Thermoelastic Characterization and Evaluation of Residual Stresses in Bi-Directional Fibrous Composites
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Thermoelastic Characterization and Evaluation of Residual Stresses in Bi-Directional Fibrous Composites G. Karami & N. Grundman & N. Abolfathi & A. Naik
Received: 6 June 2008 / Accepted: 23 October 2008 / Published online: 8 November 2008 # Springer Science + Business Media B.V. 2008
Abstract The thermoelastic behavior of bi-directional fibrous composites will be studied through the use of a finite element-based micromechanical model. The model is used to study the effect of the crossing angle of the fibers on the composite’s coefficient of thermal expansion (CTE) and the residual thermal stresses that develop after a temperature change. The effect of the fiber volume fraction (Vf) on the same results is also studied. For anisotropic materials, one can see that in addition to normal strains, shear strains will also be developed due to temperature change. This method will lend itself to evaluate the coefficients of thermal expansions not only due to normal expansion, but also due to shear expansion for composites with no principal directions. In this micromechanical model, parallelepiped unit cells incorporating the fibers at different cross angles are created to represent the periodic microstructure of the angular bi-directional composite. The volume averaged stresses per unit temperature of the individual constituents are used to study the residual thermal stresses that develop. Two different sets of materials are used to test this model. Results show that when the fiber’s cross angle is not 0o or 90o, shear strains are created. Also, residual stresses in the unit cell are functions of the cross angle between the fibers. Keywords Micromechanics . Fibrous composites . Bidirectional . Coefficient of thermal expansion (CTE) . Residual stresses
1 Introduction The ability to accurately characterize the thermoelastic expansion properties and the residual stresses within fibrous composites is important because it allows one to tailor the design of the composite to better suit its application. Fibrous composite materials typically are composed of a fiber which is used as a load carrying material and a polymeric matrix material that is used to bind the fibers together. One problem with these composites is that the polymeric matrix material typically has a thermal expansion coefficient much greater than that of the fiber [1]. G. Karami (*) : N. Grundman : N. Abolfathi : A. Naik Department of Mechanical Engineering and Applied Mechanics, North Dakota State University, Fargo, ND 58108-6050, USA e-mail: [email protected]
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Appl Compos Mater (2008) 15:259–272
This mismatch in thermal expansion properties has an influence on the overall thermal expansion of the composite and it also creates internal residual stresses in the composite materials. These residual stresses are a point of concern because in elastic structures they may superpose on the stresses from external loads and influence the load capacity of the composite. The direction of the fiber’s longitudinal axis is the direction in which load is primarily carried a
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