Multi-layer Material: Assumptions and calculations

Assumptions used by model

The structure of a layered material leads to significant differences in properties in the in-plane and through-thickness directions. Only one direction can be specified in a selection project.

As a result, the values quoted on the material datasheet represent the performance in the direction that is most important for design. The direction important properties are specified if they are in-plane or through thickness. The exceptions are the permeability data, which are through-thickness properties.

In determining the calculations for the multi-layer model, the following assumptions have been made:

• The interfacial bond between layers is perfect, with no interfacial delamination occurring under loading.

• The properties of the adhesive have little, or no, contribution to the overall panel properties (i.e. it has no thickness and no shear deformation occurs between the layers). If this is unreasonable (for instance with a very thin laminate) then it is possible to include an adhesive as a separate layer, either using a suitable existing record or creating a user defined record.

• There is no shear deformation in any of the layers; the equations for flexural strength and stiffness assume no shear.

• For thermal conductivity it is assumed that there is no thermal reflection at boundaries between layers (e.g. as can happen between ceramics and metals).

• The calculations for flexural strength assume that the multi-layer is loaded so that the top layer is in compression and the bottom layer in tension, the failure stress is calculated as the stress at which any one of the layers fails. The relative position of the layers is important for this calculation (for example, some materials such as wood and ceramics have a significantly different tensile and compressive strengths).

Due to the assumptions used, these models are not suitable for predicting the performance of laminates where significant levels of shear deformation occur in any of the layers, such as sandwich panels with low density cores. In these circumstances, it is more appropriate to use the balanced sandwich panel model.

Note: In order to compare multi-layer materials with conventional solid materials, it is necessary to consider them as a 'monolithic' material with their own set of properties. This is achieved by calculating the equivalent material properties for the multi-layer. Plotting these equivalent properties (e.g. ) on a property chart (e.g. E_f vs. ρ) allows direct comparison with all other materials in the database.

Calculations used by model

• Multi-layer materials model
• Summary of calculated properties and data required

Multi-layer materials model calculations

The equations used by the model to calculate the primary properties are summarized below. All calculated properties are equivalent properties. For more information on the derivation of these equations see derivation of calculations.

For a definition of the symbols used, see symbols.

• Volume fraction of layer i

  

  where y_i is the distance from base of multi-layer to top of layer i and so y_n is the total height of the laminate.

• Density

  

• Price

  

• Young's modulus

  

• Flexural modulus

  

  

  

  

  

• Yield strength (in-plane)

  

  

• Flexural strength,

  

  

  with σ_y,i equal to the yield or compressive strength depending on position of layer i relative to the neutral axis, and y_diff is the distance between the neutral axis and the edge of the layer that is experiencing the greatest stress.

• Specific heat capacity

  

• Thermal expansion (through-thickness)

  

• Thermal conductivity (through-thickness)

  

• Electrical resistivity (through-thickness)

  

• Dielectric constant

  

• Dielectric loss tangent

  

• Water vapor transmission

  

• Permeability (O₂)

  

• Embodied energy (primary production)

  

• CO2 footprint (primary production)

  

Summary of calculated properties and data required

A summary of the material properties required to calculate the equivalent multi-layer properties is summarized in Table 1.

Table 1. Summary of properties required to calculate equivalent multi-layer properties

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