Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

Multiaxial low cycle fatigue behavior and life prediction of CP-Ti under non-proportional stress-controlled mode

Multiaxial low cycle fatigue tests under non-proportional stress (NPSS) controlled mode were performed on commercial pure titanium (CP-Ti). Strain responses of axial and torsional channels under highly applied stress amplitudes show an initial hardening phenomenon. Non-proportional hardening coefficient of CP-Ti is independent of the controlled mode. The critical plane of CP-Ti under NPSS controlled mode is aligned with the maximum principal stress plane proved by optical microscopy observation. Optimized FSM model and KBM-PM model with mean axial and torsional strain are established. These models are further integrated into equations related to multiaxial stress ratio with high accuracy of life prediction for CP-Ti under NPSS controlled mode.     

A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

An approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.     

High-cycle fatigue mechanisms in 1045 steel under non-proportional axial-torsional loading

Detailed microscopic analyses have been made on the high-cycle mechanisms in 1045 steel under various stress-controlled axial-torsional loadings. A special attention has been paid to a critical example of non-proportional loading, i.e., 90° out-of-phase loading with different stress ratios. The replica technique has been used to monitor crack initiation and propagation from the microstructure scale. The orientations of persistent slip bands and Stage I cracks are in good agreement with the critical plane concept. The evolutions of crack length with cycle life as well as the crack aspect ratios depend on the loading condition. However at a given life, the data are consolidated in terms of crack depth versus cycle life. The McDiarmid parameter correlates stress-life data under proportional loadings. However, it underestimates fatigue lives under out-of-phase loading at high stress ratio and it overestimates them in the case where all planes experience the same shear stress amplitude (stress ratio = 0.5). More damaging mechanisms are involved in crack initiation and crack propagation. It is recommended to test the fatigue performance of materials in this last condition that involves the worst damage mechanisms.     

Short crack growth and fatigue life in austenitic-ferritic duplex stainless steel

The kinetics of short crack growth has been studied in austenitic‐ferritic 2205 duplex stainless steel. Smooth cylindrical specimens and specimens with shallow notch were subjected to constant plastic strain amplitude loading. The crack growth was studied in notched specimens. The notch area has been mechanically and electrolytically polished to facilitate the observation of crack initiation and growth. The initiated cracks were observed in an SEM (scanning electron microscope). The crack growth was studied using long distance QUESTAR optical microscope equipped with high‐resolution camera. In constant plastic strain amplitude loading the microcracks were initiated and their growth kinetics has been studied. The characteristic features of the crack growth at different plastic strain amplitudes were recorded. Two approaches to analyse the crack growth rates were adopted. The comparison of the prediction of the fatigue life using the plastic‐strain‐dependent crack growth rate was compared with Manson–Coffin law and the relation between parameters of this law and parameters of the short crack growth law were established.     

Multiaxial fatigue life prediction method in the ground vehicle industry

The extensive progress which has been made in the multiaxial fatigue area over the past 5 to 10 years has allowed wider application of the multiaxial fatigue method in component durability design in the ground vehicle industry. The method adopts the long established local strain–life approach and includes several new features. (1) A three-dimensional cyclic stress–strain model, used to simulate the elastic–plastic material behavior under complicated loadings. (2) The critical plane approach, which requires the fatigue analysis to be performed on various potential failure planes before determining the lowest fatigue life. (3) A biaxial damage criterion, to better quantify fatigue damage under various loading conditions. (4) A multiaxial Neuber equivalencing technique, used to estimate, from the elastic finite element stress results, the multiaxial stress and strain history of plastically deformed notch areas. This paper examines the application of the above features to the fatigue analyses of three generic service/test histories: a constant amplitude (baseline) test history, a history directly recorded by strain gages mounted on the critical location of a structural component, and a loading history recorded in multichannels for a complex structure.     

Multiaxial fatigue behaviour of A356‐T6

Aluminum alloy A356‐T6 was subjected to fully reversed cyclic loading under tension, torsion and combined loading. Results indicate that endurance limits are governed by maximum principal stress. Fractography demonstrates long shear mode III propagation with multiple initiation sites under torsion. Under other loadings, fracture surfaces show unique initiation sites coincidental to defects and mode I crack propagation. Using the replica technique, it has been shown that the initiation life is negligible for fatigue lives close to 10⁶ cycles for combined loading. The natural crack growth rate has also been shown to be comparable to long cracks in similar materials.     

Multiaxial fatigue of rubber: Part II: experimental observations and life predictions

Fatigue experiments were conducted with an axial‐torsion specimen covering a wide range of stretch biaxiality and a range of fatigue lives between 10³ and 2 × 10⁶ cycles. These experiments include combined torsion–compression, pure torsion, combined torsion–tension and pure axial tension. Both in‐phase and out‐of‐phase combinations of axial and torsion loading were considered. The multiaxial fatigue experiments described provide empirical evidence from which an understanding of the mechanics of the fatigue process in rubber can be developed. Each of the four equivalence parameters described in Part I has been applied to the axial‐torsion fatigue experiments described in this paper (Part II). These results provide the basis for an analysis of the effects of multiaxial loading on fatigue life, and an assessment of the degree to which the various equivalence parameters are able to rationalize the results in a unified way. For the combined axial and shear strain histories in this study, the maximum principal strain criterion gave the best correlation to fatigue life. Strain energy density gave the worst correlation. The cracking energy density criterion was generally found to give good correlation of fatigue crack nucleation lives from combined axial‐torsion tests. Because it provides a plane‐specific analysis, this criterion appears to be particularly well suited for use in crack nucleation analyses of multiaxial strain histories.     

Prediction of fatigue resistance of a hot-dip galvanized steel

The paper clarifies the effect of a galvanizing coating on the fatigue strength of a ferritic steel. Depending on experimental conditions and on the microstructure of the coating, a reduction in fatigue strength is observed especially when the coating is thick. Cracks in the galvanizing coating rapidly form under cyclic loading and then propagate into the steel substrate. This completely modifies the distribution of crack lengths. Very short cracks are not observed in the steel when galvanized. It is shown that the propagation of a crack in the substrate from the coating is only possible when the crack completely crosses the coating. By assimilating the coating thickness to a crack in the steel substrate, the fatigue resistance of hot-dip galvanized steel can be predicted using the Kitagawa–Takahashi diagram.     

Influence of non-metallic inclusions on fatigue life in the very high cycle fatigue regime

The present paper deals with the influence of non-metallic inclusions on fatigue life in the high cycle fatigue and the very high cycle fatigue regime. For that purpose, several castings of steel 42CrMo4 (AISI 4140, DIN EN 1.7225) were produced by using recently developed novel metal-melt filters. The specimens were tested in hot-isostatically pressed and heat treated condition. After fatigue failure every fracture surface was intensively investigated by scanning electron microscopy in order to define the type, the size, the chemical composition, the morphology and the location of the crack initiating discontinuity. Subsequently, Murakami’s √area model was used for the evaluation of the influence of non-metallic inclusions on the fatigue life. In the present investigation four common types of chemical compositions of crack initiating discontinuities were identified. Furthermore, four different internal failure types and their influence on the fatigue life in cast steel were investigated and described. Thus, the present contribution proposes a basic correlation determined from fatigue lives in case of various internal crack initiation types. The key parameters for fatigue life prediction in case of internal fatigue failure in the very high cycle fatigue regime are (i) the size of the crack initiating discontinuity, (ii) the inclusion depth and (iii) the crack initiating failure type.     

Frequency effect and influence of testing technique on the fatigue behaviour of quenched and tempered steel and aluminium alloy

Influences of testing technique and frequency on the fatigue behaviour of 50CrMo4 and EN AW-5083 were investigated. To clarify the effect of test frequency on the fatigue behaviour, tests with 20 kHz and f < 400 Hz were performed. The frequency effect can be caused by temperature, environment and strain rate. For the aluminium alloy, the influence of environment is responsible for the dependence of fatigue lifetime on the frequency. The fatigue lifetime of the steel showed in both environments similar frequency dependency, i.e. the strain rate is assumed to be responsible for the differences in fatigue lifetime.     

Effect of loading type on fatigue properties of high strength bearing steel in very high cycle regime

Very high cycle fatigue tests under axial loading at frequencies of 95 Hz and 20 kHz were performed to clarify the effect of loading type on fatigue properties of a high strength bearing steel in combination with experimental result of this steel under rotating bending. As a result, this steel represents the single P-S-N (probabilistic-stress-life) curve characteristics for surface-induced fracture and interior inclusion-induced fracture, just like that under rotating bending. However, fatigue strength is lower, where the run-out stress at 10⁹ cycles is evaluated to be 588 MPa, less than that under rotating bending with about 858 MPa. Occurrence probability of larger and deeper inclusion-induced fracture is much higher than that under rotating bending. Furthermore, the formation process of fine granular area (FGA) is independent of the type and frequency of loading, which is very slow and is explained as the crack nucleation process under the special dislocation mechanism. The stress intensity factor range at the front of FGA, ΔK_FGA, is approximately regarded as the threshold value controlling the stable propagation of interior crack. For the control volume of specimen under axial loading, the estimated value of fatigue limit by FGA is similar to experimental run-out stress value at 10⁹ cycles, but that by inclusion is larger. However, the corresponding estimated results under rotating bending are all conservative.     

Experimental study on very high cycle fatigue of martensitic steel of 2Cr13 under corrosive environment

Rotating bending fatigue test at very high cycle regimes was carried out on martensitic steel of 2Cr13 in air and 3.5% NaCl environment. The result showed that the S–N curve presents a stepwise tendency over the range of 10⁶–10⁸ cycles in both air and 3.5% NaCl environment. In air fatigue, cracks initiated from the sample surface and inclusions at subsurface and no typical fish eye feature in very high cycle fatigue were observed for all samples tested up to 6 × 10⁸ cycles. In 3.5% NaCl solution, a fatigue limit over the range of 10⁶–10⁸ cycles exhibited with the corrosion fatigue strength reduced by 47% compared to the air fatigue. Multiple cracks initiated from surface and the number of crack origins increased with increasing stress level and surface proportion of fatigue propagation increased as number of cycles increased.     

Influence of strain range on fatigue life reduction of stainless steel in PWR primary water

The environmental effect in the pressurized water reactor (PWR) water was investigated for various applied strain range using a type 316 stainless steel. The tests were conducted using cylindrical hollow specimens at 325°C. It was shown that the ratio of the fatigue life in the PWR water environment to that in air was about 0.3 to 0.4 regardless of the strain range when the applied strain ranges were 0.8% or more. Crack growth rates identified from spacing of striations observed on fractured surfaces were used to demonstrate that the fatigue life reduction in the PWR water environment could be attributed to the crack growth acceleration. The fractured surface observations revealed that crack initiation was enhanced by the PWR water environment. On the other hand, the reduction in the fatigue life was not significant when the strain ranges were 0.5% and 0.44%, and the specimens did not fail when the strain ranges were 0.38% or less. It was deduced that the crack initiation was not enhanced for the relatively small strain range, and the crack growth was not accelerated. Since the fatigue limit of the test material was 0.4% in the strain range in air, it was concluded that the fatigue limit was not reduced in the PWR water environment.     

Effects of annealing and quenching on fatigue behaviour in type 444 ferritic stainless steel

In order to understand the effects of annealing and quenching on fatigue behaviour in type 444 stainless steel, fully reversed axial fatigue tests have been performed using smooth specimens of heat‐treated materials in laboratory air and 3%NaCl aqueous solution. Three materials subjected to different heat treatments, annealing at 960 and 1000 °C, and water‐cooling at 960 °C, were prepared. In laboratory air, the fatigue limit of the annealed specimens was lower than that of the as‐received specimen and decreased with increasing annealing temperature. The subsequent grain coarsening from the heat treatments was primarily responsible for the lower fatigue strength in the annealed specimens. The fatigue strength of the water‐cooled specimen was lower than that of the corresponding annealed specimen. In the annealed specimens, cracks were generated within ferritic grains, while in the water‐cooled specimen, at or near grain boundaries. In 3%NaCl solution, the fatigue strengths of all specimens decreased compared with those in laboratory air. Only in the water‐cooled specimens, crack initiation at grain boundary and intergranular crack growth were observed, indicating the most sensitive to corrosion environment.     

Axial fatigue of a gas-nitrided quenched and tempered AISI 4140 steel: effect of nitriding depth

Fatigue testing under fully reversed axial loading (R=?1) and zero‐to‐tension axial loading (R= 0) was carried out on AISI 4140 gas‐nitrided smooth specimens. Three different treatment durations were investigated in order to assess the effect of nitriding depth on fatigue strength in high cycle fatigue. Complete specimens characterization, i.e., hardness and residual stresses profiles (including measurement of stabilized residual stresses) as well as metallographic and fractographic observations, was achieved to analyse fatigue behaviour. Fatigue of the nitrided steel is a competition between a surface crack growing in a compressive residual stress field and an internal crack or ‘fish‐eye’ crack growing in vacuum. Fatigue life increases with nitriding depth until surface cracking is slow enough for failure to occur from an internal crack. Unlike bending, in axial fatigue ‘fish‐eye’ cracks can initiate anywhere in the core volume under uniform stress. In these conditions, axial fatigue performance is lower than that obtained under bending and nitriding depth may have no more influence. In order to interpret the results, special attention was given to the effects of compressive residual stresses on the surface short crack growth (closure effect) as well as the effects of internal defect size on internal fatigue lives. A superimposed tensile mean stress reduces the internal fatigue strength of nitrided steel more than the surface fatigue strength of the base metal. Both cracking mechanisms are not equally sensitive to mean stress.     

Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading

A new calculation approach is suggested to the fatigue life evaluation of notched specimens under multiaxial variable amplitude loading. Within this suggested approach, if the computed uniaxial fatigue damage by the pure torsional loading path is larger than that by the axial tension–compression loading path, a shear strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage; otherwise, an axial strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage. Furthermore, the presented method employs shear strain‐based and axial strain‐based multiaxial fatigue damage parameters in substitution of equivalent strain amplitude to consider the influence of nonproportional additional hardening. The experimental data of GH4169 superalloy and 7050‐T7451 aluminium alloy notched components are used to illustrate the presented multiaxial fatigue lifetime estimation approach for notched components, and the results reveal that estimations are accurate.     

Technical note High-cycle fatigue crack initiation and propagation behaviour of high-strength sprin steel wires

An attempt has been made to characterize high-cycle fatigue behaviour of high-strength spring steel wire by means of an ultrasonic fatigue test and analytical techniques. Two kinds of induction-tempered ultra-high-strength spring steel wire of 6.5 mm in diameter with a tensile strength of 1800 MPa were used in this investigation.
The fatigue strength of the steel wires between 10⁶ and 10⁹ cycles was determined at a load ratio R = −1. The experimental results show that fatigue rupture can occur beyond 10⁷ cycles. For Cr–V spring wire, the stress–life ( S – N ) curve becomes horizontal at a maximum stress of 800 MPa after 10⁶ cycles, but the S – N curve of the Cr–Si steel continues to drop at a high number of cycles (>10⁶ cycles) and does not exhibit a fatigue limit, which is more correctly described by a fatigue strength at a given number of cycles. By using scanning electron microscopy (SEM), the crack initiation and propagation behaviour have been examined. Experimental and analytical techniques were developed to better understand and predict high-cycle fatigue life in terms of crack initiation and propagation. The results show that the portion of fatigue life attributed to crack initiation is more than 90% in the high-cycle regime for the steels studied in this investigation.