All stress and strain allowables will be calculated based on the current selection under Failure Theory in the Options frame. The failure theory will be used to determine the allowable load described in the next section. You can select more than one failure theory, which will limit the allowables of the material. For example, you can choose both Max Strain and Max Stress failure theories. If the allowable based on the maximum strain theory is 77 ksi and the allowable based on the maximum stress theory is 72 ksi, then the resulting allowable will be 72 ksi (i.e. the lower value).
Important: The allowables stored for an effective laminate, on the material form, are based on the embedded failure theory (Tsai-Hahn). When composite strength margins are reported for effective laminates these allowables are not used. Instead, the ply stress/strain allowables for the source orthotropic ply material are used to evaluate strength margins for the laminate. See Effective Laminates in Structural Analysis.
Stress allowables are generated for the material in the 1, 2, and 12 (shear) directions based on the user-selected, ply-based failure theory.
The allowables (Fu1, Fu2, Fsu12, eu1, eu2, esu12) are calculated by applying three positive (tensile) and three negative (compression) unit-valued uniaxial loads (e.g. pure Nx, pure Ny, etc.) to determine the allowable load corresponding to the first ply failure in each direction. This allowable load is converted to an average stress allowable by dividing by the total laminate thickness:
Fu1 = Nx, allow / t where Ny=0, Nxy=0
Fu2 = Ny, allow / t where Nx=0, Nxy=0
Fsu12 = Nxy, allow / t where Nx=0, Ny=0
The stress allowables can be verified directly in the Laminate Analysis form. In the figure above, a pure Nx load is applied to the laminate (the magnitude does not matter). The allowable load (using the Tsai-Hahn failure criteria) is (MS + 1) * (Applied Load) = (6.417 + 1)*(1000) = 7,417 lb/in. The Fu1 stress allowable is the allowable load divided by the thickness of the laminate. The figure above refers to the "Example Laminate 18 ply" laminate included with the HyperSizer database with a thickness of 0.099 inches.
Fu1 = Nx, allow / t = 7417 lb/in / 0.099" = 74.92 ksi
The strain allowables are the laminate strains at the allowable load. These can be backed out by inverting the ABD matrix and then by multiplying by the allowable load (vector). A practical way to do this is to use the Fu1 stress and E1 effective laminate modulus. Note that this shortcut only works if the applied load state is pure Nx.
eu1 = Fu1/E1 = 74.92 ksi / 6.81 Msi = 0.011 in/in
Notes:
Laminate allowables are copied from the parent material to the effective laminate material without modification.
Correction factors are copied from the parent material to the effective laminate material without modification.
When you view the effective laminate through the Laminate Analysis form, the stiffnesses and effective properties viewed on the form will be corrected properties. However, when you view the effective laminate properties on the Orthotropic form for a created effective laminate, the allowables will represent precorrected properties and there will be correction factors included for each property.
Consider the following example where the parent material has the following pristine tensile allowable properties:
The Correction form for this material shows a BVID correction factor of 0.42 on both Ftu1 and Ftu2, so the effective allowables for this parent material are Ftu1= 86.1 ksi and Ftu2 = 9.07 ksi.
This material is used in a laminate (not shown) and is analyzed with the Laminate Analysis form. The allowable stresses for the effective laminate are Fu1 = 30.36 ksi and Fu2 = 38.59 ksi, as shown below.
After creating an effective laminate orthotropic material, the pristine allowable stresses for this material will be shown on the Orthotropic form as Ftu1 = 72.28 ksi and Ftu2= 91.89 ksi.
To view the corrected property, open up the Correction Factor form and note that the corrected Ftu1 and Ftu2 allowable stresses (Ftu1=30.36 ksi, Ftu2=38.59 ksi) match those shown on the Laminate Analysis form.
See Correction Factors.
