# Kinematic and Isotropic Hardening

1. Mar 6, 2009

### darkelf

Hello,

Could anyone help explain what Kinematic and Isotropic hardening are. Any brief explanation or reference to a good book that explains these topics would be very useful.

Thank you

2. Mar 10, 2009

### FredGarvin

I don't spend a lot of time dealing with yielding, so my answer is going to be very basic and fundamental. You'll want to get someone like Mapes or Astronuc in here to help.

Imagine the three orthogonal axes about a point of which the axes are $$\sigma_1, \sigma_1$$ and $$\sigma_3$$. Now draw a sphere around that point. That sphere will coincide with the elastic limit. As the stress at a point increases, a path will go from the state of 0 stress to somewhere in this strress space until it eventually hits the yield surface. As you push past the yield surface by increasing stresses, the material will harden and cause a permanent set in the material when the load is released. For isentropic hardening, the yield surface will grow in size and it will have its center remain in the same place in the stress space. For kinematic, the yield surface moves but the size stays the same. There is also a mixture of the two called mixed hardening.

http://www.engin.brown.edu/courses/en222/Notes/plasticity/plasticity.htm