Prediction of threshold stress intensity for fatigue crack growth using a dislocation model

It has been shown that the ratio of threshold stress intensity for fatigue crack growth to the shear modulus is nearly a constant for many materials. This implies that fatigue crack growth is related to some fundamental phenomenon occurring at the crack tip. In the following a dislocation model has been developed to predict the threshold stress intensity. It is shown that the stress intensity can be related to the stress necessary to nucleate a dislocation at the crack tip. The most important outcome of the present analysis is that the threshold stress intensity depends more on the elastic modulus rather than on any other material property in agreement with many experimental results.

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Résumé On a démontré que le rapport de l'intensité de seuil de la contrainte provoquant une fissuration par un accroissement de la fissuration par fatigue au module de cisaillement est sensiblement une constante pour de nombreux matériaux. Ceci implique que la croissance d'une fissure de fatigue est reliée à certains phénoménes fondamentaux qui se produisent à l'extrémité d'une fissure. Dans le mémoire, on développe un modèle de dislocation qui permet de prédire l'intensité critique de la contrainte. On montre que l'intensité de la contrainte peut être mise en relation avec la contrainte nécessaire pour créer une dislocation à l'extrémité d'une fissure. La conséquence la plus importante de cette analyse est que l'intensité critique de seuil dépend davantage du module d'élasticité que de toutes autres propriétés du matériau et ce en accord avec de nombreux résultats expérimentaux.

     

A method for determining the stress intensity threshold level for fatigue crack propagation

The influence of a decreasing rate of stress intensity factor with crack propagation, $\text{d}\text{K/}\text{d}\text{a}$, on a stress intensity threshold level, $\text{δK}{}_{\mathrm{th}}$, below which fatigue crack propagation becomes insignificant is investigated. Specimens, 200 mm wide, 10 mm thick with a 40 mm-long central crack, are fatigued at the decreasing rates, $\text{∥}\text{d(δK)}\text{d}\text{a∥}$, of 2,44, 5 and 10 kg/mm^5/2 with a peak load control system and a pair of crack followers. In this range of $\text{d}\text{(δK)/}\text{d}\text{a}$, the stress intensity threshold levels, $\text{δK}{}_{\mathrm{th}}$, have the same value regardless of $\text{d}\text{K/}\text{d}\text{a}$. Therefore, the present method of decreasing the stress intensity factor at a constant rate is suitable for determining the characteristic $\text{δK}{}_{\mathrm{th}}$ of materials. Furthermore, the influence of stress ratio, $\text{R}$, is investigated at the decreasing rate, $\text{∥}\text{d}\text{(δK)/}\text{d}\text{a]}$, of 10 kg/mm^5/2.     

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.     

Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor

The relationship between fatigue crack propagation rate, da/dn, and range of stress intensity factor, ΔK, including threshold stress intensity factor, ΔK_th, is analyzed statistically. A non-linear equation, da/dn = C{(ΔK)^m-(ΔK_th)^m}, is fitted to the data by regression method to evaluate the 99% confidence intervals. Several experimental results on fatigue crack propagation properties of welded joints are compared by using these confidence intervals.     

A Dislocation barrier model for fatigue crack growth threshold

The primary mechanism of fatigue crack growth is crack-tip dislocation emission followed by the glide of the emitted dislocations. Both of these two processes are controlled by the crack-tip resolved shear stress field, which is characterized by the resolved shear stress intensity factor, . A dislocation barrier model for fatigue crack growth threshold is constructed. The model assumes that a fatigue crack stops growing when crack-tip slip bands are incapable of penetrating the primary dislocation barrier. The derived and deduced threshold behaviors agree with the observed constant threshold K_max,th in the low R region and constant threshold ΔK_th in the high R region. K_max,th is the K_max at the threshold. The constant K_max,th is related to the resistance of the primary dislocation barrier, which in most of cases is grain boundary; and the constant ΔK_th is related to the resistance of secondary barriers. Furthermore, the analysis shows that K_max,th is proportional to √d, where d is the grain size. The relation has been observed in steels. The model also helps to explain the characteristics of, and the transition from, microstructure-sensitive to microstructure-insensitive growth. This revised version was published online in July 2006 with corrections to the Cover Date.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

Phenomenology of the effective stress intensity related to fatigue crack growth thresholds

The fatigue crack growth threshold conditions for effective stress intensity amplitude are examined using simple phenomenological models for crack face interference and internal stresses. We show that behaviors correlating with all pure fatigue classifications can be generated from a single ‘ideal fatigue’ behavior by accounting for internal stress and crack face interference. The possible threshold or near-threshold manifestations of an intrinsic K_MAX threshold, independent of effective ΔK effects, are discussed.     

Determination of stress intensity factors for surface cracks using fatigue crack growth data

The fatigue growth of semi-elliptical surface cracks in a structural steel under constant amplitude tensile cycling loading is investigated. The AC potential technique is used for sizing and monitoring the profile development of the cracks. The data are used to determine the stress intensity factors along the entire crack front at different stages of crack growth where the effects of front face, finite thickness and finite width are continuously changing. Various numerical solutions are compared with the experimental results     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials under cyclic compression

For prediction of the fatigue crack growth (FCG) behavior under cyclic compression, a plasticity-corrected stress intensity factor (PC-SIF) range ΔK_pc is proposed on the basis of plastic zone toughening theory. The FCG behaviors in cyclic compression, and the effects of load ratio, preloading and mean load, are well predicted by this new mechanical driving force parameter. Comparisons with experimental data showed that the proposed PC-SIF range ΔK_pc is an effective single mechanical parameter capable of describing the FCG behavior under different cyclic compressive loading conditions.     

Effects of the transverse stress on biaxial fatigue crack growth predicted by plasticity-corrected stress intensity factor

The transverse stress has an important effect on the biaxial fatigue crack behavior. However, the experimental evidence has provided conflicting indications: it is sometimes considered to increase, decrease or have no effect. These complex phenomena cannot be rationally explained by the existing mechanical models. The effect of the transverse stress on the fatigue crack growth behavior is still one of the most puzzling questions in biaxial fatigue. Physically, this effect is a transverse stress induced plasticity phenomenon. In this paper, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effect of transverse stress on biaxial fatigue. By use of this new crack driving force some important phenomena associated with transverse stress are predicted. Comparisons with experimental results showed that the PC-SIF as an effective mechanical parameter is capable of predicting the effects of the crack length, the stress level, cyclic stress ratio, biaxial stress ratio and phase difference on the biaxial fatigue crack growth. Consequently, the alleged conflicting experimental results have been rationally explained by the PC-SIF.     

A simple model of stress intensity range threshold and crack closure stress

The cyclic stress intensity threshold (Δ$\text{K}{}_{\mathrm{TH}}$) below which cracks will not propagate varies with length for short cracks. A model is proposed which relates Δ$\text{K}{}_{\mathrm{TH}}$ to the crack closure stress arising from fracture surface roughness. This is used to predict a variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length for surface cracks in Ti 6Al-2Sn-4Zn-6Mo alloy, based upon measured values of crack opening displacement arising from roughness. The predicted variation in Δ$\text{K}{}_{\mathrm{TH}}$ with crack length is found to be similar to that obtained from the empirical model of Δ$\text{K}{}_{\mathrm{TH}}$ proposed by El Haddad et al.[5]. The application of the new model to estimate the value of crack closure stress arising from crack tip plasticity for short surface cracks is also discussed.     

A note on the stress intensity factor and crack velocity relationship for homalite 100

A series of dynamic experiments was performed to further investigate the relationship between the stress intensity factor and crack velocity for Homalite 100. Four different specimen geometries made out of the same sheet of Homalite 100 were studied using the technique of photoelasticity. The stress field around the crack tip was represented in terms of a series whose coefficients were evaluated with the multipoint over-deterministic method. The results indicate that the stress field solution depends on the number of terms in the series representation. The stress intensity factor versus crack velocity curves are distinct in the plateau and the transition region for each specimen geometry but merge in the vertical stem region. Finally the results are compared with similar results obtained with the method of caustics.     

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic-plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K_max are simulated. In comparison with a fixed K_max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.