Generalized plane strain analysis of a bimaterial composite containing a free surface normal to the interface
- PDF / 1,173,092 Bytes
- 14 Pages / 576 x 792 pts Page_size
- 60 Downloads / 230 Views
The elastic plane strain Green's function calculated in earlier papers is modified to account for generalized plane strain and applied to calculating the stress and the displacement field in a bimaterial composite containing a free surface normal to the interface and subjected to an out-of-plane load. The result is obtained in terms of a closed integral representation which is evaluated numerically as well as analytically. The method is applied to a cubic solid containing a S-5 grain boundary and to fiber-reinforced laminated composites. The singularities in the stress are identified and discussed.
I. INTRODUCTION The elastic plane strain Green's function for an infinite anisotropic bimaterial composite containing a planar interface was calculated in Refs. 1 and 2, henceforth referred to as I and II. In the preceding paper (Ref. 3, henceforth referred to as III) this Green's function was extended to a composite containing a free surface normal to the interface. In this paper we extend the mathematical technique developed in III to the generalized plane strain problem for the same solid. In particular, we calculate the displacement field and the stress distribution in a cubic solid containing a S-5 grain boundary and also in fiber-reinforced laminated composites with different fiber orientations. The solids are assumed to be subjected to an out-of-plane load. The fiber-reinforced composite materials are of special interest because of their engineering applications. The effect of a free surface on the stress distribution in a laminated composite subjected to generalized plane strain has been studied in many earlier papers4"11 (see also the references given in III). The general result is that the stress is singular at the intersection of the free surface and the interface. The main effort in the literature has been devoted to identification and characterization of these singularities. This problem is important because damage initiates at the free edges, often as ply cracks and delaminations. Usually, these delaminations are the source of compressive failure in reverse fatigue loading.12 The elastic plane strain Green's function gives the response of a solid to an applied unit force. The appli-
a)
On attachment from The Ohio State University, Columbus, Ohio 43210. ^Present address: Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.
cation of the Green's function method to a generalized plane strain problem is not quite straightforward, because in this case only the out-of-plane component of the displacements (or strain) is specified and not the applied forces. We have, therefore, extended the Green's function method as developed in I, II, and III so that it can be applied to the generalized plane strain problems. In this paper we find that, in general, the nature of singularities in the generalized plane strain problem is similar to that obtained in III. The power of a singularity depends upon the elastic constants of the constituents wh
Data Loading...
