Paris' law

About: Paris' law is a research topic. Over the lifetime, 13815 publications have been published within this topic receiving 224818 citations. The topic is also known as: Paris-Erdogan law.

A method for growing multiple cracks without remeshing and its application to fatigue crack growth

Abstract: A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

The effect of carbon nanotube dimensions and dispersion on the fatigue behavior of epoxy nanocomposites

Abstract: Fatigue is one of the primary reasons for failure in structural materials It has been demonstrated that carbon nanotubes can suppress fatigue in polymer composites via crack-bridging and a frictional pull-out mechanism However, a detailed study of the effects of nanotube dimensions and dispersion on the fatigue behavior of nanocomposites has not been performed In this work, we show the strong effect of carbon nanotube dimensions (ie length, diameter) and dispersion quality on fatigue crack growth suppression in epoxy nanocomposites We observe that the fatigue crack growth rates can be significantly reduced by (1) reducing the nanotube diameter, (2) increasing the nanotube length and (3) improving the nanotube dispersion We qualitatively explain these observations by using a fracture mechanics model based on crack-bridging and pull-out of the nanotubes By optimizing the above parameters (tube length, diameter and dispersion) we demonstrate an over 20-fold reduction in the fatigue crack propagation rate for the nanocomposite epoxy compared to the baseline (unfilled) epoxy

The effect of air and vacuum environments on fatigue crack growth rates in Ti-6Al-4V

Abstract: Fatigue crack propagation studies in vacua of 1.33 mN m-2, on Ti-6 A1-4V, at growth rates of 10-7 to 10-4 mm/cycle have shown that a threshold for growth exists at ‡K values of 6.3 to 7.6 MN m-3/2. The value of the threshold level is microstructure dependent, but growth above this value was structure insensitive according to both growth rates and fracture surface observations. Some slow (≈ 10-8 mm/cycle) crack extension was observed below the threshold values but prolonged cycling reduced the growth rate to a vanishingly small level. Fracture surface observations indicated that growth in this region was microstructure sensitive. Comparison with previously performed air work on the same material showed that while structure insensitive growth rates in vacuum were slower than those in air by a factor of 3 to 4, the low ‡K value structure sensitive rates were slower than the air ones by at least three orders of magnitude. A hypothesis is proposed to explain this in terms of a propagation mechanism for the structure sensitive mode of fatigue crack growth.

Mixed‐mode fatigue thresholds

Abstract: — Near threshold fatigue crack growth under mixed-mode loading and elastic plane-strain conditions has been studied in 316 stainless steel in laboratory air at room temperature. Particular emphasis was placed on the influence of the mode II component. Crack growth from the starter crack, although initially coplanar, branches to be perpendicular to the maximum normal stress. However the threshold for the branched crack growth is controlled not only by mode I displacement, but also by the mode II component. Upper and lower bound curves are obtained for the threshold condition and discussed in terms of crack tip reversed plastic deformation, crack surface rubbing and oxide-induced closure. A theoretical method for predicting the lower bound curve is proposed and compared with the maximum normal stress and strain energy density criteria. The new theory shows the best agreement with experimental results, giving a safe prediction for design purposes.