The title of the discussion is too categorical.

In my opinion, it is better to talk about the scope and materials for which the use of the concept of stress intensity factor is correct.

For ideally and almost perfectly elastic materials, the concept of SIF is applicable and there is no point in abandoning it at all. Only together with the rejection of continuum mechanics.

The concept of stress intensity factor and fracture toughness does not make sense for material that is not prone to stress concentration.

Thanks for your kind reply, Dr. Borovik! It is always nice to meet scientists dealing with fracture mechanics, too!

I am with you that SIF is one stress-based key parameter in LEFM since I understand you are working with stresses and therefore choose SIF as fracture criterion.

However, I would like to note here following remarks which need to be addressed here as they are highly contradictionary:

⛔ In reality, non-linear plastic failure effects prevail for #lightweight #materials, so this is the first major concern.

⛔ K is only valid for linear-elastic isotropic and homogeneous materials with vanishing plastic effects.

⛔ This is not the case neither for #metals, nor for #composites used in the #aeronautical #industry or #adhesives.

⛔ K is a prothesis in order to prevent infinite stress values, which is physically nonesrnse.

⛔ None of my student I teach can imagine the unphysical unit MPa × Squareroot (Meter).

⛔ K cannot be used as non-linear plastics failure criterion.

⛔ K full ignores plastification and yielding.

✅ K holds for #glass and #ceramics

✅ #fracture #energy GF is a modern and authentic failure criterion.

✅ #structural #software packages can easily cope with removing K with GF.

Invited to follow me on LinkedIn and YouTube!

#adhesiveadvisor #fractureanalytics #research

I agree with your analysis.

Any tool is better to use for its intended purpose. You can shave with an ax, but it's not convenient. But this does not mean that the ax is bad.

Fully aggree with your valuable contribution, Dr. Borovik!

I really doubt K is not worth the effort in determination.

But I respect the widespread usage still ongoing today.

However, what really anoys me is the wrong application of K in uncountable papers in science for "wrong materials", such as adhesives, plastics, metals, wood, concrete and composites.

I will fight against such biased and unauthentic works and claim scientific ethics to be kept by understanding the fundamental basics of fracture mechanics first before starting a related investigation.

Dear, Dr. Martin Brandtner-Hafner,

I am also saddened by the publications about the use of fracture mechanics outside the scope of its applicability.

My research interests, if you notice, are structural materials (with any chemical composition) that are not prone to stress concentration and for which fracture mechanics is not applicable. I mean materials whose morphology and mechanics of structure are borrowed from biological structural materials.

The best adhesives and glue joints have the bio-inspired morphology and mechanics too. So, the fracture mechanics is also not applicable for good adhesives :-)))

As a fact, Dr. Borovik!

We should try our best by educating and doing research in a good ethical manner!

Happy New Year 2023 to you and your team!

Dr. Martin Brandtner-Hafner

Thank you very much.

I wish you good luck in the new year. Everything else depends on us.

As an addition, I would like to draw attention to the Fracture Mechanics Paradox:

Fracture mechanics was created for structural materials. However, the better the structural material or adhesive (the less it prone to stress concentration), the less fracture mechanics is applicable to it.

As a fact! Like this philosophical paradoxon!

See you in 2023!

Best regards,

Martin

I believe we're misunderstanding the nature of Stress Intensity Factors.

1. The concept of SIF holds originally for a specific range of material behavior, i.e. the linear elastic regime, not for a specific material. Given that all solids have an initial elastic response, and the majority of them have an initial linear elastic response, it is a model applicable to all kinds of materials.

2. The SIF does NOT prevent infinite stress, it is actually a very elegant way to describe the intensity of the stress singularity at the crack tip. In linear elasticity, stress diverges as 1/sqrt(r) where r is the distance from the crack tip irrespective of boundary conditions and loading. Thus, stress does not characterize a specific solution to the crack problem (i.e. given a specific geometry, material, boundary conditions, and loads). However, it can be shown that the stress field at the crack tip can be written as a series of powers of r, the first being r^-1/2. The SIF corresponds to the first coefficient of the series, i.e. the coefficient of the leading order term. It characterizes the divergent growth of the stress, in a one-to-one relation with the geometry, material properties and BC of the problem. Thus, it specifies uniquely the solution to a particular crack problem.

3. Keeping in mind the nature of the SIF, its unit is actually quite meaningful: [K] = S*sqrt(L) (K=SIF, S=stress, L=length). Given log=natural logarithm, log(K) ~ O(1), i.e. is a finite number, while log(S*sqrt(L))=log(S) + 0.5*log(L). Thus log(S) ~ -0.5*log(L) . In plain English, the unit of SIF tells you by how much the stress increases when you move closer to the crack tip by half a decade of length units (we need to work in log-log scale).

4. A SIF criterion is useful to estimate whether a change in the load or BC would lead to failure in the elastic regime. Failure means that the crack starts to grow, but the SIF criterion does not tell you by how much. But for industrial applications, that is enough. It is still too risky today to try to design a structure with a controlled crack growth. In most safety critical applications, final designs are based on safety factors that are 3-4 times the values provided by a LEFM analysis.

5. SIFs can deal with plasticity, and there is a rich literature in what is called elasto-plastic fracture mechanics (see for example the early works of Rice). The divergent stress profile close to the crack tip reaches the yield strength of the material (Sy) at some distance Ry from the crack tip. Inside the region r

A very extensive analysis.

Unfortunately, I did not find in this analysis a point about the possibility (or impossibility) of applying the fracture mechanics and SIF to materials that are not prone to stress concentration (Fig. (c) on my slide).

As we know, SIF will always carry meaning in fracture mechanics. The idea was essential for analysis of failure in brittle solids with stress concentrations (for example cast iron). In addition, in theoretical work linear elastic solid is analyzed using SIF framework to get interesting (and sometimes counter intuitive ) solutions for example, layered materials etc.

It follows from your answer that SIF and fracture mechanics is not applicable to materials that are not subject (not prone) to stress concentration.

Did I understand you correctly?

@Arun Agrawal: I am aware that SIF was a mathematical prothesis to fix the problem of infinite stress at the crack tip.

However, if you ask a student to explain the weird units of MPa *SQRT(m), he would shrug his shoulder.

The point is you use a horse instead of a tesla to drive. This might be fine when there is jam, but is counterproductive on a highway.

Switching to energy based parameters can avoid horrific mathematical nightmares and ad enourmous value in fracture analytical interpretation.

Dr Martin Brandtner-Hafner

The units of SIF show a square-root singularity at the crack tip. It does explain infinite stress at the crack tip with a satisfactory and, rather an elegant solution. The cracks always exist in materials (in ceramics and metals). Before this people were using tensile strength (not fracture strength) based criteria in design. I guess incident of failure in liberty ships caused the initial development of fracture mechanics. It was difficult to explain. This was WWII. SIF circumvents the problem of infinite stress, using mathematical expressions. Small cracks do not lead to failure as SIF is less , although theoretically stress is infinite at the crack tip. So SIF based solutions have wide use. SIF framework is very special horse.

Energy based criteria is also used. However, SIF is simpler as it refers to stresses. There is also coupled criteria (SIF and energy) pioneered by Leguillon. The two are inter-related. And energy alone shall not be helpful. In terms of material parameters - there is fracture strength which relates to SIF and fracture toughness which relates to energy release rate for crack propagation.

We have opened the "Q&A" question What is the concept of the stress intensity factor as defined by Irwin and its utility?

It is stated what follows:

The ʺstress intensity factorsʺ concept is known from Irwin (1948, 1957) who linked these to the energy release rate (crack extension force per unit length of the crack front) in the case of a crack in a two-dimensional crack analysis. In practice (to be used in three dimensions), the crack is viewed planar (Ox1x3) with a straight front running indefinitely in the x3-direction, perpendicular to the crack propagation x1-direction. In this situation, the utility of the stress intensity factor is apparent.

In the general case in three dimensions for a crack with arbitrary crack front, the goal is to reach the crack extension force G per unit length of the crack front. We just need to ask two questions:

(1) What is the definition of G?

(2) How to obtain the crack-tip stresses necessarily involved in the expression of G?

For (1) the definition of G, we may refer to Bilby and Eshelby (1968) or to our works (for the elliptical crack, see 2021, and very recently, The rough conoidal crack, 2022).

For (2), it is required to be able to calculate the matrix (6 components) of the stresses. We are using the idea that the crack-front is a dislocation (see our works on non-planar cracks). Hence, we need a clear modelling to proceed in practice. We know no other procedure.

Then you will discover the limitation of the concept of the stress intensity factors as defined by Irwin as being able to provide all the six stress components at the tip of the crack and their connexion with G.

Excellent contributions! Thanks for putting live into this discussion.

PS: @arun, as a fact! WW2 times are thankfully over and a lot of novel research has been done since then.

I prefer methods without crack-length monitoring which means no K, GIc and JIc or R curve. Also, industry such as adhesives industry, does not apply such factors for adhesive selection since the customer does not understand their concepts nor they are willing to pay expensive fracture tests.

So, lap-shear strength is the dominant evaluation parameter related to technical datasheets and it is not expected that will change in the near future.

There are two approaches to fracture mechanics: Early Grifits-Kolosov, associated with the abstract criterion K1c, since with a linear approach, the stresses at the tip of the crack tend to an infinite value and the coefficient at the equation K1. And at K1c, the crack grows. This is a forceful non-physical approach. However, another physical approach is based on the energy of formation of a new surface G. In this way, nonlinearity and plasticity zones at the top of the fracture can be taken into account. But in the linear case, these quantities are related -. G=(K1)^ 2/E . where E -module of elasticity. The energy approach is closer to physics and can be applied to different materials

Dr Martin Brandtner-Hafner, Thanks for pointing that out. I was not so sensitive, although I traveled quite a bit in Europe. Reference of liberty ships is from fracture mechanics textbooks and we all look forward to new research.

For adhesives, with lap shear test you are measuring interface shear strength, as I understand. In fracture mechanics, we always assume a crack.

Having used linear elastic fracture mechanics for more than 30 years to safely design critical airplane parts, I am surprised to hear that the days of the stress intensity factor may be limited. Caveat, almost all of my experience is with design of metal parts. I can't imagine using LEFM on an adhesive joint; even the stress analysis is not linear.

Thousands of parts on every airplane are designed within a framework of damage tolerance, yielding safer designs from engineers without overly demanding academic backgrounds. Very safe (and very advanced) airplanes are designed by people with a BS or MS in aerospace, civil, or mechanical engineering, PhDs in fracture mechanics.

The important goal in aerospace design is not accurate but rather conservative analysis leading to a safe airplane, not one that weighs as little as possible. LEFM has made airplanes (and many other things) much safer.

Speaking of a crack, we mean the stress concentration at its tip and the stress intensity factor as its characteristic.

The specificity of adhesives is that their modulus of elasticity is usually much lower than the modulus of elasticity of the parts to be joined. Proportionately lower is the stress concentration in the adhesive joint with a crack, even for a perfectly elastic adhesive.

In plastic adhesives, and especially in so-called bio-inspired adhesives, the applicability of the apparatus of fracture mechanics is vanishingly small. In this sense, the concept of stress intensity factor for such adhesives, figuratively speaking, is living its last days.

Dr Valery Borovik, I agree. In lap shear test there is no crack (or insert crack). So SIF has no meaning. Some specimens like DCB specimen for Mode I delamination toughness of unidirectional composites have a crack. Secondly of course polymers have small linear region for applicability of LEFM ( in specimens with a crack).

That is why I prefer fracture energetical criteria such as GF - the area under the fully recorded load-CMOD diagram.

Lap shear test also is a dying species in the long run as no interface characteristics can be derived because of the missing crack propagation.

About adhesives: although there is less stress than in the adherends, there is still a propagating crack during delamination so fracture mechanics is still into play.

Luca di Stasio, congrats to your excellent analysis! It seems you are a real priest watching over the legacy of the SIF religion 😁.

However, I cannot aggree with the most points as I do believe into fracture energy religion.

Most materials do not support SIF - regardless if they have a linear elastic behaviour. This is before cracks appear so it seems like comparing apples with oranges.

The mathematical nightmare of stress based explanation of fracture is also not very appealing. Also, crack path monitoring is a necessary condition for SIF if the material is brittle. Banker-Sills did some research with anisotropy and SIF but then you got a lot of trouble mathematically with complex numbers. So why still trying to measure the process zone with r for materials with almost no process zone? This is contradictory.

Also, from my point of view, industry do not need safety factors of 3 to 4 anymore when lightweight design comes into play as this is a waste of costs.

I can speak for polymeric foams, composites and adhesives as well as wood and concrete. We have tested them all without crack length evaluation by simply recording cohesive strength over CMOD. This cohesive zone law explains enough for our clients to make firm design decisions with highest efficieny and empirical validity.

Excellent FEM models with highest fit included. Industry is not begging for more as no customer of us will or want to understand SIF. Too complex and extensive wit ph doubtful meaning.

I recommend to study Hillerborg, Bazant, Schwalbe, Nakayama, and Argon - excellent pioneers.

The problem is that energy release rate (fracture energy) is not independent of SIF. There is actually a direct relationship between the two: Gi=(Ki^2)/E', where E' is the correct elastic constant depending on mode and problem type (plane strain, plane stress). It means that 1) the strength of the singularity is directly proportional to the square root of the energy release rate, 2) a critical SIF is nothing else than a critical value of the energy release rate for which the crack starts to expand (i.e. new crack surface is formed).

Furthermore, all materials are capable of sustaining stress concentrations. Stress concentrations are due to geometry, not material properties. On the other hand, it is not physical that the stress diverges to infinity. It is a feature of the mathematical model we call elasticity (not only linear). It is from this observation that the work of Barenblatt and Dugdale stems from, i.e. the idea of concentrating whatever dissipative process happens at the crack tip in a small region around it. A critical length scale becomes a material property. Outside of this region things are still described by LEFM and SIFs. Moreover, the cohesive zone model is built upon stress intensity factors and their superposition (see for example Barenblatt).

In summary, mathematical models are tools and no tool is good for everything. Thus, I'm not claiming that SIFs are the best tool in any problem involving damage and fracture. However, they are a fundamental step-stone of most models (cohesive elements, X-FEM, phase-field fracture,...) and still of use in practical applications.

Martin Brandtner-Hafner Excellent FEM models are based on the mathematical nightmare of stress-based explanation of fracture. And without knowing the details of this mathematical nightmare, FEM results are meaningless. Garbage in, garbage out. They need to be interpreted correctly. FEM is just a calculator, so you need to know what's being computed.

to Luca Di Stasio

1. The fracture energy of the specimen, as the area under the full deformation diagram, is in no way related to the SIF and, in general, the presence of a crack in the specimen.

2. Not all materials are prone to stress concentrations. As an example, attention can be paid to biological structural materials and adhesives. The main difference between the artificial structural materials familiar to us and biological structural materials lies precisely in the tendency to stress concentration.

As an example of an artificial structural material, morphologically and mechanically similar to biological structural materials, I can offer a rope, cable or a pressed bundle of unidirectional glass fibers.

there is no SIF meaning for some polymers for example, rubber. However, SIF has very strong basis for mathematical and experimental analysis. SIF specimens for example ,CT (compact tension or SEN (single edge notch) are used for fracture toughness evaluation for metals and ceramics. Wondering which specimen is used for concrete properties

Undoubtedly, fracture mechanics and SIF have a very strong basis for mathematical and experimental analysis. Nobody objects to this.

This discussion, in my opinion, concerns the narrowing scope of this tool due to the emergence of new materials and adhesives, including those in which stress concentration does not occur near defects and inhomogeneities.

And here it does not matter whether they are polymers, metals, ceramics, etc. Only the mechanics of the material matters here.

And the fracture toughness of concrete is determined, among other things, on specimens with a notch (SENB) under the three-point bending. I saw it myself.

We are using MCT (modified compact tension) test for evaluating concrete.

It based on CT but modified used for measuring the GF value, which is the area under the stable load displacement diagram. Most important benefit: all free of crack monitoring. Only CMOD and separation force are recorded.

Easy, fast and efficient.

@Luca Di Stasio:

I aggree with Valery Borovik!

GIc is not the fracture energy G

(Nakayama 1965: Direct Measurement of Fracture Energies of Brittle Heterogeneous Materials - NAKAYAMA - 1965 - Journal of the American Ceramic Society)

GF is the specific fracture energy by G dividided by the ligament area Alig of the fractured specimen.

GF is the area under the Stress-CMOD diagramm including post-peak behaviour.

GIc is a peak value, GF a material law.

GIc ignores plasticity, GF implies it.

GIc is a small amount of the energy dissipated because of ignoring post peak area.

Besides, it is new for me that Barenblatt is using SIF.

Cohesive Zone Modelling is based on GF values according to Hillerborg (1985).

Gc is also the cohesive energy and equivalent to GF.

GIc and SIF does not correspond to GF because they are measuring crack length a.

GF and CMOD do not need crack length a.

@Martin Brandtner-Hafner

Maybe you will be interested.

For stable fracture of specimens, even from very brittle materials, I use parallel elastic elements.

Yesterday I delivered a presentation (in Russian). The report outlines the ideology of structural materials that are not sensitive to the presence of cracks, for which the concept of stress intensity factor does not make sense.

Perhaps this presentation will be of interest to the participants in this discussion.

Valery Borovik, thanks for sharing!

I am really sorry Martin, but I find that I must question almost every point that you raise on the slide.

1) Only valid for glass and ceramics?

It is widely used throughout the aerospace industry for metallic airframe structures for assessing both the durability and the damage tolerance of airframes. I can give you a number of examples which I have personally done to show that it's PREDICTIONS work and that you can use data from simple constant amplitude tests to PREDICT the durability of complex operational structures under complex operational (variable amplitude loading). A couple of examples are given in:

Jones R., Fatigue Crack Growth and Damage Tolerance, Invited Review Paper, Fatigue and Fracture of Engineering Materials and Structures, (2014), 37, 5, 463–483.

Jones R., Peng D., Singh RRK., Pu Huang, Tamboli D., Matthews N., (2015) On the growth of fatigue cracks from corrosion pits and manufacturing defects under variable amplitude loading, JOM, Vol. 67, No. 6, pp. 1385-1391

2) Too complex for applications.

This point is addressed in 1). Complex problems with real life complex geometries under complex operation load spectra are now routinely tackled. For example tis can be done in Abaqus, Nastran and Ansys in an automted fashion using the Zencrack software program, see

https://www.zentech.co.uk/zencrack_publications.htm

3) Only valid for isotropic materials.

I can give you a hundreds of examples, that I have personally done, that confirm how the stress intensity factor approach can be used to characterise the growth of materials that have anisotropic behaviour. The 50+ examples that cover crack growth in Additively Manufactured Ti-6Al-4V, where growth is dependent on the direction of the crack to the build direction and also to the build process, given in the References below is but one example.

Jones R., Peng D., (2022) A Building Block Approach to Sustainment and Durability Assessment: Experiment and Analysis, Reference Module in Materials Science and Materials Engineering, Elsevier Reference Collection.

https://www.sciencedirect.com/science/article/pii/B9780128229446000360

Much of this data can also be found in:

R. Jones , C. Rans, A. P. Iliopoulos, J. G. Michopoulos, N. Phan, D. Peng, Modelling the Variability and the Anisotropic Behaviour of Crack Growth in SLM Ti-6Al-4V, Materials 2021, 14, 1400. https://doi.org/10.3390/ma14061400

4) Ignore crack shielding.

Peoples understanding of the importance of crack tip shielding is often not commensurate with that see in service. For example as explained in

Jones R., Fatigue Crack Growth and Damage Tolerance, Invited Review Paper, Fatigue and Fracture of Engineering Materials and Structures, (2014), 37, 5, 463–483.

The USAF experience is that cracking in operational aircraft exhibits a linear relationship between the log of the crack length and flight hours, see

Berens AP., Hovey PW., Skinn DA., Risk analysis for aging aircraft fleets - Volume 1: Analysis, WL-TR-91-3066, Flight Dynamics Directorate, Wright Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base, October 1991.

This observation is supported by the RAAF experience in 35 years of operating the Boeing F/A-18 aircraft, see:

Main B., Molent L., Singh R., Barter S., Fatigue crack growth lessons from thirty-five years of the Royal Australian Air Force F/A-18 A/B Hornet Aircraft Structural Integrity Program, Int. J. Fatigue, 1330 (2020). https://doi.org/10.1016/j.ijfatigue.2019.105426

As a result, when normalised the crack growth curves associated with operational aircraft all collapse onto a single curve, regardless of the material or the flight load spectrum, see

Jones R., Singh Raman RK., McMillan AJ., (2018) Crack growth: Does microstructure play a role? Engineering Fracture Mechanics, 187, pp. 190-210.

Jones R., Peng D., Pu Huang, Singh RRK.,(2015) Crack growth from naturally occurring material discontinuities in operational aircraft, Procedia Engineering, 101, pp. 227 – 234.

So if there is significant inelastic material effects why do this happen? You will find that the fracture community was issued a challenge to explain this, amongst other things in the 2018 Eng Fract. Mech paper.

I could go on and on. But let me stop here and merely say that for operational aircraft you can PREDICT their durability using LEFM, and also predict the crack growth history from near micron size material discontinuities using LEFM.

What more could you ask from K?

Probably, similar words to car lovers were said in the century before last by people who rode horses and in horse-drawn carts.

Important discussion. Thank you. I haven't read all the comments, but I hope we recall that K is meant to be a similitude parametre. Regards L

Great comment from Lorrie. I am currently rubbing down my horse and putting her in the stable overnight, so I might leave someone else to draw out the implications wrt Lorrie's Similitude comment. I have to end here and get back and lock the stable door just incase the horse bolts.

I just wanted to draw your attention in this way that the improvement of structural materials is in the direction of reducing their tendency to stress concentration, the presence of cracks and, accordingly, the applicability of the concept of stress intensity factor to them.

Namely, the Improvement of Structural Materials counts the last days of the applicability of the stress intensity factor.

Hopefully, the development of the next generation of structural materials will take less time than the journey from a horse cart to a modern car.

Relax Valery, it's good to see people being passionate about their research fields.

I have zero knowledge about biological materials. None at all. That said, I have worked in what I would term the field of solid mechanics for many years. With the coming of age of 3D printed metallic structures I do not see the discipline of fracture mechanics and the widespread use of K disappearing in my lifetime. Quite the contrary, in the past year we have shown how K based approaches can be used to PREDICT the durability of additively managed parts, see:

Daren Peng, Rhys Jones, Andrew S.M. Ang, Alex Michelson, Victor Champagne, Aaron Birt, Samuel Pinches, and Sudip Kundu, Alankar Alankar and Singh Raman RK, Computing the durability of WAAM 18Ni 250 Maraging steel specimens, Fatigue and Fracture of Engineering Materials and Structures, 2022, 1-11. DOI: 10.1111/ffe.13828

So K based approaches are going to be around for quite a while, at least in some disciplines (aerospace, defense, etc).

Of course in adhesive bonding and composites things are best looked at using G based approaches.

Off for a horse ride.

Thank you

Yes, the first motorists, indeed, were crazy fans, I guess.

It is not clear how they managed to infect horse traction supporters with their enthusiasm.

Thank you. I am following the discussion since the start and come from solid mechanics background. So must share this:

1. In a cross-disciplinary fracture characterization project with both experiments and simulations , people from chemistry found infinite stress difficult to digest. Other group was from civil and mechanical engineering. Fracture analysis (or failure analysis) has foundation in materials science has very little overlap with fracture mechanics. Fracture analytics talks about analysis of failure and a book shall have only 5 pages out 100 on fracture mechanics. This is just my boring note about two perspectives. Interesting discussion, as K is the most important parameter for any theoretical work.

2. In my understanding the main point here is that for adhesive evaluation, it does not need fracture mechanics. K was never meant for adhesives. A DCB test or TDCB would not tell anything about the adhesive. So it would explain the composite fracture and characterize the fracture toughness of the composite (with fracture mechanics concept).

Yes, Arun. But unfortunatelly there are plenty of papers here wrongly using K for adhesives and bonded composites. So not only such authors lack in fundamentals of fracture mechanics but so are their reviewers as well.

Some basic concepts of fracture mechanics are crucial, the first attempts made by Griffith with his famous critical energy release rate and the metric introduced by Irwin which is the K factor which was linked successfully experimentally, empirically and analytically by earlier authors' works to the Griffith's energy release rate under some assumptions are the basics of the latest released concepts of fracture mechanics, these are well saved in handbooks for many solved problems and cases .

The latest regularization introduced by Francfort and Marigo, the functional introduced recently by Ambrosio and Tortorelli which has given birth to the phase-field fracture approach, all of these embed in a manner the concepts introduced by Griffith and Irwin.

@brick Amine, interesting reply. However, I disagree that GIc and K are among the latest concepts in fracture analysis since they are very old and more sophisticated approaches are already on the market.

I invite you to check out my profile to learn more and follow me on LinkedIn.

@Rhys Jones,

Thanks for your comprehensive contribution!

But I need to disappoint you as I fully agree with Valery: I don't See a bright future for K especially in my fields of activity like adhesives, composites, concrete, foams, bones, teeth, and plastics for multiple reasons.

I will stay on CMOD and GF values according to Hillerborg 1985 and will foster creating own benchmarks with FRACTURE ANALYTICS.

Regards

The stress intensity factor is valid for materials with cracks sounded by materials with a thickness equal to and greater than the length of the crack. If the material is ductile the deformation occurs at the crack tip dispersing the effect of stress concentration. K or even G cannot characterize the stresses around such cracks.

Rhys:

This is a question that has been raised for half a century or more - I can remember Keith Miller, when I was a graduate student, opining that delta-K could not be used to describe fatigue-crack growth - nevertheless fracture mechanics is still successfully used today. As long as one is properly aware of the basis and limitations of governing parameters such as K and J, I still believe that they have a powerful application. However, this is not always the case when they are used and accordingly fracture mechanics has become one of the most abused form of mechanics.

If you think that this approach should be dismissed though because of its "limited validity and questionable interpretation", could I respectively ask what you would recommend as a replacement?

cheers Rob

From the fact that the hammer is sometimes abused, it does not follow that it should be replaced. It should simply be used for its intended purpose - for driving nails.

Fracture mechanics is good for glass and other brittle materials.

The farther the material is from linear elasticity, the less linear fracture mechanics and stress intensity factor are applicable to it.