The steady state fracture kinetics of crack front spreading

Abstract

The kinetics study is based on the energetically favourable crack propagation mechanism of double kink nucleation and its subsequent sideways spreading. The analysis was carried out on linearly elastic solids for the case when kink spreading is the rate controlling mechanism. The kink spread distribution is described by a differential equation that is identical with the mass and heat transport equations. The solutions of the differential equation represent the distribution function and the crack propagation velocity as a function of the bond breaking energy AG, the work W contributed by the applied stress, and of the temperature. When W ~> AGI2 the crack velocity increases exponentially with increasing work, decreases steeply with decreasing work, and reduces to zero when W~AG[2. The theory represents well the behavior of ceramic materials and some metals in Region I and at the threshold region of stress corrosion cracking. It is of special interest for stress corrosion cracking designs that the threshold stress intensity is independent of the temperature under the conditions of the present investigation.

A fracture-mechanical theory of subcritical crack growth in ceramics

“…Measurements by Evans [1] demonstrate for glass that this power law relation is satisfied over a comparatively wide range of values for K~. In the literature a fairly large number of theoretical explanations are reported to describe measured data [2] [6]. In these various attempts, the functional dependence ~, = f(Kl) is always described -as a consequence of the Arrhenius equation by exponential functions, the arguments of which are linear, quadratic, or mixed-quadratic functions of the stress intensity factor.…”

Reliability Theory of Stochastic Fracture Processes in Sustained Loading: Part I

“…The reciprocals of these waiting times are the rates of bond breaking and of bond healing. The average rate of bond breaking, that is, the average number of bonds broken per unit time is expressed by the breaking rate constant k b as [6,11,18] In (1) and (2). AG b is the free energy needed to break the atomic bond as the crack propagates by one atomic distance, and W is the mechanical work contributed to the crack propagation by the stress through the stress intensity factor so that W = f(K).…”

“…Because both the size and the distribution of the imperfections are random, fracture life is probabilistic [1], and is usually described with the Weibull distribution function. In the following, it will be shown that the physical process of crack propagation itself is also stochastic, so that the fracture life-time is probabilistic even in homogeneous, defect-free materials [2], The resulting probability distribution is superposed on the Weibull distribution. The effect of this physical process is analyzed from the reliability point of view in Part I and the corresponding reliability theory will be developed in Part II.…”