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A probabilistic model for the entire HCF domain based on equivalent stress - Simulations and experiments
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
2012 (English)In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 36, no 1, 9-17 p.Article in journal (Refereed) Published
Abstract [en]

A probabilistic model for fatigue life is presented. It allows for inhomogeneous stress fields. The stressing of the whole body is summarized in an equivalent stress. The model is calibrated with experiments and can be formulated for a variety of different types of equivalent stresses (point, gradient, area and volume). Finite life experiments at constant load levels as well as tests around the infinite life fatigue limit are used. Using this new model, the PES-model (Probabilistic and based on Equivalent Stress), it is shown that the choice of equivalent stress has a small influence on the fit for finite fatigue life, i.e. the constant load level results. The fit for all tested equivalent stresses are similar over the entire failure probability domain. For the fatigue limit part, however, there is a larger difference between the choices of equivalent stress. It is found that a gradient adjusted point stress is most suited for the PES-model, and that it can be used in the entire SN-domain.

Place, publisher, year, edition, pages
2012. Vol. 36, no 1, 9-17 p.
Keyword [en]
Fatigue life, Experiments, Fatigue limit, Probabilistic model, Simulations
National Category
Materials Engineering
URN: urn:nbn:se:kth:diva-55226DOI: 10.1016/j.ijfatigue.2011.09.007ISI: 000297612000002ScopusID: 2-s2.0-80955157302OAI: diva2:471554

QC 20120102

Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2012-10-26Bibliographically approved
In thesis
1. Probabilistic modeling of fatigue failures
Open this publication in new window or tab >>Probabilistic modeling of fatigue failures
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Fatigue is a well known failure mode in engineering that can have catastrophic consequences, such as loss of human life. Thus design against fatigue failure is very important. There are many sources of scatter present in fatigue, for instance; the difference in load in-between users of a product, material scatter and scatter in the production. The material scatter will be studied in this thesis.

In order to quantify the material scatter, experiments have to be performed. Both finite life tests, i.e. experiments at a constant stress levels where all specimen fail and the number of cycles to failure is stored, and fatigue limit tests, experiments where some experiments are run-outs and some experiments fail, have to be performed. The SN-space contains both the finite life part and the fatigue limit part. In order to model the material scatter, the Weakest Link (WL)-integral can be used. This integral, which was derived by Waloddi Weibull at KTH, takes the entire volumetric stress distribution into account. The outcome from this integral is a fatigue failure probability for a specimen or a structure. Thus if this integral is used a structure is designed with respect to a fatigue failure probability instead of a peak stress. Such a peak stress, or hot-spot stress, is related to the fatigue limit and is typically reduced by a safety factor.

In paper A fatigue limit tests performed on a custom-made specimen with two notches of different size are presented. The predictive capabilities of the weakest link integral were studied here, where the WL-model was fitted to the experimental outcome in both notches separately and then to both notches simultaneously. It was observed that the WL-integral is in good agreement with the experimental outcome when fitted to the experimental outcome in one notch, but poor when fitted to both notches,

The weakest link integral was evaluated at the specimen surface area and as a volumetric phenomenon in paper B. The conclusions in this paper was that the area and volume formulation of the WL-integral show similar results.

A new model for the entire SN-space, the PES-model was analyzed in paper C. Here, an equivalent stress measure (a scalar stress value) was introduced in order to have the same stress measure for finite life and the fatigue limit regime. The investigated equivalent stresses were; the point stress (largest occurring stress value), the gradient adjusted point stress (largest occurring stress value reduced with the stress gradient), the area stress (an effective measure of the surface stresses using the weakest link) and the volume stress (a similar measure that summarize the volumetric stresses). It was observed that the choice of equivalent stress had a small effect for finite life both a large effect at the fatigue limit regime.

In paper D a model that combines two failure mechanisms is presented, the DS-model. This model combines a defect based model, D, that is taken to be the weakest link integral (both area and volume versions) with a stress based model, S, taken to be the normal distribution where the stress measure used is either the point stress or the gradient adjusted point stress. It is assumed that the two failure mechanisms are independent. It was observed that, the D-model was dominating for low failure probabilities and the S-model for high failure probabilities.

In order to study the experimental scatter in another way, the estimated fatigue failure locations were studied in paper E. The stress was then evaluated and the estimated fatigue failure sites and the local failure probability could be estimated. In order to better understand the spatial scatter in the estimated fatigue failure sites a modified stress gradient was used. Further, experiments where fatigue failure could occur in both notches were performed. It was seen that the spatial scatter was large, in terms of location and in stress. None of the fatigue limit models could describe the experimental trend from the competing fatigue failure site experiments.

The effect of random defect is studied in paper F. In this paper defects of different size, which are treated as circular cracks, are placed at random positions in the specimen. A fatigue crack growth analysis is performed for each crack and thus the fatigue life is obtained. The main conclusion in this paper was that the computed fatigue crack growth life does not agree with the experimentally found fatigue life.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. 40 p.
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0527
National Category
Applied Mechanics
urn:nbn:se:kth:diva-104041 (URN)
Public defence
2012-11-15, H1, Teknikringen 33, KTH, Stockholm, 10:00 (English)

QC 20121026

Available from: 2012-10-26 Created: 2012-10-25 Last updated: 2013-01-14Bibliographically approved

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