A mechanistic model for the influence of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—I. Crack-ductile materials

Concentrating on local behavior of a highly stressed zone ahead of the crack tip, a recent mechanistic approach to analyse LEFM fatigue crack growth behavior in three stages at stress ratio R = 0 is extended here to include the effect of a positive stress ratio. This paper is limited to analysing primarily the stages I and II of “crack-ductile” materials, characterised by a purely “reversed shear” (or ductile “striation”) growth mechanism in stage II. It is shown that in these materials stage I is R-sensitive and stage II is insensitive, and these can, without invoking crack closure arguments, be rationalised alternatively by considering the dominance of a K_max-controlled “Submicroscopic Cleavage” and a ΔK-controlled “ reversed shear ” fracture mechanism, respectively. Assuming Paris type power relations to hold, a predictive model is developed that contains separate growth equations with R-effect for stages I and II and shows the existence of a characteristic “master shear-curve” and a “moving pivot-point” on this curve for a class of materials. Good agreement was found between quantitatively predicted growth curves at selected R-values and a relatively large volume of available experimental data for low strength steels, aluminum alloys and titanium alloys. Besides providing more physical explanations for the observed growth behavior, the model may also be useful as a convenient alternative to crack closure for obtaining fairly accurate and conservative estimates of fatigue life for design applications.     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Cumulative damage model for fatigue crack growth based on reaction rate theory—II

A study is continued of a macro model of fatigue crack growth (FCG) that is based upon a micro result from reaction rate theory. The previously presented deterministic (mean) model is examined further, and a probabilistic model is introduced. Analysis of FCG data for periodic tensile loads reveals that three material parameters are required. The model also explicitly contains the load and the temperature T. It is shown that T and the form of the periodic load are important quantities, of which the former has interesting implications for accelerated testing. The minimum amount of testing required for predictive purposes is also discussed.     

The effect of stress ratio on fatigue crack growth rates in steels

The effects of stress ratio on fatigue crack growth thresholds and low and intermediate fatigue crack growth rates are examined on steels with ferrite-pearlite and tempered martensite microstructures, tested in air. The analysis of available experimental data shows that simple empirical relationships can be used to describe the stress ratio dependence of thresholds and fatigue crack growth rates. Results also indicate that thresholds decrease linearly with yield strength.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

The effect of stress ratio on fatigue crack growth rate in the absence of closure

A fractographic study¹ was performed on Al-alloy fatigue fracture surfaces produced by programmed load sequences. The load sequences included steps of constant amplitude cycles at three different stress ratios, each step is preceded by a small number of high amplitude cycles designed to avoid the influence of crack closure and to serve as fractographic markers. The experiments were conducted on different specimen geometries to produce conditions associated with a long crack under fully elastic conditions and a short crack in a notched coupon seeing high local post yield stress conditions. Crack sizes covered in the study ranged from 0.02 to 12 mm, and growth rates ranged from 2×10⁻⁷ to 4×10⁻⁵ mm cycle⁻¹. Fractographic evidence from the study suggests that the crack growth rate can vary by up to a factor of five with applied stress ratio change from 0.64 to 0.73. In the case of the long crack, the effect is less noticeable or totally absent. In the case of naturally initiating notch root cracks, the effect is more pronounced at higher stress level and lower crack growth rate.     

On the effect of cyclic stress ratio on the fatigue crack propagation

A new model of fatigue crack propagation is proposed which takes the effect of cyclic stress ratio into account. In the model it is assumed that the fatigue crack propagation rate is proportional to the absorbed hysterisis energy per stress cycle at the tip of a crack. The energy is calculated from stress field resulting from the Dugdak-Barenblatt Model and strain field from an experimental result. The model was applied to analyse the experiments on several materials.     

The effect of the stress ratio on fatigue crack growth in a 3% NaCl solution

Corrosion fatigue crack growth tests have been carried out at various stress ratios for a low alloy steel SNCM 2 and type 304 stainless steel.

Measurements of the effective stress intensity factor range ratio U were performed to explain the effect of stress ratio R.

The corrosive environment decreased da/dN at R = 0.1, 0.4 and little affected da/dN at R = 0.9 for SNCM 2 and increased da/dN at all R ratios for SUS 304.

It was confirmed that there exists a threshold stress intensity factor ΔK_thCF in 3% NaCl solution for both materials tested.

The corrosive environment decreased ΔK_thCF for all conditions tested except at R = 0.1 and 0.4 for SNCM 2, where ΔK_thCF-values were nearly equal to ΔK_th-values in air. ΔK_thCF/ΔK_th was 0.6 at R = 0.9 for SNCM 2 and 0.8, 0.5 and 0.7 at R = 0.1, 0.7 and 0.9 for SUS 304, respectively.

It was shown that the complicated effect of stress ratios on crack growth for SNCM 2 can be explained using effective stress intensity factor ΔK_eff.     

A fatigue crack nucleation model for anisotropic materials

Based on Tanaka‐Mura's dislocation‐dipole pile‐up configuration, a formulation of mixed mode fatigue crack nucleation is derived using the Stroh formalism for generally anisotropic materials. The fatigue life is explicitly expressed as inversely proportional to the stored plastic energy, depending on the material's anisotropic elastic matrix F ^?1, surface energy, Burgers vector, and lattice resistance. The model has been shown to agree with experimental observation on critical slip planes in PWA 1493 single crystal Ni‐base superalloy.     

A model for fatigue crack growth with a variable stress intensity factor

A model for fatigue crack growth, similar to that of Majumdar and Morrow, is proposed where the crack growth rate is determined from the low cycle fatigue and cyclic stress-strain response of the material. The model is for a constant stress range at infinity, but does allow for a variable stress intensity factor due to the changing crack length. The study also includes an analysis of the strain range in the neighborhood of the crack tip. Further it is shown that the model predicts the critical stress intensity factor. A prediction of the crack growth rate is made for 2024-T351 aluminium, copper and CU-6.3 AL alloy and is compared to the experimental observations.     

The influence of the stress ratio on fatigue crack growth in a cermet

The fatigue crack growth behavior in a cermet was investigated as a function of the stress ratio, R. At the higher K _max values the fracture path was through the cermet particles as well as through the binder phase. At low growth rates the fracture path was primarily through the binder phase. As a result the fatigue crack growth process, at a growth rate of l0^–7 m/cycle the rate was influenced by K _max, and to a lesser extent by the R value, whereas at a growth rate of 10^–11 m/cycle the growth rate depend upon K as well as the R value.     

A model of fatigue crack propagation in metals

A model of the formation and evolution of a local plastic deformation zone at the crack tip is proposed based on the analysis of the main physical processes taking place in a metallic material under the action of cyclic loads. An equation of fatigue crack growth rate curves, which explicitly accounts for the loading frequency, was derived. The equation applies to the whole range of crack lengths from short cracks to macroscopic ones. __________ Translated from Problemy Prochnosti, No. 1, pp. 35–43, January–February, 2009.     

Linear elastic fracture mechanics (LEFM) analysis of the effect of residual stress on fatigue crack propagation rate

In this research, both residual and applied stresses are converted to stress intensity factors independently and combined using the superposition principle. The fatigue crack propagation rates are predicted. Experiments using two different loading modes, constant applied stress intensity factor (SIF) range, and constant applied load modes are done for samples with and without initial tensile residual stresses. The samples with initial tensile residual stresses exhibit accelerations of the crack propagation rates. The results show that the weight function method combined with the three-component model provides a good prediction of fatigue crack propagation rates in tensile residual stress fields.     

The effect of pre-stress cycles on fatigue crack growth—an analysis of crack growth mechanism

Cyclic pre-stress increases subsequent fatigue crack growth rate in 2024-T351 aluminum alloy. This increase in growth rate, caused by the pre-stress, and the increased rate, caused by temper embrittlement as observed by Ritchie and Knott, cannot be explained by the crack tip blunting model alone. Each fatigue crack increment consists of two components, a brittle and a ductile component. They are respectively controlled by the ductility of the material and its cyclic yield strength.     

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept (dl/dN ∝ Δε_p · ω) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.     

A third-order state-space model for fatigue crack growth

A second‐order state‐space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1 - 4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075‐T6 and 2024‐T3 at constant‐amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third‐order state‐space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second‐order state‐space model is treated as the third state variable in this model. Through simulations, it is shown that the third‐order state‐space model gives better predictions than the second‐order state‐space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.