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Isotropic hardening and kinematic hardening

I've been trying to figure out difference between isotropic and kinematic hardening.

As I see,kinematic hardening can model reversible nbehaviour of metals (Bauschinger effect).

In isotropic hardening, the yield surface increase in size, but remain the same shape, as a result of plastic straining.

That is, if the yield surface is represented by a cylinder of radius "A" then an increase in the radius denotes an increase in the yield stress as a result of plastic straining.

However,this cannot capture Bauschinger effect as when unloaded and reloaded in compression (if earlier was loaded in tension) there is no sign of reduction in palstic limit.

As I see, in kinematic hardening there the yield surface translates from its original position (thus there being a change in center of cylinder) which makes the difference.

Can anyone explain this more clearly (or correct me)-with a physical intuition?


I am in the beginning of my journey to understand the differences, so please feel free to toss in your opinion or perceptions.

You can go to the textbook definitions--isotropic hardening means the yield surface can expand isotropically (same in all directions) but the origin of the yield surface is stationary, while kinematic hardening allows translation of the yield surface.

These meant little to me, so I did more searching. Most references I found discuss the 2 in context of how to model with the Finite Element method, and describe the differences schematically by drawing how each would look in a 1-D stress strain curve. What's the difference? Say you pull on a metal like aluminum--at first the stress strain curve is linear, then it starts to bend over as you get near or past yield. Stop pulling, this is Smax (max. stress). Then release the load and now go negative with the load. The stress strain curve (if the coupon doesn't buckle!) will start to bend over again, this time in compression--call this stress Sbend. If your material reaches a stress level Smax before bending over (Sbend= -Smax), that's a good indication that the material is isotropic hardening. If the difference Smax-abs(Sbend)=2*Syield, then that's a good indication you have a kinematic hardening material. Note "abs" means Absolute value of the argument.

Note that most FE codes allow you to use kinematic hardening (KH) if and only if you have a bilinear or multilinear material constitutive relation--you cannot for instance model KH with a Ramberg Osgood or power law material. I am sure there's some numerical reason for this, but I don't know the reason, wish I did.


My physical intuition is then that the difference between the 2 becomes obvious when you note have far down in stress the material will compress in a 1D stress-strain test before it starts to bend over or yield.

srikumar.gopalakrishnan's picture

Kinematic hardening - The yield surface translates

Isotropic hardening - The yield surface dilates

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