# Effective Strain of Frictionless Punch on Deep Plate

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1. Nov 4, 2015

### 1350-F

I'm trying to figure out the effective strain of a frictionless punch on a deep plate. For simplicity's sake let's say it's in plane strain. Don't quite know where to start. Closest thing I can think of is the strain from a bulge test, but that involves a thin sheet. Looked at some indentor (Vickers, Brinell etc.) strains also, but these might not be applicable, since the indenter does not travel that far into the workpiece. I also looked at some of the literature concerning ballistics but they don't really report strain or how they calculated it. I feel like there's something very simple that I'm missing here.

I'd be grateful if someone could put me on the right path.

2. Nov 4, 2015

### Nidum

Shear stress .

3. Nov 4, 2015

### 1350-F

I thought about doing σ = Ymε, but I don't have a value for Y!

 I suppose I could look it up, however

4. Nov 4, 2015

5. Nov 4, 2015

### 1350-F

Well no matter how I calculate the stress, I still need some sort of stress-strain relationship. Any method I can think of to find strain otherwise has to include reduction of length, area, etc. I could indeed calculate the new area created by the cavity but if my object is semifinite I wouldn't know the initial area.

6. Nov 4, 2015

### Nidum

Draw me a diagram so that I can understand what your actual problem is .

7. Nov 4, 2015

Here you go

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8. Nov 4, 2015

### Nidum

I think you are actually looking at a plastic flow problem . There are various theory's regarding plastic flow in metals . Modelling real situations analytically is difficult and FE methods often have to be used . A not very accurate but sometimes useful approximate solution just assumes that all metal in zone around active end of punch is at yield stress .

Not the best of explanations but it's somewhere to start :

https://en.wikipedia.org/wiki/Flow_plasticity_theory

9. Nov 4, 2015

### 1350-F

My inclination was to find P/2k from a hodograph and then use that pressure to solve for strain using th the formula I posted above. However I wasn't sure whether there was a commonly used formula or something based on the individual strains.