recovered.Unloading from a higher stress level follows a path CD,which has a smaller slope than AB.The difference in slope between the two unloading paths AB and CD is evidence that the 90 plies fail in a progressive manner.Neglect- ing the small residual strains after unloading,Hahn and Tsai [6]predicted the elastic modulus Ep of the damaged laminate as E ED=1+[(AE/AoE)-11(1-ox/o) (4.9) 4.1.1.4 Multidirectional Laminates Tensile stress-strain curves for laminates containing different fiber orientations in different laminas are in general nonlinear.A few examples are shown in Figure 4.9.For the purposes of analysis,these curves are approximated by a number of linear portions that have different slopes.When these linear portions are extended,a number of knees,similar to that observed in a cross-ply laminate,can be identified.The first knee in these diagrams is called the first ply failure (FPF)point.Many laminates retain a significant load-carrying capacity beyond the FPF point,but for some laminates with high notch sensitivity,failure occurs just after FPF (Table 4.2).Furthermore,cracks appearing at the FPF may increase the possibility of environmental damage (such as moisture pickup)as well as fatigue failure.For all these reasons,the FPF point has special importance in many laminate designs Angle-ply laminates containing [te]layups exhibit two kinds of stress- strain nonlinearity (Figure 4.10).At values of 0 closer to 0,a stiffening effect 140 1104 120 828 [0/±451s 80 552 苏 ssenS 40 [0/±45/90]s 276 [±45/90]s 0 0 0 2 6 Strain(10-5) FIGURE 4.9 Typical tensile stress-strain diagrams for multidirectional laminates. 2007 by Taylor Francis Group,LLC.recovered. Unloading from a higher stress level follows a path CD, which has a smaller slope than AB. The difference in slope between the two unloading paths AB and CD is evidence that the 908 plies fail in a progressive manner. Neglect￾ing the small residual strains after unloading, Hahn and Tsai [6] predicted the elastic modulus ED of the damaged laminate as ED ¼ E 1 þ [(AE=A0E11) 1](1 sk=sL) : (4:9) 4.1.1.4 Multidirectional Laminates Tensile stress–strain curves for laminates containing different fiber orientations in different laminas are in general nonlinear. A few examples are shown in Figure 4.9. For the purposes of analysis, these curves are approximated by a number of linear portions that have different slopes. When these linear portions are extended, a number of knees, similar to that observed in a cross-ply laminate, can be identified. The first knee in these diagrams is called the first ply failure (FPF) point. Many laminates retain a significant load-carrying capacity beyond the FPF point, but for some laminates with high notch sensitivity, failure occurs just after FPF (Table 4.2). Furthermore, cracks appearing at the FPF may increase the possibility of environmental damage (such as moisture pickup) as well as fatigue failure. For all these reasons, the FPF point has special importance in many laminate designs. Angle-ply laminates containing [±u] layups exhibit two kinds of stress– strain nonlinearity (Figure 4.10). At values of u closer to 08, a stiffening effect 140 120 80 40 0 0 2 4 Strain (10−6) [0/±45]S [0/±45/90]S [±45/90]S Stress (MPa) Stress (ksi) 6 1104 828 552 276 0 FIGURE 4.9 Typical tensile stress–strain diagrams for multidirectional laminates.
2007 by Taylor & Francis Group, LLC.