Linear thermal expansion coefficient results

The Linear thermal expansion coefficient results are used to help predict shrinkage that may occur due to temperature fluctuations.

Mesh type:

Midplane
Dual Domain

Analysis sequences that include:

Pack

For a Midplane or Dual Domain Flow (Fill+Pack) analysis of a fiber filled material, the coefficient of linear thermal expansion (CLTE) is calculated in the three principal directions of the fiber orientation tensor. Two types of results are then published:

Linear thermal expansion coefficient (averaged) results

For each element, the CLTE is calculated using an orientation average across the thickness, having averaged the fiber orientation tensors for each laminate of that element. Although the averaged CLTE data is calculated in all three directions, it is only written into the results file for the first and second principal directions. These results are used by the legacy residual strain shrinkage model, which does not use the data from the third principal direction.

Linear thermal expansion coefficient in first principal direction (averaged)
Linear thermal expansion coefficient in second principal direction (averaged)

Linear thermal expansion coefficient results

For each element, the CLTE is calculated at each laminate using the fiber orientation tensor of that element. Therefore, each laminate in the model will have a different thermal expansion result. These results are used by the CRIMS shrinkage correction model and the uncorrected residual stress model. You can check the expansion coefficient in each laminate by animating the default contour plot, which will animate the result over the Normalized Thickness.

Linear thermal expansion coefficient in first principal direction
Linear thermal expansion coefficient in second principal direction
Linear thermal expansion coefficient in third principal direction

Orthotropic assumption

The thermo-mechanical property calculation for fiber-filled composites is based on the orthotropic assumption, that fiber-filled material properties are different in three orthogonal principal directions. Under this assumption, there are 9 independent mechanical constants and three independent thermal expansion coefficients. In models analysed using Midplane or Dual Domain analysis technologies, because of the plain stress assumption in the shell structure analysis in Warp, only 4 mechanical constants (tensile modulus in first/second principal directions, Poisson ratio v12, shear modulus G12) are necessary, and only these four are offered as (averaged) results.

Using these results

Compare the results in each of the different principal directions. The material should expand less in the main direction of fiber orientation (first principal direction) than perpendicular to the fiber direction (second principal direction). If the fibers are highly or partially aligned in the first and second principal directions, then the linear thermal expansion coefficient will be different in each principal direction. If the fibers are randomly aligned, you would expect to see a uniform linear thermal expansion coefficient in each principal direction.

The averaged results are useful for looking at the CLTE at a given point and comparing it with the CLTE at different points. The profiled results can be used for an more detailed study of the CLTE values through the thickness.