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Experimental and statistical investigation of the weakest link integral and the volume effect
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0001-8068-2360
2010 (English)In: FATIGUE 2010, 2010, Vol. 2, no 1, 1451-1457 p.Conference paper, Published paper (Refereed)
Abstract [en]

A new specimen for investigation of the volume effect and scatter in fatigue data associated with different volumes is presented. This specimen contains two notches with associated volumes of different size. The WL-integral is used to estimate the probability of fatigue, and is compared to the experimental outcome. When the WL-integral is fitted to just one of the notches, the experimental outcome was well described. When fitted to both notches the fit was poor except at a failure probability of 50 %. The results are almost the same whether the WL-integral is evaluated as an area-integral at the specimen surface or as a volume-integral in the specimen volume. (C) 2010 Published by Elsevier Ltd.

Place, publisher, year, edition, pages
2010. Vol. 2, no 1, 1451-1457 p.
Series
Procedia Engineering, ISSN 1877-7058 ; 2
Keyword [en]
Volume effect, statistics, experiments, weakest link theory, fatigue limit(s), area approach
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-29694DOI: 10.1016/j.proeng.2010.03.157ISI: 000278762900155Scopus ID: 2-s2.0-77954118800OAI: oai:DiVA.org:kth-29694DiVA: diva2:397940
Conference
10th International Fatigue Conference
Note

QC 20110216

Available from: 2011-02-16 Created: 2011-02-11 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.
Series
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0527
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-104041 (URN)
Public defence
2012-11-15, H1, Teknikringen 33, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20121026

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

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