EXAMPLE PROBLEM 4.1 复合材料模量预测(1) A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having 纤维沿外力方向 modulus of elasticity of 69 GPa resin that, when hardened, displays a modulus of 3. 4 GPa. (a) Compute the modulus of elasticity of this composite in E=VmEm+ ret the longitudinal direction (b)If the cross-sectional area is 250 mmand a stress of 50 MPa is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and (c)Determine the strain that is sustained by each phase when the stress in part b is applied consists of 40 vol% of glass fibers having a modulus of elasticity consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, of 69 GPa and 60 vol% of a polyester resin that, when hardened displays a modulus of 3.4 GPa. fthe cross-sectional area is 250 mm2 and a stress of 50 MPa Compute the modulus of elasticity of this composite in the plied in this longitudinal direction, compute the magnitude of rried by each of the fiber and matrix pha Solution: First find the ratio of fiber load to matrix load SOLUTION (a) The modulus of elasticity of the composite is calculated using E=(3.4GPa)0.6)+(69GPa)0.4)=30GPa 13.5or Fm(34GPa)0.6) A continuous and aligned glass fiber-reinforced consists of 40 vol%of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened consists of 40 vol%o ter resin that. when hardened displays a modulus of 3. 4 GPa. The cross-sectional area is 250 mm?2 (b)If the cross-sectional area is 250 mm?and a stress of 50 MPaI and a stress of 50 MPa is applied is applied in this longitudinal direction, compute the magnitude the load carried by each of the fiber and matrix phases (c)Determine the strain that is sustained by each phase when the stress in part b is applied. The total force sustained by the composite F F2=A2a=(250mm250MPa)=12,500N For stress calculations, phase cross-sectional areas are This total load is just the sum of the loads carried by fiber and necessary An=V42=(060250mm2)=150mn 4=V=(0.4)250mm2)=100mm2 whereas FrFe-F.=12, 500N-860N=11, 640N3 复合材料模量预测（1） A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa. (a) Compute the modulus of elasticity of this composite in the longitudinal direction. (b) If the cross-sectional area is 250 mm2 and a stress of 50 MPa is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and matrix phases. (c) Determine the strain that is sustained by each phase when the stress in part b is applied. EXAMPLE PROBLEM 4.1 (a) The modulus of elasticity of the composite is calculated using Equation Ec = EmVm + Ef Vf : Ec = (3.4 GPa)(0.6) + (69 GPa)(0.4) = 30 GPa SOLUTION A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa. (a) Compute the modulus of elasticity of this composite in the longitudinal direction. Solution: First find the ratio of fiber load to matrix load, using Equation ， m m f f m f E V E V F F = f m m f or F F F F 13.5 13.5 (3.4 GPa)(0.6) (69 GPa)(0.4) = = = A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa. (b) If the cross-sectional area is 250 mm2 and a stress of 50 MPa is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and matrix phases. The total force sustained by the composite Fc: Fc = Acσ = (250 mm2)(50 MPa) = 12,500 N This total load is just the sum of the loads carried by fiber and matrix phases, that is 13.5 Fm + Fm = 12,500 N or Fm = 860 N whereas Ff = Fc - Fm = 12,500 N - 860 N = 11,640 N A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa. (b) If the cross-sectional area is 250 mm2 and a stress of 50 MPa is applied in this longitudinal direction, compute the magnitude of the load carried by each of the fiber and matrix phases. A continuous and aligned glass fiber-reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa. The cross-sectional area is 250 mm2 and a stress of 50 MPa is applied. (c) Determine the strain that is sustained by each phase when the stress in part b is applied. For stress calculations, phase cross-sectional areas are necessary: Am = VmAc = (0.6)(250 mm2) = 150 mm2 Af = Vf Ac = (0.4)(250 mm2) = 100 mm2