Presentation on theme: "Hygrothermal behavior of composite laminates"— Presentation transcript:
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 mismatchGraphite/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 deformationsIf 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 laminateConstraining 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 =𝜶𝛥𝑇What 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 stressesResidual strains in k-th layer 𝜺 𝑅 = 𝜺 0𝑁 + 𝑧 𝑘 𝜿 𝑁 − 𝜺 𝑘 𝐹Residual stresses in k-th layerWhat terms will be the same in two layers, under what conditions?
9 Thermal loadsIf 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 laminateLoads needed to produce same strains without temperatures
10 Thermal loads for a single isotropic layer The matrix AThermal loadsJustify letter by letter!
11 With bending Thermal moment resultants Calculating strains and curvatures under thermal loads𝐀 𝜺 0𝑁 +𝐁 𝜿 𝑁 = 𝐍 𝑁𝐁 𝜺 0𝑁 +𝐃 𝜿 𝑁 = 𝐌 𝑁
12 With Tsai-Pagano Material constants Thermal loadsThermal material constantsAny checks that we can apply?