The strains can be written as: e-→ 0 e 0 0 e ⑩ or ① Then for the composite (m+f),one has 1 E1= On the other hand,using direct calculation leads to (see Figure 10.2) △(em+ep em+er =EVm+EV m ① then: 1 1 =,+耳oy 1 E, V型+ or E=En a-+月 (10.4) Remarks: Due to the above simplifications that allow the possibility for relative sliding along the and z directions at the interface,the transverse modulus E, above may not be accurate. One finds in the technical literature many more complex formulae giving E.However,none can provide guaranteed good result. Taking into consideration the load applied (see Figure 10.2),:the modulus E,that appears in Equation 10.4 is the modulus of elasticity of the fiber in a direction that is perpendicular to the fiber axis.This modulus can be very different from the modulus along the axis of the fiber,due to the anisotropy that exists in fibers.2 This point was discussed in Paragraph 3.3.1. 2003 by CRC Press LLCThe strains can be written as: Then for the composite (m + f ), one has On the other hand, using direct calculation leads to (see Figure 10.2) then: (10.4) Remarks:
Due to the above simplifications that allow the possibility for relative sliding along the l and z directions at the interface, the transverse modulus Et above may not be accurate.
One finds in the technical literature many more complex formulae giving Et . However, none can provide guaranteed good result.
Taking into consideration the load applied (see Figure 10.2),: the modulus Ef that appears in Equation 10.4 is the modulus of elasticity of the fiber in a direction that is perpendicular to the fiber axis. This modulus can be very different from the modulus along the axis of the fiber, due to the anisotropy that exists in fibers.2 2 This point was discussed in Paragraph 3.3.1. e e
0 0 0 et 0 0 0 e z m or f Æ et 1 Et = ----st et D em + ef ( ) em + ef ------------------------ et m Vm et f = = + Vf 1 Et ----st 1 Em ------st Vm 1 Ef = + ---- st Vf 1 Et ---- Vm Em ------ Vf Ef + ---- or Et Em 1 1 – Vf ( ) Em Ef + ------Vf = = ----------------------------------- TX846_Frame_C10 Page 217 Monday, November 18, 2002 12:25 PM © 2003 by CRC Press LLC