Science topic

Fracture Mechanics - Science topic

Fracture mechanics is the study of the influence of loading, crack size, and structural geometry on the fracture resistance of materials containing natural flaws and cracks. When applied to design, the objective of the fracture mechanics analysis is to limit the operating stress level so that a preexisting crack would not grow to a critical size during the service life of the structure.
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Hello All,
I'm looking into measuring crack growth rate using the DCPD method and was wondering if it is possible to use a "bench top power supply" and a multimeter with higher accuracy? Or do I need to have specialized equipment for DCPD measurement?
The materials I'm interested are iron alloys and aluminum alloys.
Compact tensions specimen thickness =< 13mm
Cheers,
Rashiga
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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
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I'd like some opinions. What are the major challenges in fatigue and fracture mechanics?
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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.
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I need elaboration in easy language to grasp the concept.
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A part, made out of PMMA and under a remote load, can withstand a flaw until certain length before that crack grows catastrophically
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I discovered two distinct phenomena when cracks begin to form at α and β phases in titanium alloys. How does this difference mechanism come about?
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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
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It is difficult to capture the descending branch in the stress- strain diagram of the material in an experimental direct tension protocol (see Figure (a): tension behavior). The flexibility of the loading system causes premature specimen collapse. This is due to the release of stored strain energy in the loading equipement. It has been argued that it is feasible to measure this softening behavior when a sufficiently controlled strain rate is used. Given these facts, the following questions arise:
  • Is it possible to measure the softening behavior of plain concrete in an experiment?
  • Is there any experimental evidence of this measurement being possible when using a sufficiently controlled strain rate?
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  • What are the good research Areas/topics in Structural Engineering for Ph.D.?
  • Can anyone suggest to me research topics related to Fatigue and fracture mechanics of Concrete ?
  • Kindly suggest me a good review article regarding the studies performed in Structural engineering related to Fatigue life analysis of fiber reinforced concrete/ Flexural fatigue performance of concrete made with recycled materials?
  • Kindly suggest me research topics related Flexural-Fatigue Properties of Sustainable Concrete Pavement Material ?
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Dear experts in fracture mechanics, I need help in choosing a model to track crack propagation using numerical simulations. If anyone could provide me with any suggestions, articles, tutorials, or reference books where I can study (to understand the basic concept of J-integral and SIF) and which model to choose and how to implement it numerically, it will be highly appreciated.
Looking forward to your precious responses.
Thank you
Izaz Ali
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Dear Izaz,
Read these articles, it may help you in your research.
Good luck.
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Can I be assisted with guidelines to linear elastic fracture mechanics in timbers?
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Can an elliptic crack (small enough to remain a single entity, with no internal pressure or shear force) inside an isotropic material (no boundary effect) be expanded in its own plane under externally applied shearing stresses only?
If yes, how did you show that? Do we have experimental evidence for the process?
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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.
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In fracture mechanics, we accept that quasi-brittle materials such as concrete have a strain-softening branch under tensile stresses. The branch that can be obtained from a Direct Tensile Test. Accordingly to CEB-FIP, it is possible to characterize this branch by means of the fracture energy. Recently, our research team has been trying to find experimentally this branch in hollow concrete blocks (HCB) employing displacement-controlled tests, at very slow velocities (as low as 0.0005 mm/s), in a servo-hydraulic testing machine. However, it has not been possible to capture this softening branch.
The experimental results that we have had the opportunity to review, which are reported in the specialized literature, make us think that there is a problem with the testing equipment (inertia and stiffness of the machine) and that it could not be an intrinsic characteristic of the material.
After these arguments, we would appreciate your help to get some insight on the following:
1) Is it possible to obtain experimentally a strain-softening branch for quasi-brittle materials, using the Direct Tensile Test, particularly for plain concrete or HCBs?
2) Is this softening branch really a property of the material? Or is it just an apparent behavior generated by the testing machine and the measurement devices used, I mean, due to the way these devices work?
If it exists, does the speed at which it occurs need to be of an order of magnitude lower than 0.0005 mm/s? And finally, if that’s the case, does it make sense to use it in the interesting research problems?
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1) Yes, but specimen's length must be roughly smaller than wu.E/ft
wu - ultimate crack opening (see e.g. Hordijk's law);
E - Young's modulus
ft - Tensile strength
2) No. As mentioned above, it depends on specimen's length.
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In linear elastic fracture mechanics (LEFM), only the stress intensity factor seems to be used. LEFM implies the same r−1/2 singularities of stress and strain at the crack tip. Very few articles on fatigue use the strain intensity factor. Formally, the two factors could be related by Hooke's law. What is the reason why the strain intensity factor is not used in the same way as the stress intensity factor? A search for strain intensity factor returns only stress intensity factor. Why is the strain intensity factor more or less ignored?
R.M. Christensen states that "fracture mechanics in the brittle range ... require(s) formulations in terms of stress." https://www.failurecriteria.com/isitstressorstra.html
Is anything wrong with the strain intensity factor?
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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
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I am trying to find out how to identify specified parameters of ductile damage material in its stress-strain curve in Abaqus. I could identify the Young's modulus and the yield stress, but not the fracture energy. How do I identify this in my results?
For now I am simulating a simple tensile test in y-direction on a one-element model (1x0.2x1).
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Cast iron is metal, not ceramic. But it is brittle, and quite strong. What can be additives that can be added to increase its strength, corrosion resistance and high temperature stability so that it can be used in place of hard ceramics in structural application? on can it not be qualified as a ceramic even if its microstructure is predominantly intermetallic?
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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.
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I sam earching a preporcessor program for fracture mechanics analysis using abaqus, I am doubting between zencrack and feacrack, I wonder if someone has experience with these programs and can help me to select which one (or another program) is better.
I want to use it for 3D studies
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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.
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Looking for a motivated Ph.D. candidate to work in the field of additive manufacturing with the background of mechanical engineering and material science.
Deadline for application: February 14, 2020
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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
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How to model delamination results from matrix cracking with XFEM?
Dear all,
I need to do 2D multicrack propagation in a composite laminate (GFRP) in tensile load. I have 3 parts namely (0-90-0 degrees plies). And I already have existing cracks which you can see below in attached pictures. Cracks propagate well, but when it comes to the boundary I couldn’t see correct delamination behavior. Is it possible to simulate delamination because of matrix cracking in Abaqus? I both tried cohesive surface and elements. With the elements it says I cant define XFEM crack zone for the cohesive element. With the surface, during loading I see some overclosures and clearances.
Here are my material properties.
Cohesive Surface:
Knn=Kss=Ktt= 1e6 N/mm3 (which I am not so sure)
Damage Initiation: Maxs damage initiation criteria Normal=Shear1=Shear2=3.4MPa.
Damage evolution criteria: Mixed mode behavior=BK(Power=2.2)
Fracture energy: Normal=Shear1=Shear 2= 0.27 N/mm2.
Also, frictionless tangential behavior, and hard contact.
For 0 degrees ply
Damage Initiation: Maxps=807MPa
Damage evolution criteria: Mixed mode behavior=BK(Power=2.2)
Fracture energy: 0.5, 0.5, 0.01 N/mm
Elastic, type=ENGINEERING CONSTANTS 35100.,9600.,9600.,  0.3,  0.3,  0.3, 4000.,4000.4000.,
For 90 degrees ply, I just swap E11 and E33 values, and maxps=15MPa
Can someone suggest me how I can model it and if my material properties are reasonable?
Regards
Berkay
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Here it is. Good luck
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if plastic zone (rp) is obtained from maximum stress intensity (=del. K/(1-R)). How to determine plastic zone (rp) from log-log da/dN
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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
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I know this question has been asked in this forum but want to rephrase it as there have been some features that came for Ansys. Can anyone please tell from their experience which one is better? For example, I have used Ansys and felt it has some limitations e.g. in XFEM. As it can not be directly used using UI in the benchmark. Also in 3D, it is unstable. Also, all of them in Ansys fail in Anisotropic material. But I don't have experience in ABAQUS.
Kindly let us know what are your insights.
With regards
Biswabhanu Puhan
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I would probably use Abaqus. It will be easier when you implement the characteristics of your material model (user defined material or element).
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Peel stress singularities occur at the bi-material interface of the free edges of, for example, a steel-adhesive-steel sandwich specimen of say 500 mm in length, 100 mm in width, and 10 mm thickness (5 mm adhesive thickness) under longitudinal cyclic tension due to the difference in Young's modulus and Poisson's ratio of the two materials.
The singularity can be relatively economically investigated in a very fine cross-sectional finite element (FE) model representing the as manufactured geometry using the generalized plain strain approach (ANSYS), for example, see attached picture. The finer the mesh gets the larger gets the local peel stress peak at the bi-material free edge interface. The graph shows the equivalent stress according to Beltrami (similar to von Mises).
The load amplitude is chosen from a fatigue load spectrum of a cyclic test and is thus that small that linear elasticity holds for the average stress according to classical laminated plate theory (CLPT) in the adhesive. Now, this local stress peak, however, gets already as large (factor of 10 of the average equivalent stress) that it could be dedicated to a plastic deformation and failure. In reality, i.e., in the experiment, we would not see such a failure after say the first 100 load cycles. Thus, there is a discrepancy between linear elasticity theory and reality. The material seems to withstand these peaks.
For the static strength analysis one could use a non-linear stress-strain curve to circumvent the "problem" and lower the peaks and use then fracture mechanics to quantitatively evaluate such situations, but this requires the modeling and relatively expensive analysis of possible crack orientations in all possible dimensions due to the multi-axial stress state. Therefore, fracture mechanics does not seem to be an applicable method to evaluate the fatigue damage for a load spectrum whose stress vector components vary over time and thus with them the critical crack planes .
Another technique is to extract the stress value at a critical distance from the edge and then extrapolate a "more realistic" stress peak. But how to define such a critical distance on a physically sound basis and how does the extrapolation function look?
Do you have any other ideas how to extract a realistic stress value from the finite element model for a fatigue analysis?
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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.
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Hi all,
I'm interested in testing the Hydrogen Embrittlement of several metals. I
Interms of fracture testing and fatigue crack growth rate testing I want to know the difference between the following.
1. Long time H2 exposure in an environmental chamber -> conducting tests in ambient enviroment.
2. Long time H2 exposure in an environmental chamber -> conducting tests in a H2 exposed environment.
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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.
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Are there design equations for concrete sectors based on fracture mechanics parameters?
using the fracture parameters KIc or Gf to design concrete section as using compressive strength in design equation
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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
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Does a single-valued description exist for isotropic materials?
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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 σT 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.
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I'm trying to study cracked structures under a compressive load taking into account contact between the crack lips.
I would like to know if the method of extrapolation by displacement remains valid to calculate the stress intensity in this case or other valid methods.
And if you can send me some references containing the same study.
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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
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What is the best finite element modeling software packages for modeling non-linear and fracture analysis of CONCRETE? I've had some with ABAQUS standart/explicit, but I would like to learn if there is a better software for non-linear behaviour and fracture mechanics of concrete according to your experiences.
Best regards.
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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
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Hello everyone,
I am trying to develop an analytical model to study the propagation of fracture in reinforced concrete structures. I would really appreciate it if anyone could suggest to me the optimal analytical model to study the crack propagation.
Thanks in advance
Regards,
Pawan
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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.
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How to define a crack at symmetry plane? Is it right idea? Crack seam we cant specify at symmetry edge (As crack seam can be specified at interior face of 2D). How to handle this type of situation? I need to find KI for different crack lengths. Its possible to find without define seam. But I m not confident about the results. If same crac length defined inside the face (other than symmetry edge) with partition, I can get crack tip stress field. But at symmetry without seam Im not getting. (Of course we cant get, That I can understand) What may be alternate for this? Anyone have Idea, pl share.
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Thanks sir.
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Recently, I came into contact with a new discipline named chemo-mechanical coupling. I found that chemo-mechanical coupling phenomena exist in many research areas, ranging from development of advanced batteries, biomechanical engineering, hydrogen embrittlement, and high temperature oxidation, etc. Although it is very important in engineering field, I can't know the main mechanisms of coupled chemical and mechanical interactions. Can you give me some suggestions? Such as, some related publications or research project. Thanks very much.
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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
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I am planning to use the Discrete Element Method for propagation of Fracture in Reinforced concrete Structures. Which book would be the best start to study Discrete Element Method from the beginning?
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Dear All,
I want to model crack growth in a plate using ABAQUS XFEM method. Here is my question about it: How to calculate Stress intensity factor in XFEM when crack growth in ON?
At this time, when I using ABAQUS XFEM with allowing for crack growth and request for SIF through History output request,
It says that SIF could not be produced when crack growth in XFEM is ON.
Best,
adel,
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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!
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I want to simulate the growth of a crack due to fatigue. My model consists of shell elements that are non-planar. I wanted to use the XFEM available in Abaqus, but in its documentation was written that:
" XFEM is available only for three-dimensional solid and two-dimensional planar models; three-dimensional shell models are not supported. "
So the question is that are there any software to simulate crack growth in non-planar parts modeled with shell elements?
I've heard of some software like FRANC3D or ZenCrack, but I'm not sure if they're capable of doing this.
Regards
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If you wish to use FRANC3D : write to me on nls@dhioresearch.com
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Good afternoon!
FE software ANSYS provides SIFs calculation in fracture mechanics for 3 modes by CINT command for isotropic elastic material for example. Does command CINT calculate SIFs for orthotropic material or anisotropic material correctly or not? Does calculation method with CINT command in ANSYS take into account anisotropy or orthotropy of material?
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  1. Post-processing parameter, the developed macro is implemented to correlate crack tip displacement with bone crack tip displacement fields to calculate stress intensity factors in mixed mode. These examples include a flange crack in orthodontic tape and a superficial fissure in an opposing transverse plate. The results show how the results of a bone fracture may differ from those of the isotropic fracture analysis. It is also evident that this difference can be significantly large when stress analysis is performed with orthodontic properties, while fracture calculations are performed taking into account the fracture-tip fields of a fracture of a material. symmetric.
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In engineering, the damage that can be detected is usually called crack. But how to describe the small cracks which cannot be measured in the early stage of damage? Can we give a universal definition? Greatly appreciate your review.
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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
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I have reviewed some books about fracture mechanics, but I cannot explain microstructure damage with engineering fracture mechanics theory, such as fatigue damage of metals with micro-defects. Is there any outstanding work in this field? If so, can you share it with me? Greatly appreciate your answer and providing good practices in engineering.
Many thanks!
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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
Computational Materials Science
Volume 158, 15 February 2019, Pages 420-478
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It has been established that the tetragonal to monoclinic phase transformation of zirconia can be used to improve the toughness. The driving force for this transformation is the temperature gradient, which results in a change in the crystal structure of zirconia from tetragonal to monoclinic.
But, at room temperature Metastable inclusions of tetragonal Zirconia dispersed in a ceramic matrix will transform to the thermodynamically stable monoclinic form on the application of an external tensile stress, what is the driving force for such transformation to occur?
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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 Ms, 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 Ms, 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 Md temperature, the transformation is thermodynamically unfavorable and so the tetragonal zirconia cannot transform. At lower temperatures below Ms, 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 Ms < T < Md.
ROR
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FE software ANSYS provides SIFs calculation in fracture mechanics for 3 modes by CINT command for isotropic elastic material for example. Does command CINT calculate SIFs for orthotropic material or anisotropic material correctly or not? Does calculation method with CINT command in ANSYS take into account anisotropy or orthotropy of material?
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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.
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Hello everyone,
I'm working on crack propagation using a meshless method in linear elastic fracture mechanics and I want to use the Maximum Tensile Stress Criterion. I need some references or help in order to implement numerically this criterion ? And is it possible to use it without evaluating the stress intensity factors?
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Designation: ASTM D5573 − 99 (Reapproved 2012) Standard Practice for Classifying Failure Modes in Fiber-Reinforced-Plastic (FRP) Joints
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I am working on impact of proppant shape on fracture conductivity. I have found some articles and I know that some shapes as spherical will improve fracture conductivity comparing to other shapes. But now I want to simulate or calculate or model this effect when all other conditions of fracturing remains unchanged. I want to know is it possible? and if yes, what is this software?
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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.
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I am performing probabilistic fatigue analysis and need to find the distributions which could be used for material constants C and m used in Paris law.
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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.
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I have a scenario in which I need to do crack initiation & propagation study . Based on the load which is applied on the component, crack needs to be initiated . Once it is initiated, the same crack needs to be propagate if the external loads applied continuously . How to simulate this scenario using ABAQUS?
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You will need to specify the material properties based on the material of interest. Attached a link to the user manual.
Hope it helps.
Regards,
Wee
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Dear connections ,
What is the scientific relationship between stress intensity factor (SIF) and crack tip opening displacement (CTOD) with specimen double edge cracked.
So really I need your help if it is possible.
Regards,
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Hi
you can study my papers in this field
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When a planar crack is loaded in tension (mode I) in brittle materials, the velocity V of the crack is observed to increase from zero to a terminal velocity VT, then follows crack branching on further increasing V. VT falls well below the Rayleigh wave velocity VR.
To our knowledge, one attempt has been made to estimate theoretically VT. This attempt makes use of Mott (1948) extension of the Griffith concept to dynamic fracture. This is expounded by Lawn (1993). This estimate gives VT ≈ 0.38cl where cl is the velocity of longitudinal sound wave.
Does any other estimate exist?
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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.
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I have read in some articles about unstable crack growth which is sometimes referred to as RCP, however it seems that there is a clear difference between unstable crack growth and RCP. According to a paper from Leevers, P. (2001; ISBN: 0-08-0431526 📷 pp. 3322±3329 ;see attached image), he differentiated between an unstable crack growth which follows a slow crack Growth (SCG) when a critical value K1c is reached and an RCP which also follows SCG, however in a different way. I am grateful for any kind of explanation.
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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.
The major differences are enlisted below.
(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
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For a perfect column, the critical load is equal to that found analytically, but when I introduce a crack, the critical load increases, but in reality it should decrease.
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Safaa Qays thank you sir
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Fracture mechanics
Structural dynamics
Earthquake Engineering
Structural Health monitoring
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Hi, I recommend the following book
(recent trends in fracture and damage mechanics)
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Dear connections,
I encountered a problem in that the results of the stress intensity factor SIF in the two methods did not match. And I think the fault lies in abaqus (EFM intégral J).But I do not know where exactly!
So really I need your help if it is possible.
You find in attachment file which contains more information.
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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
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  In order to check the accuracy of trapezoidal form in tabular form in Abaqus, I did a single 3D element tensile example which named 3D element in attached inp file. The result seems good. Please refer to the attached plot of the Damage (SDEG) Vs Separation and Traction Vs Separation.  
  However, when I define same trapezoidal CZM for ductile carbon fiber reinforced thermoplastic material to simulate Mode I delamination fracture process in Abaqus with surface-based cohesive contact. The displacement-force curve are totally different with experiment results. The FEM and experimental are shown in attached file. I also attached the DCB-trapezoidal. inp file, please check it. 
  So anyone can help me check the reason? How to get the saw-tooth displacement-force curve like expereimental result using CZM? 
  Thank you! 
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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.
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Good mourning, could any one give me some references to standard methode used to determin fracture parameters from SENT specimens, some articles do not give any referance to a standard method that give impression that these specimens are not machined according to any standards. thanks
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You mean: Mechanical Metallurgy - Dieter George Ellwood (1961)
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I am a new user of Abaqus. I want to ask whether it's possible or not to perform fatigue life analysis using standard abaqus (without sub-routine). If possible, then how to define their loadings and where can I get their results. I hope that somebody can share their experiences here. Many thanks.
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Hi there,
I want to now if it is possible to analyze thermal fatigue of FGMs in the ABAQUS?
If, How?
Thanks
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I am looking about any useful review paper about fracture mechanics (brittle and ductile)....Have one you any suggestions?
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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
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I try to model fatigue crack growth in aluminium 2024-T3 alloy.
I have plate specimens with finite width 'W' and a circular cut-out with an additional notch, as shown in Figure.
1. The number of fatigue cycles for crack initiation could be predicted by Stress Concentration Factor, but how to find a suitable equation for that complicated notch?
2. When calculating fatigue crack growth rate by Paris-Erdogan equation:
da/dN = C * (dK) ^m
the difference in Stress Intensity Factor (dK) in a specified fatigue cycle should be calculated for crack length caused by fatigue crack growth 'a_CG'? Or as a total crack length, taking into account also initial crack length ('a_CG' + 'a_ini') ?
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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
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Due to its fined microstructure, HSC possesses different mechanical properties compared to normal strength concrete. One common characteristic is its increased brittleness. Many approaches have been used to judge the material brittleness. One method is using the ratio between the tension strength to compressive strength: the lower the ratio, the more brittle. Another is the linear portion in the stress-strain curve observed in uniaxial compressive concrete. The larger the linear portion, the more brittle. In fracture mechanics, some brittleness quantifiers have been defined according to different models In fictitious crack model (FCM), a characteristic length (lch) that is defined by combining the fracture energy (Gf) with elastic modulus E and the tensile strength of material (ft). The smaller the value lch, the more brittle the material. Another common used brittleness indicator is the critical crack extension length (ac). the larger the value ac, the less brittle. When it decreases with an increase in compressive strength, we can say the brittleness increases with strength. Apart from these, what are the other approaches that can be used to define brittleness of HSC?
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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.
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Based on the principles of fracture mechanics, a crack propagates when KI >= KIC, i.e. stress intensity factor is larger than fracture toughness, where KI=σ√(πa) for a central crack. Theoretically, as crack propagates and crack length (a) becomes larger, KI increases too. Therefore, when a crack starts to grow, it never stops! However, it is not the case in many geomechanics applications in underground structures. For example, a propagating crack in a tunnel surface will stop at a distance from the tunnel wall eventually.
In numerical modeling, a stress relaxation method may be used to lower the acting stress on the crack to model crack propagation more realistically. what are other efficient ways to model this phenomenon realistically? Good references are appreciated.
Thanks.
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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
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Any papers, books,codes, or sites as a start? Thank you.
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ASTM E-1820 recommend side grooving after fatigue pre-cracking. But I think side grooving before fatigue pre-cracking is better because the fatigue pre-crack front will be more uniform. Also, crack growth during fatigue pre-crack, will follow side grooved region.
Please give your comment and and share your experiences.
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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
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I'm looking for JIC ralated to J-integral method in fracture mechanic for Al 2024-T3 at different thickness. Who knows the reference which this parameter has been mentioned for this material at variable thickness?
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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... )
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Fracture surface after Uni-axial tensile testing of pure aluminium sub-size tensile specimen shows the presence of elongated dimples instead of equi-axed dimples. What could be the reason behind this? Does it imply that the material failed by shear?
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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.
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Suppose avg. grain size, crystal structure, young's Modulus, fracture strength, velocity of sound and surface roughness of both the crushed crystals (before and after crushing ) and the crushing surfaces, as well as load on grinding surface, static/dynamic friction coefficients are known. Then, is it possible to estimate the crushing sound of the crystals?
Conversely, if crushing sound of the crystals are analyzed, is it possible to find any mathematical relation between the variables outlined?
I am asking the questions since crushing minerals and recording-analyzing the sound require no sophisticated instrument at all.
Please provide relevant research links.
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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
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Hi. I want to plot R-curve diagram analytically for Al 2024 and evaluate nonlinear fracture mechanics of it.
I know there is ASTM standard E561 for obtaining this graph experimentally.
Is there any document that I can find this graph for this material?
I'll be grateful if you can give me any hint.
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Thanks a lot Mr Jubara for your advice.
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I am modelling an interfacial zone by cohesive elements in ABAQUS. In order to conduct a parametric study, I need to change thickness of the cohesive elements in a range (assume in the range of 0 to 0.8 mm). In a manual, it has been written that when a unit thickness is specified during defining section in the property module , penalty stiffness is the same as the elastic modulus and thickness of the layer is kind of ignored.
Herein, there are two questions;
1- Is it rational to use non-zero thickness cohesive elements at all (non-zero thickness in the model geometry and unit thickness in the cohesive section)?
2- How the penalty stiffness should be defined for the model with zero thickness up to that with 0.8 mm?
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I believe the penalty stiffness (kn) is the ratio between normal traction and the normal initial separation ~ kn=tn/delon. You can find these values for the respective materials in the literature.
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  • With a good fault and fracture dataset (displacement and length), how can I extract a mathematical data, strain rate, so to speak? Maybe programs or even formula? Do you have any indications of papers/authors or program?
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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
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(initial, minimum, maxium arc length increment and estimated total arc length) to get more accurate results?
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A simple crack system (Figure 1) can be readily studied to estimate the Hertzian conoidal crack angle and length, and also the stress intensity factor.
This is a 3-D brittle elastic half-space on the flat boundary Ox1x3 of which a rectilinear contact pressure along Ox3 is exerted by a cylinder whose axis is parallel to x3; the cylinder lies along Ox3 on the flat boundary. A planar straight-front crack inclined by an angle θ with respect to x1x3 is present under the action of the load along x2 due to the cylinder. The relevance of this modelling may be understood as follows. A slab of cylinder with thickness dx3 at spatial position O’ (0, 0, x3) exerts elastic fields (displacement and stress) proportional to those of a point load at O’ (proportionality coefficient dx3). Physically, this corresponds to the action of a spherical indenter to which is associated a conoidal fracture surface for sufficiently large load (Roesler (1956) as quoted by Frank and Lawn (1967)). The coalescence of conoidal cracks from different slabs of cylinder along Ox3 would produce planar fracture surface envelops parallel to x3 at large crack lengths. Therefore, we expect the modelling in Figure 1 to provide the experimentally observed fracture surface inclination angle θ and crack length l as a function of critical load P by both a spherical indenter and cylinder. This is the essence of the modelling depicted schematically in Figure 1.
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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.
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I am planning to teach a new class and wanted to use this specimen. Note that the black-ish line on the specimen in the LHS picture was originally along the axis of the cylinder, indicating a bulk shear strain on the order of 1. The smooth failure surface at around 50 deg from the axis in the RHS picture is thought to occur first. Note the small similar failure surfaces initiating under the blue arrow in the LHS picture. Also note the this smooth surface is predominantly under compression with the torque direction indicated. I believe there is something about molecular alignment in the tensile direction creating a weaker material in the plane perpendicular...approx. corresponding to the smooth fracture surface.
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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.
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I am using ductile damage in FE model for steel material. the damage evolution law should be specified in terms of equivalent plastic displacement (Upl) or in terms of fracture energy dissipation (Gf)
Is the correct to use the following relation for calculating equivalent plastic displacement (Upl)?
Where L is the characteristic length of element,  "epsilon.f.pl" is the equivalent plastic strain at failure and  "epsilon.0.pl" is the equivalent plastic strain at the onset of damage.
or it should be calculated using this equation?
based on abaqus documentation the fracture energy can be calculated using the following relation
Gf=(Upl*sigmayo)/2
where sigmayo is the value of the yield stress at the time when the failure criterion is reached
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Please find the attached file.
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Hello,
I am trying to simulate crack propagation between two composite plies in an in-house finite element code. I use high-order elements for better convergence and to reduce computational cost, but i have never seen in literature to release nodes instead of the whole elements in any fracture mechanics theory. Is there any specific reason based on theory that forbids this fact?
Thanks
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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.
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  • Generally, fracture mechanics parameters and terms (CTOD, J, C*, stress, load line displacement, plastic zone size) have relevant & respective dimensional units. The physical significance of their units is easily understandable like, energy per unit area or energy rate per unit area of crack growth. In case of K, why its (meter)1/2 i.e. square root of crack size, a and not simple a or 1/a or a-2 ? What is the physical significance of including square root of crack size, a in K formula?
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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
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In modeling concrete fracture, I could use fixed or rotating smeared crack model. But when could I use each of them.
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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
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Also how could I identify the pre-transition and post-transition parts of strain increment?
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Before or after cracking ??
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