Chapter 3: Longitudinal Coefficient of Thermal Expansion of a Unidirectional Lamina: Theory

See the derivation of the longitudinal coefficient of thermal expansion of a unidirectional composite lamina.

In this video, the formula for the longitudinal coefficient of thermal expansion of a unidirectional lamina is derived. The video does not cover the transverse coefficient of thermal expansion, which will be addressed in a separate module. The longitudinal direction is along the fibers, while the transverse direction is perpendicular to the fibers. The video explains that the thermal expansion coefficient depends not only on the thermal expansion properties of the fiber and matrix but also on their Young's modulus and Poisson's ratio. The video also reviews basic concepts from mechanics of solids, such as the relationship between thermal expansion and mechanical stress. It explains how mechanical stress occurs when a material is constrained and cannot expand freely. This concept is important for understanding the behavior of fiber-matrix composites, where the fiber and matrix have different thermal expansion coefficients. The derivation of the formula for the longitudinal thermal expansion coefficient involves considering the strain in the fiber, matrix, and composite. The video shows that the strain in the composite is the same as the strain in the fiber and matrix in the longitudinal direction. The stress in the fiber and matrix is related to their Young's modulus and the difference between the actual strain and the free expansion strain. Finally, the video derives the expression for the longitudinal thermal expansion coefficient by considering the overall force balance in the composite. The derived formula shows that the thermal expansion coefficient in the longitudinal direction depends on the thermal expansion properties and Young's modulus of both the fiber and matrix.