Interactions between multiple rigid lamellae in a ductile metal matrix: Shear band magnification and attenuation in localization patterns

A ductile matrix material containing an arbitrary distribution of parallel and stiff lamellar (’rigid-line’) inclusions is considered, subject to a prestress state provided by a simple shear aligned parallel to the inclusion lines. Because the lamellae have negligible thickness, the simple shear pre...

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Bibliographic Details
Published inJournal of the mechanics and physics of solids Vol. 165; p. 104925
Main Authors Giarola, Diana, Dal Corso, Francesco, Capuani, Domenico, Bigoni, Davide
Format Journal Article
LanguageEnglish
Published London Elsevier Ltd 01.08.2022
Elsevier BV
Subjects
Attenuation
Boundary integral method
Edge dislocations
Ellipticity
Failure mechanisms
Inclusions
Integral equations
Localization
Material instability
Nonlinear elasticity
Perturbation
Prestressing
Shear bands
Thickening
Material instability
Nonlinear elasticity
Shear bands
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Summary:A ductile matrix material containing an arbitrary distribution of parallel and stiff lamellar (’rigid-line’) inclusions is considered, subject to a prestress state provided by a simple shear aligned parallel to the inclusion lines. Because the lamellae have negligible thickness, the simple shear prestress state remains uniform and its amount can be high enough to drive the matrix material on the verge of ellipticity loss. Close to this critical stage, a uniform remote Mode I perturbation realizes shear band formation, growth, interaction, thickening or thinning. This two-dimensional problem is solved through the derivation of specific boundary integral equations, holding for a nonlinear elastic matrix material uniformly prestressed; the related numerical treatment is specifically tailored to capture the stress singularity present at the inclusion tips. Results show how complex localized deformation patterns form, so explaining features related to the failure mechanisms of ductile materials reinforced with stiff and thin inclusions. In particular, the influence of the inclusion distribution on the shear bands pattern is disclosed. Conditions for the magnification (the attenuation) of the localized deformations are revealed, fostering the progress (the setback) of the failure process.
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content type line 14
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2022.104925