and in developing': +0_ 60 1 2 rupture npure 2 (0,+0)+20 (rupture rupture ++ (14.5) 2 t21 Tetrupture izrupture Remark:For the case of a "three-dimensional"orthotropic material,an analogous reasoning to the previous presentation leads to a more general criterion,which can be written as: O/rupt- 12 -≤1 iz rupt. Lz(rupt. 14.2.3 Case of a Unidirectional Ply Under In-Plane Loading When the stress state is plane-stress,in the plane defined by the axes t,t (see Figure 14.2),one has 0z=Tt红=Tz=0 Equation 14.5 is simplified,and one obtains what is called "the Hill-Tsai criterion" for a ply subject to stresses within its plane: oi o OO: <1 (14.6 2 Oi rupture Remarks: The rupture strengths of the "fiber/matrix"plies are different in tension and in compression.'Do not forget to place in the denominator of each of the first three terms of Equation 14.6 the values of the rupture strengths Attention,this is not valid for a fabric that is not transversely isotropic!(see Application 18.2.10). s See values in Section 3.3.3. 2003 by CRC Press LLCand in developing 4 : (14.5) Remark: For the case of a “three-dimensional” orthotropic material, an analogous reasoning to the previous presentation leads to a more general criterion, which can be written as: 14.2.3 Case of a Unidirectional Ply Under In-Plane Loading When the stress state is plane-stress, in the plane defined by the axes
,t (see Figure 14.2), one has Equation 14.5 is simplified, and one obtains what is called “the Hill–Tsai criterion” for a ply subject to stresses within its plane: (14.6) Remarks:
The rupture strengths of the “fiber/matrix” plies are different in tension and in compression.5 Do not forget to place in the denominator of each of the first three terms of Equation 14.6 the values of the rupture strengths 4 Attention, this is not valid for a fabric that is not transversely isotropic! (see Application 18.2.10). 5 See values in Section 3.3.3. s
2 s
rupture 2 ------------------- s t 2 s z 2 + s t rupture 2 ------------------- s
s
rupture 2 + – ------------------- st + sz ( ) szst 1 s
rupture 2 ------------------- 2 s t rupture 2 – ------------------ Ë ¯ Ê ˆ + º º t
t 2 t
z 2 + t
t rupture 2 -------------------- t tz 2 t tz rupture 2 + + -------------------- £ 1 s
2 s
rupt. 2 ------------- st 2 strupt. 2 ------------ sz 2 sz rupt. 2 ------------- 1 s
rupt. 2 ------------- 1 strupt. 2 ------------ 1 sz rupt. 2 + – ------------- Ë ¯ Ê ˆ + + – s
st º º 1 strupt. 2 ------------ 1 sz rupt. 2 ------------- 1 s
rupt. 2 + – ------------- Ë ¯ Ê ˆ stsz 1 sz rupt. 2 ------------- 1 s
rupt. 2 ------------- 1 strupt. 2 + – ------------ Ë ¯ Ê ˆ – – szs
º º t
t 2 t
t rupt. 2 -------------- ttz 2 ttz rupt. 2 -------------- t z
2 t z
rupt. 2 +++ -------------- £ 1 sz = == t
z ttz 0 s
2 s
rupture 2 ------------------ st 2 st rupture 2 ------------------ s
st s
rupture 2 ------------------ t
t 2 t
t rupture 2 + – + ------------------- < 1 TX846_Frame_C14 Page 279 Monday, November 18, 2002 12:30 PM © 2003 by CRC Press LLC