JEC COMPOSITES MAGAZINE - Issue #37 - December 2007 - 65

KNOW-HOW Mechanical design g…/… Stress concentration factors Where corresponds to the stress at a point in the notch edge and to the stress at the same point but for the unnotched plate. [9] Plates with relations A/H=5 and d/H= 0.1; 0.2; 0.3; 0.4; 0.5 and 0.6 were studied, where A is the plate length, H the plate width and D the notch diameter. Figure 2 shows the stress concentration factor for different composite materials in a unidirectional laminate for φ =0° . In this case, the stress corresponds to the maximum tension stress produced at the edges of the notches over the regular diameter in the load direction. The elastic properties of the materials used in this work are shown in Table 1. It can be appreciated in Figure 2 that the stress concentration factor in a single-ply composite whose fibres are laid out in the direction of the effort is in all cases higher than in isotropic materials. Table 1: Properties of composites Fig. 3: Stress concentration factor for different fibre layouts in relation to the global axis (a. S-glass/epoxy single ply b. T300/5208 carbon/epoxy) Fibre/matrix composite T300/5208 carbon/epoxy AS4/3501-6 carbon/epoxy E-glass/epoxy S-glass/epoxy Steel Kevlar 149/epoxy E1 (GPa) 181 142 39 43 210 87 E2 (GPa) 10.3 10.3 8.6 8.9 210 5.5 G12 (GPa) 7.17 7.2 3.8 4.5 80.76 2.2 υ12 0.28 0.27 0.28 0.27 0.30 0.34 laid out in a +φ angle in relation to the effort direction (Figure 3) shows that this relation is maximum for φ= 0° and minimum for φ= 90°. For 30º, 45º and 60º, the curves remain among those mentioned before. It can be seen that carbon/epoxy composites have a higher SCF than S-glass/epoxy composites. Laminates Practically speaking, composites are built from laminates made of several layers with various orientations. In the classical laminated plate theory, [7-8] the stress resultants are defined in each layer thickness (Figure 4). Stress varies in each of the layers, so the efforts are obtained by the addition of all these stresses over each one of them: (8) where Nx , Ny , Nxy are normal and tangential forces in plane by length unit; Vx , Vy are shear forces by length unit, Mx , My , Mxy Fig.2: Stress concentration factor for φ =0° in different composite materials The increment of SCF is 57% for E-glass/epoxy composites, 100% to 120% for carbon/epoxy composites and 160% for epoxy resins with aramid fibres. It can be seen that the stress concentration factor increases with d/H, while the percentages mentioned before are kept. The highest stress is always produced at the edge of the notch, at 90º in relation to the direction of the effort applied. Figure 3a shows the stress concentration factor variation for an S-glass/epoxy single ply with fibres oriented in different angles in relation to the applied stress direction. The same variation is found for a plate of T300/5208 carbon/epoxy (Figure 3b). Analysing the stress concentration factors for plates with fibres Fig.4: Plate efforts are the plate moments by length unit, k is the layer number counting from the bottom up, N is the number of layers, and zk is the coordinate of the top surface of the k layer. Considering that plate strains are: (9) th where {å0} are the middle surface strains, and {k} its curvature; No37 December 2007 / JEC Composites Magazine

JEC COMPOSITES MAGAZINE - Issue #37 - December 2007

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #37 - December 2007