Effective Modulus of PCB
Effective Modulus of PCB
(OP)
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.
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.





RE: Effective Modulus of PCB
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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RE: Effective Modulus of PCB
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 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
RE: Effective Modulus of PCB
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.
RE: Effective Modulus of PCB
RE: Effective Modulus of PCB
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.
RE: Effective Modulus of PCB