Tham khảo tài liệu 'advanced mechanics of composite materials episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 4. Mechanics of a composite layer 197 Fig. . A cross-ply layer in a plane stress state. - s Fig. . Stress-strain diagrams of a unidirectional ply simulating its behavior in the laminate and allowing for cracks in the matrix. 1 For the first stage of loading before the cracks appear the strains are calculated with the aid of Eqs. and providing e7 ơ ey1 and ỵ y ơ where ơ ơx ơy Txy is the given combination of stresses. Using Eqs. we find stresses ơ1 ơ2 and T12 in principal material coordinates for all the plies. í í vx zi flzitỡ-rmí-nfTiZ r AtTil inofi An ofrAOCAO ZT ZT onrl T xirTìì inrliifA fTiZ A-t cf 2 we determine the combination of stresses ơ1k ơ2k and T12k Which induce the first failure of the matrix in some ply and indicate the number of this ply say k applying the appropriate strength criterion see Section . Then the corresponding stresses rr zf ZT T 1 111 1 Q I t l 1 tic t 1 2 3tzr 1 t 1 t T t 1 zf 1 qIpiiIq I í I ơ ơx ơy Txy and strains x ơ y ơ and Yxy ơ are calculated. 3 To proceed . to study the material behavior for ơ ơ we need to consider two possible cases for the layer stiffnesses. For this purpose we should write Eqs. for stiffness coefficients in a more general form . 198 Advanced mechanics of composite materials m n V M1 VTÍO A11 ỷ E1 h0 ỷ E2 h90 mn 4_VĩOĩ I V tjj A22 7 E2 h0 . E1 h90 mn 4_V . i Oiy V j -p j T -j A12 v12 E1 h0 2- 1 v12E1 h90 mn 4 . _ V r ĩ I V .jKSj A 44 G12 h0 G12 h90 u li r ỉA _ h i h h j _ h j th where h0 h0 h and h90 h90 h. a If ơ2k 0 in the kth ply it can work only along the fibers and we should calculate the stiffnesses of the degraded layer taking Ek 0 Gk12 0 and vf2 0 in Eqs. . b If ơ2k 0 in the kth ply it cannot work only in shear so we should take Gk12 0 in Eqs. . Thus we find coefficients Af st 11 12 22 44 corresponding to the second stage of loading with one degraded ply . Using Eqs. and we can determine Z U 2 J 7 1 111 1 lii l . .vni . i
