Solution of bonded bimaterial problem of two interfaces subjected to concentrated forces and couples

Abstract

A closed form solution is derived for the bonded bimaterial planes at two interfaces. The bonded planes with two interfaces are symmetric with respect to the interface, which is straight. A rational mapping function and complex stress functions are used for the analysis. The problem is reduced to a Riemann-Hilbert problem. Two interfaces problem to derive the general solution is more difficult than one interface problem. As a demonstration of geometry, semi-strips bonded at two parts at the ends of strips are considered. The solution of different geometrical shapes can be obtained by changing the mapping function. Concentrated forces and couples are applied to the each strip. The first derivative of complex stress functions which does not include integral terms with regard to variable of the mapping plane is achieved. Therefore, there is no need of numerical integration to calculate stress components and to determine unknown coefficients in complex stress function. This is very benefit. All elastic constants in complex stress functions are expressed by Dundurs' parameters. Stress distributions are shown for different lengths of the interface.

Debonding fracture of bonded bimaterial semi‐strips subjected to concentrated forces and couples

“…However, the first derivative F j 1 (t j ), F j 2 (t j ), and F j 3 (t j ) can be derived as the form without the integration regarding variable t j , though these integral cannot be carried [5]. Therefore, the numerical integration regarding variable t j is unnecessary to calculate unknown values A jk in the stress function φ j (t j ), stress components, complex intensity factors.…”

“…This is very beneficial. I j (0)(j = 1, 2, 3) is stated [5]. All material constants are expressed by Dundurs' parameters in the complex stress functions φ j (t j ) and ψ j (t j ).…”

“…, 60). δ is the arm length of couple forces [5]. The function χ j (t j ) is the following Plemelj function:…”

“…The following studies were carried out [6][7][8][9][10] and a review paper of interface fracture and delamination of composites was reported [11]. In the previous paper [5], closed stress functions of a bonded bimaterial problem of two interfaces subjected to concentrated forces and couples were derived, and as a demonstration, some figures of stress distribution for bonded bimaterial semi-strips were shown. In the present paper, using this solution of bonded bimaterial semi-strips subjected to concentrated forces and couples obtained, complex stress intensity factors and stress intensity of debondings (SID) corresponding the square root of strain energy release rate are calculated.…”

“…It is important to establish the method for the mechanical strength and to know fracture behaviors at the debonding tip. References of many bimaterial problems have been listed in [1][2][3][4][5] and in their references. The following studies were carried out [6][7][8][9][10] and a review paper of interface fracture and delamination of composites was reported [11].…”