reason for big plastic strain, thanks

[Rikuson]

Hi Everyone

I'm modeling two electronic packages subject to temperature cycling (delta T= 120C), the only difference between them is the pitch distance (0.5mm and 0.3mm), everything else is the same including material properties (elastic perfect plastic for solder alloy, purely elastic for other materials), BCs, etc. The results showed that the plastic strain in 0.3 mm (2%) is almost 10 times bigger than the 0.5 mm model(0.2%), the stress is about the same.

I'm wondering what else could cause the 2% plastic strain in 0.3 mm model besides the CTE mismatch. Seems the 0.5mm model is right (0.2%) because the alpha is 2.1E-5.

Is that just because the geometry?

I appreciate any ideas on that!

Thanks a lot!

Riku

 

[mrgoldthorpe]

I'm not sure what your geometry is, but it seems elastic components are connected by elastic-perfectly plastic solder, which is either 0.3 or 0.5 mm long. Presumably the other (elastic) components are attached to a circuit board.

I'd guess that the thermal expansions/contractions in the other elastic components must be accommodated mainly by plastic deformation in the solder, since these other components can only deform elastically.

Now a 0.3 mm section of solder accommodating a displacement of 'Delta' imposed by its neighbours will suffer a larger strain than a 0.5 mm section accommodating the same 'Delta'. Depending on the solder yield strain (yield stress/E) this will result in a larger plastic strain in the smaller pitch geometry. Add the partially constrained thermal expansion of the solder itself, and you could envisage much greater plastic strains in the smaller pitch case.

Do a sensitivity study: look at the effect of increasing DeltaT, looking at say 30, 60, 90, 120 deg C and above. I think you'll see the effect you describe emerging over a particular temperature range as the maximum strain imposed on the solder during a thermal cycle rises above its yield strain. At a rough guess: when
alpha*DeltaT=solder yield strain=yield stress/E

You'll see yield of the solder starting at a lower DeltaT in the smaller pitch geometry than the larger pitch. As DeltaT increases, this difference between the two geometries will become more apparent because the yielded solder loses its ability to fight back against its elastic neighbours. Eventually the larger pitch solder will follow the same fate, but it may take a temperature higher than 120 deg C.

As a matter of interest: are the material properties independent of temperature, or will you take account of say reduction of yield stress with increasing temperature?

 

[mrgoldthorpe]

Clarification addendum:

As you point out, the strain associated with one thermal cycle is only about 0.25%. However, because of my explanation above, there's rather more plastic strain accommodated in the smaller pitch geometry per cycle. So over several cycles the accumulated plastic strain (PEEQ) in the smaller pitch could greatly outweigh the larger pitch geometry. The ratio PEEQ(0.3mm)/PEEQ(0.5mm) would be particular large when yield is only just surpassed in the 0.5 mm pitch case.

If the strains you quote refer to only a single cycle, then the explanation must be that the solder characteristic dimension (L_s) is very much smaller than the characteristic dimension of the elastic components (L_e).

If these were considered to be two bars in series of length L_s and L_s subjected to constrained thermal expansion, the strain in the solder would be roughly alpha*DeltaT*(L_e/L_s). So is "L_s" about a tenth of "L_e"?

 

[mrgoldthorpe]

edit: "...two bars in series of length L_s and L_e subjected...."

 

[mrgoldthorpe]

I thought I'd have some displacement activity and have illustrated what I mean above in the attached xls. This models a two-bar structure comprising an Elastic bar and a smaller elastic-perfectly Solder bar. It assumes that the thermal strain always exceeds the yield strain of the Solder material, so there is a maximum load sustained by the two-bar model: given by the yield stress of the Solder multiplied by the x-section area of the Solder bar.

There's a reasonably simple equation giving the plastic strain in the Solder, but I thought I'd do the xls to demonstrate a number of cases.

Warning: check it first if you intend to use it!

 

[mrgoldthorpe]

corrected:

 

[Rikuson]

Hi, mrgoldthorpe

Thank you very much for your help!

I really appreciate!

I might use your excel file to do the presentation.
So could you tell me your name or company so that I can mention at my presentation.

Thanks again!

Riku

 

[mrgoldthorpe]

Don't worry about that. All I ask is that you make contributions to eng-tips and so return the favour to others.