# Fatigue limit, inclusion and finite lives - a statistical point of view Doktorsavhandling, 2004

An important design property of steel is the fatigue limit, i.e. the load level where a specimen has infinite life. For the material it can also be defined an endurance limit, which is the stress level at which the specimen has a certain life. It will not break before no cycles. Obviously it is of interest to estimate these limits. The maximum inclusion size in clean steels influences the fatigue limit behaviour. Therefore it is also interesting to estimate the distribution of the inclusion size which causes the failure. Here the results from staircase tests are used to estimate the fatigue limit, the endurance limit and the inclusion size distribution. By combining the fatigue limit and the finite life distribution the whole S-N curve can be estimated at the same time. The uncertainties in the estimated parameters are taken into account by using the method of information matrix or the method of profile predictive likelihood. The staircase test is combined with the $\sqrt{area_{max}}$-model to estimate the distribution of the inclusion size where the failure occurs. This can be done by using stress levels with or without inclusion measurements. By combining the $\sqrt{area_{max}}$-model and the assumption that the inclusion size above a fixed threshold follows a generalized Pareto distribution, the stresses from the staircase test can be used to estimate the probability that a component will fail. Under these assumptions the probability that the component will fail under a rotating bending test can be estimated using data from a uniaxial test on a different component and vice versa.

likelihood

profile predictive likelihood

censoring

extreme value

staircase test

## Författare

#### Sara Lorén

Chalmers, Institutionen för matematisk statistik

Göteborgs universitet

Matematik

#### ISBN

91-7291-443-2

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 2125