Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials

The finite element method (FEM) is developed for coupled thermoelastic crack problems if material properties are continuously varying. The weak form is utilized to derive the FEM equations. In conventional fracture theories the state of stress and strain at the crack tip vicinity is characterized by...

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Main Authors: Repka M., Sládek J., Sládek V., Wünsche M.
Format: Article
Language:English
Published: Sciendo 2015-11-01
Series:Journal of Mechanical Engineering
Subjects:
fgm
fem
Online Access:https://doi.org/10.1515/scjme-2016-0004
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spelling doaj-acce2467042148978820ee998ea0e1ef2021-09-05T14:00:26ZengSciendoJournal of Mechanical Engineering2450-54712015-11-01651577610.1515/scjme-2016-0004scjme-2016-0004Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded MaterialsRepka M.0Sládek J.1Sládek V.2Wünsche M.3Institute of Construction and Architecture, Slovak Academy of Sciences, 845 03 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, 845 03 Bratislava, SlovakiaInstitute of Construction and Architecture, Slovak Academy of Sciences, 845 03 Bratislava, SlovakiaDepartment of Civil Engineering, GermanyThe finite element method (FEM) is developed for coupled thermoelastic crack problems if material properties are continuously varying. The weak form is utilized to derive the FEM equations. In conventional fracture theories the state of stress and strain at the crack tip vicinity is characterized by a single fracture parameter, namely the stress intensity factor or its equivalent, J-integral. In the present paper it is considered also the second fracture parameter called as the T-stress. For evaluation of both fracture parameters the quarter-point crack tip element is developed. Simple formulas for both fracture parameters are derived comparing the variation of displacements in the quarter-point element with asymptotic expression of displacement at the crack tip vicinity. The leading terms of the asymptotic expansions of fields in the crack-tip vicinity in a functionally graded material (FGM) are the same as in a homogeneous one with material coefficients taken at the crack tip.https://doi.org/10.1515/scjme-2016-0004fgmthermoelasticityfemfracturesifst-stresses
collection DOAJ
language English
format Article
sources DOAJ
author Repka M.
Sládek J.
Sládek V.
Wünsche M.
spellingShingle Repka M.
Sládek J.
Sládek V.
Wünsche M.
Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
Journal of Mechanical Engineering
fgm
thermoelasticity
fem
fracture
sifs
t-stresses
author_facet Repka M.
Sládek J.
Sládek V.
Wünsche M.
author_sort Repka M.
title Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
title_short Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
title_full Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
title_fullStr Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
title_full_unstemmed Evaluation of Fracture Parameters for Cracks in Coupled Thermoelasticity for Functionally Graded Materials
title_sort evaluation of fracture parameters for cracks in coupled thermoelasticity for functionally graded materials
publisher Sciendo
series Journal of Mechanical Engineering
issn 2450-5471
publishDate 2015-11-01
description The finite element method (FEM) is developed for coupled thermoelastic crack problems if material properties are continuously varying. The weak form is utilized to derive the FEM equations. In conventional fracture theories the state of stress and strain at the crack tip vicinity is characterized by a single fracture parameter, namely the stress intensity factor or its equivalent, J-integral. In the present paper it is considered also the second fracture parameter called as the T-stress. For evaluation of both fracture parameters the quarter-point crack tip element is developed. Simple formulas for both fracture parameters are derived comparing the variation of displacements in the quarter-point element with asymptotic expression of displacement at the crack tip vicinity. The leading terms of the asymptotic expansions of fields in the crack-tip vicinity in a functionally graded material (FGM) are the same as in a homogeneous one with material coefficients taken at the crack tip.
topic fgm
thermoelasticity
fem
fracture
sifs
t-stresses
url https://doi.org/10.1515/scjme-2016-0004
work_keys_str_mv AT repkam evaluationoffractureparametersforcracksincoupledthermoelasticityforfunctionallygradedmaterials
AT sladekj evaluationoffractureparametersforcracksincoupledthermoelasticityforfunctionallygradedmaterials
AT sladekv evaluationoffractureparametersforcracksincoupledthermoelasticityforfunctionallygradedmaterials
AT wunschem evaluationoffractureparametersforcracksincoupledthermoelasticityforfunctionallygradedmaterials
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