Introduction

It is understood that fatigue crack growth is a consequence of the accumulation of damage by deformation in the plastic zone at the crack tip. At low loads the deformation is governed by the cyclic variation in the stress-intensity range $\Delta K$. The crack extension per cycle $(da/dN)$ becomes measurable at a threshold $\Delta K_{th}$, followed by the slower extension rate in the Paris Law regime [4,2,1,3] described by the proportionality

$$\log \Delta K \propto \log \biggl\{\frac{da}{dN}\biggr\}^m$$ (1)

where $da/dN$ is the average crack advance per cycle, and $m$ is known as the Paris exponent. The equation can be interpreted in terms of a variety of physical mechanisms [5,6], in which case the proportionality constant ($C$) becomes a function of the Young's Modulus $E$, the Poisson's ratio $\nu$, and the yield and ultimate tensile strengths $\sigma_Y$ and $\sigma_U$ respectively. Based on the possible mechanisms consistent with the Paris Law, attempts have been made to generally interpret fatigue crack growth data on the basis of just the mechanical properties of the material [5,6].

Elber modified the relation with an effective stress intensity range $\Delta K_{eff}$ to allow for variable amplitude loading, arguing that cracks grow only when their tips are open [7]:

$$\frac{da}{dN} = C_{0}(\Delta K_{eff})^m \qquad\hbox{with}\qquad C_0=C/(0.7^m)$$ (2)

These equations do not explicitly contain material properties; Duggan [8] expressed the crack growth rate in terms of the elastic modulus, toughness, and ductility:

$$\frac{da}{dN} = \bigg( \frac{\pi}{32} \bigg)^{\frac{1}{2\eta}} \f... ... ) } \Big(1 - \frac{K}{K_{Ic}} \Big) \bigg]^{\frac{1}{\eta}} K^{\frac{2}{\eta}}$$ (3)

where $\eta$ and $\epsilon$ are the fatigue ductility exponent and coefficient respectively, $E$ is the elastic modulus, $K_{Ic}$ is the critical stress intensity for fracture. Ramsamooj and Shugar have also accounted for toughness, yield strength and modulus, but not for frequency and the analysis is presumably limited to mode I loading [9]. Their model is interesting in that it generalises against iron, aluminium and titanium alloys; it does however require a prior knowledge of the threshold stress intensity range for fatigue crack growth.

The aim here was to exploit published fatigue crack growth data to create a model based on physical variables which are readily measured in a tensile test, rather than rely on inputs which depend on fatigue testing, and further, to include variables which account for test-specimen parameters. The model uses neural network analysis; although there are physically based models available in the literature, for example, [10], they require fitting parameters; a neural network is the most general way of achieving fitting without making prior assumptions about the relationship to which the data are fitted [11]. There have been other attempts to use neural networks for this purpose [12] but they do not adequately treat the uncertainties of modelling so it is not possible to properly assess the predictions made. The original intention here was to study steels, but as will be seen later, the model was, without modification, found to generalise to other alloy systems.