Question About Strain-Hardening

[Saladsamurai]

In Shigley's Design there is a brief discussion in chapter 2 about strain hardening. At one point he says,

A little thought will reveal that a bar will have the same ultimate load in tension after being strain-hardened in tension as it had before...

Is this just because you cannot stress the bar beyond S_u and thus cannot improve upon that number?


He also says that

the new strength is of interest...because the fatigue strength improves--since fatigue strengths are correlated with the local ultimate strengths

What does this mean? What are "local ultimate strengths?" And how are they correlated to fatigue strengths?

Any thoughts are appreciated

 

[Cyrus]

The ultimate strength is the ultimate strength. It's as good as the material can do. When you strain harden the bar, you increase the linear portion where yeilding starts to occur, but you loose 'safety'. In other words, if you over stress the metal, it will yield. Next time you get to that stress level, it will remain linear. Go past that level, and you strain harden it further. You can keep on doing this, until you get to the point where the material has no more forgiveness. Instead of yeilding when you over stress the bar, it will reach Su and suddenly fail quite dangerously like cast iron.

 

[Saladsamurai]

The ultimate strength is the ultimate strength. It's as good as the material can do. When you strain harden the bar, you increase the linear portion where yeilding starts to occur, but you loose 'safety'. In other words, if you over stress the metal, it will yield. Next time you get to that stress level, it will remain linear. Go past that level, and you strain harden it further. You can keep on doing this, until you get to the point where the material has no more forgiveness. Instead of yeilding when you over stress the bar, it will reach Su and suddenly fail quite dangerously like cast iron.

Thanks Cyrus, this makes sense.

When you say

you increase the linear portion where yeilding starts to occur, but you loose 'safety'

what does that implicate for the stress-strain diagram? That is, does the slope of the linear region change? Or does it 'shift' while retaining the same slope?

I am not sure if I am wording my question correctly.

 

[Cyrus]

Thanks Cyrus, this makes sense.

When you say


what does that implicate for the stress-strain diagram? That is, does the slope of the linear region change? Or does it 'shift' while retaining the same slope?

I am not sure if I am wording my question correctly.

I believe it just makes the linear portion extend further up.

PS: I hope you are not using that book to learn. It's really a design book and not a 'learning' book. It's terrible for the theory. It's great for, "I want to do THIS". Look it up, do it.

 

[Saladsamurai]

I believe it just makes the linear portion extend further up.

PS: I hope you are not using that book to learn. It's really a design book and not a 'learning' book. It's terrible for the theory. It's great for, "I want to do THIS". Look it up, do it.

No. I already took materials science, I am just exploring some of the nuances that we didn't go into with much detail.

It's for my ME Design course that I am taking. Hope I get some use out of this book; at $200 USD, it's the most expensive one I have purchased yet.

 

[Cyrus]

No. I already took materials science, I am just exploring some of the nuances that we didn't go into with much detail.

It's for my ME Design course that I am taking. Hope I get some use out of this book; at $200 USD, it's the most expensive one I have purchased yet.

I had to look into making springs a few months ago. This book is very good for looking up how to do things. I didn't care about the theory of how you make springs. I just wanted to make one. This is what the book is strong for. "I want to make car brakes" ...go to chapter 16.

 

[minger]

I believe it just makes the linear portion extend further up.

For the most part correct. When you pass the yield point, you reach areas of permanent deformation. When you then unload the part, even though you are past the proportional (linear) area, you unload at the Elastic Modulus. That is, when you get down to zero stress, you have a non-zero value for strain, that is your permanent deformation.

As Cy mentioned, because the linear line is now "shifted" over, it increases the yield strength...I'm rambling...I need a cup of coffee.

 

[Cyrus]

For the most part correct. When you pass the yield point, you reach areas of permanent deformation. When you then unload the part, even though you are past the proportional (linear) area, you unload at the Elastic Modulus. That is, when you get down to zero stress, you have a non-zero value for strain, that is your permanent deformation.

As Cy mentioned, because the linear line is now "shifted" over, it increases the yield strength...I'm rambling...I need a cup of coffee.

Yeah, I saw that in the chart but I didn't mention it because I didn't want to say something incorrect about it.