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Mechanics Analysis Composite Materials Episode 6

Tham khảo tài liệu 'mechanics analysis 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 | Chapter 4. Mechanics of a composite layer 161 where a _ 5__ . r J_ Ex 72Ợtv 1 - Consider two limiting cases. For an infinitely long strip 7 oo we have Ex Eỵ. This result corresponds to the case of free shear deformation specified by Eqs. 4.77 . For an infinitely short strip 7 0 we get In accordance with Eqs. 4.83 this result corresponds to a restricted shear deformation yvv 0 . For a strip with finite length Ex E x B . Dependence of the normalized modulus on the length-to-width ratio for a 45 carbon-epoxy layer is shown in Fig. 4.29. As can be seen the difference between and Ex becomes less than 5 for I 3a. 4.3.2. Nonlinear models Nonlinear deformation of an anisotropic unidirectional layer can be rather easily studied because stresses ff Ơ2 T 2 in the principal material coordinates see Fig. 4.18 are statically determinate and can be found using Eqs. 4.67 . Substituting these stresses into nonlinear constitutive equations Eqs. 4.60 or Eqs. 4.64 we can express strains and y 2 in terms of stresses TV ơy and Tvv. Further substitution into Eqs. 4.70 yields constitutive equations that link strains and yvi. with stresses ơx Ợ and TV . thus allowing US to find strains in the global coordinates X y z if we know the corresponding stresses. E 1.4 r Fig. 4.29 Dependence of the normalized apparent modulus on the strip length-to-width ratio for a 45J carbon-epoxy layer. Mechanics and analysis of composite materials ơx MPa As an example of application of a nonlinear elastic material model described by Eqs. 4.60 consider a two-matrix fiberglass composite whose stress-strain curves in the principal material coordinates are presented in Fig. 4.16. These curves allowed us to determine coefficients è and c in Eqs. 4.60 . To find coupling coefficients m we use a 45 off-axis test. Experimental results circles and the corresponding approximation solid line are shown in Fig. 4.30. Thus constructed material model can be used now to predict its behavior .