Application of imperfect interface weight function techniques for modelling of glued structures containing cracks and small defects

International Symposium on Dynamic Deformation and Fracture of Advanced Materials 2013

物理学;材料科学

Vellender, A.^1,2 ; Mishuris, G.^1,2 ; Piccolroaz, A.^3

Institute of Mathematics and Physics, Aberystwyth University, Physical Sciences Building, Aberystwyth, Ceredigion, SY23 3BZ, United Kingdom^1

Enginsoft Trento, Via della Stazione 27-fraz. Mattarello, 38123, Trento, Italy^2

Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy^3

关键词: Adhesive substances;    Fracture criteria;    Imperfect interface;    Material stiffness;    Perturbation Analysis;    Semi-infinite crack;    Special solutions;    Wiener-Hopf techniques;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/451/1/012013/pdf
DOI  :  10.1088/1742-6596/451/1/012013

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

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.