Fatigue-Crack Growth

According to equation (5.2), the stress intensity factor K depends on the external stress a and the crack length a. Transferring this to the case of cyclic loads with a stress range Act, we arrive at the cyclic stress intensity factor 

The crack propagation is described using the crack-growth rate da/dN, defined as the crack growth da per cycle. 

In principle, the R ratio for K should be denoted Rk- However, because Rk = Krcdn/Kraayi — min/ max = R holds, we can simply write R instead. 

Because the crack growth is not continuous during the cycle, the crack-growth rate is defined as da/dN = limAN i Aa/AiV [113]. Mathematically, it is thus not a differential quotient. Nevertheless, it is common to write it in this way. 

Equation (10.4) seems to imply that AAth depends linearly on the R ratio. However, it has to be taken into account that Aop itself also depends on R. For practical applications, it would be useful to know the exact A-dependence, for this would allow to make measurements at one R ratio only and to extrapolate from there. Several, sometimes contradictory, approaches can be found in the literature, for example in Schott [130]  

Curves like those of Fig. 10.1 suggested researches that the FCGR do/ dA should be a function of the crack size a and the applied stress a 

However, one of the first knots to loosen if not the first one was the stress entering Eq. (10.1). It was, in fact, necessary to choose which stress to consider among the external stress o, the average stress o on the section containing the crack and the local stress O/ ahead of the crack tip, but in this latter case the distance from the crack tip at which to calculate the local stress remained unknown. Generally, the attention of researchers was concentrated on either the external stress cr or the mean stress on the cracked section, both of simple determination at least on regular sections as those of the specimens used. The functional dependency more considered, always of empirical nature, was of the type [4, 5] 

10 Fracture Mechanics Approach to Fatigue Crack Propagation 

The reference system for Eqs. (10.3) and (10.4) is the polar one shown in Fig. 10.2. Similar expressions exist for the shear stresses. The function/-,-(0) is an non-dimensional factor whose value depends only on the anomaly 6. Note that the stress field given by Eq. (10.3) exists only in a near vicinity of the crack tip where the terms of higher order of the ratio a/r can be neglected. In practice, at few millimeters from the crack tip this stress field already does not exists any longer. Equations (10.3) and (10.4) indicate that the crack tip stress field has a singularity of the type r being the distance from the tip, whose intensity is given 

The subscript I means that we are examining the Mode I of aperture of a crack, among the three possible shown in Fig. 10.3. The first, or Mode I, is certainly the most severe since it requires less energy to produce the same effects among the three (fracture of the work-piece). Equation (10.3) indicates that the crack tip stress field is always self-similar, independent of geometry. Only the intensity 

Typical crack growth rate (da/dN) versus AK or K ax curves are shown in Fig. 7.8 [4] as a function of AK, or K ax, and other loading, environmental, and material variables. Ideally, it is desirable to characterize the fatigue crack growth behavior in terms of all of the pertinent loading, material, and environmental variables, namely. 

The lower hmit of integration (at or ai) is usually defined on the basis of nondestructive inspection (NDl) capabilities, or on prior inspection the upper limit is defined by fracture toughness or a predetermined allowable crack size that is consistent with inspection requirements (a/ or 2)- Equations (7.5) and (7.6) may be rewritten in terms of the stress intensity factor K  

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Eig. 9. Schematic fatigue crack growth data showing the regions of growth rate. 

Eracture mechanics concepts can also be appHed to fatigue crack growth under a constant static load, but in this case the material behavior is nonlinear and time-dependent (29,30). Slow, stable crack growth data can be presented in terms of the crack growth rate per unit of time against the appHed R or J, if the nonlinearity is not too great. Eor extensive nonlinearity a viscoelastic analysis can become very complex (11) and a number of schemes based on the time rate of change of/have been proposed (31,32). 

ASTM E647-93, "Measurement of Fatigue Crack Growth Rates," Annual Book of ASTM Standards, ASTM Puhhcations, Philadelphia, 1993. 

Fig. 15.8. Fatigue crack-growth rates for pre-cracked material.

Example 2.22 A certain grade of acrylic has a Kc value of 1.6 MN and the fatigue crack growth data as shown in Fig. 2.77. If a moulding in this material is subjected to a stress cycle which varies from 0 to 15 MN/m, estimate the maximum internal flaw size which can be tolerated if the fatigue endurance is to be at least 1(P cycles. 

A series of fatigue crack growth tests on a moulding grade of polymethyl methacrylate gave the following results... 

Fig. 8.59 Features of a corrosion fatigue crack growth curve...

Fig. 8.63 Effect of environment on fatigue crack growth rate in 1% Cr-Mo-V steel at 550°C (after Tomkins and Wareing )...

Fig. 8.64 Influence of hydrogen pressure, frequency and waveform on the enhancement of fatigue crack growth in 708M40 steel A/f = 30 (after McIntyre )...

Fig. 8.65 Corrosion fatigue crack growth data for structural steel in seawater at 0.1 Hz, / = -I to 0.85 and -1.10 V (Ag/AgCI) (after Scott...

In common with many of the alloy-environment systems described so far, if the alloy is not susceptible to stress-corrosion cracking under constant stress or stress intensity, then little or no effect of environment on fatigue crack growth is observed. In these cases, frequency, R ratio and potential within the passive or cathodically protected ranges for titanium have no effect on growth rates. 

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