Hi Ilker, for neutral loading you must maintain the stress state on the yield surface exactly without either loading or unloading, yet while at the same time moving to a new location on the yield surface. In the idealization of our yield surface for J2 plasticity, this means that xi_ij xi_ij = 2/3sigma_0^2 all the time even though the stresses are changing. Think about the phrase I mentioned "the stress state walks along the yield surface". This is not easy to do even in the idealization of our plasticity model, and I suspect this would be really difficult to do experimentally where the shape of the yield surface is less well defined and not necessarily isotropic (material-wise). I believe there were some early works related to yield surface probing experiments. You may want to look for papers by Taylor, Quinney, and Lode for more information. Sorry, I do not have titles for the exact papers.
So perhaps to get an example of a stress state that would work, suppose you were with sigma_x, sigma_y, and tau_xy and plotted a Mohr's circle. This stress state would be exactly at yield by the von Mises criterion. If you were to change the values of the stresses in such a way that the size of the Mohr's circle does not change (and the principal stress values do not change) and could do so smoothly (i.e. small simultaneous changes in stress) then you should be in neutral loading condition (in the idealized case).
Could you please give a few loading path example for neutral loading? Can biaxial tension of a plate in an out-of-phase manner be an example of it?
Hi Ilker, for neutral loading you must maintain the stress state on the yield surface exactly without either loading or unloading, yet while at the same time moving to a new location on the yield surface. In the idealization of our yield surface for J2 plasticity, this means that xi_ij xi_ij = 2/3sigma_0^2 all the time even though the stresses are changing. Think about the phrase I mentioned "the stress state walks along the yield surface". This is not easy to do even in the idealization of our plasticity model, and I suspect this would be really difficult to do experimentally where the shape of the yield surface is less well defined and not necessarily isotropic (material-wise).
I believe there were some early works related to yield surface probing experiments. You may want to look for papers by Taylor, Quinney, and Lode for more information. Sorry, I do not have titles for the exact papers.
So perhaps to get an example of a stress state that would work, suppose you were with sigma_x, sigma_y, and tau_xy and plotted a Mohr's circle. This stress state would be exactly at yield by the von Mises criterion. If you were to change the values of the stresses in such a way that the size of the Mohr's circle does not change (and the principal stress values do not change) and could do so smoothly (i.e. small simultaneous changes in stress) then you should be in neutral loading condition (in the idealized case).