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Numerical Modelling of Short Fatigue Crack Growth

Hansson, Per LU (2008)
Abstract (Swedish)
Popular Abstract in Swedish

I en komponent som blir utsatt för en upprepande på- och avlastning, så kallad cyklisk belastning, kan små sprickor initieras och börja växa i materialet. Detta fenomen kallas för utmattning och kan få katastrofala följder, såsom haveri. För att med god säkerhet kunna dimensionera mot utmattning är det viktigt att på en mikro skala förstå de fenomen som ligger bakom spricktillväxten, och att ha tillförlitliga modeller för beräkning av en komponents livslängd.

I denna avhandling har jag studerat tillväxten av korta utmattningssprickor. Med korta sprickor menas här sprickor som är kortare än ett fåtal korn i materialet. Så korta sprickor är kända för att växa på ett sätt som skiljer sig... (More)
Popular Abstract in Swedish

I en komponent som blir utsatt för en upprepande på- och avlastning, så kallad cyklisk belastning, kan små sprickor initieras och börja växa i materialet. Detta fenomen kallas för utmattning och kan få katastrofala följder, såsom haveri. För att med god säkerhet kunna dimensionera mot utmattning är det viktigt att på en mikro skala förstå de fenomen som ligger bakom spricktillväxten, och att ha tillförlitliga modeller för beräkning av en komponents livslängd.

I denna avhandling har jag studerat tillväxten av korta utmattningssprickor. Med korta sprickor menas här sprickor som är kortare än ett fåtal korn i materialet. Så korta sprickor är kända för att växa på ett sätt som skiljer sig från hur långa sprickor växer. Korta sprickor kan börja växa vid lägre laster och i högre hastighet än långa sprickor. Därför kan man inte använda de vedertagna metoder som finns för beräkning av tillväxt av långa sprickor på korta sprickor. Det avvikande beteendet beror på att korta sprickor är mycket känsliga för mikrostrukturen hos materialet, samt för de lokala förhållandena vid sprickspetsen. Även mekanismerna som styr spricktillväxten skiljer sig mellan långa och korta sprickor. För att förbättra livslängdsberäkningar är det därför av intresse att få en bättre förståelse för vilka mekanismer som är viktiga för spricktillväxten hos korta sprickor, och hur dessa påverkar förloppet. Detta är målet med denna avhandling.

Den första delen av avhandlingen behandlar en mikrostrukturellt kort kantspricka inom ett korn i en halvoändlig kropp. Kroppen är utsatt för upprepade av- och pålastning med antagandet av plan töjning. Sprickan antas att växa på grund av skjuvning, och öppning av sprickytorna som resultat av nukleering, glidning och annihilering av diskreta kantdislokationer i materialet. En kantdislokation kan ses som ett fel i en annars perfekt kristallstruktur, och ger upphov till singulära spänningsfält i materialet. Dislokationerna bygger upp en plastisk zon framför sprickan och påverkar spänningsfältet vid sprickspetsen. Dislokationerna kan röra sig i materialet längs speciella glidplan så länge kraften som driver dem är större än gittermotståndet. De kan även hindras av eventuella korngränser i materialet. Även den yttre randen, definierad som den fria kanten tillsammans med sprickan själv, modelleras med hjälp av dislokationer i form av dipolelement i en randelementformulering. Denna modell används sedan för att utvärdera vilken effekt på spricktillväxten en rad olika parametrar har. Parametrar som undersökts är kornstorlek, yttre laster, överlaster, spricklängd, sprickans initiella vinkel, och sätt korngränsens egenskaper.

Den andra delen av avhandlingen är ett delvis experimentellt arbete, utfört i sammarbete med Volvo Aero Corporation (VAC). Målet med detta arbete var att utvärdera ett befintligt beräkningsprogram för utmattningsdimensionering, NASGRO, utvecklat av Southwest Research Institute. Av speciellt intresse för VAC var att utvärdera om programmet var användart för bedömning av tillväxten av korta, halvelliptiska ytsprickor i tunna titanplåtar. För att utvärdera detta gjordes tio utmattningsprov på 2 mm tjocka plåtar, alla med en initiell notch. Från notchen initierades sedan en kort utmattningsspricka som tilläts växa igenom platen, tills provstaven gick av. Under provets gång mättes spricklängden med hjälp av potentialfallstekniken. Resultaten från experimenten jämfördes med beräkningar utförda med NASGRO, både gällande spricktillväxt, sprickform och brottkriterie. Relativt bra överenstämmelse mellan experimenten och NASGRO erhölls gällande livsländ, medan predikteringen av sprickformen skiljde sig något, speciellt för långa, nästan genomgående, sprickor. (Less)
Abstract
Fatigue implies repeated loading and unloading of a structure, and components subjected to fatigue might experience nucleation of cracks, and subsequent crack propagation. This might lead to catastrophic consequences, such as complete failure of a structure. In order to accurately dimension against fatigue it is of uttermost importance to have a thorough understanding of the mechanisms behind the growth of fatigue cracks, and from this develop reliable methods for estimating the fatigue life.

In this Thesis, the growth of short fatigue cracks is addressed. In this context, a short crack is defined as a crack shorter than a few grains of the material. It is well known that such short cracks can grow at lower applied loads and at... (More)
Fatigue implies repeated loading and unloading of a structure, and components subjected to fatigue might experience nucleation of cracks, and subsequent crack propagation. This might lead to catastrophic consequences, such as complete failure of a structure. In order to accurately dimension against fatigue it is of uttermost importance to have a thorough understanding of the mechanisms behind the growth of fatigue cracks, and from this develop reliable methods for estimating the fatigue life.

In this Thesis, the growth of short fatigue cracks is addressed. In this context, a short crack is defined as a crack shorter than a few grains of the material. It is well known that such short cracks can grow at lower applied loads and at higher growth rates than long cracks. Therefore, well established methods for predicting the growth of long cracks cannot be used for short cracks. The difference in growth behaviour is due to the sensitivity to the microstructure of the material and influence of the local conditions at the crack tip, for short cracks. Also short cracks are known to propagate through a different growth mechanism than long cracks. In order to formulate more accurate crack growth models, the mechanisms behind their crack growth and the impact on the growth behaviour must be known. This constitutes the scope of this Thesis.

The first part of the Thesis deals with a microstructurally short edge crack, located within one grain of a semi-infinite body, loaded by a remote fatigue load under plane strain conditions. The crack is assumed to grow due to shearing and opening between the crack surfaces as a consequence of nucleation, glide and annihilation of discrete edge dislocations in the material. An edge dislocation can be seen as an error in a, otherwise, perfect crystal gitter, and gives rise to a singular stress field in its surroundings. Such dislocations, forming in front of the crack, represent the plastic zone in the material and have a strong effect on the stress field at the crack tip. The dislocations are free to move along specific slip planes in the material as long as the force exerted on them exceeds the lattice resistance, and as long as they do not collide with grain boundaries of the material. Also the external boundary, here defined as the free edge together with the crack itself, is modelled by dislocation dipole elements in a boundary element approach. The model have been used to evaluate the influence on the crack growth for a number of different situations such as variations in grain size, external load, overloads, crack length, initial crack angle, different descriptions of the grain boundary, and so on.

In the second part of this Thesis, an experimental study was performed in cooperation with Volvo Aero Corporation (VAC). The aim of was to evaluate a computer program used for fatigue calculations, NASGRO, developed by Southwest Research Institute. Of special interest was to investigate if the program could be used for predicting the growth of short, semi-elliptical, surface cracks in thin titanium sheets. For the evaluation, ten titanium sheets of 2 mm thickness, each with a small starter notch, were used. From the initial notch a small fatigue crack was initiated. The growth of the crack was monitored until complete failure of the specimen. The crack length was continuously calculated by the use of the potential drop technique. The results from the experiments were compared to the results obtained from NASGRO, both regarding crack growth rate, crack shape and failure criteria. The results from the experiments and from NASGRO showed reasonable good agreement, up until just before final failure, were the correct crack path could not be simulated correctly. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Pippan, Reinhard, University of Leoben, Austria
organization
publishing date
type
Thesis
publication status
published
subject
keywords
discrete dislocation, Fatigue, grain boundary, short crack
pages
158 pages
defense location
Room M:E, M-building, Ole Römers väg 1, Lund university, Faculty of Engineering
defense date
2008-06-05 13:15
ISBN
978-91-633-2786-5
language
English
LU publication?
yes
id
b8c48e80-15d9-4238-a195-96fc77efcabc (old id 1148832)
date added to LUP
2008-05-12 15:36:17
date last changed
2016-09-19 08:45:17
@misc{b8c48e80-15d9-4238-a195-96fc77efcabc,
  abstract     = {Fatigue implies repeated loading and unloading of a structure, and components subjected to fatigue might experience nucleation of cracks, and subsequent crack propagation. This might lead to catastrophic consequences, such as complete failure of a structure. In order to accurately dimension against fatigue it is of uttermost importance to have a thorough understanding of the mechanisms behind the growth of fatigue cracks, and from this develop reliable methods for estimating the fatigue life.<br/><br>
In this Thesis, the growth of short fatigue cracks is addressed. In this context, a short crack is defined as a crack shorter than a few grains of the material. It is well known that such short cracks can grow at lower applied loads and at higher growth rates than long cracks. Therefore, well established methods for predicting the growth of long cracks cannot be used for short cracks. The difference in growth behaviour is due to the sensitivity to the microstructure of the material and influence of the local conditions at the crack tip, for short cracks. Also short cracks are known to propagate through a different growth mechanism than long cracks. In order to formulate more accurate crack growth models, the mechanisms behind their crack growth and the impact on the growth behaviour must be known. This constitutes the scope of this Thesis.<br/><br>
The first part of the Thesis deals with a microstructurally short edge crack, located within one grain of a semi-infinite body, loaded by a remote fatigue load under plane strain conditions. The crack is assumed to grow due to shearing and opening between the crack surfaces as a consequence of nucleation, glide and annihilation of discrete edge dislocations in the material. An edge dislocation can be seen as an error in a, otherwise, perfect crystal gitter, and gives rise to a singular stress field in its surroundings. Such dislocations, forming in front of the crack, represent the plastic zone in the material and have a strong effect on the stress field at the crack tip. The dislocations are free to move along specific slip planes in the material as long as the force exerted on them exceeds the lattice resistance, and as long as they do not collide with grain boundaries of the material. Also the external boundary, here defined as the free edge together with the crack itself, is modelled by dislocation dipole elements in a boundary element approach. The model have been used to evaluate the influence on the crack growth for a number of different situations such as variations in grain size, external load, overloads, crack length, initial crack angle, different descriptions of the grain boundary, and so on.<br/><br>
In the second part of this Thesis, an experimental study was performed in cooperation with Volvo Aero Corporation (VAC). The aim of was to evaluate a computer program used for fatigue calculations, NASGRO, developed by Southwest Research Institute. Of special interest was to investigate if the program could be used for predicting the growth of short, semi-elliptical, surface cracks in thin titanium sheets. For the evaluation, ten titanium sheets of 2 mm thickness, each with a small starter notch, were used. From the initial notch a small fatigue crack was initiated. The growth of the crack was monitored until complete failure of the specimen. The crack length was continuously calculated by the use of the potential drop technique. The results from the experiments were compared to the results obtained from NASGRO, both regarding crack growth rate, crack shape and failure criteria. The results from the experiments and from NASGRO showed reasonable good agreement, up until just before final failure, were the correct crack path could not be simulated correctly.},
  author       = {Hansson, Per},
  isbn         = {978-91-633-2786-5},
  keyword      = {discrete dislocation,Fatigue,grain boundary,short crack},
  language     = {eng},
  pages        = {158},
  title        = {Numerical Modelling of Short Fatigue Crack Growth},
  year         = {2008},
}