Negative Stress Ratio Research Articles

Fatigue Crack Growth for Ferritic Steel Under Negative Stress Ratio

Abstract The phenomenon of crack closure is important in the prediction of fatigue crack growth behavior. Many experimental data indicate crack closures during fatigue crack growths both under tensile–tensile loads and tensile–compressive loads at constant amplitude loading cycles, depending on the magnitude of applied load amplitudes and stress ratios. Appendix A-4300 of the ASME Code Section XI provides two equations of fatigue crack growth rates for ferritic steels expressed by stress intensity factor ranges at negative stress ratios. The boundary of the two equations is classified with the magnitude of applied stress intensity factor ranges, in consideration of the crack closures. However, the boundary value provided by the ASME Code Section XI is not technically well known. The objective of this paper is to investigate the influence of the magnitudes of the applied stress intensity factor ranges on the crack closures. Fatigue crack growth tests using ferritic steel specimens were performed in air environment at room and high temperatures. From the crack closures obtained by the tests, it was found a new boundary which is smaller than the definition given by the Appendix A-4300.

Influence of WC-Co hard metal microstructure on defect density, initiation and propagation kinetics of fatigue cracks starting at intrinsic and artificial defects under a negative stress ratio

The fracture behavior of WC-Co hard metals depends on the size of material inhomogeneities or defects from which cracks emanate. The size and frequency of these defects is of high significance to the quantitative understanding of the failure behavior of structural components and metalworking tools made of hard metal. Currently, the interdependence of a hard metal's microstructure, its defect density, its crack nucleation and growth kinetics and its observed fatigue behavior is not completely understood. The current work provides information on the defect density, fatigue limits, fatigue crack initiation thresholds and growth kinetics at a cyclic mean stress of zero for various hard metal grades as a function of their microstructure. The average WC grain size of the investigated materials varied from ultrafine to medium; the Co binder content ranged from 9 to 15 wt.%. The distribution of size and density of defects was determined by analytic relations based on Weibull theory applied to strength distributions determined in three-point bending experiments performed under monotonously increasing load. Fatigue limits were derived from stress amplitude-life curves determined in a six-point bending arrangement under a stress ratio R = σmin/ σmax = –1. Crack growth kinetics were determined for the same stress ratio for artificially cracks in eight-point bending, as well as for cracks emanating from intrinsic subsurface material defects in six-point bending. The observed differences in the fatigue behavior are discussed based on the determined defect densities and the influence of ambient air / vacuum conditions on crack initiation and growth.

Microstructure refinement and grain size distribution in crack initiation region of very-high-cycle fatigue regime for high-strength alloys

The microstructural features underneath the fracture surfaces of high-strength alloys experienced very-high-cycle fatigue were further investigated to show the nanograin layer in crack initiation regions under negative stress ratios due to numerous cyclic pressing (NCP) mechanism. The grain size and the thickness of nanograin layer in fine granular area of high-strength steels and rough area of titanium alloys were measured. A normalized quantity d* was proposed to characterize the distribution of the nanograin size. A new schematic to express NCP process was depicted to describe the contacting actions between crack surfaces, which causes the microstructure refinement of the high-strength alloys.

Study of the variation of contact state near the contact boundary in a dovetail attachment under different loads

It is very important to characterize the variation of cyclic parameters near the contact edge in dovetail attachments for understanding the fretting fatigue mechanism. In this paper, the variation of contact state in a dovetail attachment was studied by using the finite element method (FEM), which is affected by two key factors i.e. the relative slip and the mutual compaction. When the flank angle and the coefficient of friction are constant, the influence of compaction seems much more obvious under centrifugal loads, and the edge of contact zone would move up along the contact surface. However, the influence of relative slip becomes much more obvious under tensile loads, and the edge of contact zone would move down. The movement of contact edge shows a similar trend under cyclic loads, which may result in the movement of position where the high stress gradient locates, and the numerical results show that the negative stress ratio would occur near the contact edge.

Fatigue Crack Growth Thresholds under Negative Stress Ratio for Aluminium Alloys

When fatigue crack growth rate da/dN = 0, the stress intensity factor range ΔKI is a threshold and it is expressed by ΔKI = ΔKth. The threshold ΔKth is important for design, repair/replacement, particularly, trouble shooting for cracked components. However, the thresholds were not well codified. Authorized and consensus ΔKth are required. This paper introduces the current thresholds provided by fitness-for-service codes and the definition of ΔKth under negative stress ratio R is discussed. Finally, the threshold ΔKth for aluminum alloys in air environment is proposed for fitness-for-service codes.

High‐cycle and very‐high‐cycle fatigue behaviour of a titanium alloy with equiaxed microstructure under different mean stresses

AbstractThe fatigue behaviour of a titanium alloy Ti‐6Al‐4V with equiaxed microstructure (EM) under different values of tensile mean stress or stress ratio (R) was investigated from high‐cycle fatigue (HCF) to very‐high‐cycle fatigue (VHCF) regimes via ultrasonic axial cycling. The effect of mean stress or R on the fatigue strength of HCF and VHCF was addressed by Goodman, Gerber, and Authors' formula. Three types of crack initiation, namely, surface‐with‐RA (rough area), surface‐without‐RA, and interior‐with‐RA, were classified. The maximum value of stress intensity factor (SIF) at RA boundary for R < 0 keeps constant regardless of R in HCF and VHCF regimes. The SIF range at RA boundary for R > 0 also keeps constant regardless of R in VHCF regime, but this value decreases linearly with the increase of R for surface RA cases. The microstructure observation at RA regions gives a new result of nanograin formation only in the cases of negative stress ratios for the titanium alloy with EM, which is explained by the mechanism of numerous cyclic pressing.

Further investigation on microstructure refinement of internal crack initiation region in VHCF regime of high-strength steels

The profile samples prepared by focused ion beam (FIB) in crack initiation region (CIR) and fish-eye (FiE) region of failed specimens subjected to rotary bending (RB) and ultrasonic axial (UL) fatigue testing with various stress ratios (R) were observed by transmission electron microscopy (TEM) with selected area electron diffraction (SAD) detection for two high-strength steels. The grain size and the thickness of nanograin layer along the crack growth path in CIR underneath fine-granular-area (FGA) were measured for the cases of R 0 and the FiE region outside CIR for either negative or positive stress ratio cases, which suggests that the formation of nanograin layer in the FGA region is due to the numerous cyclic pressing (NCP) process and the plastic deformation ahead of the crack tip may cause certain extent of microstructure deformation but is insufficient to form nanograin layer on crack surfaces.

Fatigue Crack Growth Thresholds at Negative Stress Ratio for Ferritic Steels in ASME Code Section XI

Thresholds of fatigue crack growth rates are important characteristics for fatigue crack growth assessment for the integrity of structural components. ASME Code Section XI provides fatigue crack growth thresholds for ferritic steels in air and water environments. The threshold is given as a constant value under a negative stress ratio. However, the thresholds are not clearly defined in the range of negative stress ratios. The definition seems to be maximum stress intensity factors. Besides, the thresholds expressed by the maximum stress intensity factors decrease with decreasing stress ratios. This means that the thresholds under negative stress ratios become unconservative assessments. The objective of this paper is to discuss the definition of fatigue crack growth threshold and to propose the threshold equation for the ASME Code Section XI, based on experimental data obtained from a literature survey.

The Mechanism of Internal Fatigue-Crack Initiation in a Titanium Alloy with Lamellar and Equiaxed Microstructure

Traditionally, the primary or equiaxed α grains of titanium alloys are regarded as the defects to cause crack initiation due to their cyclic brittleness, and fatigue cracks will initiate from the α grains rather than the lamellar microstructure (LM) clusters. Here, we found that fatigue crack is prone to initiate from a large microstructure domain of a big α+β cluster or an α grain in a titanium alloy with the composition of coarse LM clusters and fine equiaxed α grains. Then, the mechanisms of crack initiation for the cases of high-cycle fatigue and very-high-cycle fatigue under stress ratio R = -1, 0.1 and 0.5 are addressed, showing that the numerous cyclic pressing process dominates the microstructure evolution with grain size refinement and nanograin formation underneath the fracture surfaces in the crack initiation region under negative stress ratios.

Fatigue crack growth in wheelset axles under bending and torsional loading

In the past, unexpected failures in wheelset axles lead to catastrophic consequences. To avoid those failures inspection intervals must be defined. The definition of the inspection intervals is based on fracture mechanical approaches. In the present work, the railway axle steel 34CrNiMo6 is investigated. For this material fatigue crack growth data have been experimentally determined for a range of different negative and positive stress ratios. Furthermore, the FORMAN/METTU parameters for different probabilities of survival are identified. In wheelset axles different geometry factors influence the crack growth behaviour. Therefore, different shouldered solid shafts with transition radii and a press fit seat are designed and tested under rotating bending. Moreover, the load situation also has an influence on the crack growth. The main bending load is overlapped with torsional loading at special wheel-rail-situations. With the developed mixed mode test rig, the influence of different load situations on wheelset axles are examined.

The effect of compression loading on fatigue crack propagation after a single tensile overload at negative stress ratios

Experiments on fatigue crack propagation under a loading history with a single tensile overload at an overload ratio of ROL = 1.8 were performed at different baseline stress ratios of R = 0, −0.25, and −1 for aluminium alloy 2A12-O. The widely accepted fatigue crack propagation retardation due to a single tensile overload (OL) in the case of a positive stress ratio (R) was observed at R = 0. However, the retardation effect gradually decreased from R = 0 to R = −0.25 and disappeared at R = −1. These results indicate that the applied compressive load has a significant effect on the fatigue crack propagation after a single tensile overload for aluminium alloy 2A12-O. To reveal the mechanism of this effect of compression loading, a detailed elastic-plastic finite element (FE) analysis was performed. Based on the results of finite element analysis, a mechanism of additional reverse plastic damage caused by compression loading was proposed to explain the interaction of tensile overload and compressive load. The parameter of reverse plastic zone size was applied to characterize the additional reverse plastic damage. A parameter describing the effect of compression loading on fatigue crack propagation retardation due to a single tensile overload was developed. Using this parameter it was verified that the mechanism of additional reverse plastic damage is effective to explain the compression loading effect on the fatigue crack propagation retardation due to a single tensile overload.

Very high cycle fatigue of surface carburized CrNi steel at variable stress ratio: Failure analysis and life prediction

High cycle fatigue and very high cycle fatigue properties of a surface-carburized CrNi steel were examined under axial loading with stress ratios of −1 and 0. The positive stress ratio overcomes the effect of carburized layer and promotes crack initiation from the carburized layer. The morphology of fine granular area (FGA) is more distinct under the negative stress ratio with more obvious crack closure effect. Two models concerning the inclusion-fisheye failure and the inclusion-FGA-fisheye failure are proposed. The predicted fatigue lives based on the concept of crack initiation are in good agreement with experimental results.

The role of local plasticity during very high cycle fatigue crack initiation in high-strength steels

Cracks leading to failure in very high cycle fatigue (VHCF) of high-strength steels often initiate at subsurface inclusions with stress intensity factors (SIF) below the classical threshold SIF Kth for long cracks, especially for negative stress ratios. A characteristic fine granular area (FGA) can then be observed at the fracture surface in the vicinity of those crack-initiating inclusions. According to various researchers, the FGA formation might be responsible for the late initiation of a propagable long crack. Microstructural investigations reveal strong local grain refinement along the fracture surface inside the FGA. The origin of the FGA and its influence on the crack initiation in VHCF is discussed controversially in the literature. The grain refinement might be the result of local plasticity around inclusions in VHCF prior to crack initiation or propagation and thereby causal for the late failure. If this is true, there should be a correlation between the FGA dimension and the local plastic zone size. This hypothesis is investigated in detail in this study. For this purpose, the spatial geometry of FGA is systematically analyzed for different fatigued specimens of the high-strength steel 100Cr6. The results are compared to plastic zone size models and the influence of local plasticity on VHCF is discussed. Based on the results, the VHCF failure mechanism proposed by Grad et al. (2012) [1] is extended and improved.

Study on Fatigue Design Method of an Engine Component Produced by Flake Graphite Cast Iron for Different Loading Modes and Mean Stresses

In order to improve reliability of an automotive engine, a fatigue design method was studied based on the fatigue mechanisms in flake graphite cast iron. In the present study, fatigue test specimens were cut from an actual engine component. The material used showed nonlinear behavior in stress–strain relationship from lower stress level during tensile testing. Rotating bending fatigue testing and axial load fatigue testing were performed. Fatigue crack initiation and propagation behavior were observed during the fatigue tests by a replication technique. Fatigue cracking initiated from the tip of flake graphite in early stage of the total fatigue life when the applied stress was higher than the fatigue limit. On the other hand, fatigue cracking was not observed in the specimen tested with applied stress below the fatigue limit. The threshold stress intensity factor obtained with a small surface crack was lower than that obtained with a through-thickness crack. Fatigue limits under various loading conditions such as bending loading and axial loading were predicted well based on fracture mechanics using the $$ \sqrt {\text{area}} $$ parameter. Threshold stress intensity factor for a small surface crack and the maximum graphite size assumed as an initial crack were used for the prediction. Axial load fatigue tests with different stress ratios were performed. The fatigue limit diagram obtained by the fatigue tests did not follow the modified Goodman relation. On the other hand, fatigue limits prediction based on fracture mechanics approach showed good agreement with fatigue limit obtained with fatigue tests in a wider range of mean stresses σmean varying from − 150 to 50 MPa, in negative stress ratio. In case of σmean higher than 50 MPa, in a positive stress ratio, a smaller effect of stress ratio in the fatigue limit diagram was observed. It was considered that this phenomenon could be explained by the lower effect on the crack closure in a small surface crack initiated from the tip of graphite flake and also influence of local plastic behavior of the matrix around the tip of graphite flake. It can be summarized that the fracture mechanics approach is an effective way to predict fatigue limits of an engine component produced by flake cast iron in different loading conditions and in wider range of mean stress conditions.

Subcycle fatigue crack growth formulation under positive and negative stress ratios

A new fatigue crack growth model at the subcycle scale is proposed for both positive and negative stress ratios. The term “subcycle” refers to the crack growth modeling within a cyclic loading duration rather than the classical cycle averaged crack growth rate (i.e., da/dN). The proposed model includes two major components: a subcycle crack growth rate function and a crack opening stress estimation algorithm for tension–tension and tension–compression cyclic loading. The subcycle crack growth rate function is proposed based on existing in situ scanning electron microscopy testing results. Following this, separation of far field crack contact and near tip crack contact are discussed for both positive and negative stress ratios. A simple linearized model is proposed to estimate the crack opening stress. The developed simplified crack opening stress estimation model is compared with several other models available from open literatures. Next, the proposed subcycle fatigue crack growth methodology is validated with several sets experimental data for various metallic materials under different positive and negative stress ratios. Some discussions and conclusions are drawn based on the proposed model.

Fatigue crack growth at negative stress ratios: On the uncertainty of using ΔK and R to define the cyclic crack tip load

At negative stress ratios, the cyclic crack tip loading cannot be defined by ΔK and R. Little attention has been paid on this issue and most of the existing fatigue crack growth data at negative stress ratios is treated in the same way as positive stress ratios. The aim of this note is to call attention on this topic and to sensitize the reader for possible uncertainties in life time prediction. Simple examples are discussed which show that neither reversal crack tip plasticity nor the crack growth rate is controlled by Kmax and R at negative stress ratios. Instead the parameter σtip seems to be a controlling parameter for minimum crack tip load at negative stress ratios. A discussion is provided with the focus on transferring the findings to other specimen or structures. Perspectives for the treatment of negative stress ratios in the context of fatigue crack growth are briefly discussed.

Threshold values for very high cycle fatigue failure of high‐strength steels

AbstractCracks leading to failure in very high cycle fatigue (VHCF) of high‐strength steels mostly initiate at subsurface inclusions at stress intensity factors (SIF) below the classical threshold value Kth for long cracks, especially for negative stress ratios. Here, a characteristic fine granular area (FGA) can be observed at the fracture surface in the vicinity of these initiating inclusions. According to various researchers, the FGA formation might be responsible for the late initiation of a propagable long crack. This study aims to clarify the threshold values of SIF for crack initiation for VHCF failure with FGA formation at nonmetallic inclusions. For this purpose, ultrasonic fatigue tests (R = −1) with the high‐strength steel 100Cr6 (SAE 52100) were carried out until an ultimate number of cycles of 109. In addition, very high cycle stress increase tests were performed. A serial grinding investigation of fatigued specimens acted as a technique to evaluate the distribution of unharmful inclusion in the tested volume. By the combination of these tests, a threshold value of the SIF for the VHCF by FGA formation at inclusions can be derived. This threshold value depends on the size of the crack initiating inclusion.

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.

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

AbstractThe maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN − ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.

A Fatigue Life Prediction Method Based on Strain Intensity Factor.

In this paper, a strain-intensity-factor-based method is proposed to calculate the fatigue crack growth under the fully reversed loading condition. A theoretical analysis is conducted in detail to demonstrate that the strain intensity factor is likely to be a better driving parameter correlated with the fatigue crack growth rate than the stress intensity factor (SIF), especially for some metallic materials (such as 316 austenitic stainless steel) in the low cycle fatigue region with negative stress ratios R (typically R = −1). For fully reversed cyclic loading, the constitutive relation between stress and strain should follow the cyclic stress-strain curve rather than the monotonic one (it is a nonlinear function even within the elastic region). Based on that, a transformation algorithm between the SIF and the strain intensity factor is developed, and the fatigue crack growth rate testing data of 316 austenitic stainless steel and AZ31 magnesium alloy are employed to validate the proposed model. It is clearly observed that the scatter band width of crack growth rate vs. strain intensity factor is narrower than that vs. the SIF for different load ranges (which indicates that the strain intensity factor is a better parameter than the stress intensity factor under the fully reversed load condition). It is also shown that the crack growth rate is not uniquely determined by the SIF range even under the same R, but is also influenced by the maximum loading. Additionally, the fatigue life data (strain-life curve) of smooth cylindrical specimens are also used for further comparison, where a modified Paris equation and the equivalent initial flaw size (EIFS) are involved. The results of the proposed method have a better agreement with the experimental data compared to the stress intensity factor based method. Overall, the strain intensity factor method shows a fairly good ability in calculating the fatigue crack propagation, especially for the fully reversed cyclic loading condition.