Assignment of chapter 4 Table 2.1 Typical Mechanical Properties of a Unidirectional Lamina (SI System of...

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Assignment of chapter 4 Table 2.1 Typical Mechanical Properties of a Unidirectional Lamina (SI System of Units) Glass/ Boron/ Property Symbol Units epoxy epoxy Graphite/ epoxy Fiber volume fraction V 0.45 0.50 0.70 Longitudinal elastic modulus E GPa 38.6 204 181 Transverse elastic modulus E2 GPa 8.27 18.50 10.30 Major Poisson's ratio V12 0.26 0.23 0.28 Shear modulus G12 GPa 4.14 5.59 7.17 Ultimate longitudinal tensile strength (ult MPa 1062 1260 1500 Ultimate longitudinal compressive strength (ult MPa 610 2500 1500 Ultimate transverse tensile strength (0)ult MPa. 31 61 40 Ultimate transverse compressive strength (0%) ult MPa 118 202 246 Ultimate in-plane shear strength (512) uit MPa 72 67 68 Longitudinal coefficient of thermal expansion m/m/C 8.6 6.1 0.02 Transverse coefficient of thermal expansion m/m/C 22.1 30.3 22.5 Longitudinal coefficient of moisture expansion B m/m/kg/kg 0.00 0.00 0.00 Transverse coefficient of moisture expansion m/m/kg/kg 0.60 0.60 0.60 (Source: Reprinted with permission from Tsai, S. W. and Hahn, H. T., Introduction to Composite Materials, Technomic Publishing Co., Inc., Lancaster, PA, Table 1.7, p. 19; Table 7.1, p. 292; Table 8.3, p. 344.) 4-1 A [45]s glass fiber/epoxy matrix laminate (V=0.45) and thickness of each ply is 0.5mm, find it's stiffness matrix of [A], [B] and [D]. 4-2 The laminate in 4-1 is subjected to a load of NN, = 250N/mm. Find the local strain and stress in each lamina. 4-3 Find the in-plane and flexural effective elastic moduli of the laminate in 4-1. In-plane effective elastic moduli of a laminate E = 1 hA* 3/4 effective in-plane extensional modulus in X-direction; Ein = 1 hA* 22 3/4 effective in-plane extensional modulus in Y-direction; 1 hA* 66 A* in 12 V vin 3/4 effective in-plane shear modulus; 4* 3/4 effective in-plane major Poisson's ratio; A* 12 A* 22 3/4 effective in-plane minor Poisson's ratio; with in V in xy yx E. Ey Flexural effective elastic moduli of a laminate E E 12 hD 3/4 effective flexural modulus in X-direction; 12 = Gy = xy hD* * 22 3/4 effective flexural modulus in Y-direction; 12 hD* D* 12 = xy D* with 66 3/4 effective flexural shear modulus; *11 3/4 effective flexural major Poisson's ratio; D*.. 12 D* v VJ 22 3/4 effective flexural minor Poisson's ratio; = E E Assignment of chapter 4 Table 2.1 Typical Mechanical Properties of a Unidirectional Lamina (SI System of Units) Glass/ Boron/ Property Symbol Units epoxy epoxy Graphite/ epoxy Fiber volume fraction V 0.45 0.50 0.70 Longitudinal elastic modulus E GPa 38.6 204 181 Transverse elastic modulus E2 GPa 8.27 18.50 10.30 Major Poisson's ratio V12 0.26 0.23 0.28 Shear modulus G12 GPa 4.14 5.59 7.17 Ultimate longitudinal tensile strength (ult MPa 1062 1260 1500 Ultimate longitudinal compressive strength (ult MPa 610 2500 1500 Ultimate transverse tensile strength (0)ult MPa. 31 61 40 Ultimate transverse compressive strength (0%) ult MPa 118 202 246 Ultimate in-plane shear strength (512) uit MPa 72 67 68 Longitudinal coefficient of thermal expansion m/m/C 8.6 6.1 0.02 Transverse coefficient of thermal expansion m/m/C 22.1 30.3 22.5 Longitudinal coefficient of moisture expansion B m/m/kg/kg 0.00 0.00 0.00 Transverse coefficient of moisture expansion m/m/kg/kg 0.60 0.60 0.60 (Source: Reprinted with permission from Tsai, S. W. and Hahn, H. T., Introduction to Composite Materials, Technomic Publishing Co., Inc., Lancaster, PA, Table 1.7, p. 19; Table 7.1, p. 292; Table 8.3, p. 344.) 4-1 A [45]s glass fiber/epoxy matrix laminate (V=0.45) and thickness of each ply is 0.5mm, find it's stiffness matrix of [A], [B] and [D]. 4-2 The laminate in 4-1 is subjected to a load of NN, = 250N/mm. Find the local strain and stress in each lamina. 4-3 Find the in-plane and flexural effective elastic moduli of the laminate in 4-1. In-plane effective elastic moduli of a laminate E = 1 hA* 3/4 effective in-plane extensional modulus in X-direction; Ein = 1 hA* 22 3/4 effective in-plane extensional modulus in Y-direction; 1 hA* 66 A* in 12 V vin 3/4 effective in-plane shear modulus; 4* 3/4 effective in-plane major Poisson's ratio; A* 12 A* 22 3/4 effective in-plane minor Poisson's ratio; with in V in xy yx E. Ey Flexural effective elastic moduli of a laminate E E 12 hD 3/4 effective flexural modulus in X-direction; 12 = Gy = xy hD* * 22 3/4 effective flexural modulus in Y-direction; 12 hD* D* 12 = xy D* with 66 3/4 effective flexural shear modulus; *11 3/4 effective flexural major Poisson's ratio; D*.. 12 D* v VJ 22 3/4 effective flexural minor Poisson's ratio; = E E