Dear Dietmar

I do not know the ISO13 586, but for tests on SENB as in CT the fracture energy is obtained from Stress Intensity Factors solutions and the Irwin fromula for G if the specimen remains elastic. If not, you should take into account the plastic part which is deduced from the area under the load-plasticc displacement curve (plastic work). In this formula the plastic work is multiply by a coefficient 2/net section for SENB specimens giving the plastic part of the energy release. The net section does not represent the crack extension. If the material is brittle you should not have stable crack growth. See old papers on the net like the one of T Anderson. The formulae in the elastic domain is exact. In the plastic domain, the energy release rate formula is an approximation working well for deeply cracked specimens.

This estimates the enregy at fracture initiation and the energy spent during the unstable phase is not included in your measurement.

best regards

Philippe Gilles

You are right. This happen because we neglect the constraint issues in the normal calculation. The scientific results  possibly match with the experimental results only at lower loads till the LEFM constraint is valid. You may plan your research to account the difference in the energy through some parameters. Best wishes.

Dr. Shashidhar Kudari

Your assumption that "In an SENB test, the GIc is basically the mechanical energy at max. load (i.e., at fracture), divided by the residual cross-section area of the specimen." is not correct.  Remember, that GIc is the incremental change in the strain energy with the incremental change in the crack area.  You have taken the entire strain energy of the sample divided by the total residual fracture area as G.  That can be very different from the incremental changes. 

The assumption that the fracture is the same across the sample is based on sample size: plane stress is always to be small with respect to plane strain so the size of the samples tested is an important consideration. 

Dear Dietmar,

I do not know  ISO 13586. I gess it should be  similar to the ESIS TC4 protocoles.

If you just follow the protocole the value obtaiend should be a correct value.

Polymers are rather different form metlas since E is a sensitive parameter  contrary to steel that display the same  value independently of the loading conditions and composition. So that the relationship between Gic and kic is not  always so straight.

And sometimes it is recomended to determine Gic independently of the determination of Kic because the uncertatinty in the apparent E value.

However if you are in a plane strain- elastic situation only initiation matters. I belive that you are in a "stick -slip" fracture propagation mode.

This is very common in polymers and there is much work done in the past. 

If possible is better to determine Kic than Gic because it dependes only of the measurement of critical load .

Regards, Patricia Frontini

Dear all,

As I work exclusively on brittle materials, the calculation of G via Irwin's formula always gives results that are very similar to those calculated from the area under the curve, but this is not surprising, looking at the force--displacement curve as the area under the triangular curve is essentially force*force/modulus and considering that the KIc is proportional to the force.

I am just wondering how this calculation agrees with the fundamental definition of the GIc, which is "decrease in energy per increase in area". We don't measure the change in energy, nor do we measure the change in area (other than in other fracture mechanics tests, like in the DCB test). What we do measure is the total energy per total residual area.

Do you know what Anderson's paper is called?

Dietmar

Dear Ditmar,

In any case, the G1c has more scientific sense than other estimations. ...

To get the right answer, you have to study the fracture mechanisms and the situation at  notch tip. In any case, we have to understand that any test on the fracture toughness is test for strength of a notched sample. We must know what we have in withinity of the notch tip before the final failure could happen. Your machine is loading the sample till it will not stop to resist... To get the right answers, you have to know fractographical details of loading and fracture. SEM will help you, I think. As I could understand, your samples are much stronger and tougher than you have expected.

If you have any questions, I could talk.

Kind regards

Oleksandr Vasylyev

Good morning

I would like to add more from a practical side. In brittle homogeneous materials under bending, there is a region (1) under tension separated from a region (2) under compression by a neutral (undeformed) plane; shear stresses may also be present. G1 the crack extension force (per unit length of the crack front) pertaining to region (1) is larger than G2 that of region (2). When incorporating an edge notch in region (1), another quantity is Gc (same mathematical definition) associated with the initiation of the motion of a starter crack. A question is to which G, I have to compare my experimental measurement? Also, am I able to link my finding to physical quantities such as the surface energy...? Proposing a failure stress should be associated to a controlling mechanism: crack nucleation, initiation of starter crack motion (this corresponds generally to transitory crack configurations), or crack propagation (over macroscopic distance).

In fracture mechanics, no general principle can be applied universally. if your material is sufficiently brittle, Griffith's theory will be enough; if it has somehow little ductility, a modified brittle theory will work. In case of brittle polymers, applicability of these theories need to be considered first. fracture here does not necessarily means complete tearing or separation of the tested specimen into two pieces but the condition in which the material ceases to bear any further load. G is defined as the change of strain energy for unit change of crack area, or more correctly, release in strain energy with unit increase in crack area. Thus, it is one of the most fundamental parameter in the fracture mechanics field. Now, for answering your question, you should note that with the onset and propagation of the crack, G changes with load and crack length or area. In the limiting case, G1C is defined as the condition, when crack driving force, i.e. dG/da exceeds or equals the equivalent derivative of maerial's resistance w.r.t. crack length i.e. dR/da and also when G is either equal to or more than R. In all cases, both conditions do not necessarily satisfied at Pmax. This happens because the assumption of continuum does not satisfy completely for real materials and during deformation and prior to fracture at the localized region the material behavior is different from the rest due to presence of triaxiality stemming from constraint. Hence, if the obtained G1C is truely a material property, may be ascertained if you carry out more SENB tests with different sizes and notch dimensions to determine the conditions where the effect of constraint does not change your obtained result. Again, the same experiments should be repeated with specimens with different sizes and other geometry. In principle, for G1C to be certified as a material property for scientific importance, it must be independent of constraints.