where Ao =net cross-sectional area of the 0 plies 490=net cross-sectional area of the 90 plies A=A0+A90 At the knee,the laminate strain is equal to the ultimate tensile strain sru of the 90 plies.Therefore,the corresponding stress level in the laminate is ok ESTU, (4.6 where ok is the laminate stress at the knee. If90 plies are assumed to be completely ineffective after they fail,the second- ary modulus(slope after the knee)Es of the laminate can be approximated as E= A0 En. (4.7) A Failure of the laminate occurs at the ultimate tensile strain sLu of the 0 plies. Therefore,the laminate failure stress oF is CF =Ok +Es(SLU -STU). (4.8) Unloading of the cross-ply laminate from a stress level oL above the knee follows a path AB (Figure 4.8)and leaves a small residual strain in the laminate.Reloading takes place along the same path until the stress level oL is recovered.If the load is increased further,the slope before unloading is also A OL k BD Strain FIGURE 4.8 Unloading and reloading of a [0/90]s laminate. 2007 by Taylor&Francis Group.LLC.where A0 ¼ net cross-sectional area of the 08 plies A90 ¼ net cross-sectional area of the 908 plies A ¼ A0 þ A90 At the knee, the laminate strain is equal to the ultimate tensile strain «TU of the 908 plies. Therefore, the corresponding stress level in the laminate is sk ¼ E«TU, (4:6) where sk is the laminate stress at the knee. If 908 plies are assumed to be completely ineffective after they fail, the second￾ary modulus (slope after the knee) Es of the laminate can be approximated as Es ¼ A0 A E11: (4:7) Failure of the laminate occurs at the ultimate tensile strain «LU of the 08 plies. Therefore, the laminate failure stress sF is sF ¼ sk þ Esð Þ «LU «TU : (4:8) Unloading of the cross-ply laminate from a stress level sL above the knee follows a path AB (Figure 4.8) and leaves a small residual strain in the laminate. Reloading takes place along the same path until the stress level sL is recovered. If the load is increased further, the slope before unloading is also A sL sk C B D Stress Strain FIGURE 4.8 Unloading and reloading of a [0=90]S laminate.
2007 by Taylor & Francis Group, LLC.