highly anisotropic material and loaded at the ends,it was demonstrated that the stress approached the uniform St.Venant solution much more slowly than the corresponding solution for an isotropic material [23]. The size of the region where end effects influence the stresses in a rectan- gular strip loaded with tractions at the ends is given by [23] 2但，c2 (2.41) where b is the maximum dimension of the cross section,and E and G2 are the longitudinal elastic and shear moduli,respectively. In this equation A is defined as the distance over which the self-equilibrated stress decays to 1/e of its value at the end.When the ratio E/G2 is large, the decay length is large and end effects are transferred a considerable distance along the gage section.Testing of highly anisotropic materials thus requires special consideration of load introduction effects.Arridge et al.[26], for example,found that a very long specimen with an aspect ratio ranging from 80 to 100 was needed to avoid the influence of clamping effects in tension testing of highly anisotropic,drawn polyethylene film.Several other cases are reviewed in Reference [25]. 2.5 Lamina Strength Analysis When any material is considered for a structure,an important task for the structural engineer is to assess the load-carrying ability of the particular material/structure combination.Prediction of the strength of composite materials has been an active area of research since the early work of Tsai [27].Many failure theories have been suggested,although no universally accepted failure criterion exists [28].As pointed out by Hyer [41,however, no single criterion could be expected to accurately predict failure of all composite materials under all loading conditions.Popular strength criteria are maximum stress,maximum strain,and Tsai-Wu criteria(see References [1-6,28]).These criteria are phenomenological in the sense that they do not rely on physical modeling of the failure process.The reason for their popu- larity is that they are based on failure tests on simple specimens in tension, compression,and shear(Chapters 5-7)and are able to predict load levels required to fail more complicated structures under combined stress loading. In the following presentation,failure of the lamina will first be examined and then failure of the laminate will be briefly considered.It is assumed that the lamina,being unidirectional or a woven fabric ply,can be treated as a homogeneous orthotropic ply with known,measured strengths in the prin- cipal material directions.Furthermore,the shear strength in the plane of the ©2003 by CRC Press LLChighly anisotropic material and loaded at the ends, it was demonstrated that the stress approached the uniform St. Venant solution much more slowly than the corresponding solution for an isotropic material [23]. The size of the region where end effects influence the stresses in a rectan￾gular strip loaded with tractions at the ends is given by [23] (2.41) where b is the maximum dimension of the cross section, and E1 and G12 are the longitudinal elastic and shear moduli, respectively. In this equation λ is defined as the distance over which the self-equilibrated stress decays to 1/e of its value at the end. When the ratio E1/G12 is large, the decay length is large and end effects are transferred a considerable distance along the gage section. Testing of highly anisotropic materials thus requires special consideration of load introduction effects. Arridge et al. [26], for example, found that a very long specimen with an aspect ratio ranging from 80 to 100 was needed to avoid the influence of clamping effects in tension testing of highly anisotropic, drawn polyethylene film. Several other cases are reviewed in Reference [25]. 2.5 Lamina Strength Analysis When any material is considered for a structure, an important task for the structural engineer is to assess the load-carrying ability of the particular material/structure combination. Prediction of the strength of composite materials has been an active area of research since the early work of Tsai [27]. Many failure theories have been suggested, although no universally accepted failure criterion exists [28]. As pointed out by Hyer [4], however, no single criterion could be expected to accurately predict failure of all composite materials under all loading conditions. Popular strength criteria are maximum stress, maximum strain, and Tsai-Wu criteria (see References [1–6,28]). These criteria are phenomenological in the sense that they do not rely on physical modeling of the failure process. The reason for their popu￾larity is that they are based on failure tests on simple specimens in tension, compression, and shear (Chapters 5–7) and are able to predict load levels required to fail more complicated structures under combined stress loading. In the following presentation, failure of the lamina will first be examined and then failure of the laminate will be briefly considered. It is assumed that the lamina, being unidirectional or a woven fabric ply, can be treated as a homogeneous orthotropic ply with known, measured strengths in the prin￾cipal material directions. Furthermore, the shear strength in the plane of the λ π ≈ ( ) b 2 E G1 12 1 2 TX001_ch02_Frame Page 24 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC