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Author:Andersson, Tom
Title:Analysis of Discontinuities in Metallic Materials With the Extended Finite Element Method
Epäjatkuvuuksien analysointi metallisissa materiaaleissa XFEM-menetelmällä
Publication type:Master's thesis
Publication year:2010
Pages:(8) + 80      Language:   eng
Department/School:Sovelletun mekaniikan laitos
Main subject:Lujuusoppi   (Kul-49)
Supervisor:Tuhkuri, Jukka
Instructor:Laukkanen, Anssi
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  4834   | Archive
Keywords:FEM
XFEM
fracture mechanics
crack propagation
murtumismekaniikka
särönkasvu
Abstract (eng): The goal of this work was to develop a finite element method code able to handle strong and weak discontinuities in two dimensional cases.
The code is able to model crack (strong discontinuity) propagation and take into account the presence of precipitates.
Precipitates (weak discontinuity) are modelled as small material domains with Young's modulus differing from the rest of the specimen.

The code is written in Matlab utilizing the Getfem general purpose finite element (FE) library.
Getfem-library is an open source library developed with C++.
As case studies three edge crack configurations in a two dimensional tensile type fracture mechanics square specimen are considered.
In these cases the specimen is loaded from its upper boundary and the lower boundary is fixed.
In first case a stationary crack, with length of 3/10 the whole specimen is analyzed with the aim of verifying the code.
In the eases to follow the crack propagation capabilities of the implementation are investigated.
The initial crack length in these cases is 1/10 of the whole specimen.
The maximum circumferential tensile stress criterion is used to calculate the crack propagation angle.
In second case three different crack propagation variants are considered: one with loading perpendicular to the crack, one with loading parallel to the crack, and one with a 45° angle.
The third case is similar to the first variant of case two only difference is that precipitates are included into the material.
Constitutive properties of the precipitates differ in these analyses.

The code was verified by crosschecking computed stress intensity factor values with the analytical ones.
The computed results were in good agreement with the theory.
The crack propagation was analyzed by comparing the computed crack growth angles and the ones given by the used crack growth criterion.
The crack propagation and its behaviour near regions with discontinuously varying material properties were in good accordance with theoretical crack propagation.
The Getfem-library is found to be effective and user friendly, regardless of the lack of documentation, in building XFEM codes.
The code developed during this work will be used as a base for more sophisticated and effective XFEM codes.
Abstract (fin): Tämän työn tarkoituksena oli kehittää elementtimenetelmää soveltava koodi.
Koodilla mallinnetaan särön kasvua erkaumia sisältävässä materiaalissa.
Särö mallinnetaan vahvana epäjatkuvuutena.
Erkaumat ovat mallinnettu pieninä alueina, joiden kimmokerroin poikkeaa muusta materiaalista.
Nämä alueet erottuvat perusaineesta heikkoina epäjatkuvuuksina.
Työn puitteissa koodia sovelletaan vain kaksiulotteisissa tapauksissa.

Koodi on toteutettu Matlab ympäristössä, käyttäen hyväksi Getfem kirjaston ominaisuuksia.
Getfem on avoimen lähdekoodin C++ elementtimenetelmä kirjasto.
Koodi testataan mallintamalla reunasärö kappaleeseen.
Kappaleen alareuna on jäykästi kiinnitetty ja yläreunaan asetetaan voimareunaehto.
Särön pituus on 3/10 koko kappaleen pituudesta.
Tämän lisäksi koodilla simuloidaan särön kasvua kolmella toisistaan eroavalla tapauksella.
Alkusärön pituus näissä tapauksissa on 1/10 kappaleen pituudesta.
Särön kasvun kulma määritetään suurimman vetojännitys ehdon mukaisesti.
Ensimmäisessä tapauksessa kappaletta kuormitetaan pystysuoralla voimalla, toisessa tapauksessa kuormittava voima on särön suuntainen ja viimeisessä tapauksessa kuormittava voima on asetettu 45° kulmaan säröön nähden.

Laskentarutiinin antamia jännitysintensiteettikertoimia verrattiin analyyttisesti saatuihin.
Laskentarutiini tuotti särön kärjen lähelle oikeanlaisen jännityskentän ja sen antamat jännitysintensiteettikertoimet ovat teorian mukaisia.
Laskentarutiiniin antamia särön kasvukulmia verrattiin käytetyn särönkasvukriteerin antamiin.
Laskentarutiini tuotti oikeanlaisen särörintaman ja sen tuottama säröpolku materiaaliominaisuuksiltaan pääaineesta poikkeavien alueiden läheisyydessä vastaa kirjallisuudessa esiintyviä tapauksia.
Koodia tullaan käyttämään pohjana tuleville ohjelmille, joiden avulla voidaan simuloida särön kasvua todellisessa materiaalissa.
ED:2010-03-18
INSSI record number: 39313
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