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 𝛼 1 =0.02× 10 −6 ∘ 𝐶 ,   𝛼 2 =22.5× 10 −6 ∘ 𝐶 .
A 200 𝑜 𝐶 drop in temperature will produce a strain of 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 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 𝜺 𝐹𝑇 =𝜶𝛥𝑇
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 𝜺 𝑁 for “non-mechanical”
The “residual strains” or the mechanical strains of non-mechanical origin are 𝜺 𝑀 = 𝜺 𝑁 − 𝜺 𝐹

8. Residual stresses
Residual strains in k-th layer 𝜺 𝑅 = 𝜺 0𝑁 + 𝑧 𝑘 𝜿 𝑁 − 𝜺 𝑘 𝐹
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
The matrix A
Thermal loads
Justify letter by letter!

11. With bending Thermal moment resultants
Calculating strains and curvatures under thermal loads
𝐀 𝜺 0𝑁 +𝐁 𝜿 𝑁 = 𝐍 𝑁
𝐁 𝜺 0𝑁 +𝐃 𝜿 𝑁 = 𝐌 𝑁

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