Effective Strain of Frictionless Punch on Deep Plate

In summary: Drawing a diagram might help you to understand the problem better.In summary, the person is trying to figure out the effective strain of a frictionless punch on a deep plate. They are not sure where to start and are looking for help.
  • #1
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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  • #2
Shear stress .
 
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  • #3
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
 
  • #5
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.
 
  • #6
Draw me a diagram so that I can understand what your actual problem is .
 
  • #7
Here you go
 

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  • #8
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
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.
 

Related to Effective Strain of Frictionless Punch on Deep Plate

1. What is the definition of effective strain in the context of a frictionless punch on a deep plate?

The effective strain is a measure of the deformation or elongation of a material due to an applied force. In the context of a frictionless punch on a deep plate, it refers to the amount of stretching or compression of the plate caused by the impact of the punch.

2. How is the effective strain of a frictionless punch on a deep plate calculated?

The effective strain can be calculated using the formula ε = (δ-t)/t, where ε is the effective strain, δ is the displacement of the plate, and t is the initial thickness of the plate. This formula assumes that the material is homogeneous and has a uniform thickness.

3. What factors can affect the effective strain of a frictionless punch on a deep plate?

Several factors can affect the effective strain, including the force applied by the punch, the shape and size of the punch, the material properties of the plate, and the thickness of the plate. Additionally, any friction or lubrication between the punch and the plate can also impact the effective strain.

4. Why is it important to consider the effective strain in the design of a frictionless punch on a deep plate?

The effective strain can provide valuable information about the behavior of the plate under the impact of the punch. It can help determine the maximum load the plate can withstand before failure, as well as the potential for buckling or other forms of deformation. Understanding the effective strain can aid in optimizing the design of the punch and plate to ensure structural integrity and efficiency.

5. How can the effective strain of a frictionless punch on a deep plate be controlled?

The effective strain can be controlled by adjusting the parameters of the punch and plate, such as the force applied, the shape and size of the punch, and the material properties and thickness of the plate. Additionally, the use of lubricants or other friction-reducing techniques can help minimize the impact of friction on the effective strain. It is also important to carefully consider the design and structural integrity of the punch and plate to ensure they can withstand the desired level of force without excessive strain.

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