plane stress is a stress field in two directions (the two in-plane directions) implies strain in all three directions (strain in the thickness direction is due to poission effects).
personally I think it is exactly the same as bi-axial stress.
on the other hand, plane strain implies stress in three directions, usually in thick plates where there is enough material to restrain (prevnet) the plate straining in the thickness direction by creating a stress in the thickness direction.
having taken the time to read the OP again, bi-axial loads can give rise to either plane stress or plane strin conditions depending on the thickness of the panel. if the panel is thin there will be 3D strain (and plane stress). if the panel is thick there will be 2D strain (at the mid-plane of the plate) as the material in the thickness direction has enough stiffness to react the strain in the thickness direction (creating a 3D stress field).
I think rb is on the right track with his latest post. The question is more: In the bi-axial loading case, is it identically bi-lateral along the thickness direction. You can "bi-axially" load a part at a discreet location along it's length, but the stress distribution along that length will not be identical (it will be higher directly under the loading and reduce the farther you get from the loading). For a "plane stress" case, the stress gradient along the thickness is '0'. This doesn't mean that the stress in the plane is '0', just that from node to adjacent node through the thickness, the stress doesn't change (or doesn't change significantly). Plane stress can be reduced to a 2-D problem. Bi-axial loading can't.
"if the panel is thick there will be 2D strain (at the mid-plane of the plate)"
why 2D strain only... if;e.g, you subject a cube to the stresses SigmaX and SigmaY and left the faces normal to Z axis free of Stresses (this is biaxial loading/BC case.. is not it?), then you will have variant strain along the Z axis (due to Poission ratio effect) but your stress along z axis will be zero.
Please correct me if I am wrong
i'd say that the stress at the surface would be zero but at the center of your cube you'd probably have 3D stress.
BUT a cube is not a good example of the point I was making (because you're not talking about a size, and size is important). If you have a plate 10"x10"x1" thick and you apply bi-axial in-plane loads to it, I would say that this is going to develop a 3D stress field. If you have a sheet 10" x10"x0.01" then under bi-axial loads this sheet will exhibit 2D stress (ie 3D strain) 'cause there's not enough material to restrain deflections in the thickness direction caused by poission effects).
bi-axial loads can produce bi-axial (plane) stress or tri-axial stress (plane strain).
I believe what you have described, if I understand you correctly, is plane stress...a special case of bi-axial loading. I would suggest you find a good Mechanics of Materials text and review the requirements for "Plane Stress".
I change my mind that biaxial loading on a specimen is not necessary plain strain case.
I think what rb1957 said is correct: bi-axial loads can give rise to either plane stress or plane strain conditions depending on the thickness of the panel and the constraint conditions.
For soildynamics: at your post 8.8.2007 12:17, I think there is something missing. A cube is not the same as thick panel. For a think panel, you can say it's plane strain problem.
For a cube under biaxial loading, i think it'll be plain stress as GBor also said. Imagine the cube is vertically loaded compression pressure while horizontal pressure 1 is kept constant and no loading pressure for the other horizontal direction.
Doesn't 'biaxial' imply non zero normal stresses (or all the other stresses, normal and shear, are near zero or zero) in only two directions? Though I have never seen that used any other way besides for a thin, rectangular plate (plane stress that is), loaded with tension or compression normal to the outside edges, I can guess that this definition of 'biaxiality' would be too restrictive. What would you call the stress state in a structure with all stresses (normal and shear) zero except for two (say two shears, or a normal and a shear)? The axial part of biaxial implies in the direction of one of the coordinate axes; however, why exclude shear stresses from the discussion? Because of historic convention?
