Modeling the Dimensional Variations of Composites Using Effective Coefficients of Thermal Expansion

With the increasing demands for energy efficiency and environmental protection, composite materials have become an important alternative to traditional materials. Composite materials offer many advantages over traditional materials including low density, high strength, high stiffness to weight ratio, excellent durability, and design flexibility. Despite all these advantages, composite materials have not been as widely used as expected because of the complexity and cost of the manufacturing process. One of the main causes is associated with poor dimensional control. 'Spring-in' is a common dimensional variation of composite angled parts. Due to the layerwise structure of composites, traditionally the spring-in was calculated numerically by defining each lamina as an element along the through-thickness direction and assigning its material properties and orientation. This method is usually too time-consuming for practical applications. In this article, the effective coefficients of thermal expansion of symmetric laminates were derived. Using the effective CTE, spring-in can be calculated by a simple mathematical formula. This approach was validated by finite element analysis and experiments. The effective CTE are very useful in 3-D finite element analysis. The effective CTE provide a feasible approach to the 3-D finite element analysis. Compared with the layerwise approach, the number of elements is significantly reduced. This was illustrated by an example.