Hygrothermal behavior of composite laminates

1. Hygrothermal behavior of composite laminates • Composite materials can absorb moisture and expand in the same way that they expand due to temperature. • We can use the same kind of analysis to deal with stresses that arise from both. • In this course we will focus on thermal behavior. • The effect of temperatures on composite laminates is more pronounced than on metals because of large disparity in coefficient of thermal expansion.

2. Effect of mismatch • Graphite/epoxy typical thermal expansion coefficients are . • A drop in temperature will produce a strain of -0.0045 in the transverse direction, and almost nothing in the fiber direction. • In a 0/90 laminate the fibers in one ply will not allow the matrix in the other ply to shrink by more than a fraction of the -0.0045 strain. • This will eat up a substantial part of the load carrying capacity. • For cryogenic conditions (e.g. liquid hydrogen tanks) the temperature drop is more than doubled, and the laminate can fail just due to thermal loads. • What can we do?

3. Thermal deformations • If ply can expand or contract due to hygrothermal effects, only strains, but no stresses. • Stress free expansion strain in a unidirectional layer (Fig. 3.2)

4. Strains and stresses • “Free” strains • Hooke’s law when total strains are different from free strains.

5. Interaction between plies • 0/90/45 laminate • Constraining effect of adjacent laminates

6. (0/90)s laminate • Stress-free expansion of layers • Constrained deformation

7. Residual strains • Free strains in x-y system (Checks?) • In vector form • What is the coefficient of thermal expansion in the 45-deg direction? • The actual strains in the ply due to thermal loads are denoted as for “non-mechanical” • The “residual strains” or the mechanical strains of non-mechanical origin are

8. Residual stresses • Residual strains in k-th layer • Residual stresses in k-th layer • What terms will be the same in two layers, under what conditions?

9. Thermal loads • If a laminate is subjected to temperature change without any loads then the stress and moment resultants should be zero. • Substituting from previous slide for in-plane equation for symmetric laminate • Loads needed to produce same strains without temperatures

10. Thermal loads for a single isotropic layer • For a single isotropic layer • The matrix A • Thermal loads • Justify letter by letter!

11. With bending • Thermal moment resultants • Calculating strains and curvatures under thermal loads

12. With Tsai-Pagano Material constants • Thermal loads • Thermal material constants • Any checks that we can apply?