The influence of grain size variation on metal fatigue
Introduction
Supposedly identical components made of metal often show substantial differences in fatigue lives. The differences are apparent even during controlled tests with identical stress levels. Miller writes in [3] that the scatter in fatigue data needs to be put in a perspective by for example detailed studies of the effect of material structure on early crack growth. One model of early (short) crack growth has been developed by Navarro and de los Rios in [5], [6], [7], [8], [9], [10]. The purpose of this study is to investigate the effect of grain size variation on fatigue life. Since the main part of the fatigue life is explained by the crack initiation, the model of Navarro–de los Rios will be used, as in [12], but modified to handle grains of varying sizes. A stochastic grain structure will be obtained by simulation. Similar ideas have been used by Ahmadi and Zenner [1] in a study of the growth of microcracks under the influence of cyclic loading. They compared simulations of cracks in a two-dimensional hexagonal lattice with experiments and the distribution of cracks was claimed to be in quantitatively good agreement between simulations and experiments. The main differences in the ideas from the present paper is the deterministic grain structure and our focus on scatter. A stochastic grain structure, a Voronoi tessellation, is used by Meyer, Brückner-Foit and Möslang [2] but focusing more on the crack patterns when several cracks are allowed to grow. Here also the results were found to be in good agreement with experiments.
The grain model is introduced in Section 2.1 and the Navarro–de los Rios model with modifications is described in Section 2.2 along with some computational details. The results are presented in Section 3 and analysed in Section 4.
Section snippets
Grain structure
In the proposed model the metal grain structure is a Voronoi tessellation in two or three dimensions of points generated from a Poisson process (see Fig. 1). The reason for using a Voronoi tessellation can be argued as follows. If, in the crystallisation process of a one phase metal, all grains begin to grow simultaneously and at the same rate the resulting grain structure would be a Voronoi tessellation. The tessellation could be modified by allowing the grains to begin their growth at
Results
Simulations were made of two-dimensional Voronoi tessellations where the number of nuclei were taken from a Poisson distribution with expectation (denoted λA) 2000, 4000 and 9000, which corresponds to looking at components of increasing size. More specifically, squares of sides 2, 4 and 6 giving the area A to be 4, 16 and 36, respectively, were used with an intensity, λ, of points per unit area as 250. The unit of the area is not important since the grain size is only included implicitly in the
Discussion
The discussion following is purely qualitative because of lack of real data. There is no evaluation of the Voronoi model as a grain structure apart form the comparison of the intercepts with the lognormal distribution. The agreement is not very good since the observations are not on a straight line. In this context, however, this is not the crucial thing to compare but rather the distribution of large grains which is more important for the crack growth. Probably the common knowledge of the
Acknowledgements
I am grateful to my supervisors Jacques de Maré and Thomas Svensson for starting me on this project and helpful discussions.
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