3D modeling of subsurface fatigue crack nucleation potency of primary inclusions in heat treated and shot peened martensitic gear steels

A computational strategy is developed to characterize the driving force for fatigue crack nucleation at subsurface primary inclusions in carburized and shot peened C61^® martensitic gear steels. Experimental investigation revealed minimum fatigue strength to be controlled by subsurface fatigue crack nucleation at inclusion clusters under cyclic bending. An algorithm is presented to simulate residual stress distribution induced through the shot peening process following carburization and tempering. A methodology is developed to analyze potency of fatigue crack nucleation at subsurface inclusions. Rate-independent 3D finite element analyses are performed to evaluate plastic deformation during processing and service. The specimen is subjected to reversed bending stress cycles with R = 0.05, representative of loading on a gear tooth. The matrix is modeled as an elastic–plastic material with pure nonlinear kinematic hardening. The inclusions are modeled as isotropic, linear elastic. Idealized inclusion geometries (ellipsoidal) are considered to study the fatigue crack nucleation potency at various subsurface depths. Three distinct types of second-phase particles (perfectly bonded, partially debonded, and cracked) are analyzed. Parametric studies quantify the effects of inclusion size, orientation and clustering on subsurface crack nucleation in the high cycle fatigue (HCF) or very high cycle fatigue (VHCF) regimes. The nonlocal average values of maximum plastic shear strain amplitude and Fatemi–Socie (FS) parameter calculated in the proximity of the inclusions are considered as the primary driving force parameters for fatigue crack nucleation and microstructurally small crack growth. The simulations indicate a strong propensity for crack nucleation at subsurface depths in agreement with experiments in which fatigue cracks nucleated at inclusion clusters, still in the compressive residual stress field. It is observed that the gradient from the surface of residual stress distribution, bending stress, and carburized material properties play a pivotal role in fatigue crack nucleation and small crack growth at subsurface primary inclusions. The fatigue potency of inclusion clusters is greatly increased by prior interfacial damage during processing.     

Influence of inclusion size on S-N curve characteristics of high-strength steels in the giga-cycle fatigue regime

Fatigue fracture of high-strength steels often occurs from small defect on the surface of a material or from non-metallic inclusion in the subsurface zone of a material. Under rotating bending loading, the S-N curve of high-strength steels consists of two curves corresponding to surface defect-induced fracture and internal inclusion-induced fracture. The surface defect-induced fracture occurs at high stress amplitude levels and low cycles. However, the subsurface inclusion-induced fracture occurs at low stress amplitude levels and high-cycle region of more than 10⁶ cycles (giga-cycle fatigue life). There is a definite stress range in the S-N curve obtained from the rotating bending, where the crack initiation site changes from surface to subsurface, giving a stepwise S-N curve or a duplex S-N curve. On the other hand, under cyclic axial loading, the S-N curve of high-strength steels displays a continuous decline and surface defect-induced or internal inclusion-induced fracture occur in the whole range of amplitudes. In this paper, influence factors on S-N curve characteristics of high-strength steels, including size of inclusions and the stress gradient of bending fatigue, were investigated for rotating bending and cyclic axial loading in the giga-cycle fatigue regime. Then, based on the estimated subsurface crack growth rate from the S-N data, effect of inclusion size on the dispersion of fatigue life was explained, and it was clarified that the shape of S-N curve for subsurface inclusion-induced fracture depends on the inclusion size.     

Corrosion fatigue crack initiation and growth in 18 Ni maraging steel

Nucleation of fatigue cracks in air and 3.5 wt% NaCl solution has been studied in an 18 wt% Ni maraging steel. Specimens tested on reverse bending fatigue machine showed a marked decrease in fatigue strength of the steel in NaCl solution reducing the 10⁷ cycles endurance limit from 410 MPa in air to 120 MPa. Microscopic studies revealed crack initiation to be predominantly associated with non-metallic silicate inclusions in both cases. In air, initiation is caused by decohesion of the inclusion/matrix interface, while in NaCl solution complete detachment of inclusions from the matrix results due to the dissolution of the interface. 70% more inclusions are quantitatively shown to be associated with cracks in NaCl solution than in air at the same stress levels. Experimental and theoreticalS-N curves and inclusion cracking sensitivity data are consistent with the mechanism suggested. The final fracture occurs by the main crack consuming the inclusions ahead of it by the “unzipping” of the shear band produced between the crack tip and the inclusion ahead.     

Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method

In this paper, Voronoi cell finite element method (VCFEM), introduced by Ghosh and coworkers (1993), is applied to describe the matrix-inclusion interfacial debonding for particulate reinforced composites. In proposed VCFEM, the damage initiation is simulated by partly debonding of the interface under the assumption of the critical normal stress law, and gradual matrix-inclusion separations are simulated with an interface remeshing method that a critical interfacial node at the crack tip is replaced by a node pairs along the debonded matrix-inclusion interface and a more pair of nodes are needed to be added on the crack interface near the crack tip in order to better facilitate the free-traction boundary condition and the jumps of solution. The comparison of the results of proposed VCFEM and commercial finite element packages MARC and ABAQUS. Examples have been given for a single inclusion of gradually interfacial debonding and for a complex structure with 20 inclusions to describe the interfacial damage under plane stress conditions. Good agreements are obtained between the VCFEM and the general finite element method. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials. The financial support by the Special Funds for the National Major Fundamental Research Projects G19990650 and the National Natural Science Foundation of China No. 59871022 are gratefully acknowledged.     

Detrimental effect of nitride and aluminium oxide inclusions on fatigue life in rotating bending of bearing steels

Abstract

Rotating bending fatigue tests were performed on hardened AISI type 52100 bearing steel. Fracture surfaces after testing at a stress amplitude of 950 MPa showed that the Ti(C,N) inclusions which caused fatigue failure were significantly smaller than the corresponding alumina inclusions. The smallest crack initiating Ti(C,N) inclusion had a size of 3 μm and the smallest alumina inclusion was 17 μm. It was also shown that fatigue life was significantly shorter for a steel which showed cracked alumina inclusions on the fracture surfaces than for a steel which had non-cracked inclusions. Finite element calculations were performed to determine the driving forces of short cracks at Ti(C,N) and alumina inclusions. Two configurations were studied in each case, based on both non-cracked and cracked inclusions. The calculations incorporated heat treatment simulation and cyclic loading with successive growth of cracks. It was found that the Ti(C,N) configurations gave the highest driving forces for crack growth. The alumina configuration with a non-cracked inclusion gave the lowest driving force. It was concluded based both on experimental evidence and theoretical considerations that Ti(C,N) inclusions are more detrimental to fatigue life than alumina inclusions of the same size. It is their shape and thermal properties which make Ti(C,N) inclusions more detrimental than alumina inclusions. Internal cracking of alumina inclusions leads to reduced fatigue life.     

Microstructure-based fatigue modeling of cast A356-T6 alloy

High cycle fatigue (HCF) life in cast Al-Mg-Si alloys is particularly sensitive to the combination of microstructural inclusions and stress concentrations. Inclusions can range from large-scale shrinkage porosity with a tortuous surface profile to entrapped oxides introduced during the pour. When shrinkage porosity is controlled, the relevant microstructural initiation sites are often the larger Si particles within eutectic regions. In this paper, a HCF model is introduced which recognizes multiple inclusion severity scales for crack formation. The model addresses the role of constrained microplasticity around debonded particles or shrinkage pores in forming and growing microstructurally small fatigue cracks and is based on the cyclic crack tip displacement rather than linear elastic fracture mechanics stress intensity factor. Conditions for transitioning to long crack fatigue crack growth behavior are introduced. The model is applied to a cast A356-T6 Al alloy over a range of inclusion severities.     

Initiation and early growth of short fatigue cracks at inclusions

In this study, the initiation and early growth behaviour of short fatigue cracks in En 7A steel with a high content of elongated MnS inclusions was investigated, by generating and evaluating data on the growth of short fatigue cracks under various stress levels and stress ratios for the six principal specimen orientations. Short cracks usually initiated at the debonded interfaces between the matrix and the inclusions. If there was no debonding, cracking sometimes occurred in the inclusions. In the early stages, short cracks propagated by a mechanism of inclusion influenced growth. Under low stress levels, usually one short crack was initiated which dominated most of the fatigue life, while under high stress levels there was multicrack interaction.

MST/3249A     

Rotating bending fatigue properties of two case hardening steels after nitriding treatment

Fatigue properties of two Al-containing steels have been investigated by rotating bending fatigue tests. Results show that the fatigue limits (the fatigue strength at 10⁷ cycles) were improved remarkably by plasma nitriding due to the high hardness of 1000 Hv and compressive stress of 400 MPa in the nitrided layer. Scanning electron microscopic observations show that after nitriding the fatigue crack initiation sites moved from the surface flaws or near-surface matrix into the AlN inclusions at around the case-core interface. Degassing treatment can increase the fatigue limit because it prevented fatigue crack initiation at AlN inclusions due to the reduced [N] contents and refined inclusion size.     

Study on bending fretting fatigue of LZ50 axle steel considering ratchetting by finite element method

Based on the finite element simulation, the crack nucleation location and failure life of bending fretting fatigue are analysed and predicted for LZ50 axle steel, respectively. In the simulation, a simplified two‐dimensional finite element model with an equivalent normal force is proposed and the role of ratchetting is also considered by using a new cyclic elastoplastic constitutive model. The crack nucleation location and fatigue life are finally predicted by Smith–Watson–Topper (SWT) critical plane criteria referring to the finite element calculation. It is shown that the predicted results are in fairly good agreement with the experimental ones.     

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.     

Multi-axial fatigue initiation at inclusions and subsequent crack growth in a bainitic high strength roller bearing steel at uniaxial experiments

The behaviour of inclusion initiated fatigue was studied for a high strength bearing steel with a bainite micro-structure. The analysis included experiments and numerical simulations. It was realized that the stress-state was multi-axial in the matrix material that met the inclusion also for a uniaxial far field stress. Fatigue initiation risk at the interface between the inclusion and matrix material was therefore predicted with the Findley multi-axial critical plane criterion. The fatigue parameters were determined from independent experiments on smooth specimens with tensile surface stress gradients. Crack growth from the inclusion to final rupture was modelled as a penny shaped crack with closure compensated effective material parameters. The growth simulations suggested that the majority of the fatigue life was consumed as fatigue crack initiation at the non-metallic inclusion.     

Fatigue Fracture of a High-Resistance Structural Steel Component Destined to Sustain Severe Loads Under Service Conditions

A structural steel component that failed under fatigue was examined with the aim to identify the root causes of this failure. Fractographic examination revealed the presence of multiple beach marks; the position and arrangement of those signified the occurrence of fatigue fracture under the presence of combined loading conditions, involving torsion and bending stress components. Crack initiation was observed also at the corners of the steel plate where non-metallic inclusions were located. Stereo-microscopical examination of the fracture surface likely revealed the presence of casting inclusions, probably fluxes or slag particles, near the surface and in the interior of the component. These inclusions could be considered inherent—metallurgical stress raisers, behaving as locations of prominent crack nucleation under cyclic fatigue loading, stimulating subsequent crack propagation and final ultimate rupture.     

A computer simulation of four-point bending fatigue of a rear axle assembly

The bending fatigue test of a rear axle assembly is simulated by using a FE-integrated fatigue analysis methodology. The presented technique is based on local stress–strain approach in conjunction with two critical plane damage parameters. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Linear elastic FE stress analyses are used in the calculation of local fatigue loading. All computational modules are implemented into the software tool and used in the four-point bending fatigue test simulation of rear axles made of a high-strength alloy steel. In fatigue models, proportional loadings with a static preload are considered, and the effects of residual stresses are neglected. The fatigue test cycles and crack initiation locations are predicted using Smith–Watson–Topper and Fatemi–Socie fatigue damage parameters. Both damage parameters provided conservative test cycle estimates for the test conditions simulated. It is also observed that von Mises stress distributions cannot be used to predict fatigue crack initiation locations while Smith–Watson–Topper critical plane parameter estimated the cracking location suitably. Comparisons with the prototype tests showed the applicability of the proposed approach.     

Crack growth induced delamination on steel members reinforced by prestressed composite patch

ABSTRACT Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive‐plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive‐plate interface debond.     

Fretting fatigue crack nucleation in Ti–6Al–4V

Fretting fatigue crack nucleation in Ti?6Al?4V when fretted against itself is investigated to determine the influence of contact pressure, stress amplitude, stress ratio, and contact geometry on the degradation process. For the test parameters considered in this investigation, a partial slip condition generally prevails. The resulting fatigue modifying factors are 0.53 or less. Cycles to crack nucleation, frictional force evolution, crack orientations and their relationship to the microstructure are reported. The crack nucleation process volume is of the same order as the microstructural length scales with several non‐dominant cracks penetrating 50 μm or less. The effective coefficient of friction increases during early part of fretting. Observations suggest that cyclic plastic deformation is extensive in the surface layers and that cyclic ratchetting of plastic strain may play a key role in nucleation of the fretting cracks. A Kitagawa–Takahashi diagram is used to relate the depth of fretting damage to the modifying factor on fatigue life.     

A probabilistic total fatigue life model incorporating material inhomogeneities,stress level and fracture mechanics

Testing on notched specimens from thin sheet aluminum 2024-T3 was carried out to investigate the formation of fatigue cracks at constituent particles and to quantify the critical distributions and their stress level dependence. The distributions of fatigue lives, nucleation lives, and crack nucleating (CN) particle sizes were determined for each specimen and exhibited a significant stress level dependence. The measured distributions provided the foundation for the total fatigue life model, which uses a probabilistic Monte Carlo method in conjunction with Newman's fastran ii crack closure model. The total life model closely predicted the cumulative distribution function (CDF) of fatigue lives for the three stress levels examined and specifically predicted the shortest fatigue lives, critical from a design for reliability standpoint, and their variability. The total life model accounted for both nucleation and propagation lives; however, the results based on modeling the total life entirely as crack propagation were accurate and slightly conservative. Additionally, a probability of crack nucleation (POCN) concept to relate the distribution of all particles to the distribution of CN particles was developed based on the experimental observations and provides a better representation of the data than traditional threshold approaches.     

The effect of residual stress due to interference fit on the fatigue behavior of a fastener hole with edge cracks

The fatigue property of riveted lap joint is greatly related to the riveting-induced residual stress. However, an accurate study of the fatigue property considering the influence of residual stress quantitatively can be very difficult. A 3D interface element based on the virtual crack closure technology (VCCT) was developed to calculate the stress intensity factor (SIF) for through cracks at the hole edge. The riveting process was analyzed prior to the tensile test in the finite element code, so that the residual stress can be taken into account to get the eventual value of SIF. The result shows that, with the presence of fatigue cracks, the initial stress-strain state in the structure would change, especially near the crack tip, where great compressive stress can be found. The eventual residual stress cannot be derived by simply superimposing the riveting-induced residual stress with the crack-induced residual stress. The 3D-VCCT interface element shows strong ability to solve the SIFs. The FE analysis results agree well with the reported models both in the fatigue crack growth rate (FCGR) and in the shape of the crack front. However, when the crack is extremely short, not only the reported models, but also the present numerical model would fail. Besides, unlike Elber's model and Schijve's model, this study shows that the crack opening stress should not be a function of the stress ratio solely, but also with the crack length included.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

Effect of inclusion on subsurface crack initiation and gigacycle fatigue strength

The effect of inclusions on crack initiation and propagation in gigacycle fatigue was investigated experimentally and analytically in six high strength low alloy steels. Fatigue testing was performed at very high numbers of cycles through ultrasonic fatigue tests at 20 kHz. Inclusions at subsurface are common sites for fatigue crack nucleation in these alloys when cycles to failure was >10⁷ cycles. A significant change in the slope of the S–N curve was observed accompanying the transition from surface to subsurface crack initiation. A deterministic model has been developed to predict the total fatigue life, i.e. crack initiation life and crack propagation life, from the measured inclusion sizes. The predicted fatigue strength agreed reasonably well with the experimental results. It is a tendency that smaller inclusions are associated with longer fatigue life. The results demonstrated that the portions of life attributed to subsurface crack initiation between 10⁷ and 10⁹ cycles are >99%.