Effective Modulus of PCB

[Transient1]

In regards to Printed Circuit Boards, after I find the equivalent stiffness of a laminate, EI, I would like to extract the effective young's modulus E. My goal is to perform a FEA analysis using just a solid with equivalent properties rather than modeling each layer.

The equation I used for equivalent EI is

EI_equiv = Sum for each layer [ (E_i*I_i)+ (y_i - y_n)^2 * E_i*A_i]

y_i=neutral axis for the layer i
y_n=neutral axis of PCB

For Stress calculations I could estimate I=EI_equiv/I_layer

Dividing EI by the sum of I_i, doesn't seem to yield a logical answer. I get a young's modulus less than the young's modulus of each individual layer.
Can anyone shed some light on effective young's modulus calculations? Thanks in advance.

 

[wes616]

What FE system are you using? Your software may do this for you. Otherwise, it's not difficult, but not quite so straighforward.

For In plane

Ex = 1/(h x A*11)

Ey = 1/(h x A*22)

For Flexural

Efx = 1/(h x D*11)

Efy = 1/(h x D*22)

Note: A*11 would read A Star one one not A times 11.

[A]* = [A]^-1 and [D]* = [D]^-1

If you don't have a CLPT program for developing the ABD matrix, then there are several cheap/free ones you can get, then just use excel to get the inverse matrix.

h is measured thickness of the laminate.

I recognize the theory that you are using in your question, but I can not seem to find it. If i remember right, this develops a circular argument. I believe that I made this mistake before. Could you tell me what book you are using?



Wes C.
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No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[Transient1]

Wes,

Thanks for your response. I'm working with ANSYS, predomiantly in the workbench environment. I've just begun delving into making a more accurate model of our PCBs. The equations I started working with are from a laminate excel spreadsheet off of MIT opencourseware's website. It seems like its referenced from

http://www.wood-handbook.com,

but currently I can't check due to some of our IT departments internet controls. I can see how they end up making a circular argument. I'm studying up on CLPT. Can you suggest a text to begin with, perhaps the one you referenced these equations from? I'm searching around for a spreadsheet to develop the ABD matrix, but I encountered the same surf controls...anyways once my IT department comes in I'll handle that. Thanks again.

-Chris

 

[wes616]

Chris,

Your IT dept really needs to lighten up

You are probablly not going to find a spreadsheet to develop your abd matrix. There are a number of specialized programs to do this. A couple are freeware/shareware. Search around on this forum. There are some links.

It's an old text but I like to use Composites Design by Stephen Tsai. There are many that are good though.

Also, the internet has a great many lectures on Lamination Theory posted online.

Wes C.
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No trees were killed in the sending of this message, but a large number of electrons were terribly inconvenienced.

 

[sreid]

If you could live with bulk propertities search G-10, FR-4 and Garolite.

 

[Transient1]

Wes- Thanks for your help. I've continued reading up on composites. I'll probably end up buying a text, although I've found plenty of resources on the web.

sreid- We've used the bulk properties of the boards in the past. In general, its acceptable. However, knowing the effective modulus of the PCB due to the ground plane and a couple other high coverage planes would be really useful.

 

[Transient1]

Also, I searched on this forum for the ABD calculation program as well as on the web. I can't seem to find a simple one to do what I need. Any suggestions?