Fracture Mechanics - Science topic

Hi, you don't need any special equipment. We don't use it in our lab either. But it is easier to buy a DCPD. On the other hand, you are a little proud when the system finally runs. :)

We use a nanovoltmeter and a PC with a self-written software in Labview.

You have to measure on your sample the voltage drop at your crack ("active signal") and the voltage at a spot without crack ("reference signal"). In addition, total voltage and total current.

We do the evaluation with Matlab. In the standards, you will find the corresponding formulas for the ratio of electrical voltage to crack length.

I recommend the insertion of striations during the crack propagation test for a better correlation of the crack length. A reference test may be necessary.

Regards,

Michael

Respected A. C. O. Miranda Sir,

Based on my limited personal experience which I gained during mode I and mixed mode fracture and fatigue testing of various materials and specimens:

Apart from the very high cost associated with experimental studies, other challenges for conducting fatigue and fracture experimental studies are:

(1) Except for the mode I fatigue and fracture testing procedures specified in ASTM E399 and ASTM E647standards, no standard methodology and specimen are available to perform the fatigue and fracture studies for mixed mode loading.

(2) The fabrication of metallic specimens for fatigue testing itself is very costly due to the requirement of sharp notches which are cut using the wire EDM process. A slight manufacturing error in the specimen results in unexpected crack growth. Creating a proper natural pre-crack in metallic specimens is very challenging.

(3) The loading fixtures required for conducting fatigue and fracture experiments are not easily available. Most of the time you have to fabricate customized loading fixtures for your particular study.

(4) Unavailability of trained operators and fatigue testing machines. Very few specialists are there who exactly know how to perform fatigue and fracture experiments carefully. Also, fatigue and fracture experiments are very time-consuming and require continuous observation (fatigue pre-cracking and further actual experiments).

(5) Unavailability of crack length measurement approaches in mixed mode fatigue loading. For mode I, COD gauges are available to measure the instantaneous crack length, but for mixed mode fatigue tests no such crack measuring gauge is available; mostly optical methods are employed which are not very efficient.

(6) High variability of fatigue and fracture results. It is very challenging to control the repeatability of tests. There are many uncontrollable factors that affect the fatigue and fracture results like pre-crack length, materials intrinsic defects, loading pattern, alignment of the specimen, and many others. The variability in experimental data poses the biggest challenge in formulating the general conclusions from the experimental study.

(7) Need for extensive finite element numerical simulations for determining SIFs of the actual crack path in mixed mode fatigue. No closed-form SIFs solutions are available for an actual crack path for any geometry of specimen used for mixed mode fatigue and fracture testing.

Aftab Khan

A part, made out of PMMA and under a remote load, can withstand a flaw until certain length before that crack grows catastrophically

Dear Hasfi,

The reasons for the initiation of cracks are related accumulated internal stresses between the α and β phases in titanium alloys. These external stresses in the process of operation tend to balance. Cracks can be observed in both solid particles and softer particles of the structure. To avoid this negative effect, normalization is performed to a certain extent or the chemical composition of the spawn is changed in order to reduce external stresses.

With respect

Emil Yankov

Dear Guillermo Elizondo Botello . See the following useful link: http://www.framcos.org/FraMCoS-4/403.pdf

Also check please the following good link: https://www.studentsmeet.org/structural-engineering-phd-thesis-topics-to-consider/

Dear Izaz,

Read these articles, it may help you in your research.

Good luck.

hi,

I recommend you a few papers about fracture toughness:

In the present modelling, the elliptical crack under arbitrary loading is represented by a continuous distribution of infinitesimal dislocations. The conditions under which the crack can be expanded in its own plane are investigated. We show that under applied shearing stresses parallel to the plane of the loop, an expansion is not feasible. Please see "Elliptical crack under arbitrarily applied loading: dislocation, crack-tip stress and crack extension force" in our contributions in Research Gate.

1) Yes, but specimen's length must be roughly smaller than w_u.E/f_t

w_u - ultimate crack opening (see e.g. Hordijk's law);

E - Young's modulus

f_t - Tensile strength

2) No. As mentioned above, it depends on specimen's length.

Professor Manfred Staat ,

Very interesting question indeed. In my opinion the use of strain is more meaningful than stress. I had the same question with regards to the cracking criterion. The criterion is used to find the location of cracking. In the literature, the criteria are mostly based on stress, whether it is the Rankine criterion, Mohr-Coulomb criterion, Drucker-Prager/ Von Mises criteria. Mostly, a combination of shear-based criterion and a tensile criterion is used. I think one of the reasons that strain has been left out of LEFM analyses (and from other fields of mechanical engineering as well) is that the cracking criteria (or failure criteria in general) based on extensional strain were not found successful in estimating the location of the cracking around the crack tip (or failure of material in general). Still, our intuitive understanding is that cracking in opening mode has an extensional nature in essence.

During my PhD research, I tried to look at the problem from a new perspective, discussing the use of a 3D extensional strain-based criterion for opening mode cracking (under low-confinement or tension) and a 3D shear-based criterion for shear mode cracking (under intermediate to high confinement). I discussed this in detail in Chapters 2 and 3 of my dissertation (Directional and 3-D confinement-dependent fracturing, strength and dilation mobilization in brittle rocks (Access: https://dx.doi.org/10.14288/1.0384518)) and explained why the use of a 1-D extensional strain-based criterion that does not consider the influence of confinement on suppression of cracking leads to a wrong estimate of the location of cracking, while use of a 3-D extensional strain-based criterion that considers the influence of confinement on suppression of cracking can give the correct location for crack propagation. I also discussed the application of the criterion to larger scales, including fracturing around tunnels (meso-scale), and regional faults (macro-scale). I hope this would encourage the researchers to re-examine the application of extensional strain-based criteria.

Kind regards,

Masoud

Dear Vanda Nur Ilmi

It is suggested to read following papers:

Dear Sumit Bhowmick

Higher alloying elements like, Cr, Ni, Mo and/ or Al can improve both corrosion, wear and heat resistance due to carbides, intermetallic compounds and austenite formation, Otherwise addition higher percentage of most pervious element decrease toughness of cast iron.

If there is still interest, you might also consider Franc3D. It creates well-configured crack tip meshes, works well with ABAQUS, and calculates very accurate SIFs using M-integrals from the results.

Dear sir,

during my master degree my research work was on laser additive manufacturing.

i would like to pursue my doctor degree on additive manufacturing because of my previous work.

if there is any vacancy on additive manufacturing please let me know.

thank you

Here it is. Good luck

Dear Hasfi:

Both m and C in the simple Paris power-law, for (strictly speaking, the mid-range of) fatigue-crack growth rates, are merely scaling constants set by experiment for a given material. There should be little to no fundamental correlation between them, other than C will tend to decrease as the value of m increases. To my knowledge, no one has attempted such a correlation which, in my humble opinion, would be largely futile. The value of the exponent m does vary in a somewhat systematic manner. If we focus simply on the mid-range of growth rates (as m is naturally higher in the near-threshold and near-instability regimes), its value for metallic materials is typically in the range of 2 to 4. As materials become more brittle, m tends to increase; it can be as high as 15 or so for intermetallics and for ceramics can reach values as high as of 20 to 50 (where an exponential version of the Paris law is probably more suitable).

Incidentally, what happened to your da/dN vs. delta K curve at very high growth rates? - that simply cannot be real!

ROR

I would probably use Abaqus. It will be easier when you implement the characteristics of your material model (user defined material or element).

by the way, for the free edge stress based on elasticity, you don't have a use a 3D FEA with very fine mesh, you can simply analyze a cross-section using mechanics of structure genome and its companion code SwiftComp.

In simple terms, the difference between those two conditions is whether or not the environment during testing is allowing the hydrogen to escape from the metal. After removal from a hydrogen environment, most metals will start to lose their hydrogen content, as the hydrogen atoms diffuse out of the material and recombine to escape as hydrogen gas. The rate of this loss depends on the material (particularly characteristics like diffusivity and solubility of hydrogen); a material like a ferritic steel may lose enough hydrogen content within the order of minutes that mechanical tests will no longer show an effect of hydrogen while an austenitic steel may take days to lose enough to no longer show an effect. Testing in a hydrogen environment removes (or at least reduces, depending on pressure) the driving force for the hydrogen to leave the sample.

So, which test conditions you want to use depends on the material being tested and the length of the test. If the hydrogen content loss in on the order of minutes, by the time the sample is removed from the environment, the test is set-up, and then run, it is unlikely that the results will show any effect of hydrogen. If the hydrogen content loss is on the order of days, then shorter tests (tensile, fracture toughness) can probably be run before losing too much hydrogen, but fatigue crack growth rate tests, which can take months, will show a decreasing effect of hydrogen as the test continues.

There is still developing and rich literature on fracture mechanic in "quasi--brittle" materials. One of the early and consistent researchers in the area is Zdeneck Bazant at Northwestern and numerous others around the world. You might start with ACI committee 446 on Fracture Mechanics of Concrete structures and pick up the thread from there.

cmd

When the crack (be it planar or non-planar) is associated with crack-tip plasticity, the relations between the failure stresses in specimens tested in tension, compression and bending given above (see our answer 1) remain valid, except that σ_T is now multiplied by a quantity that contains the crack-tip plastic zone size, crack-front shape and orientation of average crack surface. Please see “NON-PLANAR CRACK WITH CRACK-FRONT PLASTIC YIELDING UNDER GENERAL LOADING” in our contributions in ResearchGate.

Hi Simon,

Thank you for finding time to reply, Indeed there are modes II, I do model also the frictional resistance to the sliding of the faces, and if the load is high enough I notice the upper lips slide over the lower lips. As far as I know, I didn't found any publication studying the contact between crack lips which makes it difficult to validate my model. I'm only using an elastic isotropic material for now.

Regards,

Oussama

Three nonlinear material models available in ATENA

1.crack band model based on fracture energy,

2.fracture-plastic model with non-associated plasticity

3.microplane material model

What I am trying to say is that this field been has been killed with research and others spent years working on it and had teams of students exploring it. If you are starting thesis research maybe you could consider whether this is the right direction to explore, or could you select a more timely topic with more potential for novelty and better prospects of success. If you are passionate about fracture and feel that you can add to the state-of-the-art then that is a different discussion. Good luck.

Thanks sir.

Dear Gang Zhu

The applications of chemo-mechanical coupling discipline are going on for the time being into two directions that covering by materials research and development activity:

Designing and manufacturing a multifunctional components that characteristics in a variety of applications e.g. artificial organs.

Highlight the mechanism of material degradation and failure case study e.g. high temperature oxidation process.

Now, in the case of high temperature oxidation the mechanical coupling with the oxidation chemical reaction results in stress generation in the oxide scale formed which in turn affects the chemical reaction rate and the diffusion process of the reactants and therefore, the process become a complex chemo-mechanical as the stress is diffusion dependent during the oxidation and the oxide growth is stress induced.

In other hand, the story may be different with the hydrogel coupling behavior as external mechanical load can induce redistribution of ionic concentration, while a chemical stimulus lead to swelling or shrinking of the hydrogel.

So for this multi-field coupling behavior in a medium, there are many approaches that have been proposed by many researchers leading to a bundle of knowledge for the same coupling behavior .Thus, I think that makes the topic appears as foggy to understand by many of the followers.

I hope the above contribution is helpful.

Best regards

Isabel Herreros Thanks

Hi Adel,

Currently, Abaqus doesn't support SIF or any contour integral for moving cracks. Abaqus supports it for stationary crack only. The contour integral are path dependent, so request at least 5 contours, ignore first 2 contours and take average of remaining 3.

Try different values of enrichment radius. Too small value of ER predicts larger and unrealistic values of SIF. ER should be some factors of element length to get reliable results.

All the best!

If you wish to use FRANC3D : write to me on nls@dhioresearch.com

Gang:

How to define a crack? Your question is essentially how small can a crack be to still be considered as a crack, and more specifically what dimensions preclude the use of continuum and fracture mechanics to analyze such a crack. In general, for a continuum approach, which has the advantage of being widely applicable, a crack naturally needs to have at least one dimension larger than an atomic (or lattice) spacing.

As there are no size-scales in elasticity, in principle any sized elastic crack could be analyzed. However, from a fracture mechanics perspective, for the use of linear-elastic fracture mechanics (LEFM), its is any violation of the elastic constitutive law used that must be considered, i.e., this region of violation needs to be small enough to be ignored, e.g. the crack size (and the remaining uncracked ligament) should to be some 10 to 15 times larger than the crack-tip plastic zone.

For nonlinear elastic fracture mechanics (NLEFM) approach, the crack size (and remaining uncracked ligament) need to be at least a order of magnitude larger than the region of unloading, i.e., increment of crack advance) and the crack-tip zone of non-proportional loading. Indeed, the prevailing constitutive laws used to develop the fracture mechanics approach which is utilized will be in general determine what sized cracks (and what sized components) can be analyzed, as in the LEFM and NLEFM examples given above.

The physical definition, however, of when a crack is actually a crack is very relevant to the question of crack initiation for fatigue analysis and life prediction. Traditional total life (S/N) approaches to fatigue life estimation of course include initiation, but one doesn't generally need to know the dimensions of any crack formed as only the applies stress (or strain) and the number of cycles to failure are measured. For damage-tolerant life-prediction strategies, conversely, the crack size does become important, as conventionally the lifetime is calculated in terms of the cycles for the largest undetected crack to grow to failure. LEFM approaches work well here, e.g., by integration of the Paris law for fatigue-crack growth, but there are problems with small cracks which can display non-conservative behavior, i.e., faster growth rates (and lower fatigue thresholds) than larger cracks at the same applied stress-intensity range. For a brief classification of the relevant crack sizes here, the reader is referred to the attached reference on small fatigue cracks.

If we could perform such damage-tolerant life-prediction calculations and include crack initiation, this would dramatically enhance predicted lifetimes but, in addition to the question at hand as to when a crack is actually a crack, this is a tall order as the initiation life is invariably a marked function of the nature of the component surface, and to reliably characterize the surface condition in, for example, every turbine blade in every gas turbine, would be impossible. However, a recent study has attempted to characterize the precursor microstructural damage prior to the formation of an actual crack (Lavenstein et al., Science, 370 (2020) 190), and if this approach can ever be feasibly harnessed industrially, then maybe the question of when a crack is actually a crack may not be so important!

ROR

Good question.

Indeed, classical engineering fracture mechanics does not consider the role of microstructure on damage initiation and evolution.

When you aim to reconcile these two fields I find it helpful to go back to the original works of Griffith.

In his basic consideration he derives a fracture criterion from the trade-off between the elastic energy that gets stored inside a homogeneous material (without any microstructure for the moment) upon mechanical loading and the free surface energy that has to be provided when a crack opens up.

The lesson that can be learned here with respect to your question is that this energetic principle can be nicely generalized and cast into a functional form.

This means that you can construct a (free) energy functional, which includes the elastic energy, the plastic energy (for instance the energy that is stored through the statistically accumulated and the geometrically necessary dislocations for instance or some other analogue / mean-field formulation for the inelastic portion of the stored deformation energy), and the surface energy.

The specific relation to the microstructure comes from the fact that for instance the surface energy for a cohesion process inside the grain interior is different from that at a triple point or at the grain boundary for instance, which means that such general energy balance formulations can be rendered microstructure dependent and then be solved specifically (microstructure-dependent) for a local integration point that carries a certain MS ingredient.

And when thinking even beyond this, all these microstructure features such as the dislocation-related parameters or interfacial energy values etc can of course depend on the chemical decoration and partitioning values.

We have made good experience with casting these contributions for instance in a generalized Ginzburg-Landau formalism.

This can then be solved in principle by phase field simulations and can be also coupled with crystal plasticity mechanics etc.

Good luck

PS

Here are some reference suggestions where we outlined this:

Computer Methods in Applied Mechanics and Engineering

Volume 312, 1 December 2016, Pages 167-185

A phase field model for damage in elasto-viscoplastic materials

( )

Journal of the Mechanics and Physics of Solids

Volume 99, February 2017, Pages 19-34

Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture

(https://www.sciencedirect.com/science/article/abs/pii/S0022509616304513)

Computational Materials Science

Volume 158, 15 February 2019, Pages 420-478

( )

Ahmed:

Fred Lange's article is a good one to read on this point, although a better one in my opinion is Tony Evans' and Bob McMeeking's J. Am. Ceram. Soc. article (vol. 65, 1982, 242) on "Mechanics of transformation toughening in brittle materials".

In simple terms though, in ceramic materials such zirconia toughened alumina and partially stabilized zirconia, the composition is adjusted so that the zirconia phase is in its cubic and tetragonal form at ambient temperatures. Cubic zirconia doesn't play any role, but under these conditions the tetragonal phase is partially stable. If the temperature was lowered below M_s, the martensite start temperature, this tetragonal phase would athermally transform, via a martensitic (sometimes called a "military") transformation to the lower energy monoclinic phase - but this has little to no effect on the toughness of the ceramic. However, as the tetragonal zirconia is only partially stable, it can be induced to transform at temperatures above M_s, by stress to the lower energy monoclinic phase. Since this is promoted around any crack tip (where the local stresses are much higher) a transformation zone is formed around any advancing crack. However, the transformation is accompanied by a several percent increase in volume; accordingly, due to the dilation associated with the transformation, this zone will be in compression due to constraint from the surrounding ceramic matrix further from the crack, which has been subjected to correspondingly lower stresses and therefore has not transformed (an "Eshelby transformation"). The crack thus has to grow into a zone of compression and the resulting crack-tip shielding leads to marked rising R-curve behavior and transformation toughening (incidentally, there is also a contribution from the shear associated with the transformation).

The transformation toughening effect though is only pertinent at temperatures where the tetragonal zirconia phase is partially stable. At higher temperatures, above the so-called M_d temperature, the transformation is thermodynamically unfavorable and so the tetragonal zirconia cannot transform. At lower temperatures below M_s, as noted above, all the tetragonal zirconia spontaneously transforms and so there cannot be any constraint by untransformed zirconia on the transformation zone surrounding the crack wake.

Thus, transformation toughening in these zirconia-containing ceramics is only realized at temperatures where M_s < T < M_d.

ROR

Dear Artem,

There are simple and right ways to estimate the parameters of fracture, I recommend to estimate first the CTOD from results and then use it to obtain the SIF and compare the results with the literature. I used the CTOD to obtain the J-integral in my last publication in computational materials science, you can use it to estimate the SIF.

Designation: ASTM D5573 − 99 (Reapproved 2012) Standard Practice for Classifying Failure Modes in Fiber-Reinforced-Plastic (FRP) Joints

Dear Mr. Sasan, I would like to suggest a paper about your question, wrote by M. M. Mollanouri-Shamsi, et al, from University of Southern California, SPE-190024-MS (2018). The title is "Proppant Shape Effect on Dynamic Conductivity of a Fracture Filled with Proppant". I hope this can help you. Best regards.

Conduct the trial of fatigue crack growth as per ASTM E647, on your material and test condition. Now you can use a curve fitting technique to fit a curve on the data received for FCG and then determine the governing equation of the curve. This will give you the value of C and m the pairs constants.

Hi Guru Moorthy

You will need to specify the material properties based on the material of interest. Attached a link to the user manual.

https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usi/default.htm?startat=pt03ch12s08.html

Hope it helps.

Regards,

Wee

Hi

you can study my papers in this field

The conservation of energy corresponds to Griffith Energy-balance concept. This is stated as

G(I)max=2*Gamma

where Gamma is the surface energy. Observe that this is valid at G(I)max only. Here, G(I)max is known independently first, before we can reach the Griffith equation. You are telling nothing new.

Dear Mario,

RCP-Rapid crack propagation (RCP) is a phenomenon in which a long fast-moving brittle crack can propagate in a material body. Cracking of glass plates and frozen lakes is an example of RCP. RCP can also occur in pipes. Cast iron pipes and plastic pipes under certain conditions may also experience this phenomenon. Cracks are thought to initiate at internal defects on an impact of impulse event and can travel long distances quickly. RCP occurs in pressurized systems with enough stored energy to drive cracks faster than energy is released. Cracks tend to have a smooth fracture surface. RCP is affected by temperature, energy driving force, material, pipe size and processing efforts.

Unstable crack occur at load control, when the maximum load is reached, i.e. as soon as the preceding stable growth tends to occur under constant load.

(a) RCP can occur at fatigue striation load and material can get failed. There are fluctuations of stress. Maximum load is not required. There is no constant load. it can be instant fail.

Unstable crack growth occurs when the maximum load is reached, i.e. as soon as the preceding stable growth tends to occur under constant load.

(b) RCP occurs in pressurized systems with enough stored energy to drive cracks faster than energy is released.

For unstable crack, the stress-strain energy released, together with the energy supplied from the outer load goes to kinetic energy and to what is required by the dissipative region at the crack edge to sustain crack growth.

(c) RCP is smooth surface while unstable depicts brittle surface.

(d) RCP or Stable- Onset of stable crack growth (RCP) occurs at point S and fracture occurs at point F.

Unstable- During unstable crack growth, the stiff machine cannot supply the energy needed for dissipation in the crack edge region, and therefore all this energy is supplied by energy release from the stress-strain field in the specimen.

(e) RCP- RCP can be characterized by high crack speed, smooth surface with large plastic deformation, wavy propagation of the crack along the extrusion direction. It can be described by LEFM parameters, dynamic fracture resistance and dynamic fracture toughness. RCP is most common in plastic pipe as the majority of field failures in piping are attributable to slow crack growth (SCG) fractures or rapid crack growth. Shape is almost uniform. The crack edge generally accelerates to a very high velocity, often several hundred meters per second, and sometimes to a few thousand meters per second. The energy required for conversion from a static to a dynamic state of the structure is provided by stress-

Unstable- Shape of a small crack is generally non‐uniform growth. In addition, the deceleration and subsequent acceleration of crack growth corresponds to the transition from unstable to stable crack growth. Strain energy release from the body, sometimes assisted by energy supply from the loading device.

Ashish

Safaa Qays thank you sir

Hi, I recommend the following book

(recent trends in fracture and damage mechanics)

Hi Bounedjar Adel

I had a look at the attachment and noticed it might be in French. But at least I think I understand what you are working on.

I think you have used a quarter model. Since it is in symmetry, did you half the stress or force applied on the boundary condition to the left? If not, you will will need to double the stress you apply in the analytical solution.

Next is on dimensional consistency. Not sure what parameters you used in the geometry, but Abaqus does not specify dimensions, and you will need to be careful when inputting them. Example, if you used mm in dimension-ing the model, stress in Nmm^-2 will be in MPa instead of Pa and so on.

Try doing a quick check, might be a simple fix. Hope it helps.

Regards,

Wee

Hi Qitao,

This is a problem of unstable crack propagation (i.e., fast crack propagation). In the quasi-static CZM analysis, the gradual CZM model should be established in the crack propagation process from initiation to arrest. We have a paper published recently for you to refer if you contact to me.

Looking forward we may to more communication.

You mean: Mechanical Metallurgy - Dieter George Ellwood (1961)

Here is the link: https://www.academia.edu/34896003/Mechanical_metallurgy_-_Dieter_George_Ellwood.pdf

Hi there,

I want to now if it is possible to analyze thermal fatigue of FGMs in the ABAQUS?

If, How?

Thanks

Ahmed:

The topic of fracture mechanics is somewhat broad to describe in one review paper but there are several books that I can recommend. The first book written on the topic was John Knott's Fundamentals of Fracture Mechanics (Halstead Press, 1973) which I can send you a copy of, if you want it. However, by far the best recent text is Ted Anderson's Fracture Mechanics: Fundamentals and Applications (CRC Press, now in its 4th ed., 2017). This is a truly educational description of the mechanics of linear elastic and nonlinear elastic fracture mechanics - there's not too much on the materials science of fracture, but his description of the mechanics is excellent.

ROR

Dear Konred,

Generally, for 2024-T3 most common aluminum copper heat treated alloy values have stress intensity factor in range of 36-40 MPa√m and △K= 10-11 MPa√m.(you can check with heat treatment materials ASM handbook). Use SENT specimens for the same.

Use appropriate formula for calculation. AFGROW developed code by NASA is used for simulation of fatigue crack growth with and without residual stress. Many models for fatigue crack growth are implemented so far. The effect of loading ratio and heat treatment (tempered situation) for aluminum alloy 2024 can be investigated. The effect of condition temper for aluminum alloy on fatigue crack growth rate can be presented using paris....miller and take the slope, use the equation da/dn to find your values. find f= kop/Kmax, use this value in da/dn calculation.

Refer this paper: file:///C:/Users/3020/Cookies/Desktop/Downloads/FatiguecrackgrowthofdifferentAluminiumalloys2024.pdf

Hope it is helpful to you.

Ashish

Hello

I think fracture energy is the area under load disp curve, it could be one the factors in judging the brittleness of the concrete. more energy might provide less brittleness for the material. if you look at characteristic length formula, you will find other factors such as E , ft ... there.

Hi Abolfazl,

Thanks for your interesting question. I think it might be good to consider strains rather than stresses, if you are dealing with brittle and semi-brittle materials. I would, in particular, recommend looking at the critical tensile strain criterion by Fujii and the extension strain criterion by Stacey. I hope you find this useful. Regards, Ebrahim

Thank you Alireza Safari Tarbozagh

Side grooving intends to remove the plane stress region around the sides of the crack, which influences the fracture toughness results.

One thing to note is that when fatigue pre-cracking without side-grooves, it will produce a 'thumbnail' shaped crack tip. When side-grooving is machined into the specimen after pre-cracking, it removes the crack tip contour near the sides of the specimen, resulting in a fairly straight and uniform crack tip.

However, if fatigue pre-crack is applied after sidegrooving, you might get an interaction of perpendicular stress fields around the side-groove-notch tip interface. This might potentially lead to a reverse 'thumbnail' shaped crack tip. I do not think this matter too much for research as it would behave like a 'blunted' chevron crack tip, but one will need to check if it confroms to the standards for use in industry.

Regards,

Wee

1. www.researchgate.net/publication/289152143...

Characterization of fracture behavior of 2024-O and 2024-T3 aluminum alloys, November 2004,Revista de Metalurgia 40(6):431-435;A. Monsalve,R. Morales.

2. FAILURE ANALYSIS OF AN AL 2024-T3 PLATE USING FRACTURE MECHANICS, December 2017,Conference: Meeting on Aeronautical Composite Materials and Structures – MACMS 2017.( www.researchgate.net/publication/321946259... )

Akash:

It depends on the size and geometry of your test specimens.

Elongated dimples which form in shear are very common in uniaxial tensile test fracture surfaces. The classical example is the "cup-and-cone" failure mode. In the center of the samples - the "cup" - where the stress-state is dominated by the applied tensile stresses, the process of ductile dimple formation occurs by microvoid coalescence, i.e., voids nucleate at particles (either by the particle cracking or separation at the particle/matrix interfaces); these voids then grow, primarily driven by the triaxial stresses at the center of the sample, until they coalesce or more likely the separating ligaments between the voids "neck down" due to plastic instability. Nominally the same process occurs near the surface of the sample - the "cone" - but now the process is dominated by the near-surface shear stresses. The result is the coalescence of voids formed around particles in shear, which naturally results in elongated dimples.

As you describe your aluminum sample as "sub-size", it is highly likely that the process of microvoid coalescence is dominated by the near-surface shear stresses, in which case elongation dimples would be the result.

ROR

P.S. It is interesting to note here that the formation of dimples both in tension and in shear can even occur at the center of a uniaxial tensile sample in the "cup" region. In many low-alloy steels, the initial voids responsible for their microvoid coalescence ductile fracture are formed at inclusions, e.g., MnS inclusions which readily debond from the matrix. These voids then grow under the triaxial stresses, as described above, but the necking down between these larger voids by a plastic instability can occur by shear-induced microvoid coalescence of cracks in the much smaller carbide particles. The latter is know as a void sheet instability.

Dear Sumit,

Sound of cracking crystals between two hard surface depends on couple of important metallurgical as well as mechanics factors such as increasing strains, grain distribution reaches log normal packing, coarsening of crystal grains, mis orientation angles, level of temperature distribution due to fraction between two surface with grain misalignment effect , critical grain size micro-cracking and thermal enhancement, cohesion crack nucleation, defects, cavities etc.

In general, If the size of the crystal grains is closed to the wavelength of the supersonic ray, the part will not be transparent to ultrasound, in this case the there will be no ultrasound bottom of signal. it is also seen that size of the crystal grain increases the intensity of supersonic wave decreases.

Sound products can be listen at high extrusion speeds.

Atomistic modeling is highly applicable in easy understanding of crack sound between hard metal.

Ashish

Ahmed M. J. Ali

Thanks a lot Mr Jubara for your advice.

I believe the penalty stiffness (k_n) is the ratio between normal traction and the normal initial separation ~ k_n=t_n/del^o_n. You can find these values for the respective materials in the literature.

Dear Kauê and colleagues,

In case your study only deals with outcrop data, I can add another perspective working with neotectonic data.

In compressive settings, we have found good results by using pristine surfaces (alluvial surfaces, lava floods, etc) as strain markers or by reconstructing the paleo-enveloping surface of partially eroded features where pre-deformed geometry is known (at different details and scales).

These markers can be modeled through balancing techniques and thus extension/shortening values and rates can be obtained/estimated.

This approach does not rely only on fault data, but attempt to quantify continuous volumetric deformation.

In some compressive settings, when you plot the amount of shortening accrued by the main thrust or causative fault versus the shortening widely distributed in the hanging wall related to distributed minor faults, results suggest that total deformation at these secondary structures is not minor and might challenge somehow the relationships indicated by Scholz&Cowie.

In the event these comments were useful, I leave a couple of links of potential interest below (and references therein)

Best,

Carlos

Aamir Sultan

see these articles :

Part I:

Part II:

In a recent work intitled “Fracture Mechanics in a three-dimensional elastic half-space under the rectilinear contact pressure of a cylinder” (see our contribution in ResearchGate), this crack system has been investigated. Expressions of the relative displacement of the faces of the crack, crack-tip stresses and crack extension force G per unit length of the crack front are given. G displays a maximum at an angle θ that is confronted to experiment. dG / dθ = 0, the condition that determines the crack angle, is seen to depend on Poisson’s ratio only.

Hi Bart. Sorry for the delay in respons. I am still learning to use this...

There was no intentional discontinuity introduced. On a macro-scale the specimen appeared as a uniform cylindrical shape. It looks as though it was cut from a larger sheet and the turned with a lathe which would leave circumferential tool marks but these woul be perpendicular to the fracture surface.

Dear Dhanraj Rajaraman

Please find the attached file.

Hi Abedin,

I think my question was not clear. I am trying to use vcct in a 12-node cubic element and when the criterion is satisfied, it would be convenient for me to release a node instead of the whole element. More specifically, i want to calculate the strain energy release rate in a node, and if is bigger than critical fracture energy, the node of a high order element (instead of the whole element) will be released.

Mr. Kumar,

As explained by many others, the unit of K is due to the sqrt(r) singularity.

Describing a similar parameter for HRR singularity might have a unit with MPa.m^n, where n can have a fraction value.

The physical significance could be that for an applied stress, K describes by what factor the stress will intensify at a distance of 'r' from the crack tip. The definition of K comes from theory of elasticity, and so it should describe the stress field at the boundary of plastic zone.

As I said another parameter can be described at a boundary of plastic zone and process zone, and that factor would describe the stress field at that boundary.

To make it more fancy, its similar to the Event Horizon, the boudnary of singularity in a Black Hole.

With regards,

Abhishek

Normally fixed crack models need crack tracking strategies for avoiding global stress locking, which is numerically more stable.

Rotating crack models on the other hand are more flexible, some of which can be tricky and very similar to classical smeared crack model (the crack can rotate 90 degree during loading process). There are also some stable versions standing somewhere between smeared and fixed models, such as Cracking Elements method (unfortunately only 8 node quadrilateral element works by now).

Better try different models and try to develop some novel versions.

Some papers are recommended:

[1] 3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations

[2] Embedded crack vs. smeared crack models: a comparison of element wise discontinuous crack path approaches with emphasis on mesh bias

[3] Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

[4] Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations

[5] Cracking elements: a self-propagating Strong Discontinuity embedded Approach for quasi-brittle fracture

[6] Geometrically non-linear and consistently linearized embedded strong discontinuity models for 3D problems with an application to the dissection analysis of soft biological tissues

[7] Smeared crack approach: back to the original track

Before or after cracking ??