Applied Stress Intensity Factor Range Research Articles

Fatigue crack growth behavior in an aluminum alloy Al–Mg–0.3Sc produced by wire based directed energy deposition process

AbstractAdditive manufacturing (AM) of Al–Mg–Sc alloys has received considerable interest from the aerospace industry owing to their high specific strength and suitability for AM processes. This study has investigated the fatigue crack growth behavior in an Al–Mg–0.3Sc alloy made by wire and arc additive manufacturing. Tests were conducted with two different crack orientations at cyclic load ratios of 0.1 and 0.5. At the lower load ratio, the horizontal crack showed a faster growth rate owing to the smaller grains and coarser second‐phase particles that the crack tip had encountered when it propagated along the material build direction. The anisotropy in crack growth rate was mainly caused by the grain size effect. When the applied stress intensity factor range exceeded the value of 10 MPa m1/2, an isotropic crack growth rate between the two crack orientations was measured. This is due to the microstructural influence being overcome by the governing parameter of fracture mechanics. At the higher load ratio of 0.5, crack growth rate is isotropic, and the threshold stress intensity factor range was much lower than that tested under load ratio 0.1. Finally, the modified Hartman–Schijve equation has been successfully employed to represent the crack growth rates in all three regions.

Equivalent crack growth model for correlation and prediction of fatigue crack growth under different stress ratios

An equivalent crack growth model that accounts for the effect of stress ratio is proposed for the correlation and prediction of crack growth under different stress ratios. A previously proposed equivalent driving force ΔKeq that yields the same growth rate (da/dN)R as combined applied stress intensity factor range ΔKR and stress ratio, R is modified, and its corresponding equivalent growth rate (da/dN)eq is derived. This yields an equivalent crack growth model of (da/dN)eq versus ΔKeq capable of collapsing data of different R-ratios unto a common curve. The model was validated with excellent agreement between the model and published data.

On the fatigue crack growth behavior of Ti–10V–2Fe–3Al in gaseous hydrogen

The fatigue crack growth behavior of Ti–10V–2Fe–3Al in gaseous hydrogen (H2) was assessed through comparative experiments conducted in laboratory air and 8.3 MPa H2. The measured fatigue crack growth rate (da/dN) versus applied stress intensity factor range (ΔK) relationships and observed fracture morphologies for laboratory air and H2 were comparable up to ΔK ≈ 6.9 MPa√m, when tested at a load ratio of 0.1 and frequency of 10 Hz. At higher ΔK values, significant crack deflection and subsequent catastrophic failure occurred in the specimen tested in H2. This degradation was not observed in a specimen pre-exposed to 8.3 MPa H2 for 96 h and then immediately tested in laboratory air. X-ray diffraction of the failed H2-tested specimen revealed that the material remnants were predominantly composed of TiH2, suggesting that hydride formation was the catalyst for catastrophic failure in H2. The mechanistic implications of these results and their impact on current material compatibility assessments for Ti alloys in hydrogen service are then discussed.

Very high cycle fatigue properties of high‐strength spring steel 60SiCrV7

AbstractThe very high cycle fatigue properties of spring steel 60SiCrV7 for automotive suspension system with different hydrogen contents were studied by using ultrasonic fatigue testing and fatigue crack growth testing. The results show that the S–N curves exhibit continuous drop of fatigue lives and no obvious horizontal line exists. Similar fracture surface features were observed for all the specimens that failed mainly from internal inclusions with surrounding granular bright facet (GBF). Fatigue strength decreases remarkably with increasing hydrogen content. The applied stress intensity factor range at the periphery of GBF ΔKGBF is approximately proportional to 1/3 power of the square of GBF area. The average values of ΔKGBF for uncharged specimens are close to crack growth threshold ΔKth, which indicates that ΔKGBF could be regarded as the threshold value governing the beginning of stable fatigue crack propagation. The increase of hydrogen content tends to reduce ΔKGBF.

Near-threshold fatigue propagation of physically short and long cracks in Titanium alloy

Damage tolerance is today imposed by the regulations to dimension aeronautical turbine critical parts. Thus resistance of these parts to potential anomalies is assessed. It requires to study, besides standard long cracks, the propagation of cracks of little dimension (some tenth of mm for initial length) which can have an atypical behavior consisting in crack propagation at lower stress intensity factor range than the threshold for long crack. In this context, this study is focused on a bimodal Titanium alloy (TA6V) tested at different temperatures: room temperature and 400°C at a low load ratio R of 0.1, which corresponds to loading of manufactured compressor impellers in these materials.Tests are run on compact tension specimens initially pre-cracked at constant applied stress intensity factor range (ΔK) and then cracked to threshold in view of obtaining a long crack of a/W˜0,5. Physically 2D through-thickness short fatigue cracks are created by gradually removing the plastic wake of this long crack in order to obtain a crack length as short as possible (0.1 mm). Next the short crack obtained is propagated in view of getting different thresholds for different crack lengths according to a procedure of load decrease. Crack closure contribution is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. 2D short crack propagation behavior is compared to long crack behavior with a special attention given to crack closure. The threshold evolution in function of the crack length is investigated using a Kitagawa diagram approach for determining a non-propagation criterion of short cracks.

Granular bright fact crack propagating under very high cycle fatigue

The different crack initiation modes from different internal defects of a high carbon chromium bearing steel are investigated in the present paper. The relative granular bright facet (GBF) size is approximately proportional to . The critical applied stress intensity factor range at the periphery of inclusion ΔKinc,th, above which the GBF will no longer be formed, was obtained. For the present SUJ2 steel, ΔKinc,th = 8 MPa m1/2. The crack growth process in GBF is further investigated by the low–high two-step variable amplitude loading tests. The crack growth process in GBF can be described by . The exponent m0 is a material constant independent of the applied stress amplitude and the inclusion size and increases with increasing of HV.

Dynamic Strain Evolution around a Crack Tip under Steady- and Overloaded-Fatigue Conditions

We investigated the evolution of the strain fields around a fatigued crack tip between the steady- and overloaded-fatigue conditions using a nondestructive neutron diffraction technique. The two fatigued compact-tension specimens, with a different fatigue history but an identical applied stress intensity factor range, were used for the direct comparison of the crack tip stress/strain distributions during in situ loading. While strains behind the crack tip in the steady-fatigued specimen are irrelevant to increasing applied load, the strains behind the crack tip in the overloaded-fatigued specimen evolve significantly under loading, leading to a lower driving force of fatigue crack growth. The results reveal the overload retardation mechanism and the correlation between crack tip stress distribution and fatigue crack growth rate.

On effect of hydrogen on very high cycle fatigue behaviours of high strength steels

In order to analyse the effect of hydrogen on very high cycle fatigue properties, hydrogen was precharged into two high strength steels. The applied stress intensity factor range at the periphery of inclusions before and after being precharged is approximately proportional to the cubic root of inclusion size. In addition, the applied stress intensity factor range at the periphery of inclusions after being precharged was lower compared with uncharged specimens. The additional stress intensity factor range generated by hydrogen ΔKH is raised after the hydrogen was precharged. A simple prediction equation of S–N curve was proposed by introducing the hydrogen influence factor. The proposed prediction equation can reasonably describe the S–N curves for precharged specimens.

The effects of overload on the fatigue crack growth in ductile materials predicted by plasticity-corrected stress intensity factor

On the basis of plastic zone toughening theory, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effects of overload on the fatigue crack growth in ductile materials. By use of this new crack driving force parameter a theoretical correlation of the Paris law with crack tip plastic zone is established. Comparison with extensive experimental data showed that the PC-SIF describes fairly well the effects of the crack length and different loading variables, including the applied stress intensity factor range, load ratio, overload extent and overload number, on the overload retardation.

Incorporating small fatigue crack growth in probabilistic life prediction: Effect of stress ratio in Ti–6Al–2Sn–4Zr–6Mo

The effect of stress ratio on the statistical aspects of small fatigue crack growth behavior was studied in a duplex microstructure of Ti–6Al–2Sn–4Zr–6Mo (Ti-6-2-4-6) at 260°C with particular emphasis on incorporating small-crack data into probabilistic life prediction and the influence of stress ratio on probabilistic lifetime limits. A Focused Ion Beam (FIB) was used to machine micro-notches in test specimens, which served as crack-initiation sites and enabled the acquisition of multiple small-crack growth data sets from single experiment. Stress ratios of −0.5, 0.05, and 0.5 were employed, and small-crack growth was monitored by the acetate replication method. Qualitatively, change in the stress ratio produced almost negligible influence on the small-crack growth behavior when plotted as crack growth rate (da/dN) vs. applied stress intensity factor range (ΔK). A probabilistic method was employed to represent the variability in the small-crack growth behavior and the statistical differences with respect to stress ratio where a method of optimization of the small-crack growth model parameters, based on a minimization of the error between the predicted and the measured crack length vs. cycles (a vs. N) data, was used. In spite of qualitative similarity, differences in the statistical parameters of small-crack growth as a function of stress ratio were found to be significant in life prediction. The methods for representation and probabilistic treatment of small-crack data were also shown to be important factors in incorporation of the small-crack regime in probabilistic life prediction.

Application of a failure assessment diagram under rolling contact to components with hardness variable along the depth

A development of a failure assessment diagram for the evaluation of the safe working area of components subjected to rolling contact loading is here presented regarding the application to components whose hardness varies along the depth. The approach takes into account the influence of inherent defects in determining subsurface rolling contact fatigue, depending on working conditions, material properties and hardness profile along the depth. For this aim, crack propagation from inherent defects is assessed in terms of applied stress intensity factor range normalized with respect to short crack growth threshold, defect – free fatigue is assessed in terms of Dang Van stress normalized with respect to shear fatigue limit, where the material quantities depend on hardness variable with depth. These two normalized quantities are the coordinates of the points of a “reference curve” in the failure assessment diagram, which location indicates whether and where failure is expected to occur. By analysing different combinations of loading condition, inclusion dimension and hardness profile, it was possible obtaining a design diagram of general validity, which allows a fast prediction of safety against subsurface rolling contact fatigue.

Fatigue crack growth through particulate clusters in polycarbonate material

The interaction of a crack with a perfectly bonded inclusion or a cluster of inclusions in polycarbonate matrix was investigated through both numerical simulations and fatigue tests. Stress intensity factors (KI) were evaluated by boundary element method for several particle sizes, position and finally for inclusion cluster as a precursor study for the experiments. The numerical simulation has shown the crack tendency to circumvent the inclusions with consequential reduction of the growth rate. Fatigue crack growth tests were carried out on several particle-filled specimens at constant value of the applied stress intensity factor range (ΔKIapp) highlighting the crack delay due to the presence of the stiff second phase. The experiments demonstrated that the inclusion effect on the crack growth rate can be explained with a model based on the crack shielding effect in which the particle would act to reduce the effective stress intensity factor at crack tip (KIeff). Finally, the crack growth rate was predicted with an analytical model, and then compared to that obtained by the fatigue testing. Possible explanations for differences are discussed.

Wake history effect on closure of short and long fatigue crack in 304L stainless steel

The effect of crack length and of crack wake history on crack closure is investigated in 304L austenitic steel. Tests are run on CT specimens initially pre-cracked at constant applied stress intensity factor range ΔK, at a load ratio R=0.1. After precracking, the crack wakes are machined to obtain 2D physically short cracks. Then propagation of these short cracks is still performed at constant ΔK for length ranging from 0.1 mm up to 4 mm. A numerical analysis of load-displacement data allows improved closure detection for the smaller short cracks. The ratio γ=Kop/Kmax is shown to decrease with decreasing crack length a for a <1.2mm; for a >1.2mm, the long crack domain is reached and γ is shown constant and equal to 0.352 independently of ΔK. For tests usually run at increasing ΔK or decreasing ΔK, γ is dependent on the variation of ΔK with a, and the relation da/dN vs ΔK is shown dependent on the loading history. But in all cases, the crack propagation rates are rationalized in term of ΔKeff.

Fatigue crack growth behaviour and life prediction for 2324-T39 and 7050-T7451 aluminium alloys under truncated load spectra

This paper presents a study of crack growth behaviour in aluminium alloys 2324-T39 and 7050-T7451 subjected to flight-by-flight load spectra at different low-stress truncation levels. Crack branching was observed in the higher truncation levels for the 2324 and in all truncation levels for the 7050. Mode I crack growth life can be predicted for the 2324 alloy by the NASGRO equation and the Generalised Willenborg retardation model. However, quantitative prediction of the fatigue life of a significantly branched crack is still a problem. Material properties, test sample’s orientation and applied stress intensity factor range all play dominant roles in the fracture process.

Characterisation of the fatigue properties of cast irons used in the water industry and the effect on pipe strength and performance

As part of an on going programme to characterise the residual properties and understand the failure mechanisms of in-service grey cast iron water pipes, the fatigue crack propagation behaviour of grey cast iron samples has been studied. Specimens were sourced from three ex-service pipes. For each pipe the microstructure and composition were characterised and the fracture toughness was determined. The fatigue behaviour was investigated in terms of the crack growth rate (da/dN) as a function of the applied stress intensity factor range. Clear differences in the fatigue behaviour of the samples from different pipes were observed. The result from these investigations, which indicate that microstructural differences play a role in mechanical behaviour, will support the development of asset management tools for use in the water industry.

Effect of crack depth on fatigue crack growth rates for a C–Mn pipeline steel in a sour environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge owing to the number of variables that have a significant effect on material behaviour. The fatigue behaviour of API 5L X65 pipeline steel parent material tested in a sour environment has been investigated. Fatigue crack growth rate (FCGR) tests have been performed to evaluate the influence of crack depth on crack growth rate (d a/d N), over the range 2–10 mm. The results obtained showed crack growth rates for deep flaws to be a factor of 5–30 higher in the sour environment than in air, dependent on the applied stress intensity factor range (Δ K). Shallow flaws have been shown to grow up to an order of magnitude faster than deep flaws in a sour environment at the same value of Δ K. The results highlight a potential non-conservatism associated with using deep-crack data to predict the behaviour of shallow flaws. The observed behaviour is attributed to the uptake of hydrogen at specimen surfaces exposed to the sour environment.

The Behavior of Shallow Cracks in a Pipeline Steel Operating in a Sour Environment

Setting conditions for the avoidance of in-service crack growth in aggressive corroding environments has long been a major challenge due to the number of variables that have a significant effect on material behavior. One area where both experimental data and a validated assessment methodology are lacking is the behavior of shallow cracks. This paper describes the early results of an ongoing research program aimed at addressing the shortfall in experimental data to characterize material behavior in the shallow-crack regime, with the long-term aim of improving the understanding and assessment of the early stages of environment assisted cracking. There is an industry need for a better understanding of material behavior under these conditions and for the development of a more robust assessment methodology. API 5L X65 pipeline steel parent material was tested in a sour environment with initial flaw sizes in the range 1–2 mm. Fatigue crack growth rate tests have been performed to investigate the influence of crack depth on crack growth rate (da/dN). Initial results suggest that crack growth rates for deep flaws can increase by a factor of 5–100 compared with air depending on the applied stress intensity factor range (ΔK). Shallow cracks have been shown to grow up to 130 times faster in a sour environment than in air and up to an order of magnitude faster than deep cracks in a sour environment at the same value of ΔK. Constant load tests have also been performed to investigate the influence of crack depth on the threshold stress intensity factor for stress corrosion cracking (KISCC). Preliminary results suggest that in this case there is no crack depth dependence in the range of flaw sizes tested. While further experimental work is required, the results obtained to date highlight the potential nonconservatism associated with extrapolating deep-crack data. Guidance is therefore provided on how to generate appropriate experimental data to ensure that subsequent fitness for service assessments are conservative.

The evolution of the stress–strain fields near a fatigue crack tip and plasticity‐induced crack closure revisited

ABSTRACTThe evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.

Non-destructive detection of damage in an austenitic stainless steel SUS 304 by the use of martensitic transformation

The present study investigates a method for the non-destructive detection of damage in an austenitic stainless steel SUS 304 by the use of martensitic transformation. Volume fraction of � martensite transformed in uniformly stretched SUS304 plates was measured and expressed as a function of the applied strain level e. The distributions of � phase in the plastic wake regions produced around fatigue cracks were then electromagnetically measured in fatigued SUS 304 plate specimens. The results were compared with the distributions of magnetic flux density Bz above the fatigue cracks in the specimens magnetized by a strong magnetic field higher than 0.4 T. It was revealed that the Bz distributions reflected the α phase distributions in the wake regions: i.e., the distance between the points where Bz reached the minimum and the maximum had a high correlation with the fatigue crack length, and the minimum and the maximum values of Bz showed a linear relationship with the applied stress intensity factor range ∆K. These results imply that not only the crack length but also the fatigue damage can be detected effectively in an electromagnetic non-destructive way.

Discrete dislocation modeling of fatigue crack propagation

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small-scale yielding are carried out using discrete dislocation dynamics. Cracks along a metal–rigid substrate interface and in a single crystal are studied. The formulation is the same as that used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. The cyclic crack growth rate log(d a/d N) versus applied stress intensity factor range log(Δ K I) curve that emerges naturally from the solution of the boundary value problem shows distinct threshold and Paris law regimes. Paris law exponents in the range 4 to 8 are obtained for the parameters employed here. Furthermore, rather uniformly spaced slip bands corresponding to surface striations develop in the wakes of the propagating cracks.