Whether one is under fatigue loading or monotonic loading, a state of plane strain ("plane", not "plain" please) will be achieved when the plastic zone at the crack tip is small (by about an order of magnitude), as compared to the out-of-plane thickness dimension of the component. Under cyclic loading during fatigue crack propagation, the critical zone size is that of the maximum plastic zone at the maximum load of the fatigue cycle. With the crack growing and the maximum stress intensity of the fatigue cycle (probably) increasing, conditions may transition from plane strain to that of non-plane strain (often loosely referred to as plane stress) as the plastic zone gets larger with crack growth. The effects of this transition can be several fold; for example, in many materials the fatigue fracture can transition from a flat to a 45 degree slant fracture, which often can accelerate the crack-growth rate. However, the effects of stress-state are not as large during fatigue crack propagation as one might see when measuring the fracture toughness. If anyone is interested, I discussed these stress-state effects on fracture and fatigue crack growth in a very old paper of mine; please see Ritchie, Smith & Knott, "Effects of thickness on fibrous fracture from a notch and on fatigue-crack propagation in low-strength steel," Metal Science, vol. 9, Nov. 1975, pp. 485-92.

Fracture surface examination a good way to qualitatively distinguish stress states.

Pl. refer this following article, 

M. Nani Babu, , C.K. Mukhopadhyay, G. Sasikala, B. Shashank Dutt, S. Venugopal, Shaju K. Albert, A.K. Bhaduri, T. Jayakumar Fatigue Crack Growth Characterisation of RAFM Steel using Acoustic Emission Technique, Procedia Engineering, Volume 55, 2013, Pages 722–726

At plain stress state under cyclic tension the  plastic deformation rate much more in comparison with plane stress condition.

The growth of plastic zone may differentiate between plane strain and plane stress conditions. In plane stress case growth of plastic zone is faster.

In plain stress condition the ratio of crack mode II in comparison with mode I is more than in plain strain.

Dear Professor Ritchie:

generally, how the stress state infuence the brittle and ductile fracture process and their fracture surface morphology?

Dr. Hou:

The effect of stress-state, often defined as the ratio of the hydrostatic to equivalent stress, is critical to the development of fracture and the resulting measured fracture toughness in metallic materials. The most damaging (or effective) stress-state is a triaxial stress field, which is developed in highly constrained geometries in plane strain, such as deep-cracked bend samples (and even deeply circumferential-notched tensile samples), where the ratio of the hydrostatic stress to the equivalent (Mises) stress can reach as high as 2, as compared to 1/3 for (unnotched) uniaxial tension.

Such a triaxial stress-field is very effective in promoting brittle cleavage fracture, as the highest tensile (opening) stresses are developed (on the order of two crack-tip opening displacements ahead of the crack tip), the plastic-zone size is limited and through-thickness yielding is inhibited - the latter by the state of plane strain - all of this restricts any relaxation of the high stresses to promote brittle transgranular cleavage fracture (or sometimes intergranular cracking).

Such triaxiality is also important for ductile fracture involving microvoid coalescence.  There is evidence that the high mean stress associated with a constrained hydrostatic stress field can promote crack initiation, either by cracking a particle (e.g., like carbides in steels) or promoting its debonding from the matrix (e.g., as many inclusions in steels).  However, the major effect is in the growth of the resulting voids that form around these particles; clearly, it is more effective to pull the material apart in three directions as opposed to merely one direction as in uniaxial tension (until maximum load when necking commences, that is).  According to the simple Rice and Tracey model, the resulting ductility, which is the fracture strain when these voids link up, will be proportional to the reciprocal function of the exponential of the ratio of the hydrostatic to equivalent stress, i.e., the ductility  can be reduced by more than an order of magnitude when comparing values (measured for ductile fracture) in a triaxial (plane-strain) stress-state compared to that in simple unnotched uniaxial tension.

The bottom-line here is that a triaxial stress-state can have a major effect in promoting both brittle and ductile fracture.

ROR

Dear Prof. Ritchie,

When CT sample  thickness is reduced, there is tendency of buckling. The buckling will also leads to slat fracture. How can we distinguish whether slat fracture is due to buckling or plain stress condition? How can we calculate limiting thickness to avoid buckling in CT specimen?

Dr. Bind:

Compact-tension C(T) specimens, or any other fracture mechanics sample for that matter, should only have a tendency to buckle when they are thin, of course, but also when the loads go compressive, and so I have to assume here that you are referring to fatigue crack growth measurements where loads could be below zero.  In these situations, it is customary to make use of anti-buckling guides positioned directly adjacent and either side of the sample. These are simply unloaded plates which prevent any asymmetry of loading of the specimen.  However, as this restricts any off-axis displacements, these guides may act to inhibit somewhat the onset of slant fractures and so if you're really concerned about this aspect - whether it's due to some degree of buckling or the existence of nominally plane-stress conditions, I would perform the tests with and without anti-buckling guides and see if there is a difference. However, I wouldn't be using compact-tension samples for these tests; it is not an ideal geometry for compression loading unless you have a full stress analysis for these samples under such compressive applied loads - this analysis is unlikely to be simply the reverse of the customary one under tensile loading. For through-zero loading fatigue-crack growth testing in samples with reduced thickness (whatever that actually means quantitatively), I think that you would be better off with using a center-cracked sheet - now called middle-cracked tension MC(T) - sample geometry, where the K-solutions have been used for decades for both positive and negative load ratio loading of thin section sheet.

ROR

Dear Zhengkun:

I'm uncertain how to answer your question as to whether you should perform one or two simulations for the two cases of plane stress and plane strain conditions, as it will depend on the actual numerical analysis that you're using.  I would talk to someone more familiar with the details of your CAE model.

ROR

Dear Prof. Ritchie:

Are the principal strain and principal stress in the same orientation in the complex plastic deformation?

in the plain strain state definition, the Z-direction has stress ,but no strain. is it possible a direction have stress but no strain?

Dr. Hou:

The principal stress and principal strain axes will be the same, but ti is certainly possible to have strain without a stress in a particular direction and by the same token a stress without a strain.  To consider the first case, if you do a uniaxial tensile test on a cylindrical sample, you have a uniaxial state of stress along the axis of the sample but in the radial directions the sample will "Poisson's contract" meaning that the deformation state is a uniaxial state of stress but a triaxial state of strain (as until a neck develops there will be no stress in the radial directions).  A state of plane strain is the other case.  Here for example with a fracture toughness specimen which is very thick in the z-direction compared to the size of the plastic zone, a through-thickness stress will be set up in this z-direction but because the sample is thick, the strain will approach zero.

ROR

Dear Robert,

you mentioned

".. hydrostatic stress to the equivalent (Mises) stress can reach as high as 2 .."

in theory this might be a case..

in the reality to achieve this condition is hmm..!? just wounder to see the sample geometry and notch configuration to make hydrostatic stress as high as 2 of deviatoric V-M. Moreover how it is possible to apply stress in three axes direction to the notch (while we test the sample in just one axial direction with lets say R=-1).

OR we need to consider a type of grain lattice structure and grains orientation within the material tested? in this case everything turns out with more hmm...?!

Thank you (just learning),

Dmitry