Stress Intensity Factor Range ΔK Research Articles

Crack propagation modelling for service life prediction of large slewing bearings

Slewing bearings in wind turbines are meant to last 20 years or longer. But wind turbine accidents (structural failure) occur nevertheless in some cases earlier. Minimizing the risk and with this enhancing the public acceptance of wind turbines is of great importance for the increase of alternative energy production. For a more accurate prediction of the service life of slewing bearings XFEM calculations with crack initiation and crack propagation are developed using Abaqus XFEM. The material parameters such as Paris coefficients for crack propagation and fracture toughness values (KIC) were measured in advance on samples of different heat treatment conditions. With a linear elastic fracture mechanics approach the local stress intensity factor range ΔK for a given starting crack front is calculated. Coupling this information with the Paris-law and a maximum crack propagation interval of 0.1-0.3 mm, the number of cycles to failure during crack propagation is determined. The crack is extended stepwise until ΔK reaches the limiting fracture toughness of the material. The crack propagation model was first validated on different test specimen geometries. Correlating these first simulated test results with experimental data the crack initiation phase can be estimated. The simulation of real components, such as bearings, will be developed subsequently, using calculated stress distributions provided by other partners in the project as input parameters (sub-structure approach). Fatigue tests are also done on pre-corroded specimens since bearing failure may also be promoted by an unfavorable combination of overloads and corrosion damage.

Characterization of fatigue crack propagation of pitting-corroded rebars using weak magnetic signals

In this study, mode-I high-cycle fatigue tests were conducted on smooth standard specimens manufactured from HRB400 steel bars, prefabricated with a semi-ellipsoid corrosion pit. Fatigue crack growth (FCG) behavior was predicted using the FCG model, based on linear elastic fracture mechanics (LEFM). During the fatigue process, an online piezomagnetic signals was detected, while the residual magnetic field (RMF) distribution near the corrosion pit was recorded after the specimen was unloaded. The range of the magnetic tangential induction ΔBt and the gradient of the normal component of the RMF distribution Gmax were selected as the characteristic weak magnetic parameters, which exhibited a three-stage evolution law with fatigue progression. Next, the evolution mechanism of the weak magnetic field during the FCG process of the pitting-corroded rebars was comprehensively explored. Subsequently, quantitative relationships between the stress intensity factor (SIF) range ΔK and ΔBt as well as the fatigue crack length a and Gmax were separately established. The errors between the predicted and validation experimental results of ΔK, a, and FCG life were all within 20%. Furthermore, the influence of the pit geometry and stress ratio on the variation of ΔBt versus ΔK, and Gmax versus a was investigated. The increments of ΔBt and Gmax in different 1000-cycle intervals during various FCG stages were recorded, which could help estimate FCG behavior of pitting-corroded rebars in practical applications.

Compliance method to measure crack length and crack closure for automated fatigue crack propagation test of nanocrystalline nickel film

Experimental techniques for measuring the crack length and crack closure behavior of single edge crack tension [SE(T)] specimens with fixed ends were developed with compliance method employing a high-resolution laser displacement meter together with data processing for noise elimination. Then, an automatic force-shedding fatigue crack propagation test system was developed. Using this system, we measured the crack length and crack closure behavior of thin films with a thickness of 5 or 10 µm and width of 10 mm, with which the accuracy of crack length measurement was better than 0.46 mm. The crack closure behavior could also be identified by the compliance method. The relationship between the crack propagation rate da/dN and the stress intensity factor range ΔK for nanocrystalline (NC) and ultrafine-grained (UFG) thin film was independent of the force ratio, and the relationship for the 10 µm-thick film was almost identical to that for the 5 µm thick film. No crack closure was observed in the UFG and NC thin films, whereas it occurred in the medium-size-grained (MG) thin film. The da/dN–ΔKeff relationships for thin films were independent of the force ratio and film thickness. In the Paris law region, da/dN for the MG film was higher than that for an MG plate at comparable ΔKeff, showing that crack closure could not account for the thickness effect. However, no difference in ΔKeff,th was observed for both the MG film and the MG plate. In the Paris law region (Region B), no effect of grain size on the da/dN–ΔK relationship was observed for the 10-µm-thick film; however, the crack propagation rate was higher for a film with smaller grain size and thickness from 100 to 180 µm. For NC and UFG films, the crack propagation rate of the 100-µm-thick film was higher than that of the 10-µm-thick film, but it was almost identical for MG films; however, the rate for a thin film was higher than that for a bulk plate. The threshold stress intensity factor range was always lower for a film with smaller grain size.

Influence of cold rolling on the fatigue crack growth behavior of tungsten

The influence of cold rolling on the fatigue crack growth (FCG) behavior of pure tungsten was investigated. For that tungsten sheets with three different thicknesses (2 mm, 1 mm and 100 μm) corresponding to different degrees of deformation were selected to prepare compact-tension (CT) and single edge notched tension (SENT) specimens. To account for orientation influences the crack propagation direction parallel, perpendicular and under 45° to the rolling direction was investigated. It could be shown that a pronounced cyclic R-curve behavior evolves, leading to relatively high thresholds of stress intensity factor range ΔK th , even at high load ratios. Furthermore, for the smallest grain size a pronounced anisotropy of the FCG behavior was observed where the crack growth direction perpendicular to the rolling direction exhibits the highest ΔK th and the lowest crack growth-rates. Especially the tungsten foils with 100 μm thickness showed stable crack growth with a pronounced Paris-regime. As a consequence, cold rolled tungsten qualifies as a fatigue resistant laminate material applicable for future structural applications in harsh environments.

Effect of Specimen Thickness and Stress Intensity Factor Range on Plasticity-Induced Fatigue Crack Closure in A7075-T6 Alloy.

Fatigue crack growth experiments are performed using A7075-T6 compact tension (CT) specimens with various thicknesses t (1–21 mm). The stress intensity factor at the crack opening level Kop is measured, and the effects of t and the stress intensity factor range ΔK on Kop are investigated. In addition, the change in Kop value due to specimen surface removal is investigated. Furthermore, we clarify that the radius of curvature of the leading edge of the fatigue crack decreases as t becomes thinner. Using the three-dimensional elastoplastic finite element method, the amount of plastic lateral contraction (depression depth d) at the crack tip after fatigue loading is calculated quantitatively. The following main experimental results are obtained: In the region where ΔK is 5 MPam1/2 or higher, the rate of fatigue crack growth da/dN at a constant ΔK value increases as t increases from 1 to 11 mm. The da/dN between t = 11 and 21 mm is the same. Meanwhile, in the region where ΔK is less than 5 MPam1/2, the effect of t on da/dN is not observed. The effects of t and ΔK on the da/dN–ΔK relationship are considered physically and quantitatively based on d.

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.

The Mechanism of Creep during Crack Propagation of a Superalloy under Fatigue-Creep-Environment Interactions.

In this study, we examine the mechanism of fatigue-crack propagation in 718Plus superalloy at 704 °C under fatigue–creep–environment interactions, in this case, a new turbine disc material used in aero-engines at high temperatures. The effect of creep on the fatigue-crack propagation of the superalloy at high temperature was also researched. There was an unusual inhibitory effect on the propagation of fatigue cracks in 718Plus alloy, in which the propagation rate of fatigue cracks decreased with the increase of creep time through exploration of dwell-fatigue-crack growth (DFCG) test with different creep times. In particular, under lower stress intensity factor range (ΔK) conditions, the fatigue-crack growth rate with a 90 s hold-time was one order of magnitude lower than that with a 5 s hold-time. Conversely, the gap between the two DFCGs gradually decreased with the increase of ΔK and the creep effect became less apparent. The mechanism of crack propagation in 718Plus alloy under two creep conditions was investigated from a viewpoint of the microstructure, oxidation rate at high temperature and crack path morphology under different conditions.

Characteristic Dependency of Hydrogen-Affected Fatigue Crack Growth and Crack Tip Plasticity on Low Loading Frequency in α-Iron

Aiming to investigate the dependency of hydrogen-affected fatigue crack growth (HAFCG) on the loading frequency f, this study experimentally characterized the HAFCG in a commercially pure iron as a function of f ranging from 0.02 to 20 Hz as well as a stress intensity factor range ΔK and hydrogen gas pressure $$ P_{{{\text{H}}_{2} }} $$ . The crack tip plasticity was analyzed by interferometric microscopy and transmission electron microscopy in addition to the fracture surface observation. As a result, the amount of FCG rate acceleration by hydrogen increases as f decreases until it reaches a critical value (f = 2 Hz at $$ P_{{{\text{H}}_{2} }} $$ = 3.5 MPa, f = 0.2 Hz at $$ P_{{{\text{H}}_{2} }} $$ = 35 MPa), while the HAFCG rate greatly decreases once f decreases below the critical value. At the same time, the fracture mode at $$ P_{{{\text{H}}_{2} }} $$ = 3.5 MPa changes from brittle quasi-cleavage to a more ductile manner showing no clear hydrogen influence. On the other hand, the size of cleavage-like facets becomes large in case of $$ P_{{{\text{H}}_{2} }} $$ = 35 MPa suggesting that the number of lattice planes causing cleavage is reduced because of less hydrogen effect. The crack tip plasticity reduction by hydrogen is clearly confirmed while the HAFCG enhancement occurs above the critical value of f. In contrast, at f below the critical value, the crack tip plasticity is recovered to almost the same level as in the inert environment. Based on a theoretical estimation of hydrogen diffusion from the crack tip, the critical value of f causing this reversal f dependency is likely determined by the hydrogen concentration gradient in the vicinity of the crack tip. Although the associated mechanism is still unclear, it is suggested that the dynamic interaction between mobile dislocations and diffusing hydrogen atoms is important in clarifying the mechanism of HAFCG.

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.

A concise and novel binomial model for creep-fatigue crack growth behaviors

A concise binomial model including time-dependent term and cycle-dependent term is proposed in this paper in order to characterize fatigue crack growth rate at high temperature. The specific functional forms of the time-dependent term are derived for several materials, and then the characteristic dwell times corresponding to the most significant interaction effect are determined. Besides, the contribution of the time/cycle-dependent term to the total crack growth rate of the model at different stress intensity factor range ΔK levels is discussed. The research achievements are helpful to support the damage tolerance analysis of high temperature structures in service.

Magnification Factor Mk and its Parametric Solutions for Fatigue Crack Growth Assessment of Flaws at Weld Root Toes in Girth Welds

Abstract To account for the effect of the stress concentration factor (SCF) at the weld toe on stress intensity factor range ΔK, a magnification factor Mk is used. The existing Mk solutions given in BS 7910 were developed for the fatigue assessment of flaws at the toes of fillet and butt welds and may not be suitable for assessing flaws at single-sided girth weld root toes, where fatigue cracking often initiates and the weld width is relatively small. Finite element (FE) modeling was performed to determine a 2D Mk solution for engineering critical assessment (ECA) of a flaw at the weld root bead toe. The weld root bead profile was uniquely characterized by five variables including weld root bead width, weld root bead height, hi-lo, weld root bead angle, and weld root bead radius. Following a parametric sensitivity study, defect size, weld root bead height, and hi-lo were identified as the governing parameters. A total of 6000 FE simulations was performed, covering different combinations of weld root bead height and hi-lo. A series of automation scripts were developed in the python programming language and the Mk solution for each type of defect model was developed and provided in a parametric equation. The accuracy of the 2D Mk solutions was confirmed by the experimental data. It was found that the methods and Mk solutions currently recommended in BS 7910 and DNVGL-RP-F108 are inappropriate for assessing a flaw at a girth weld root toe.

Comparison of fatigue crack propagation behaviour in two steel grades S235, S355 and a steel from old crane way

Utilization of various steel grades in civil engineering allows designing bridges, bridge elements or simple structures according to their fracture mechanical properties. The service intervals of structures, which are going to be in use for a long time, cannot be calculated only on the basis of tensile and brittle fracture properties but also on the knowledge of the resistance to the fatigue crack growth. This contribution presents a comparison of the fatigue behaviour of two modern steel grades S235 J2, S355 J2 and a steel extracted from an old crane way. The comparison of these steel grades is done by fatigue crack propagation tests (the results of the experimental tests are described using concept of the stress intensity factor range ΔK). The fatigue properties are discussed and recommendations for the use of the steels are stated.

Experimental characterisation of fatigue crack growth based on the CTOD measured from crack tip displacement fields using DIC

The current work presents an experimental study on the use of the crack tip opening displacement (CTOD) to evaluate its ability to characterise fatigue crack growth. A methodology is developed to measure and to analyse the CTOD from experimental data. The vertical displacements obtained by implementing digital image correlation (DIC) on growing fatigue cracks are used to measure the CTOD. Two fatigue tests at stress ratios of 0.1 and 0.6 were conducted on compact tension (CT) specimens manufactured from a 1 mm thick sheet of commercially pure titanium. A sensitivity analysis to explore the effect of the position selected behind the crack tip for the CTOD measurement was performed. The analysis of a full loading cycle allowed identifying the elastic and plastic components of the CTOD. The plastic CTOD was found to be directly related to the nonlinear zone (i.e., plastic deformation) generated at the crack tip during fatigue propagation. Moreover, a linear relationship between da/dN and ΔCTODp independent of the stress ratio was found. Results show that the CTOD can be used as a viable alternative to the stress intensity factor range (ΔK) in characterising fatigue crack propagation since the parameter considers the fatigue threshold and crack shielding in an intrinsic way.

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.

Fatigue Crack Growth Study in P91 and 316LN Steels Using Acoustic Emission

Fatigue crack growth (FCG) behavior of ferritic steel P91 and austenitic stainless steel 316LN (SS 316LN) has been studied at ambient temperature. Acoustic emission (AE) signals generated during FCG tests were captured using 375 kHz resonant transducer. The FCG and AE results were compared for both steels in Paris and threshold regimes. The AE results indicated five and four substages of FCG for P91 steel and SS 316LN, respectively. Several parameters of AE signals such as rise time, peak amplitude and event duration were used to differentiate between various substages of the FCG. AE cumulative count was correlated with stress intensity factor range (ΔK) in Paris regime for both the steels. For SS 316LN, the exponent of the correlation of AE cumulative count with ΔK is in good agreement with Paris exponent. For P91 steel, higher value of the exponent of the AE cumulative count—stress intensity factor range correlation compared to Paris exponent is observed. Monitoring of AE continuously during fatigue crack growth of these two steels enables understanding the mechanisms of crack growth operative at different regions of the FCG curve.

Fatigue Crack Growth Rate of an Al-Cu-Mg Alloy

In this study, fatigue crack growth rates of industrial 2524-T3 aluminium alloy plates under various stress ratios R (R = 0.1, 0.2, 0.3, and 0.5) were examined. The microstructure was observed by using a scanning electron microscope (SEM). The results showed that, for a given stress intensity factor range ΔK, the increase in stress ratio led to an increase in fatigue crack growth rate. Besides, the SEM images showed that the fatigue striations were predominant in the fracture, and the spacing of the fatigue striations also drastically increased as the stress ratio increased in different samples. This phenomenon can be explained well by crack closure effects.

Modeling R-dependence of near-threshold fatigue crack growth by combining crack closure and exponential mean stress model

A previously proposed equivalent driving force model was modified to account for crack closure for modeling stress ratio, R, dependence of fatigue crack growth in near-threshold regime. A new fatigue crack growth driving force model was established in the form of ΔK⋅f(R), where the f(R) includes both crack closure and mean stress contributions, and well informs the shift from dominance of stress intensity factor range ΔK to maximum stress intensity factor Kmax with increasing R. The model was validated widely with sound agreement between modeling results and experimental data.

Influence of crack closure and local near-tip stress on crack growth life estimation

Currently, among other models for crack growth prediction, crack closure models that consider the decrease in stress intensity factor (SIF) range associated with cyclic loading asymmetry are more popular. One of drawbacks of these models is impossibility of considering the loading history sequence.The theory related threshold SIF range and ΔKth and local near-tip stresses, induced by overloads, and postulated that the overload effect in the near-threshold region of growth rates is caused by residual local stresses. The proposed model applies the local stress and strain approach to estimate stress σ* in the stress concentration region for fatigue analysis. This region is characterized by local near-tip stress σ*, whose amplitude is determined by cyclic inelastic reaction at crack tip. Further development of the model is due to varying nature of the threshold SIF range ΔKth.As a basis, the Forman-Mettu formula was adopted, which describes the fatigue crack growth curve in all three regions of fatigue crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the Schijve equation, considering the asymmetry of the half-cycle U = f(R), and effective SIF was estimated by ΔKeff = ΔK*U. Given known SIF range ΔK, the value of the local stress σ* at distance from the crack tip r* was determined for each half cycle by Neuber and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical formula of Кth=f(σ). Thus, known loading history made it possible to determine ΔKeff, Kmax, and Kth on each cycle for fatigue life estimation.Mathematical modeling of fatigue crack growth life, especially in near-threshold region of its growth, according to the Sunder’s scheme, showed that investigated aluminum alloy 2024-T3 exhibited crack growth sensitivity to various types of force action, including various types of random loading.

Hydrogen-affected fatigue crack propagation at various loading frequencies and gaseous hydrogen pressures in commercially pure iron

Hydrogen-Affected Fatigue Crack Growth (HAFCG) in commercially pure iron has been characterized in terms of hydrogen gas pressure, loading frequency and stress intensity factor range ΔK. A higher hydrogen gas pressure decreases the critical value of ΔK triggering the HAFCG enhancement, and a lower loading frequency increases the HAFCG enhancement. Intergranular FCG in the non-accelerated regime is likely caused by the hydrogen-induced microvoid coalescence along the grain boundary, while a brittle cyclic cleavage fracture in the accelerated regime can be explained in terms of crack tip sharpening and hydrogen-enhanced decohesion process.

Numerical and experimental method for the prediction of the propagation life of fatigue crack on metallic materials

A prediction method for the propagation life of fatigue crack for cracked components was provided and verified in this study to predict the propagation life of fatigue cracks on components in engineering applications conveniently and directly. In the simulation aspect, a finite element (FE) model of cracked specimen was created to obtain the stress intensity factor range ΔK. The FE model was verified by comparing simulated ΔK to a formulary calculated one. The simulated ΔK could be used for studying the relationship with crack size. In the experimental aspect, the fatigue crack propagation test was conducted on three specimens. The material coefficients C and m were fitted according to Paris’ law. The load cycles with different crack depths were recorded in the testing process. The propagation life of fatigue cracks of specimen was predicted via the relationship between ΔK and crack size a according to Paris’ law. The comparison between predicted life and experimental life of specimens indicated the feasibility of the method. The proposed prediction method in this study for the propagation life of fatigue cracks can be used in engineering applications.