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ADVANCED MECHANICS OF COMPOSITE MATERIALS Episode 6

Tham khảo tài liệu 'advanced mechanics of composite materials episode 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 162 Advanced mechanics of composite materials As an example consider a boron-aluminum unidirectional composite whose experimental stress-strain diagrams Herakovich 1998 are shown in Fig. 4.17 circles along with the corresponding approximations solid lines plotted with the aid of Eqs. 4.65 . 4.3. Unidirectional anisotropic layer Consider now a unidirectional layer studied in the previous section and assume that its principal material axis 1 makes some angle Ộ with the x-axis of the global coordinate frame see Fig. 4.18 . An example of such a layer is shown in Fig. 4.19. 4.3.1. Linear elastic model Constitutive equations of the layer under study referred to the principal material coordinates are given by Eqs. 4.55 and 4.56 . We need now to derive such equations for the global coordinate frame x y and z see Fig. 4.18 . To do this we should transfer stresses O1 O2 T12 T13 T23 acting in the layer and the corresponding strains S1 S2 Y12 Y13 Y23 into stress and strain components Ox Oy Txy Txz Tyz and Sx Sy Yxy Yxz Yyz using Eqs. 2.8 2.9 and 2.21 2.27 for coordinate transformation of stresses and strains. According to Fig. 4.18 the directional cosines Eqs. 2.1 for this transformation are we take x 1 y 2 z 3 lx1x c lx 1 y S lx1z 0 ly1x -S ly1y c ly1z 0 4.66 lz1x 0 lz1y 0 lz1z 1 where c cos Ộ and 5 sin ệ. Using Eqs. 2.8 and 2.9 we get O1 ơxC2 OyS2 2ĩxyCS O2 OxS2 ơyC1 - 2txyCS T12 Oy - Ox cs Txy c2 - S2 4.67 T13 Txzc TyzS T12 TxzS Tyzc The inverse form of these equations is Ox 01c2 Ơ2S2 - 2T12cs Oy O1S2 02c2 2T12cs Chapter 4. Mechanics of a composite layer 163 ơ2 MPa t12 MPa 140 r 0 I_I_I_I_I_I_I_I_I g 12 012345678 b Fig. 4.17. Calculated solid lines and experimental circles stress-strain diagrams for a boron-aluminum composite under transverse loading a and in-plane shear b . 164 Advanced mechanics of composite materials Fig. 4.18. A composite layer consisting of a system of unidirectional plies with the same orientation. Fig. 4.19. An anisotropic outer layer of a composite