We analyse a problem of anti-plane shear in a bimaterial plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. The problem can be considered as modelling bimaterial ceramics which are joined with a thin adhesive substance. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener-Hopf techniques and allows us to obtain an expression for an important constant σ0 (which may be used in a fracture criterion) that describes the leading order of tractions near the crack tip for the unperturbed problem. We present computations that demonstrate how σ0 varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion's presence having an amplifying or shielding effect on the propagation of the main crack.

Application of Imperfect Interface Weight Function Techniques for Modelling of Glued Structures Containing Cracks and Small Defects / Vellender, A.; Mishuris, G.; Piccolroaz, Andrea. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - 451:1(2013), pp. 1-6. [10.1088/1742-6596/451/1/012013]

Application of Imperfect Interface Weight Function Techniques for Modelling of Glued Structures Containing Cracks and Small Defects

Piccolroaz, Andrea
2013-01-01

Abstract

We analyse a problem of anti-plane shear in a bimaterial plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. The problem can be considered as modelling bimaterial ceramics which are joined with a thin adhesive substance. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener-Hopf techniques and allows us to obtain an expression for an important constant σ0 (which may be used in a fracture criterion) that describes the leading order of tractions near the crack tip for the unperturbed problem. We present computations that demonstrate how σ0 varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion's presence having an amplifying or shielding effect on the propagation of the main crack.
2013
1
Vellender, A.; Mishuris, G.; Piccolroaz, Andrea
Application of Imperfect Interface Weight Function Techniques for Modelling of Glued Structures Containing Cracks and Small Defects / Vellender, A.; Mishuris, G.; Piccolroaz, Andrea. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - 451:1(2013), pp. 1-6. [10.1088/1742-6596/451/1/012013]
File in questo prodotto:
File Dimensione Formato  
1742-6596_451_1_012013.pdf

accesso aperto

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 457.26 kB
Formato Adobe PDF
457.26 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/32858
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact