How to obtain Effective Laminate Strain Allowables from Ply data?

[mraedel]

Hi,

I defined an orthotropic ply (Et1=Ec1=141GPa, Et2=Ec2=9.34GPa, G12=4.5GPa) with the lamina strain allowables etu1=etu2=4500microstrain, ecu1=ecu2=3500microstrain, esu12=4500microstrain.

From this ply I create effective laminates, which I then use in a pre-design structural analysis. Therein, I use max strain criterion to evaluate the effective laminate strength.

For my understanding, using an effective laminate, you have no information about the number of plies or their stacking.

So, my question is: How do I calculate the effective laminate strain allowables from the ply values?

E.g. for a 50% 0°, 30% +-45° and 20% 90° effective laminate: Does HyperSizer built a discrete laminate internally to compute the A-Matrix and thus calculate the effective engineering constants? Does HyperSizer use such an internal discrete laminate for the determination of the effective laminate strain allowables, as mentioned in this post for the stress allowables? If yes, which criterion is used for this analysis?

For the 50% 0°, 30% +-45° and 20% 90° effective laminate with the mentioned ply values I get etu1=10758.29microstrain; etu2=10952.44microstrain; ecu1=7190.529microstrain; ecu2=7358.728microstrain; esu12=12433.95.

I'd like to understand how I come to these values.

[James]

The effective laminate analysis has been changed in versions 6.4, 7.0, 7.1 and newer. The new analysis approach does not use the allowables displayed on the form for any strength analysis. The allowables stored for the effective laminate, on the material form, are based on the embedded failure theory (Tsai-Hahn). These allowables are not used to write margins of safety for strength. The ply stress/strain allowables for the source orthotropic ply material are used to evaluate strength margins for the laminate. The IML and OML laminate strains are used with very thin plies at these locations evaluate ply failure of an effective laminate. This is a conservative assumption made for effective laminate analysis because HyperSizer doesn't know exactly which ply is at the IML/OML surface.

Here is a help topic that discusses how the composite strength analysis is performed for an Effective laminate.
http://hypersizer.com/help/#Materials/EffLam/el-using_struct_analysis.php%3FTocPath%3DFeatures%7CMaterials%7CEffective%2520Laminates%7CUsing%2520Effective%2520Laminates%7C_____1

Notice how the software builds a laminate with a thick middle layer to get the appropriate laminate Aij and Dij stiffnesses. Since the stack-up sequence is unknown, The Dij for an effective laminate is approximated based on an an orthotropic approach Et^3/(12(1-v^2)). This is another assumption which may be conservative or un-conservative.

Sorry for the confusion. For future version we're likely going to remove the effective laminate allowables since they are now meaningless.

-James

[mraedel]

Thanks @James,

the smeared stiffness approach is clear to me. The pseudo three stack laminate is clever.

Anyway, could you please explain the "old" way using the Tsai-Hahn criterion? How do I get the effective laminate strain allowables?

BTW, I guess due to the small thickness of the IML and OML it is not of relevance, but shouldn't the IML and OML have opposite stacking to retain symmetry for effective laminates and deliver comparable strains ? Thus, if OML [0/90/45/-45] and IML [-45/45/90/0].

[James]

In older versions the effective laminate (EL) allowables were based on the failure theory you select when you create the EL. HyperSizer was basically building a laminate, then applying unit forces in each direction (+Nx, -Nx, +Ny, -Ny, Nxy) and running the selected ply-based failure criteria to determine first ply failure in the laminate. From the lamina margin-of-safety calculation (Tsai-Hahn, Tsai-Wu, etc.) for each unit force application, HyperSizer can determine the stress/strain allowables for a laminate with the ply percentages, corresponding to a particular composite failure mode.

Your observation about the IML/OML plies is correct. The layup created for the EL analysis is in fact symmetric. The image in the help documentation needs to be updated.

-James