Crack Growth Threshold Research Articles

Estimation of P‐S‐N curves in very‐high‐cycle fatigue: Statistical procedure based on a general crack growth rate model

AbstractExtensive experimental investigations show that internal defects play a key role in the very‐high‐cycle fatigue (VHCF) response of metallic materials and that crack growth from internal defects can take place even if the stress intensity factor associated to the initial defect is below the threshold for crack growth. By introducing a reduction term in the typical formulation of the threshold for crack growth, the authors recently proposed a general phenomenological model, which can effectively describe crack growth from internal defects in VHCF. The model is able to consider the different crack growth scenarios that may arise in VHCF and is enough general to embrace the various weakening mechanisms proposed in the literature for explaining why crack can grow below the threshold.In the present paper, the model is generalized in a statistical framework. The statistical distributions of the crack growth threshold and of the initial defect size are put into the model. The procedure for the estimation of the Probabilistic‐S‐N curves and of the fatigue limit distribution is illustrated and numerically applied to an experimental dataset.

Oxidation and creep interactions during high temperature high-R fatigue crack growth threshold determination

While knowledge relating to the determination and practical application of fatigue crack growth threshold stress intensity factors (ΔKth) for defect assessment is relatively well established for many circumstances, this is not the case for materials and conditions which are sensitive to time dependent mechanisms. In particular, current testing standards do not address determination of the property for very high R (Kmin/Kmax) ratios, and those conditions when the environment can be influential and ΔKth is sensitive to the adopted da/dN(ΔK) criterion. The incidence of creep crack growth in association with very slowly growing high-R high cycle fatigue cracks is not always discernable by the direct examination of near-to-threshold da/dN(ΔK) test records, but can be predicted by means of a time dependent failure assessment diagram analysis. In addition to a general state of knowledge review, particular attention is paid to circumstances relating to high-R ΔKth in power plant steels at high temperatures for which oxide induced closure and creep cracking can be influential. Evidence for a low alloy 1%Cr steel, a martensitic 9%Cr steel and an austenitic 18%Cr steel is considered, and the practical implications are examined.

Fatigue crack growth of a railway wheel

Abstract Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed. Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold. To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K I and K II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques. The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.

Behavior of small cracks under negative stress ratio fatigue loading

In this paper we analyze growth of small cracks initiated from microscopic notches and loaded near the growth threshold under different stress ratios. The results of in-situ optical measurements during high cycle fatigue testing show that small cracks initiate and grow quickly after which there is a long period of slow growth until the large crack growth threshold is reached. The crack growth rate data from different loading ratios indicates that the positive portion of the stress amplitude or the maximum stress intensity factor can be used to compare crack growth rates. The test data also shows that increasing only the compressive stress portion of the loading will cause an arrested small crack to grow again.

Fatigue Crack Growth Behavior of a New Type of 10% Cr Martensitic Steel Welded Joints with Ni-Based Weld Metal

In the present work, the fatigue crack growth (FCG) behavior of a new type of 10% Cr martensitic steel welded joints with Ni-based weld metal was comparatively studied for different regions including base metal (BM), heat-affected zone (HAZ) and weld metal (WM). FCG results indicated that the tempered lath martensite BM has a higher fatigue crack growth resistance than the tempered granular martensite HAZ that without a typical lath structure. In comparison, the austenitic WM has the highest fatigue crack growth threshold. Meanwhile, due to the microstructural and chemical compositional differences between BM and WM, a clear interface existed in the welded joints. At the region of the interface, the microstructures were physically connected and an element transition layer was formed. Although the starter notch was positioned at the region of interface, the fatigue crack gradually deviated from the interface and ultimately propagated along the inter-critically heat-affected zone. The difference in microstructure is considered as the primary factor that resulted in the different fatigue crack growth behaviors of the welded joints. In addition, the continuous microstructure connection and composition transition at the interface contributed to the good fatigue resistance at this region.

Enhancing fatigue resistance and damage characterisation in adhesively-bonded composite joints by carbon nanofibres

In the present work we report on the use of carbon nanofibres (CNFs) to simultaneously improve the cyclic fatigue resistance and the detectability of disbonding in adhesively-bonded structures made of carbon-fibre reinforced-plastic (CFRP) composites. The effects of the concentration of the CNFs (i.e. 0.4, 0.7 and 1.0 wt%) and their orientation (i.e. random versus aligned) in the epoxy-adhesive layer between two CFRP substrates are investigated. The results show that increasing the concentration of randomly-oriented CNFs (a) improves greatly the mode I fatigue resistance of the adhesive layer, including raising the crack growth threshold of the cyclic strain-energy release-rate, and (b) increases the quasi-static fracture toughness. Further improvements in the fatigue resistance occur when the CNFs are aligned perpendicular to the plane of the joint, i.e. normal to the crack plane, as opposed to being randomly-oriented in the adhesive layer. In addition, the CNFs form a conductive network that makes it possible to detect and characterise fatigue-induced disbonding using an electrical-resistance technique. A simple model is developed for the relationship between the disbond (i.e. crack size) and the electrical resistance of a bonded joint with conductive substrates. Finite element analyses are carried out to quantify the applicability of this model as a function of the conductivity of the adhesive from 10−4 S/m to 1 S/m. The results confirm that the proposed simple model is highly accurate for joints where the composite substrates have a through-thickness electrical conductivity exceeding a hundred times that of the adhesive. This research paves the way for new multi-functional adhesives with greatly enhanced fatigue resistance and disbond detection capability.

Effect of Stress Ratio on Fatigue Crack Growth Threshold for Austenitic Stainless Steels in Air Environment

The fatigue crack growth threshold ΔKth is an important characteristic of crack growth assessment for the integrity of structural components. However, the accurate threshold ΔKth values for austenitic stainless steels in air environment are lacking in many fitness-for-service (FFS) codes, although fatigue crack growth tests have been performed and many test data had been published. This paper focuses on fatigue crack growth threshold ΔKth values for austentic stainless steel in air environment. The paper introduces the current ΔKth values provided by four major FFS codes and summarizes the available test data based on the literature survey. The paper then discusses the applicability of the existing ΔKth for stainless steels and proposes a new relation as a function of the stress ratio (the R ratio) for use by FFS codes.

Effect of microstructure on the fatigue crack growth behavior of laser solid formed 300M steel

In this research, the effect of microstructure on the fatigue crack growth rate (FCGR) of laser solid formed (LSFed) 300M steel was investigated. The results showed that the as-deposited microstructure of LSFed 300M steel consisted of martensite and coarse bainite. After heat treatment, the microstructure became homogeneous and was primarily composed of tempered martensite, bainite and a small amount of retained austenite. The FCGR of LSFed 300M steel gradually increases with increasing stress ratio (for a given stress intensity factor range and stress ratios between 0.1 and 0.5). The refined austenite grain of heat-treated LSFed 300M steel reduced the fatigue crack growth threshold (FCGT) and the FCGR. The fractography of as-deposited LSFed 300M steel was different from that of heat-treated LSFed 300M steel.

Does a nucleated crack propagate?

Conditions for propagation or non-propagation of an incipient crack from stress concentrations such as notches, holes, etc., are evaluated using elastic-plastic fracture mechanics methods and the Kitagawa-Takahashi diagram, hence linking smooth specimen behavior to fracture mechanics. The analysis differs from all other previous models which are either empirically based or assume that short crack growth behavior differs from that of long cracks due to crack closure or lack of it. It is shown that the stress intensity factor of an incipient crack decreases and then increases as it moves away from the internal stress field of a notch. Crack propagation is ensured only when the minimum is equal to or greater than the unique fatigue threshold for crack growth. Otherwise non-propagation conditions prevail. Equations are developed to establish the conditions for the minimum stress required for continuous propagation of the originated crack. It is shown that by analyzing published results on notch-fatigue that specimen failure occurs only if the applied stresses exceed the minimum stress required for crack propagation. Otherwise crack arrest occurs resulting in non-propagating cracks. The analysis can be readily used to determine the conditions for failure of a notched specimen if the elastic stress concentration factor, kt, the notch-tip radius, ρ, and fatigue crack threshold, Kth, for the material are known. The analysis, in principle, is applicable to all subcritical crack growth processes.

A general model for crack growth from initial defect in Very-High-Cycle Fatigue

Abstract: It is well-known in the literature that internal defects play a major role in the Very-High-Cycle Fatigue (VHCF) response of metallic materials. Generally, VHCF failures nucleate from internal defects characterized by a limited size. Unexpectedly, it has been found that cracks can grow from the initial defect even if the Stress Intensity Factor (SIF) is quite below the characteristic threshold for crack growth. Even though researchers unanimously accept this singular experimental evidence, they still dispute about its physical justification. Different micromechanical explanations have been proposed in the literature: local grain refinement, carbide decohesion, matrix fragmentation, hydrogen embrittlement, numerous cyclic pressure and formation of persistent slip bands are the most famous proposals. Regardless of the specific micromechanical explanation, it is generally acknowledged that a weakening mechanism occurs around the initial defect, thus permitting crack growth below the SIF threshold. The present paper proposes an innovative approach for the quantitative modeling of the weakening process around the initial defect. The proposed model considers an additional SIF that reduces the SIF threshold of the material. Starting from a very general formulation for the additional SIF, possible scenarios for crack growth from the initial defect are also identified and described. It is theoretically demonstrated that, depending on the scenario, a VHCF limit may also be present and its final formulation recalls the well-known expression previously proposed by Murakami.

Quantitative Evaluation of the Flaking Strength of Rolling Bearings with Small Defects: (Part 1: FEM Analyses of the Stress Intensity Factor, KII, under Rolling Contact)

It has been demonstrated that the rolling contact fatigue (RCF) test, using a specimen with a small drilled hole, is a useful means of evaluating the influence of a minor defect on the flaking strength of steels. In this study, RCF tests were conducted on rolling bearings with small drilled holes. Flaking failure was determined to be caused by the shear-mode fatigue cracks that emanated from the small defects. As a first step to quantifying the crack-growth threshold according to fracture mechanics principles, using the finite element method (FEM), it was necessary to analyze the Mode II stress intensity factor (SIF) range, ΔKII, of a ring-shaped crack, as emanated around the edge of a drilled hole after the passage of a rolling element. Subsequently, the derived values were correlated with the ΔKII values of penny-shaped cracks in an infinite body under uniform shear via a correlation factor, fdrill. The SIF of the ring-shaped crack was also uniformly correlated with that of the penny-shaped crack, using the single factor, fdrill, irrespective of the hole diameter, d, the depth of the hole-edge, h′, and the maximum contact pressure, qmax, within the following ranges: d = 0.05 ~ 0.2 mm, h′ = 0.05 ~ 0.345 mm and qmax = 2.0 ~ 3.0 GPa. The obtained results were later applied towards the quantification of the RCF test results, as detailed in Part 2 of the report on this research.

転がり軸受のはく離強度に及ぼす微小欠陥寸法の影響（第1報:転がり接触下のモードII応力拡大係数のFEM解析）

It has been shown that rolling contact fatigue (RCF) test using specimen having a small drilled hole is a useful method for evaluating the effect of small defect on flaking strength of steels. In this study, RCF tests of rolling bearings having a small drilled hole were carried out. The flaking failure was considered as a problem of shear-mode fatigue crack emanating from the small defect. As a first step to quantify the crack-growth threshold on the basis of fracture mechanics, mode II stress intensity factor range, ΔKII, of a ring-shaped crack emanated around the edge of a drilled hole under the passing of a rolling element was analyzed by using finite element method. And then, the obtained values were correlated with the ΔKII values of penny-shaped cracks in an infinite body under uniform shear through the intermediary of a correlation factor, fdrill. The stress intensity factor of the ring-shaped crack was uniformly correlated with that of the penny-shaped crack by the single factor fdrill irrespective of hole diameter, d, depth of hole edge, h’, and maximum contact pressure, qmax, within the ranges: d = 0.05 ~ 0.2 mm, h’ = 0.05 ~ 0.345 mm and qmax = 2.0 ~ 3.0 GPa. The obtained results will be applied for the quantification of RCF test results shown in the subsequent paper.

Impacts of weld residual stresses and fatigue crack growth threshold on crack arrest under high-cycle thermal fluctuations

High cycle thermal crazing has been observed in some residual heat removal (RHR) systems made of 304 stainless steel in PWR nuclear plants. This paper deals with two types of analyses including logical argumentation and simulation. Crack arrest in networks is demonstrated due to the presence of two cracks of the same depth in the network. This identical depth may be proved assuming that mean stress acts only on crack opening and that cracks are fully open during the load cycle before arrest.Weld residual stresses (WRS) are obtained by an axisymmetric simulation of welding on a tube with a chamfer. Axisymmetric and 3D parametric studies of crack growth on: representative sequences for variable amplitude thermal loading, fatigue crack growth threshold (FCGT), permanent mean stress, cyclic counting methods and WRS, are performed with Code_Aster software using XFEM methodology. The following results are obtained on crack depth versus time: the effect of WRS on crack growth cannot be determined by the initial WRS field in absence of crack, but by the associated stress intensity factor. Moreover the relation between crack arrest depth and WRS is analyzed.In the absence of FCGT Paris’s law may give a significant over-estimation of crack depth even if amplitudes of loading smaller than FCGT have not been considered. Appropriate depth versus time may be obtained using different values of FCGT, but axisymmetric simulations do not really show a possibility of arrest for shallow cracks in contrast with logical argumentations.

Prediction of effective mode II fatigue crack growth threshold for metallic materials

The fatigue crack growth threshold consists of the intrinsic component (effective threshold) and the extrinsic component (crack closure). Theoretical formulae for prediction of the mode II effective threshold in metallic materials are presented. The model is based on physical interpretation of experimental findings. For a given material the dominant local crack growth mode at the kinked crack front of a remote mode II loaded crack is identified and the local stress intensity factor is expressed, which represents a new concept for estimation of the mode II effective threshold. The local crack growth mode depends on microstructure and crystallographic structure of the material. Moreover, new experimental data for mode II effective thresholds of the Ti6Al4V alloy (ΔKIIeff,th=1.8MPam1/2) and pure zirconium (ΔKIIeff,th=1.3MPam1/2) are presented. These data extended the available database for metallic materials and confirmed a broad validity of the proposed theoretical relationships.

Research on Transition from Short to Long Fatigue Crack Propagation of GH4133B Superalloy Used in Turbine Disk of Aero-Engine

The fatigue crack propagation tests for circular notched compact tension specimens of GH4133B superalloy used in a turbine disk of aero-engine are carried out at room temperature. The test data shows that in the transition region from short to long crack growth, the crack growth rate appears as a fluctuation form with acceleration following deceleration. A quasi harmonic function is constructed to model the fatigue crack growth in the transition region, and the result indicates that such function is suitable to describe the crack growth behavior. A metallographic analysis with respect to microscopic observation for the specimen’s surface suggests that the wave period, that is, a step length of a cycle fluctuation from acceleration to deceleration on the crack growth rate curve is agree well with the intrinsic scale of grain size, which indicates that in the transition region from short to long crack growth, grain boundary plays a dominant role in crack growth rate. Finally, the fracture surfaces of specimen are observed using a scanning electron microscopy. It can be found from the fracture surface morphologies that in the transition region from short to long crack growth, the stress intensity factor range is still lower than the fatigue crack growth threshold ΔKth, the effect of microstructure, such as grain size, grain boundary, secondary phase particle, and inclusion ahead of the crack tip, and the effect of crack closure on crack growth behavior should be considered, the local further plastic deformation at crack tip will meet larger resistance, so some twin bands are observed on the fracture surface. As crack length increases with increasing fatigue cycle, the crack propagation is noted to change from a transgranular crack propagation mode, a mixed transgranular and intergranular crack propagation nature, to intergranular crack propagation manner.

Fatigue Crack Growth Threshold Determination for Welded Joint Constituents of a Steam Turbine LP Rotor

Fatigue Crack Growth Threshold Determination for Welded Joint Constituents of a Steam Turbine LP Rotor

S‐N curves in the very‐high‐cycle fatigue regime: statistical modeling based on the hydrogen embrittlement consideration

AbstractThe continuous increment of durability and reliability requirements for many machinery components is significantly enhancing the research activity in the Very‐High‐Cycle Fatigue (VHCF) characterization of metallic materials, in particular of high‐strength steels for critical structural applications.According to the model, the VHCF strength of high‐strength steels can be estimated from the projected area of the ‘Optically Dark Area’ (ODA), which plays a key role in the VHCF response of high‐strength steels: more than 95% of the total VHCF life is consumed in the ODA formation, with crack growing even though the Stress Intensity Factor (SIF) is below the threshold for crack growth. Following the hydrogen embrittlement theory proposed by Murakami, hydrogen is supposed to assist crack growth within the ODA.The present paper proposes a general SIF formulation for the analytical model of the hydrogen assisted crack growth within the ODA. Starting from the general SIF formulation, a general expression for the material fatigue limit is obtained in the paper. The statistical method for the estimation of the parameters involved in the proposed model is finally illustrated in the paper and numerically applied to an experimental dataset.

Delayed Fracture of Glass Bulbs Used in Fire Sprinklers

Very rarely, glass bulb sprinkler heads activate when there is no fire or elevated temperatures. In such cases, the bulb fragments are never recovered. Speculation may arise that there was a defect in the bulb from manufacturing or installation, which led to its eventual failure. We investigated the growth of such defects using the principles of fracture mechanics and the well-known laws of slow crack growth in glass. These laws include the existence of a threshold, below which cracks do not grow at all, and above which cracks grow at a velocity that is greater than a minimum value. As a result, bulbs either never fail, or fail within a relatively short time after the crack or defect is created. Finite element and fracture mechanics analyses for a typical bulb indicates that the maximum delay is of the order of hours or weeks, not years. Experiments confirm this phenomenon. Over 100 bulbs were intentionally damaged, then placed under a constant load. A total of 44 bulbs, for which the combination of damage and load happened to be above the threshold for crack growth, failed within days (up to 36 days), while all other 58 bulbs survived over 2 years without failure. The theoretical analysis and the experiments demonstrate that fracture of sprinkler bulbs occurs relatively quickly after the introduction of a defect: if a bulb fractures in service without apparent cause, there must have been some event to damage the bulb or the sprinkler head in the days or weeks before the activation.

Effects of laser shock processing on high cycle fatigue crack growth rate and fracture toughness of aluminium alloy 6082-T651

The effects of laser shock processing without protective coating on high-cycle fatigue crack growth and fracture toughness were investigated. Laser shock peening treatment was performed on compact tension specimens from both sides perpendicular to the crack growth direction, followed by subsequent grinding. Fatigue crack growth tests were performed at frequencies between 116 and 146Hz, at R=0.1 and a constant stress intensity range during the fatigue crack initiation phase and K-decreasing test. A lower number of cycles was required to initiate a fatigue precrack, and faster fatigue crack growth was found in tensile residual stress field of LSP-treated specimens. The crack growth threshold decreased by 60% after LSP treatment. The fracture toughness decreased by 28–33% after LSP treatment. The fatigue-to-ductile transition boundary on fractographic surfaces show linear fatigue crack fronts in non-treated specimens and curves after LSP treatment.

Fatigue crack growth threshold as a design criterion - statistical scatter and load ratio in the Kitagawa-Takahashi diagram

Cracks in components reduce the endurable stress so that the endurance limit obtained from common smooth fatigue specimens cannot be used anymore as a design criterion. In such cases, the Kitagawa-Takahashi diagram can be used to predict the admissible stress range for infinite life, at a given crack length and stress range. This diagram is constructed for a single load ratio R. However, in typical mechanical engineering applications, the load ratio R varies widely due to the applied load spectra and residual stresses. In the present work an extended Kitagawa-Takahashi diagram accounting for crack length, crack extension and load ratio is constructed. To describe the threshold behaviour of short cracks, a master resistance curve valid for a wide range of steels is developed using a statistical approach.