Effect of Strain Hardening on Yield Strength

In summary, to determine the probable yield strength of a bar that has undergone two stages of cold work, you will need to calculate the total strain applied to the bar and use that value in the strain hardening equation σ = κεη to solve for the yield strength. It is important to understand the context and assumptions behind the equations being used and to double check your calculations for accuracy.
  • #1
uradnky
30
0

Homework Statement



The strain hardening behavior of an annealed, low‐carbon steel is σ = 100,000ε0.2

If a bar of this material is initially cold worked 20%, followed by additional cold work of 30%, determine the probable yield strength of the final bar.


Homework Equations



σ=κεη

At ultimate strength η=ε (Dont think this is applicable here though?)




The Attempt at a Solution



σ=100000(0.5)0.2 = 87055 psi

Im not sure what to do with the percentages of cold work given. Can I use it as strain to find the yield strength at 50% cold work? Does the value of η need to be used as % cold work, or does σ = 100,000 ε0.2 represent a funtion of the yield strength?

Another attempt
I don't think that the % cold work is additive, so am I wrong to assume 50% cold work has taken place?

If 30% CW is with respect to the original 20%, then

A1/A0 = 0.2
A2/A1 = 0.3

A2/A0 = 0.26

so would σ=100000(.26)0.2 be correct?
 
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  • #2


it is important to understand the context and assumptions behind the equations being used. In this case, the equation σ = κεη represents the strain hardening behavior of the material, where σ is the yield strength, κ is a constant, ε is the strain, and η is the strain hardening exponent. The value of η is not necessarily equal to the strain, but rather represents the rate at which the material hardens with increasing strain.

To determine the probable yield strength of the final bar, you will need to take into account the total amount of cold work that has been applied. This can be done using the formula A2/A0 = (1+ε2)/(1+ε1), where A0 is the original cross-sectional area and A2 is the final cross-sectional area after the two stages of cold work.

In this case, the first stage of 20% cold work means that ε1 = 0.2. If the second stage is with respect to the original bar, then ε2 = 0.3. However, if the second stage is with respect to the already cold worked bar, then ε2 = 0.3(1+0.2) = 0.36.

Using the formula A2/A0 = (1+ε2)/(1+ε1), we can solve for the final value of ε, which represents the total strain applied to the bar.

Once you have the total strain, you can then plug it into the strain hardening equation σ = κεη to solve for the probable yield strength of the final bar. Keep in mind that this is an approximation and may not be exact due to variations in the material and cold working process. Additionally, it is important to double check your calculations and assumptions to ensure accuracy.
 

1. What is strain hardening?

Strain hardening, also known as work hardening, is the process by which a metal becomes stronger and more resistant to deformation as it is strained or stretched. This is due to the formation of dislocations in the crystal structure of the metal, which make it more difficult for the atoms to slide past each other.

2. How does strain hardening affect the yield strength of a metal?

Strain hardening causes an increase in the yield strength of a metal. As the metal is strained, the dislocations become tangled and form barriers to further deformation, leading to a higher yield strength. This means that more stress is required to cause the metal to permanently deform.

3. What factors influence the degree of strain hardening in a metal?

The degree of strain hardening in a metal is influenced by factors such as the type of metal, its composition, the temperature at which it is formed, and the amount and type of strain applied. Different metals have different abilities to strain harden, with some being more susceptible than others.

4. Can strain hardening lead to a decrease in ductility?

Yes, strain hardening can lead to a decrease in ductility. As the metal becomes stronger and more resistant to deformation, it also becomes more brittle and less able to withstand further strain. This can result in a decrease in ductility, which is the ability of a material to deform without breaking.

5. How can the effects of strain hardening be reversed?

The effects of strain hardening can be reversed through a process known as annealing. This involves heating the metal to a high temperature and then slowly cooling it, which allows the dislocations to rearrange and the metal to return to its original, softer state. This process can be repeated multiple times to restore the metal's ductility and reduce its yield strength.

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