Hall-Petch law and hardness-yield strength correlation 1

[seep]

Hello everyone!

I have a question:
I am currently working on an austenitic steel and after applying Hall-Petch law, the slop of a curve (on HV vs d^-1/2 graph) is different than taken from the literature... How can I explain this? May it be connected with "k" coefficient?

Another question:
There is a well known law for metals, connecting hardness and yield strength:
H = α x YS

α for metals should be around 3... But it's not working once again in my case - it's about 1,2. How can I explain this?

I would be grateful for any indications!

 

[EdStainless]

Or you may need to look at the definition of yield strength.
The arbitrary 0.2% offset value does not have a theoretical basis, it is an engineering convenience.
This is especially true in low strength, high work hardening alloys.
I have only ever seen these relationships used for alloys that have a high yield strength and large elastic region.

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Plymouth Tube

 

[TVP]

What kind of austenitic stainless steel? Fully annealed, very low yield strength? Or highly cold-worked, spring temper wire or strip?

 

[Guest102023]

H = α x YS?

I cannot recall having learned such a relationship, certainly not for austenitic SS.

Are you working on steel or an assignment?

"If you don't have time to do the job right the first time, when are you going to find time to repair it?"

 

[OGMetEngr]

There is no universally accepted correlation between yield strength and hardness. As Ed stated, it's a construct of engineering to standardize a point just past the deviation from the linear elastic region of a stress-strain curve. ASTM A370 does, however, give a rough correlation between ultimate tensile strength and hardness.

Also, the Hall-Petch relationship is between the yield strength and grain size, not hardness or ultimate tensile strength.

 

[CoryPad]

The relationship hardness = 3x yield stress can be shown by plane strain indentation analysis using slip lines.

 

[EdStainless]

Cory, that would be true yield though not the arbitrary offset value, correct?

= = = = = = = = = = = = = = = = = = = =
Plymouth Tube

 

[seep]

Thanks for tips about the correlation between H and YS, I thought it is working for all metal alloys. I have relatively low YS (200MPa) and high %A (40$), so it will not be working in this case?

Do you have any suggestions have can I explain that my slope of H-P law is different that in the articles? It means that I obtained higher values of hardness for the approximately same grain size (for the samples in the same thermomechanic state).

 

[OGMetEngr]

As we previously stated, the correlation between hardness and grain size is very rough, at best. You can explain the difference from the slope in the articles by stating that there is no accepted correlation between hardness and grain size. Grain size according to H-P correlates to yield (not ultimate tensile), which very roughly, if at all, correlates to hardness.

Also for a high work-hardening FCC metal (austenitic), any cold work will increase yield strength without decreasing grain size. You could simply have cold-worked material and the paper you have uses solution annealed material.

 

[seep]

Thank you!

 

[seep]

Last thing - is it possible that after short-time annealing at 1000C (homogenization), I would have smaller hardness but lower YS than for only forged samples? Grains are bigger so logically hardness gets lower, but YS and even shape of the stress-strain curve doesn't change.

 

[CoryPad]

Ed,

Flow stress in shear, k. Definitely not arbitrary offset value.

If k = Y/[√]3, then applied pressure during hardness testing is p = 3Y, where Y is yield stress.

 

[OGMetEngr]

Your result after a solution treatment would depend on many factors. The grains will recrystallize and, depending on ramp rates, hold times, exact chemical composition, holding temperature, and prior thermomechanical history your grains could grow to be smaller or larger. Your mechanical properties after forging without a heat treatment would depend on the forging steps, finishing temperature, etc.

To summarize, predicting the results after the heat treatment would require knowledge of many more variables than you have provided so far. This is the reason for testing to verify properties after heat treatment.