ENBIS: European Network for Business and Industrial Statistics

A Load-strength Model for Fatigue Applications

21 September 2009, 14:45 – 15:05

Abstract

Submitted by

Pär Johannesson

Authors

Pär Johannesson(a) and Thomas Svensson(b)

Affiliation

(a) Fraunhofer-Chalmers Research Centre for Industrial Mathematics, Gothenburg, Sweden; (b) SP Technical Research Institute of Sweden, Borås, Sweden

Abstract

For components in service, fatigue is an extremely complex phenomenon. Material proper-ties, non-metallic inclusions, surface finish, scratches, geometric variations and other defects are all highly influential on the fatigue strength. Since many of these influential variables are not measurable beforehand, any fatigue life prediction is very uncertain. The service loads that will act on the component in the future are also very uncertain. They vary with time for each single user, but more importantly they differ between different users, missions, and envi-ronments. Uncertainties for both strength and load can be taken into account either by using overall safety factors based on engineering judgement or by using probabilistic methods, modelling the influential factors as random variables. The overall safety factor approach has the weakness that it is difficult to update, whereas the statistical methods have the weakness that the knowledge about the involved random variables is vague, especially in the tails of the distributions.
Here, we therefore propose a compromise between a probabilistic design method and a de-terministic safety factor approach. We use a second order statistical method to determine the prediction uncertainties, but include an extra safety factor covering uncertainties we have not been able to take care of by the probabilistic model, e.g. because of uncertain distribution tails. Second order statistics is used, since it complies with the information usually available about influential variables. It only uses mean values and variances of the input variables; combines them into means and variances of the logarithm of the strength and the load, respectively, and finally compares these two resulting random properties for a reliability assessment. The un-certainties in load and strength can come from variation in material properties, tolerances, customer usage, and so on. However, also statistical uncertainties and model uncertainties are easy to incorporate, e.g. uncertainties in parameter estimation, and model errors in fatigue life or finite element calculations.
For the load-strength model we need a simple and robust model for the fatigue life. Here we propose the Basquin equation, together with the Palmgren-Miner damage accumulation rule. The strength variable is defined as the endurance limit at fixed number of cycles, N0, say, e.g. one million cycles. The load variable is defined as an equivalent load amplitude, which is defined as the amplitude of a constant amplitude load with N0 cycles, which gives the same damage as the measured load scaled to the target design life.
The reliability assessment is based on the comparison of the load and strength variables. The result can be expressed in terms of a central safety factor for the medians of the strength and load, namely a multiplication of a deterministic and a statistical safety factor, where the statistical safety factor depends on the required reliability index and the prediction uncertainty.
The proposed method will be demonstrated for an automotive application. The strength of the component is determined from variable amplitude fatigue tests, and the load is found from measurements in service.

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