alloy sheets prepared by varying solution heating rates are discussed systematically. The results reveal that both the intensity of Goss texture and grain dimensions are improved with the decreased solution heating rates. Upon an identical stress intensity factor range (ΔK), the increased Goss texture of the sample with a solution heating rate of 2 ℃/min (2HR) promotes crack deflection, causing a decrease in FCP rates compared to that of the sample with a solution heating rate of about 100 ℃/min (FHR). The dislocations clustered near grain boundaries are more significant with increasing grain size during cyclic loading, which intensifies the strain localization. The accumulation of dislocations increases the possibility of micro-voids formation and creates the conditions for crack deflection, which results in a decrease in FCP rate. Besides, based on the calculation of the reversible plastic zone (RPZ) size, the initial ΔK entering the rapid propagation region increases with decreasing solution heating rates and exhibits a strong linear relationship with grain size.

Fatigue Crack Growth Analysis in Modified Compact Tension Specimen with Varying Stress Ratios: A Finite Element Study

In this study, the primary objective is to analyze fatigue crack propagation in linear elastic fracture mechanics using the SMART crack growth module in the ANSYS Workbench, employing the finite element method. The investigation encompasses several crucial steps, including the computation of stress intensity factors (SIFs), determination of crack paths, and estimation of remaining fatigue life. To thoroughly understand crack behavior under various loading conditions, a wide range of stress ratios, ranging from R = 0.1 to R = 0.9, is considered. The research findings highlight the significant impact of the stress ratio on the equivalent range of SIFs, fatigue life cycles, and distribution of deformation. As the stress ratio increases, there is a consistent reduction in the magnitude of the equivalent range of stress intensity factor. Additionally, a reciprocal relationship is observed between the level of X-directional deformation and the number of cycles to failure. This indicates that components experiencing lower levels of deformation tend to exhibit longer fatigue life cycles, as evidenced by the specimens studied. To verify the findings, the computational results are matched with the crack paths and fatigue life data obtained from both experimental and numerical sources available in the open literature. The extensive comparison carried out reveals a remarkable level of agreement between the computed outcomes and both the experimental and numerical results.

Atomistic fracture in bcc iron revealed by active learning of Gaussian approximation potential

The prediction of atomistic fracture mechanisms in body-centred cubic (bcc) iron is essential for understanding its semi-brittle nature. Existing atomistic simulations of the crack-tip under mode-I loading based on empirical interatomic potentials yield contradicting predictions and artificial mechanisms. To enable fracture prediction with quantum accuracy, we develop a Gaussian approximation potential (GAP) using an active learning strategy by extending a density functional theory (DFT) database of ferromagnetic bcc iron. We apply the active learning algorithm and obtain a Fe GAP model with a converged model uncertainty over a broad range of stress intensity factors (SIFs) and for four crack systems. The learning efficiency of the approach is analysed, and the predicted critical SIFs are compared with Griffith and Rice theories. The simulations reveal that cleavage along the original crack plane is the atomistic fracture mechanism for {100} and {110} crack planes at T = 0 K, thus settling a long-standing issue. Our work also highlights the need for a multiscale approach to predicting fracture and intrinsic ductility, whereby finite temperature, finite loading rate effects and pre-existing defects (e.g., nanovoids, dislocations) should be taken explicitly into account.

Fatigue life prediction of AA2524 thin plate strengthened using compound laser heating and laser shot peening method

AA2524 is a aluminum alloy based on damage tolerance design, and it is mainly used for the manufacturing of aircraft skins. Aircraft skins often occur fatigue failure due to harsh working conditions. To improve the fatigue resistance of aircraft skins and to accurately predict the fatigue life of AA2524 compact tension (CT) samples. The compound strengthening method of lsear heating (LH) and lsear shot peening (LSP) is proposed to improve the fatigue life of AA2524 in this paper. Considering the effect of stress ratio (R), residual stress (RS), stress intensity factor range (ΔK), and maximum stress intensity factor (Kmax) on the fatigue crack growth rate (FCGR), the fatigue life of CT samples was predicted applying artificial neural networks, support vector regression models. The results show that laser heating and laser shot peening can obviously improve the fatigue life by 30.703% at R = 0.1 and 4.701% at R = 0.5, compared with base materials. The neural networks have better fatigue life prediction ability, and the fit coefficients for the neural networks predicting fatigue life reach 0.97, which is better than that of Walker model (0.91). The prediction value for ANN model is 75,462 cycles, the magnitude for SVR model is 78,234 cycles, and the experimental value is 74,204 cycles. The deviation are 1.7% and 5.43%, respectively. Meanwhile, the effect of R on the FCGR of AA2524 is closely associated with the crack closure effect.

Correlating stress ratio effects on the fatigue crack growth rate behavior of a nickel-based superalloy GTM718

Damage tolerance evaluation under service loads requires a unified constant amplitude fatigue crack growth law for the material which takes care of stress ratio effects. Several types of crack driving force parameters have been proposed in the past to correlate stress ratio effects on fatigue crack growth rates. In the present investigation, a unified crack growth law is derived for a nickel-based superalloy by considering various crack driving force parameters to eliminate stress ratio effects. Initially, the constant amplitude fatigue crack growth rate (FCGR) behavior of GTM718 alloy was experimentally determined at various stress ratios, R ranging from R = 0.1 to 0.7. As expected, increasing the stress ratio, increased crack growth rates, and decreased threshold stress intensity factor range, ΔKth. The conventional crack growth rate, da/dN vs stress intensity factor range, ΔK data was then modified and re-plotted as a function of different crack driving force parameters viz., (a) Elber’s parameter, ΔKeff, (b) Walkers’ parameter, Kw (c) Kujawski’s parameter, K*, (d) Forman’s parameter, Kf, and (e) Two-parameter crack driving force, ΔK*. It was observed that Kf and ΔK* crack driving force parameters were correlating stress ratio effects better than other models in all three regimes of crack growth rates. Further, a unified crack growth law was derived based on the Kf and ΔK* crack driving force parameters which is useful in predicting FCG behavior under service loads.

Computing the stress intensity factor range for fatigue crack growth testing at 20 kHz

AbstractInertia and damping influence the values of the stress intensity factors (SIFs) at high‐frequency loading and they must be included in computations. In the present study, different dynamic simulation procedures were carried out for two types of specimen geometries and the achieved SIF values were compared. Fast computation procedures such as harmonic modal analysis and direct steady‐state analysis were compared to the computationally expensive transient dynamic analysis. Two different methods for calculating the SIF, the J‐integral and the crack tip opening displacement (CTOD) methods, were applied and compared and the results showed a near perfect agreement in calculation of the mode I SIF. The Rayleigh damping model was introduced into the dynamic computation to investigate its effect and the results revealed a clear effect on the SIF at 20 kHz frequency. The fast direct steady‐state analysis showed good agreement to both harmonic modal and transient analysis with the different damping values used and is, after this study, the recommended procedure.

Fatigue crack propagation behavior in Ti−6Al−4V alloy with surface gradient structure fabricated by high-energy shot peening

A gradient structure was successfully fabricated on the surface of Ti−6Al−4V alloy by high-energy shot peening (HESP), and its effect on fatigue crack propagation was investigated. Optical microscope, scanning electron microscope, transmission electron microscope and X-ray diffractometer were used to characterize the microstructure and residual stress evolution during HESP. The results show that a gradient nanostructure with residual compressive stress layer of 220 μm in depth is formed. The generation of gradient nanostructures improves the strength−ductility combination of the alloy. Maximum residual compressive stress is generated on the subsurface, which gradually increases with the increase of shot peening time. HESP treatment effectively reduces the crack propagation rate and increases the fatigue crack propagation life. The residual compressive stress reduces the effective stress intensity factor range at crack tip, thereby generating the crack closure effect and delaying the crack propagation. At the same time, the synergy effects of increase in grain boundaries, decrease in effective slip length and the plastic zone at the crack tip caused by the refinement of the surface grains can increase the crack propagation resistance as well.

Multi-level Uncertain Fatigue Analysis of a Truss under Incomplete Available Information

We predict the fatigue life of a planar tubular truss when geometrical parameters, material properties, and live loads are non-deterministic. A multi-level calculation uncertainty quantification framework code was designed to aggregate the finite element method and fatigue-induced sequential failures. Due to the incompleteness of the aleatory-type inputs, the maximum entropy principle was applied. Two sensitivity analyses were performed to report the most influencing factors. In terms of variance, the results suggest that the slope of the curve crack growth rate × stress intensity factor range is the most influencing factor related to fatigue life. Furthermore, due to the application of the entropy concept, the fatigue crack growth boundaries and fatigue crack size boundaries obtained provide the most unbiased fatigue crack design mapping. These boundaries allow the designer to select the worst-case fatigue scenario, besides being able to predict the crack behavior at a required confidence level.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

The effect of material defect orientation on rolling contact fatigue of a ball bearing

In this study, finite element method (FEM) is applied to investigate the effect of material defect orientation on subsurface crack initiation in rolling bearings. First, the history of stress intensity factors (SIFs) of a subsurface cubic material defect is calculated. SIFs calculation is conducted when it is parallel to the rolling surface of a bearing ring (varphi = 0^circ) under a ball rolling on the ring. Then, the effect of defect orientation, varying from varphi = 0^circ to varphi ; = ;30,; 45; {text{and}} ;60^circ, on the history of SIFs is investigated. It is deduced that changing the defect orientation results in a threefold increase in the equivalent SIF range compared to parallel orientation.

Effects of grain structures on fatigue crack propagation behavior of an Al-Cu-Li alloy

The effects of two different grain structures on fatigue crack propagation (FCP) behavior of an Al-Cu-Li alloy were investigated. The results indicate that the fibrous grained and equiaxed grained samples exhibit significantly different FCP resistances. The FCP rates are particularly different at the Paris stage at the stress intensity factor range (ΔK) is about 20 MPa∙m1/2, the equiaxed grained sample is 8.23 × 10-4 mm/cycle, while the fibrous grained sample is up to 1.65 × 10-3 mm/cycle. The results of electron backscattered diffraction (EBSD) analysis of the crack propagation paths show that about 58.7 % of crack paths are transgranular and 67.6 % of the cracks are deflected in the fibrous grained sample, most crack segments are parallel to {111} 〈101〉 slip system. While in the equiaxed grained sample, the probabilities of transgranular and intergranular propagation are both about 50 % and 73.2 % of the cracks are deflected, most crack segments are parallel to {111} 〈011〉 slip system. The grain reference orientation deviation (GROD) and the kernel average misorientation (KAM) maps show that the degree of deformation at the grain boundaries of the fibrous grained sample is higher than the equiaxed one.

Comparison of the continuum damage and fracture mechanics in fatigue assessment of components containing residual stresses

In the present study, the fatigue crack growth life of standard and smooth notched specimens containing residual stresses are evaluated based on the continuum damage and fracture mechanics approaches. It is indicated that fatigue crack growth lives assessed by the continuum damage model are closer to the experimental results, with a difference of <10% in the specimens containing residual stresses. The total stress intensity factor range is used to consider the effects of residual stresses in the estimation of fatigue crack growth life based on the fracture mechanics. It is found that in existing residual stresses, the stress intensity factor K is not a proper parameter to evaluate crack tip zone. Fatigue crack initiation life is experimentally obtained based on assessing variations of the slope of unloading curve in the force-displacement diagram of fatigue experiments. The cycle including a change in the slope is considered as fatigue crack initiation event. Isotropic and kinematic hardening parameters of ASTM A516 pressure vessel steel are considered in finite element analyses. Tensile residual stresses are introduced into the notched specimens by employing four-point-bending with a magnitude of around 90% of the yield stress of the material. The results indicate that at least 65% of the fatigue life of the specimens is decreased due to the presence of tensile residual stresses. Tensile residual stresses are measured using the hole-drilling technique.

Effect of Pore Defects on Very High Cycle Fatigue Behavior of TC21 Titanium Alloy Additively Manufactured by Electron Beam Melting

Titanium alloys additively manufactured by electron beam melting (EBM) inevitably obtained some pore defects, which significantly reduced the very high cycle fatigue performance. An ultrasonic fatigue test was carried out on an EBM TC21 titanium alloy with hot isostatic pressing (HIP) and non-HIP treatment, and the effect of pore defects on the very high cycle fatigue (VHCF) behavior were investigated for the EBM TC21 titanium alloy. The results showed that the S-N curve of non-HIP specimens clearly had a tendency to decrease in very high cycle regimes, and HIP treatment significantly improved fatigue properties. Fatigue limits increased from 250 MPa for non-HIP specimens to 430 MPa for HIP ones. Very high cycle fatigue crack mainly initiated from the internal pore for EBM specimens, and a fine granular area (FGA) was observed at the crack initiation site in a very high cycle regime for both non-HIP and HIP specimens. ΔKFGA had a constant trend in the range from 2.7 MPam to 3.5 MPam, corresponding to the threshold stress intensity factor range for stable crack propagation. The effect of pore defects on the very high cycle fatigue limit was investigated based on the Murakami model. Furthermore, a fatigue indicator parameter (FIP) model based on pore defects was established to predict fatigue life for non-HIP and HIP specimens, which agreed with the experimental data.

Fatigue crack growth behavior in additive manufactured Ti6Al4V alloy with intentionally embedded spherical defect

The present study aims at elucidating the impact of unavoidable defects in selective laser melting (SLM) additive manufactured alloys on fatigue performances. The novel idea is to reveal the relationship between the printing defect and fatigue crack growth, by intentionally embedding a 500 μm spherical defect in an SLM-Ti6Al4V alloy exerted to low-cycle fatigue (LCF). The results show that the cyclic softening of the specimen was not affected by the embedded defect and surprisingly its fatigue life was nearly the same as the virgin specimens free of embedded defects at low strain amplitudes. The performance is attributed to the single crack initiation site and only small change in the stress intensity factor range (ΔK). In contrast, when subjected to higher strain amplitudes during LCF, the embedded defect dominates the crack initiation and crack propagation occurs readily. It is shown that the experiments support a model description based on the competitive failure mechanisms between the surface defects and internal defects.