Mean stress effects in stress-life fatigue and the Walker equation

Mean stress effects in finite-life fatigue are studied for a number of sets of experimental data for steels, aluminium alloys and one titanium alloy. Specifically, the agreement with these data is examined for the Goodman, Morrow, Smith–Watson–Topper and Walker equations. The Goodman relationship is found to be highly inaccurate. Reasonable accuracy is provided by the Morrow and by the Smith–Watson–Topper equations. But the Morrow method should not be used for aluminium alloys unless the true fracture strength is employed, instead of the more usual use of the stress-life intercept constant. The Walker equation with its adjustable fitting parameter γ gives superior results. For steels, γ is found to correlate with the ultimate tensile strength, and a linear relationship permits γ to be estimated for cases where non-zero mean stress data are not available. Relatively high-strength aluminium alloys have γ≈ 0.5, which corresponds with the SWT method, but higher values of γ apply for relatively low-strength aluminium alloys. For both steels and aluminium alloys, there is a trend of decreasing γ with increasing strength, indicating an increasing sensitivity to mean stress.     

A Walker exponent corrected model for estimating fatigue life of metallic materials in loading with mean stress

Mean stress significantly influence the fatigue life predictions of metallic materials. The Walker mean stress equation with its additional material parameter w provides good predictions for a wide range of materials. Unfortunately, additional tests are necessary to determine the Walker exponent w. In order to overcome this shortcoming, for aluminum alloys, the Walker exponent w was correlated linearly with the sum of ultimate tensile strength and true fracture strength. Then, a Walker exponent corrected effective strain energy density criterion was developed by incorporating the Walker mean stress equation into the strain life curve. The capability of fatigue life prediction for the developed model was checked against the tested data of 304 L stainless steel, SAE 1045 steel, 7075‐T651 aluminum alloy, and Incoloy 901 superalloy, and comparisons were also performed by using the Lv's Walker exponent corrected model. The developed model provides more satisfactory results, especially for the considered materials in loading with mean stress.     

Ratcheting behaviour and mean stress considerations in uniaxial low-cycle fatigue of Inconel 718 at 649 °C

The ratcheting behaviour of Inconel 718 was investigated at 649 °C under uniaxial cyclic loading. Stress-control tests have been conducted at various combinations of stress amplitude and mean stress. The ratcheting strain at failure increases with increasing mean stress for a given stress amplitude and with decreasing stress amplitude for a given mean stress. Fatigue lives were correlated using three mean stress models: the Goodman equation, the Smith–Watson–Topper (SWT) parameter and the Walker parameter. It has been shown that the Goodman equation and the SWT parameter do not correlate life data, while the Walker parameter yields acceptable correlation. The SWT parameter was modified to incorporate the ratcheting effect. The new parameter is found to yield correlation similar to that of the Walker parameter.     

A mean stress correction model for tensile and compressive mean stress fatigue loadings

A new mean stress fatigue model based on the distortional strain energy is proposed to account for the mean stress effects on fatigue life. The proposed model is compared with the Morrow and the Smith‐Watson‐Topper (SWT) mean stress correction models using a number of experimental data sets for one cast iron, two steels and two aluminium alloys under tensile and compressive mean stress loadings. It is found that both the proposed mean stress correction model and the SWT model yield similar results and provide very good correlation for positive mean stress data and moderate negative mean stress data. For high compressive mean stresses, the proposed model shows reasonably good correlations, while the SWT model fails to correlate the fatigue data. The Morrow model was found to give poor correlations for all fatigue data analysed by yielding conservative results for compressive mean stresses and non‐conservative results for tensile mean stresses.     

Parametric representation of fatigue in alloys and its relation to microstructure

Abstract

Low cycle fatigue properties of austenitic steels and aluminium alloys are discussed. Curves of stress S–number of cycles to failure N for three alloys are presented. The form of the S–N curve is described and the various equations used by designers to represent the curve are discussed. It is suggested that microstructurally related parameters could be inserted in these parametric design equations. Attempts at achieving this objective using a disclocation stress and a fracture toughness related model are described. It is shown that reasonable fits between predicted and experimental S–N curves result from the application of the dislocation stress model, whereas the fracture toughness approach seems less successful.

MST/1163     

Neue Auswertungsmethode zur Bestimmung der Kennwerte der Dehnungswöhlerlinie und der Spannungs‐Dehnungs‐Kurve unter Berücksichtigung der Kompatibilität

New method for evaluation of the Manson‐Coffin‐Basquin and Ramberg‐Osgood equations with respect to compatibility A new method for determining the stress‐strain and strain‐life curves for metals is presented. The method involves fitting the curve to experimental data points in a three‐dimensional strain‐stress‐life space. With the plastic part of strain, stress and fatigue life as coordinates, a straight line is used for fitting the experimental data points. The material constants are calculated directly from the directional vector R and the coordinates of the point P , which determines the fitted straight line. It is shown that the assumption of equality of the plastic and elastic components in Manson‐Coffin‐Basquin and Ramberg‐Osgood equations leads to the so called compatibility condition. This new method retains the mathematical and physical relationships between the considered curves. The results obtained from this new method using high‐strength aluminium alloys subjected to different manufacturing conditions and different test temperatures are presented. These results are compared to results obtained with a conventional method for determining the fatigue parameters.     

Creep behaviour of P91/GTR-2CM/12Cr1MoV dissimilar joint predicted by the modified Theta method

Creep behaviour of P91, 12Cr1MoV steels and the P91/12Cr1MoV dissimilar joint were investigated at 823 K. Results show that the creep strength of P91 is much higher than 12Cr1MoV and than the dissimilar joint. The stress dependence of minimum creep rate and rupture life for both steels and the dissimilar joint obeyed Norton’s power law. The values of stress exponent are similar for 12Cr1MoV steel and the dissimilar joint in high stress region, indicating similar creep mechanism. However, the creep behaviour at 140 MPa for the dissimilar joint showed deviation from the other higher stresses, indicating different creep mechanism as the stress is decreasing. Microstructure showed that creep ruptured on the 12Cr1MoV side of the dissimilar joint as conducted in the high stress region, whereas ruptured on the carbon decarburized zone as conducted in the low stress region. Fracture location changed from 12Cr1MoV base metal to inter-critical heat affected zone as the creep time going. A modified theta equation was proposed to predict the creep behaviour, and the random errors from fitting to experimental creep data were smaller than obtained from the traditional theta method. The predicted creep behaviour showed good agreement with experimental ones.     

CORRELATION OF FATIGUE CRACK GROWTH RATE AT DIFFERENT STRESS RATIOS FOR QUENCHED AND TEMPERED STEELS AND OTHER ALLOYS

Abstract— Measurements of the effect of stress ratio on the constant amplitude fatigue crack growth rates in four quenched and tempered steels in the Paris regime are reported. This data and published data for other alloys (including lower strength steels and non-ferrous alloys) are evaluated, and a correlation function suitable for practical fatigue life calculations is derived. In addition to stress intensity factor range and stress ratio, other significant parameters are the yield stress of the material and its thickness. For the four steels on which new measurements were made, the degree of dependence of the crack growth rate on stress ratio may be related to sensitivity to environmental conditions.     

THE EFFECT OF STRESS RATIO ON THE FATIGUE THRESHOLD CONDITION OF PHYSICALLY SMALL CRACKS

An approach is proposed to predict the intrinsic threshold of physically small cracks without invoking crack closure considerations. The basic assumption invoked is that a Δ K representation is valid for short cracks, hence the lower-bound threshold value, ΔK_0(s)(min) for short cracks can be numerically equated with the lower-bound threshold value of long cracks, ΔK*_{0(l)(min), s} of the same material. Several experimental observations provide a basis for this rationalization. The approach allows a quantitative prediction of stress ratio and crack length dependence of Δ K _0(S) which provides good agreement with experimental data for several low-strength steels and aluminium alloys. This alternative procedure may be found useful in design applications.     

Modeling mean stress relaxation in variable amplitude loading for 7075-T6511 and 7249-T76511 high strength aluminum alloys

Mean stresses in fatigue life calculations for critical structural components are a source of great uncertainty in any engineering design. Correction of life predictions in strain or stress based approaches to fatigue are necessary when dealing with mean stresses; the Goodman, Morrow, Smith–Watson–Topper and Walker models are widely used mean stress models for mean stress correction in life calculation. Aluminum alloys 7075-T6511 and 7249-T76511 are tested in fatigue. Relaxation tests are performed with the intent of characterizing the cyclic relaxation of mean stresses for variable amplitude loading when loading conditions approach the irregularity of service loadings. Several plasticity models are studied to reproduce the observed behavior, and simulations are compared to identify the best candidate for implementation in a life prediction software. An incremental plasticity model introduced by Jiang and Sehitoglu in 1996 is fitted to test data for both alloys to obtain all the model parameters. Constant and variable amplitude loading simulations are run to compare the results with experimental data. A multisurface plasticity model developed by Wetzel in 1971 is also implemented to simulate material behavior. Then modifications are suggested on the model formulation so that the mean stress relaxation response is closer to the experimental data. Life calculations for the variable amplitude loading patterns are performed without considering relaxation effects, and with the use of the plasticity models described, to compare the advantages of introducing transient effects in the analysis.     

INVERSION OF THE STRAIN-LIFE AND STRAIN-STRESS RELATIONSHIPS FOR USE IN METAL FATIGUE ANALYSIS

Abstract— Two methods are described for inverting the strainrange/life and strainrange/stressrange equations commonly used in fatigue analysis in order to obtain closed-form expressions for life and stressrange in terms of strainrange. In the Collocation approach the form used is N _f= A (Δε—Δε₀)γ or N _f= A (Δε)Ψ(Δε—Δε₀)γ. In the Spline-Function approach the curve is divided into two regions. At strainranges above where the elastic and plastic lines intersect the equation is N _f= N _T R ^1/c exp δ R α; at lower strainranges it is N _f= N _T R ^1/b exp δ R β, where N _T is transition life, R is strainrange normalised to transition strainrange, and b, c , α, β, δ are constants determinable from the constants of the equation to be inverted. Similar expressions are derived for the cyclic stress/strain curve in terms of the same constants. The methods are illustrated by an example, and found to have close conformity to the basic equations to be inverted.     

FATIGUE CRACK PROPAGATION IN AUSTENITIC STAINLESS STEEL UNDER LOW FREQUENCY LOADING AND SALT WATER CONDITIONS

Fatigue crack growth rates (FCGR) for a steel similar to AISI 316LN have been evaluated in air and salt water. At free corrosion potential, a short crack effect appeared for crack lengths shorter than 4  mm. For longer cracks, a segment (called region I) of the corrosion FCGR curve can be described by an equation with the same coefficients as for steels of ordinary resistance to corrosion. Thus, the process controlling crack propagation is presumably the same for both steels. Corrosion FCGR in region II (range of longer crack lengths and higher Δ K values, where the curve cannot be described by the previously mentioned equation) are slower than for ordinary steels. The plateau in FCGR observed at a cathodic potential corresponds to the higher plateau at the free corrosion potential. An interpretation is presented for the shape of the corrosion FCGR curves at both potentials.     

Ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress

Stress-control fatigue tests have been conducted on a copper alloy at room temperature with and without mean stress. Ratcheting strain was measured to failure under four sets of stress amplitude and mean stress. The ratcheting strain versus cycle curve is similar to the conventional creep curve under static load consisting of primary, steady-state and tertiary stages. The steady-state rate and ratcheting strain at failure increase with mean stress for a given stress amplitude and with stress amplitude for a given mean stress. Ratcheting strain increases as the stress rate decreases. The S–N curve approach and mean stress models of Smith–Watson–Topper and Walker yielded good correlation of fatigue lives in the life range of 10²–10⁵ cycles.     

Fatigue crack propagation characteristics of high‐tensile steel wires for bridge cables

The viability of single edge cracked sheet test method for rapidly determining the crack propagation characteristics of steel wires was investigated. First, fatigue tests under 3 different stress ratios were conducted on the sheet specimens which were manufactured from a kind of widely used cable wires. The test data were analysed, and the crack growth rates of sheet specimens were constructed by Walker model. Then, a series of fatigue tests were performed on notched round‐bar specimens to verify the predictability of Walker model parameters. Moreover, the experimental results obtained in different studies on crack propagation characteristics of steel wires were discussed. The results show that the crack propagation characteristics of sheet specimens behave a certain dependence on depth. The sheet crack growth laws can be well used to predict the fatigue life of notched bar specimens when the mechanical heterogeneity is considered. For bridge cable steels, the rational values for the exponent parameter of Paris law, m, should be close to 3.     

Variation of the cyclic strain-hardening exponent in advanced aluminium alloys

The cyclic strain-hardening exponents for five fatigue-resistant aluminium alloys were determined throughout the fatigue life to study the degree of cyclic stability of these alloys. Data were compared with results for 2024-T4 aluminum and for two high-pressure steels. The strain-hardening exponent increased logarithmically in all cases except 2024-T4, although the increase was small and did not exceed 33% over the fatigue life. 7475-T351 aluminium alloy was found to be entirely stable, and 7075-T7351 almost so. These were followed in order of rising sensitivity by 2014-T6, 7050-T73651, and 2124-T851 aluminium alloys, and 28NiCrMo7.4 and 30CrNiMo8 steels. 2024-T4 aluminum alloy demonstrated a strong decrease in strain-hardening exponent with fatigue life.     

Applicability of life prediction methods to the low cycle fatigue of braze clad AlMn1.0Mg0.5 alloys

The original and modified universal slope methods, the uniform material law, and the modified Diercks equation have been applied to the low cycle fatigue life prediction in the braze clad AlMn1.0Mg0.5 alloys. The experimental data from clad and non-clad, pre-strained and non-pre-strained AlMn1.0Mg0.5 alloys at room temperature and at 75 and 180°C have been used to evaluate the applicability of the life estimation methods. It is likely that there is no universal method to predict the low cycle fatigue lives of all kinds of aluminium alloys. However, the modified universal slope method and the modified Diercks equation provide reasonably good predictions in these braze clad aluminium alloys.     

The effect of mean stress on fatigue crack propagation a literature review

Most investigations of fatigue crack propagation have been carried out using pulsating tension loading and rate of crack propagation (da/dN) expressed in terms of range of stress intensity factor (ΔK). However, mean stress can have a significant effect on da/dN, so that generally it should be expressed in terms of mean and range of stress intensity factor. Literature relating to the effect of mean stress on da/dN, mainly in steels and aluminium alloys, is reviewed in the present report. Empitical relationships which allow the correlation of crack propagation data obtained at different mean stresses, crack propagation theories which predict the effect of mean stress, and fundamental explanations of the effects of mean stress are discussed. Suggestions for future research are made.     

Study of the fatigue lifetimes and crack propagation behaviour of a high speed steel as a function of the R value

High speed steels, such as the alloy H‐13, when used as forging dies are subjected to both wear and cyclic loading, and both of these factors can affect the useful life of such dies. It follows that it is of some importance to determine the fatigue characteristics of such steels. However, fatigue studies of such alloys are limited, especially with respect to fatigue crack propagation (FCP) behaviour as a function of mean stress, and therefore more detailed studies are necessary. In the present study, the fatigue lifetimes and the crack propagation behaviour of a high speed steel were experimentally investigated in laboratory air under different stress ratios, R. A modified linear‐elastic fracture mechanics (LEFM) approach was applied to analyze the experimentally‐obtained FCP behaviour. The predicted S–N curves and crack growth behaviour for a wide range of R ratios agree well with the experimental data, and the modified LEFM approach is therefore considered to be useful for evaluation of the fatigue behaviour of this class of high strength steels.     

A map for wear mechanisms in aluminium alloys

A quantitative wear map for aluminium and its alloys has been constructed using normalized test variables and the physical modelling approach proposed by Lim and Ashby for steels. New model equations based on a different state-of-stress criterion suitable for aluminium alloys have been developed and found to match well with reported experimental wear data on aluminium alloys. The field boundaries between various interfacing wear mechanisms were constructed by using critical values of experimental wear data which manifest themselves in discontinuities in the slope of wear curves. However, within a given wear regime, the model equations developed here agreed fairly well with the reported wear data. The wear mechanisms successfully modelled here include oxidation dominated wear, delamination wear, severe plastic deformation wear, and melt wear.