A variational constitutive model for the distribution and interactions of multi-sized voids

Handle URI:
http://hdl.handle.net/10754/594229
Title:
A variational constitutive model for the distribution and interactions of multi-sized voids
Authors:
Liu, Jinxing; El Sayed, Tamer S.
Abstract:
The evolution of defects or voids, generally recognized as the basic failure mechanism in most metals and alloys, has been intensively studied. Most investigations have been limited to spatially periodic cases with non-random distributions of the radii of the voids. In this study, we use a new form of the incompressibility of the matrix to propose the formula for the volumetric plastic energy of a void inside a porous medium. As a consequence, we are able to account for the weakening effect of the surrounding voids and to propose a general model for the distribution and interactions of multi-sized voids. We found that the single parameter in classical Gurson-type models, namely void volume fraction is not sufficient for the model. The relative growth rates of voids of different sizes, which can in principle be obtained through physical or numerical experiments, are required. To demonstrate the feasibility of the model, we analyze two cases. The first case represents exactly the same assumption hidden in the classical Gurson's model, while the second embodies the competitive mechanism due to void size differences despite in a much simpler manner than the general case. Coalescence is implemented by allowing an accelerated void growth after an empirical critical porosity in a way that is the same as the Gurson-Tvergaard-Needleman model. The constitutive model presented here is validated through good agreements with experimental data. Its capacity for reproducing realistic failure patterns is shown by simulating a tensile test on a notched round bar. © 2013 The Author(s).
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division
Citation:
Liu J, Sayed TE (2013) A variational constitutive model for the distribution and interactions of multi-sized voids. International Journal of Damage Mechanics 23: 124–152. Available: http://dx.doi.org/10.1177/1056789513486907.
Publisher:
SAGE Publications
Journal:
International Journal of Damage Mechanics
Issue Date:
29-Jul-2013
DOI:
10.1177/1056789513486907
Type:
Article
ISSN:
1056-7895; 1530-7921
Sponsors:
This work was fully funded by the KAUST baseline fund.
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Jinxingen
dc.contributor.authorEl Sayed, Tamer S.en
dc.date.accessioned2016-01-19T14:43:52Zen
dc.date.available2016-01-19T14:43:52Zen
dc.date.issued2013-07-29en
dc.identifier.citationLiu J, Sayed TE (2013) A variational constitutive model for the distribution and interactions of multi-sized voids. International Journal of Damage Mechanics 23: 124–152. Available: http://dx.doi.org/10.1177/1056789513486907.en
dc.identifier.issn1056-7895en
dc.identifier.issn1530-7921en
dc.identifier.doi10.1177/1056789513486907en
dc.identifier.urihttp://hdl.handle.net/10754/594229en
dc.description.abstractThe evolution of defects or voids, generally recognized as the basic failure mechanism in most metals and alloys, has been intensively studied. Most investigations have been limited to spatially periodic cases with non-random distributions of the radii of the voids. In this study, we use a new form of the incompressibility of the matrix to propose the formula for the volumetric plastic energy of a void inside a porous medium. As a consequence, we are able to account for the weakening effect of the surrounding voids and to propose a general model for the distribution and interactions of multi-sized voids. We found that the single parameter in classical Gurson-type models, namely void volume fraction is not sufficient for the model. The relative growth rates of voids of different sizes, which can in principle be obtained through physical or numerical experiments, are required. To demonstrate the feasibility of the model, we analyze two cases. The first case represents exactly the same assumption hidden in the classical Gurson's model, while the second embodies the competitive mechanism due to void size differences despite in a much simpler manner than the general case. Coalescence is implemented by allowing an accelerated void growth after an empirical critical porosity in a way that is the same as the Gurson-Tvergaard-Needleman model. The constitutive model presented here is validated through good agreements with experimental data. Its capacity for reproducing realistic failure patterns is shown by simulating a tensile test on a notched round bar. © 2013 The Author(s).en
dc.description.sponsorshipThis work was fully funded by the KAUST baseline fund.en
dc.publisherSAGE Publicationsen
dc.subjectconstitutive modelen
dc.subjectDistribution of multi-sized voidsen
dc.subjectinteractions of multi-sized voidsen
dc.subjectporous mediaen
dc.subjectvoid growth and coalescenceen
dc.titleA variational constitutive model for the distribution and interactions of multi-sized voidsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalInternational Journal of Damage Mechanicsen
kaust.authorLiu, Jinxingen
kaust.authorEl Sayed, Tamer S.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.