Effective Strain of Frictionless Punch on Deep Plate

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SUMMARY

The discussion focuses on calculating the effective strain of a frictionless punch on a deep plate under plane strain conditions. The user explores various methods, including shear stress calculations and references to indentation tests like Vickers and Brinell, but finds them unsuitable due to the depth of penetration. The conversation highlights the need for a stress-strain relationship and suggests that plastic flow theory may be applicable, with finite element methods (FEM) often used for modeling such scenarios. A reference to flow plasticity theory is provided as a starting point for further exploration.

PREREQUISITES
  • Understanding of shear stress calculations
  • Familiarity with plastic flow theory in metals
  • Knowledge of finite element methods (FEM)
  • Basic principles of stress-strain relationships
NEXT STEPS
  • Research "Flow Plasticity Theory" for insights on plastic deformation
  • Explore "Finite Element Analysis (FEA)" techniques for modeling strain
  • Study "Shear Stress in Punching" to understand stress distribution
  • Look into "Stress-Strain Relationships" for different materials
USEFUL FOR

Mechanical engineers, materials scientists, and anyone involved in metal forming processes or stress analysis will benefit from this discussion.

1350-F
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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.
 
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Shear stress .
 
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Nidum said:
Shear stress .

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

[Edit] I suppose I could look it up, however
 
Nidum said:
https://www.google.co.uk/search?q=s...oTCKLqksi-98gCFUsaPgodFwgI_g&biw=1680&bih=939



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

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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
 
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.