Failure resistance of three-layer structural elements being bent with a crack in the layer in tension

Abstract

UDC 539.3 The strength of bodies of laminar structure depends to a significant degree upon the condition of the interfaces of the layers. An increase in the failure resistance of such structures is provided by the formation of shear separations absorbing a portion of the elastic energy liberated during crack development [i]. An analysis of the stresses at the tip of a crack passing through an interface [2] shows that shear separations of constant dimensions promote a decrease in the stress intensity factors and, consequently, an increase in the critical loads. The purpose of this work was to investigate on the basis of the force hypotheses of strength the limiting state of a laminar structure with a crack the front'of which enters into the interface of the layers and with a separation the dimensions of which are determined by the stressed state of the structure. Let us consider a three-layer plate with a rigid reinforcing layer and a thickness significantly ls than the thickness of the matrix layers. The plate is loaded by the bending moment M and the layer in tension is weakened by a through craok with free edges (Fig. i). Since the tensile strength of the center reinforcing layer is significantly higher than the tensile strengths of the matrix layers, the propagation of the crack is determined by the stressed state in the layer in compression. Let us represent the stresses in the plate by the sum of the stresses of pure bending in a continuous three-layer panel and the stresses in the vicinity of the crack. In order to solve the first problem let us use for each layer the equations of the theory of plates taking into consideration the Kirchhoff-Love hypothesis [3]. Then we obtain: