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.     

Influence of stress ratio on the threshold level for fatigue crack propagation in high strength steels

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔK_th were measured over the range of stress ratio, R, from ?1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔK_th was well represented as |ΔK_th/2|_R=(1?R)γ|ΔK_th/2|_R=0; and the propagation rate, as da/dn = A(1?R)^γm[(ΔK/2)^m ? {(1 ? R)^γ|ΔK_th/2|R=0}^m] for ?1≦R≦0.33 or da/dn = A(1 ? 0.33)^?γm [(ΔK/2)^m {(1 ? R)^γ |ΔK_th/2|R=0}^m] for 0.33 < ≦ 0.8.     

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.

     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Determination of the length dependence of the threshold for fatigue crack propagation

A rising load amplitude crack growth test on specimens pre-cracked in cyclic compression is presented as a procedure to determine the length dependence of the threshold of fatigue crack propagation described by the R(resistance)-curve for the threshold of stress intensity factor range. The experimental results show that the residual stress field in front of the pre-crack can significantly influence the R-curve.In order to measure the material specific R-curve which is not affected by the pre-cracking condition it is important to use the smallest possible load amplitude. To achieve this goal, a very small notch root radius is essential. It is shown that at notches machined by razor blade polishing technique the load amplitude for pre-cracking can be reduced to values where the load history does not influence the R-curve for the threshold of stress intensity range.     

A model for fatigue crack propagation

A model for fatigue crack propagation is presented which incorporates low cycle fatigue, mechanical properties and a microstructurally-associated process zone. Comparison of the model to published date for 4340 (hard and soft), a series of TRIP steels, Ti-6A1-4V, 2024-T6 and 300 grade maraging steel shows good agreement.     

A theory for fatigue crack propagation

A new continuum mechanics model is developed for predicting fatigue crack propagation rates using a fracture mechanics approach. The model demonstrates the critical dependence of fatigue crack growth on the fatigue ductility exponent, the fatigue ductility coefficient, the elastic modulus and the fracture toughness; it is related to the stress intensity range, implying that fatigue crack growth is critically dependent upon the condition at the tip of the crack.Four materials are studied, namely a creep resistant stainless steels, FV535; a $\text{2}\text{1}\text{2}$ per cent nickel-chromium-molybdenum direct hardening steel, 2S96D; a nickel base heat resisting alloy INCO 901; and a ferrous alloy containing titanium carbide in a medium alloy tool steel matrix, known as Ferrotic C.The developed model provides a means of predicting crack propagation rates based on mechanical properties, and the simplified model provides a fundamental basis for a more general form of the Paris relationship.     

A comparison of different methods to determine the threshold of fatigue crack propagation

Three different methods for determining the threshold value for fatigue crack growth — the load-shedding technique, the stepwise increase of load amplitude on specimens precracked in cyclic compression, and decrease of stress intensity range at a constant maximum stress intensity — were applied to a high-strength aluminium alloy. The load-shedding technique tended to lead to higher values of the threshold, especially at low R-ratios. The threshold determined with decreasing stress intensity range at a constant maximum stress intensity was larger than the effective threshold determined with stepwise increasing of load amplitude on specimens precracked in cyclic compression.     

The influence of stress intensity and microstructure on fatigue crack propagation in ferritic materials

New and published fatigue crack growth data for a wide range of steels have been categorized in terms of different growth mechanisms, namely striation formation, microcleavage, void coalescence and intergranular separation. General principles emerged concerning the influence of mean stress, specimen thickness, flow stress and toughness on rates of fatigue crack propagation through their effect on growth mechanism.

Crack propagation rates associated with striation formation were insensitive to changes in mean stress (except at very low stress intensities) and specimen thickness. Increase in flow stress resulted in a small decrease in growth rate, although the path of a crack through complex structures like welds was, nevertheless, strongly influenced by plastic relaxation. Crack propagation rates increased when deformation led to net-section yielding (general yielding) and the increase was related to specimen thickness and geometry. It has been shown that simple relationships between the rate of propagation and alternating stress intensity are adequate for describing fatigue crack growth by the striation mechanism.

Departures from exclusively striation formation to include micro-cleavage, void coalescence or intergranular separation were found to result in accelerated growth rates. Where growth occurred by combined striation formation and microcleavage, the increase in fatigue crack growth rate was dependent on the maximum tensile stress and hence on the mean stress and specimen thickness. Similarly, when fatigue involved the void coalescence mechanism the rate was increased by raising the mean stress. The role of microstructure and fracture toughness in promoting the different growth mechanisms is discussed. Modification of the simple growth law is necessary in order to describe the observed results.     

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 new method of analysing fatigue crack propagation data

A new method of assessing the validity of fatigue crack propagation laws is described. The method is illustrated by correlating experimental data collected using compact tension specimens for several steels and several testing environments. At no stage in the analysis is it necessary to estimate crack growth rates from the crack length-cycles data, a procedure which is extremely difficult to carry out accurately in practice. Six different fatigue crack growth laws are considered and it is shown that a simple law derived from a damage accumulation theory consistently offers the best correlation for the limited sets of data so far tested. This fatigue crack growth law when used in conjunction with compact tension specimens could provide a very useful method of assessing by comparison the fatigue crack growth properties of metals and it could therefore be a valuable tool for use in materials selection procedures.     

A numerical method of processing fatigue crack propagation data

A least squares spline function method of estimating crack growth rates from a discrete set of experimental fatigue data is presented and an errors analysis is carried out in detail.     

A new microcomputer-aided system for measuring fatigue crack propagation threshold and selecting testing parameters

A new mathematical model is proposed for measuring fatigue crack propagation (FCP) threshold by using K-decreasing and K-increasing method. The formulae for efficiently selecting load-variation coefficients and crack growth increments (Δa) , (Δa) , in the case of K-decreasing and K-increasing tests are given and a correct method for determining FCP rate in the near-threshold region is recommended. On the basis of the above-mentioned work, a personal microcomputer-aided system is set up and successfully used for the FCP rate measurement in Lc9 aluminum alloy in 3.5% NaCI salt water environment. Compared with other systems, this system can increase the measurement accuracy, shorten testing time and obtain more information. Furthermore, the hardware is inexpensive.