An investigation of the isotropy of epoxy polymers
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Donald F. Adams Department of Mechanical Engineering, University of Wyoming, Laramie, Wyoming 82070 (Received 16 April 1992; accepted 6 August 1992)
Measurements of the engineering constants E, G, and v are routinely made for polymeric materials. If these materials are isotropic, these measurements should satisfy the relationship G = E/2{\ + v). However, many past measurements have indicated that this relationship is not satisfied. This raises questions about the assumptions of material isotropy and the applicability of Hooke's law. The methods used to measure these engineering constants for a number of different polymers are first described. Then, new results obtained in the current investigation are presented, indicating that the elastic constants do in fact satisfy the isotropic relationship for strains up to 0.5%. However, it is shown that at strain levels above this level, the relationship between stress and strain is nonlinear. I. INTRODUCTION
termed the isotropic relationship, is shown in Eq. (2).
The materials of interest in the present study are epoxies, i.e., highly crosslinked amorphous polymers. An important use for these materials is as matrix materials in fiber-reinforced composite materials. Such polymers are usually assumed to be homogeneous and isotropic,1'2 at least on the scale of present interest, i.e., macroscopically. Homogeneity requires material properties to remain constant from point to point in the material. Therefore, all other factors being equal, experimental measurements will be insensitive to the test location. Isotropy requires the elastic properties to be independent of direction. These commonly accepted assumptions indicate that Generalized Hooke's law for an isotropic medium, as shown in Eq. (1) in terms of engineering constants, should be applicable.2 In these equations E is Young's modulus, G is the shear modulus, and v is Poisson's ratio. 1
V 0-33
~E
J_ £22
E
^22
0-33
v ~E £23 £31 £12
;o-33
G Q-31
G Q-12
G
(1)
It can be shown that a relationship among the engineering constants E, G, and v exists.3 This relationship, 3352 http://journals.cambridge.org
J. Mater. Res., Vol. 7, No. 12, Dec 1992 Downloaded: 12 Apr 2015
G =
E 2(1 + v)
(2)
Experimentally determined engineering constants should satisfy this relationship. For example, data from a classical textbook on elasticity by Sokolnikoff3 for isotropic materials other than polymers indicate the isotropic relationship to be satisfied to within 2%. Experimental observations that are not in agreement with this relationship suggest that the assumptions of homogeneity, isotropy, and/or the applicability of Hooke's law are not valid. One of the materials selected for the present study, Hercules 3501-6 epoxy,4 has been in use since the early 1970s,5 and therefore has been studied by a number of investigators during the intervening years.5"30 A summary of the mechanical properties reported in some of these studies is presented in Table I. The data in Table I indicate considerable variation in the measured values of t
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