Fatigue Crack Growth Laws for Brittle and Ductile Materials Including the Effects of Static Modes and Elastic‐plastic Deformation

Abstract

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.The growth rate equations are expressed in terms of the near field value of the J-integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached. NOMENCLATURE da/dN = fatigue crack growth rate Aa,da = increment of crack extension Aa,,da, = tear component of Aa and 6a 6af = fatigue component of 6a f ( a / w ) = function defining the plastic collapse stress m = exponent in Paris-Erdogan growth law s = size of fatigue plastic zone w = specimen width A = constant in Paris-Erdogan growth law D = crack tip damage parameter D, = critical value of D AD = cyclic change in D E = Young's modulus F, = a dimensionless constant related to the fatigue process zone length E 237 F t M S 1 4 A 238 G. G. CHELL F ( z ) = a function defining the plastic displacement G = strain energy release rate J = J-integral J, = value of J at initiation of ductile tear Jlc = initiation value of J determined in a toughness test J, = critical value of J for fast fracture .Imax = J corresponding to maximum load AJ =cyclic change in J JR = crack growth resistance value of J J, = saturation JR value K = stress intensity factor K,,, = K at maximum load Kmin = K at minimum load K,, = fracture toughness AK = cyclic change in K K, = K/K,c M = constant relating J to CD N = number of fatigue cycles P,,, = maximum load P,,, = minimum load R = Pm,n/Pmax s, = a/ol T = tearing modulus T,,, = T at maximum load T,,, = T evaluated from J R resistance curve T,,,, = T,,, at initiation of tear a = constant relating D to (D p = exponent relating D to CD S = material constant related to fatigue process zone E = fat...

An Investigation of Fatigue Crack Growth in a Ductile Material at High Growth Rates

“…Some of these data are shown in Fig. 5(a) where the measured rates are shown plotted against the rates predicted using the Paris law, equation (9). This figure emphasizes the conclusion drawn from Fig.…”

“…Kaiser [ 101 and Chell [9] have independently proposed similar mechanical models for evaluating the effects of ductile static modes of fracture on fatigue crack propagation. The models assume that the crack extension per cycle due to fatigue (da/dN),, and ductile tearing, (da/dN),, may be independently evaluated and linearly added to give the total rate of propagation, da/dN, i.e.…”

“…where a is the current crack depth. Recognizing that (dJ,,,,,/dN) = (dJ,,,/da) x (da/dN) then equation (4) may be rearranged into the growth rate law given by Chell [9] as…”

“…see Ref. [9]). Different modifications to the Paris law are necessary if the static modes correspond to ductile mechanisms, such as void growth and coalescence.…”

Static and Fatigue Failure Response of Woven Carbon Fiber Specimens with Double Edge Notches

“…Fibers began to popout of matrix, but did not tear. Cracks in carbon fiber propagate at super-sonic speeds 18 so there is no photo from this research of these parts in the process of failing. The horizontal face cracking that can be seen above the horizontal tearing in Figure 60 did not appear until the part…”