Where is the Neutral Axis for High Manganese Steel?

I may be wrong but as far as I know the neutral axis is function of deformation and not of stress level. If it is function of deformation then it is function of the Young modulus and of the fact that after bending a plane section will rotate but stay plane.

If all this which is a base of formula as in Roark or others is true the neutral axis position does not depend on the "hardening".

The internal stress distribution will depend on the extent of the plastic deformation and the subsequent release: either full release or partial release (as in the formation of square and rectangular hollow sections). The geometric neutral axis of the section does not change and the eventual stresses in the section can generally be based on plastic theory for justification of the section. However, the deflections will be influenced by the residual internal stresses and, if a second order analysis is required, the stresses may also be influenced. Not a full explanation, I know, but if this points you in the right direction then perhaps you could explain a little more as to your problem.

Sorry for taking so long to reply, computer problems.

I use 3D CAD Solid Modelling software in my work and with the package it has a Sheet Metal environment. This environment allows you to unfold &/or unroll SM parts so that you can create a flat-pattern for the profile cutter.

The application comes with a standard K-Factor of 0.44 and this is used to define where, through the thickness of the material, you'll find the neutral axis. The neutral axis is needed by the application to calculate the flat pattern. As far as I understand this the neutral axis is calculated for each bend/fold from the inside of the bend/fold and for the number given it is 44% away from the inside of the bend/fold or 56% away from the outside of the bend/fold.

A K-Factor of 0.44 is for Mild Steel only - AFAIA - and other materials have different K-factors.

The application has another method for calculating the flat-pattern that relies upon a bend table. This data is gather empirically, but as this machine I'm involved with designing is a prototype I don't have sufficient data to create a bend table when you consider I need to bend/fold all of the thickness of material, with all of the various internal radii and to all of the various angles. Plus, as this is empirical I will need at least three of each to get an accurate average.

So I need to know the K-Factor for 14% Manganese Steel. Manganese Steel work-hardens very quickly. For example, take a 10mm plate and hit it with a hammer, then try folding/bending that plate through where the hammer struck, you'll see where the hammer hit the material. This is why I assume that work-hardening would affect the position of the neutral axis in Mn-Steel and therefore the K-Factor.

AFAIA it isn't beyond the realms of possibility for the neutral axis to be outside of the material, particularly for very hard materials that have a low ductility andwhich workharden, which will cause me all sorts of problems as the 3D-CAD application only accepts values 0<K<1 - greater than zero and less than one.

TIA

Actually, I was surprised to find so much information on k-factors from a simple google. Having read through, is it possible for you to do say 6 tests on samples for which you know the results and can predict them with the formulae and also on your manganese steel for the same type of sample? A simple correlation factor might then be easily defined. It may even be that there is no noticeable difference between the two types of steel. At least as far as your process is concerned.

There is quite a bit about K-Factors, but nothing about the K-factor for Manganese steel :(

I found in another CR4 thread the following link: http://www.ciri.org.nz/bendworks/bending.pdf It gives a method for calculating the k-factor from one test. The CR4 thread is similar to yours "Determining the K-Factor for Sheet Metal"

The neutral axis a geometric property - nothing to do with hardness.

I agree with nick about Roark - good source of info on the subject

I think what the questioner is trying to get at is that the "effective" neutral axis varies. i.e. the work hardening and the built-up internal stresses affect the subsequent deformation. The subsequent deformation can then be worked back to give an effective inertia and the effective displacement of the neutral axis. One other point is that when a plate is bent, the change of volume per unit length due to the bending process (which are most apparent at the ends of the plate where bulges and thinnings occur) show that the plate has undergone an overall thinning out. Not much, but a little nevertheless. There is therefore a change in the moment of inertia. The neutral axis, assuming a normalising process takes place, would stay in the middle of the section.

I think what the questioner is trying to get at is that the "effective" neutral axis varies. i.e. the work hardening and the built-up internal stresses affect the subsequent deformation.

The deformation yes but the geometric properties of the section NO.

The subsequent deformation can then be worked back to give an effective inertia and the effective displacement of the neutral axis.

You cannot call it inertia! The definition of the "inertia" is ∫l^2*dA applied to the whole section.

One other point is that when a plate is bent, the change of volume per unit length due to the bending process (which are most apparent at the ends of the plate where bulges and thinnings occur) show that the plate has undergone an overall thinning out.

The deformation in transverse direction you mention are not due to the volume changes but mainly to the fact that the Poisson-strains are not compensated, so that the material state of strain does change;

There is therefore a change in the moment of inertia. The neutral axis, assuming a normalising process takes place, would stay in the middle of the section.

NO and NO and NO What happens is if the stuff is stressed over the elastic limit that there is no more a linear proportionality between deformation and stress. This DOES NOT change the moment of inertia of the section.

I am sorry to say that you mix up notions coming from different directions. I would suggest, if you do not mind, to have a look at some books to make it for you clear. The risk is that misunderstand the origin for different phenomena and this can be under circumstances dangerous.

I think what the questioner is trying to get at is that the "effective" neutral axis varies. i.e. the work hardening and the built-up internal stresses affect the subsequent deformation.

The deformation yes but the geometric properties of the section NO.

I agree that the true geometric properties cannot be thought of as variable; it is geometry after all. Perhaps I'm wrong, but to try to follow up my initial point I was saying that what will actually be seen in real life in terms of the deflections (which may be modelled but is rather complex and not something I would embark upon without some futher reading as you helpfully suggest) could be then given an approximation in terms of an effective inertia.

We have used this technique to good effect in large span structures where plastic behaviour was only present in a particular part of the section. It is not directly applicable here but is an example of where an effective inertia due to strain hardening/plastic behaviour could be modelled.

The subsequent deformation can then be worked back to give an effective inertia and the effective displacement of the neutral axis.

You cannot call it inertia! The definition of the "inertia" is ∫l^2*dA applied to the whole section.

It is effective inertia i.e. what can be used in the calculations in the place of the actual geometric inertia so that the calculations give results that correlate to reality or at least a better approximation than with the geometric inertia.

One other point is that when a plate is bent, the change of volume per unit length due to the bending process (which are most apparent at the ends of the plate where bulges and thinnings occur) show that the plate has undergone an overall thinning out.

The deformation in transverse direction you mention are not due to the volume changes but mainly to the fact that the Poisson-strains are not compensated, so that the material state of strain does change;

That's interesting. I hadn't thought of describing it in these terms. However, I would add that in the bending processes generally, where the material is bent it thins out a little.

There is therefore a change in the moment of inertia. The neutral axis, assuming a normalising process takes place, would stay in the middle of the section.

NO and NO and NO What happens is if the stuff is stressed over the elastic limit that there is no more a linear proportionality between deformation and stress. This DOES NOT change the moment of inertia of the section.

The thinning of the material will lower the inertia won't it? The normalising process (annealing in the deformed state without the ability to release the internal stresses by movement) will release the internal stresses and bring the material back tom the elastic state. Deformations would then be truly elastic again - unless the plastic limit is again exceeded.

I am sorry to say that you mix up notions coming from different directions. I would suggest, if you do not mind, to have a look at some books to make it for you clear. The risk is that misunderstand the origin for different phenomena and this can be under circumstances dangerous.

You do not call it "inertia" but "section characteristic parameter" or as you wish but not inertia.

The "inertia" came out from the elastic analysis of the section stresses in bending. If parts of section are plastically loaded then the integral to relate stresses to bending moment has an other aspect:

a first integral for the elastic core and a second one for the elasto plastic zone outside the elastic core.

It is not any more what is usually called "inertia".

No comment on last §?

I'm just happy to discuss things. A small comment on your last paragraph is in my first paragraph. Effectively, when I realise that I don't know enough, I go away and read up. I suspect it will require some number crunching too, so as to properly understand the magnitude of the effects. Thanks for your advice and comments. Do you have any further comment in response to the thinning of material and the corresponding reduction of the second moment of area?

To make it more clear. In the assumption generally accepted that a section which was plane before loading stays plane after loading. The difficulty is to make the clear difference between strain and stress.