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Probabilistic modeling of fatigue failures
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
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: urn:nbn:se:kth:diva-104041OAI: oai:DiVA.org:kth-104041DiVA: diva2:562748
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
List of papers
1. A study of the volume effect and scatter at the fatigue limit: experiments and computations for a new specimen with separated notches
Open this publication in new window or tab >>A study of the volume effect and scatter at the fatigue limit: experiments and computations for a new specimen with separated notches
2011 (English)In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 33, no 3, 363-371 p.Article in journal (Refereed) Published
Abstract [en]

In this paper a new fatigue specimen is presented that has been developed in order to conduct detailed investigations of the volume effect and the scatter of fatigue data in the fatigue limit regime The specimen has two separated notches A and B with different size of the loaded volume associated with them respectively By changing the location of the applied load the fatigue failure in the experiments can be controlled to occur in either notch A or B Comparisons were made with simulations based on statistical weakest link (WL) theory In the weakest link statistics the three parameter Weibull distribution is used for estimation of the fatigue failure probability It is shown that the predictive capability of WL-models is poor for high and low failure probabilities when the two separated notches A and B are considered If only one notch (either A or B) is considered and the other one is disregarded the predictive capability of WL is drastically improved Experiments with almost equal failure WL-probability in A and 8 (28% and 27%) did not result in equal experimental failure probability WL-statistics can not predict the experimental outcome when separated notches are present.

Keyword
Experiments, High cycle fatigue, Statistics, Volume effect, Weakest link theory
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-29531 (URN)10.1016/j.ijfatigue.2010.09.012 (DOI)000285170500008 ()2-s2.0-78649316253 (Scopus ID)
Note

QC 20110207

Available from: 2011-02-07 Created: 2011-02-07 Last updated: 2017-12-11Bibliographically approved
2. Experimental and statistical investigation of the weakest link integral and the volume effect
Open this publication in new window or tab >>Experimental and statistical investigation of the weakest link integral and the volume effect
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.

Series
Procedia Engineering, ISSN 1877-7058 ; 2
Keyword
Volume effect, statistics, experiments, weakest link theory, fatigue limit(s), area approach
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-29694 (URN)10.1016/j.proeng.2010.03.157 (DOI)000278762900155 ()2-s2.0-77954118800 (Scopus ID)
Conference
10th International Fatigue Conference
Note

QC 20110216

Available from: 2011-02-16 Created: 2011-02-11 Last updated: 2012-10-26Bibliographically approved
3. A probabilistic model for the entire HCF domain based on equivalent stress - Simulations and experiments
Open this publication in new window or tab >>A probabilistic model for the entire HCF domain based on equivalent stress - Simulations and experiments
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.

Keyword
Fatigue life, Experiments, Fatigue limit, Probabilistic model, Simulations
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-55226 (URN)10.1016/j.ijfatigue.2011.09.007 (DOI)000297612000002 ()2-s2.0-80955157302 (Scopus ID)
Note

QC 20120102

Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2017-12-08Bibliographically approved
4. An investigation of a fatigue model with two competing failure mechanisms
Open this publication in new window or tab >>An investigation of a fatigue model with two competing failure mechanisms
2012 (English)Report (Other academic)
Abstract [en]

Fatigue limit tests where there are two competing fatigue failure locations, two notches of different size, are performed in this paper. The normal distribution is used for describing the experimental outcome, where the largest occurring stress value or the gradient adjusted stress is used as a stress measure. Another model for describing the experimental outcomeis the Weakest Link (WL)-integral where the integration is performed over the specimen surface area or the specimen volume. The longitudinal positions of the estimated fatigue failure sites are measured and investigated as well. Neither the normal distribution (point stress and gradient adjusted point stress), nor the WL-integral can explain the experimental outcome from the competing notch tests. They all predict the same trend, but not the same trend as in the experiments. When looking at the estimated longitudinal location of fatigue failure it can be seen that it differs considerably from experiment to experiment. If the stress is evaluated at the estimated fatigue failure location, it is seen that the local stress is much lower than the maximal stress. The load cases where there should be an equal amount of failures in both notches according to the different models do not agree with the experimental findings. It is concluded that stress based continuum models can not describe the experimental outcome when there are competing fatigue failure sites (notches) present.

Publisher
19 p.
Series
Trita-HFL, ISSN 1104-6813 ; 525
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-103858 (URN)
Note

QC 20121025

Available from: 2012-10-25 Created: 2012-10-22 Last updated: 2012-10-26Bibliographically approved
5. An investigation of the location of fatigue initiation: deterministic and probabilistic aspects
Open this publication in new window or tab >>An investigation of the location of fatigue initiation: deterministic and probabilistic aspects
2012 (English)Report (Other academic)
Abstract [en]

Fatigue limit tests where there are two competing fatigue failure locations, two notches of different size, are performed in this paper. The normal distribution is used for describing the experimental outcome, where the largest occurring stress value or the gradient adjusted stress is used as a stress measure. Another model for describing the experimental outcome is the Weakest Link (WL)-integral where the integration is performed over the specimen surface area or the specimen volume. The longitudinal positions of the estimated fatigue failure sites are measured and investigated as well. Neither the normal distribution (point stress and gradient adjusted point stress), nor the WL-integral can explain the experimental outcome from the competing notch tests. They all predict the same trend, but not the same trend as in the experiments. When looking at the estimated longitudinal location of fatigue failure it can be seen that it differs considerably from experiment to experiment. If the stress is evaluated at the estimated fatigue failure location, it is seen that the local stress is much lower than the maximal stress. The load cases where there should be an equal amount of failures in both notches according to the different models do not agree with the experimental findings. It is concluded that stress based continuum models can not describe the experimental outcome when there are competing fatigue failure sites (notches) present.

Publisher
20 p.
Series
Trita-HFL, ISSN 1104-6813 ; 526
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-103861 (URN)
Note

QC 20121025

Available from: 2012-10-25 Created: 2012-10-22 Last updated: 2012-10-26Bibliographically approved
6. On the effect of random defects on the fatigue notch factor at different stress ratios
Open this publication in new window or tab >>On the effect of random defects on the fatigue notch factor at different stress ratios
2012 (English)In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 41, 179-187 p.Article in journal (Refereed) Published
Abstract [en]

The effect of randomly distributed defects of different sizes on the fatigue performance of a notched member has been studied. Both the effect of the volume density of defects and the size distribution of the defects have been studied. The fatigue life and the fatigue limit distributions of a smooth or notched specimen have been estimated. Using this probabilistic approach, the fatigue notch factor as function of failure probability can be estimated. It is shown that the approach with randomly distributed defects has better predictive capabilities than classical methods. The weakest link approach can be seen as an alternative to simulation of the randomly distributed defects. The two methods have similar predictive capabilities. The stress based methods generally do not take the load ratio into account when estimating the fatigue notch factor. It is also shown that the fatigue limit estimated with defect analysis is lower than the experimental one.

Keyword
Fatigue notch factor, Experiments, Fatigue crack growth, Probabilistic model, Simulations
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-95483 (URN)10.1016/j.ijfatigue.2011.07.011 (DOI)000303486800023 ()2-s2.0-84859429675 (Scopus ID)
Note

QC 20120528

Available from: 2012-05-28 Created: 2012-05-28 Last updated: 2017-12-07Bibliographically approved

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other locale
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Output format
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