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.
Questions related to Fracture Mechanics
  • asked a question related to Fracture Mechanics
Question
1 answer
In fracture, the various expressions of G the crack extension force per unit length of the crack-front (or energy release rate) show invariably a linear dependence of G with the crack half-length c. This is true whatever the shape (planar or non-planar) of the crack and the form f of the crack-front (f can be developed in Fourier forms). Hence some expressions of G (see relation (2.25), page 37 in Lawn (1993) Second Edition, for example) provided for the DCB specimens are under question. Are these concerned with crack propagation?
Relevant answer
Answer
We provide G values for Double-Cantilever Beam (DCB) specimens that depend linearly on the crack length c: see " DOUBLE-CANTILEVER BEAM SPECIMEN BENT BY PAIRS OF OPPOSITE TERMINAL TRANSVERSE LOADS" (2024) in our contributions in Research Gate.
  • asked a question related to Fracture Mechanics
Question
8 answers
For failure analysis, sometimes parts received contains fully rusted fracture surface and surrounding areas. Is there an acid solution out there for soaking the parts or spraying solution to the corroded area to remove the corrosion products and obtain a clean surface for analysis?
Relevant answer
Answer
In our lab we use commercial products based on orthophosphoric acid. However, it should be remembered that after this a protective oxide film is created on the surface. If you need to examine the surface structure, this can be a problem.Recently I tried using a cheaper option - citric acid. It takes more time. However, there is an effect.
  • asked a question related to Fracture Mechanics
Question
1 answer
Hi, I want to analyze a crack in 2d and 3d and find displacement of the Part Block due to that Crack and loading.
My question is as I want to create periodic Sine load applying for several second or minutes, which Solver in Step module suits best and also which method of crack analysis (XFEM, contour integral or VCCT)?
Relevant answer
Answer
follow this link it will help you. its a Udemy course that creates the model you are asking for in details.
  • asked a question related to Fracture Mechanics
Question
1 answer
Dear RG Members,
I’m currently working on extracting data of multiple .rst/.rth files, which are having same mesh and same node numbering, using PyANSYS/PyMAPDL. The end target is to use this data for LCF/Creep/Creep-fatigue/fracture calculations. Currently this data extraction is done manually, we want to automate this process.
The elements I am using is plane77 (with axisymmetric option) for thermal analysis and plane 183 (axisymmetric) for structural analysis (in ANSYS).
Please look at the figure attached.
I want to provide path for all my rth/rst files and respective load/substep numbers for which I want to extract data. On pressing confirm a popup will ask for node number and desired data (temperature/stress/strain/creep strain) for that node number should be there in the output column from all these files (that's the wish). First row data (temperature from a rth file for steady state thermal run) I was able to extract. Got stuck in the second row where I want von Mieses stress from a steady state structural run.
However, when I attempt to parse the result sets using result.parse_step_substep(), I receive only integer indices representing the result sets, rather than a tuple containing the actual load step and substep numbers. For example, my .rst file shows 3 result sets, but the step info returned is simply 0, 1, and 2, without any clear mapping to the original load step and substep numbers from the simulation. Is there a current method within PyMAPDL to directly retrieve data based on specific load step and substep numbers (e.g., Load Step 3, Substep 5), rather than relying on the result set indices?
Thank you for your help and support in advance.
Regards
NC
Relevant answer
Answer
I asked this question for PyANSYS team also. Here is their reply:
This was a mistake from my side as I just started using PyANSYS. Functionality I was seeking is related to the PyMAPDL Reader, not PyMAPDL itself.
Regards
  • asked a question related to Fracture Mechanics
Question
3 answers
The aim of the research here is to prevent the propagation of the crack in the fabricated elastic medium with useful applications.
Relevant answer
Answer
1) Your answer is on a purely assumption level.
2) Assuming no pre-existing crack, le material would deform plastically only.
3) In presence of a pre-existing crack, expansion of the latter would be observed on the elastic applied stress range first until the blunting of the crack (crack arrest), clearly in a two-dimensional crack scheme.
  • asked a question related to Fracture Mechanics
Question
2 answers
I am looking to purchase a photography kit for onsite metallurgical investigations, such as capturing photos of worn areas, hot tears, cold tears etc. Could anyone suggest me a good macro-photography kit / camera combination for this purpose. Thank you.
Relevant answer
Answer
Hello Mohammad,
The biggest problem that has not been solved yet is the depth of field. Any USB microscope with output to the laptop screen is quite suitable for field analysis of small defects. For large defects, it is better to use a camera (with a tripod). It requires special lenses or adapter rings. For high-quality photos for reports or articles, you will need to take several shots with different depths of field in manual mode and then combine them.
  • asked a question related to Fracture Mechanics
Question
15 answers
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?
Relevant answer
Answer
Recent works confirm that elliptical cracks cannot expand under applied shearing stresses parallel to their planes. Please see: Conoidal crack with elliptic bases, within cubic crystals, under arbitrarily applied loadings-I. Dislocation, crack-tip stress, and crack extension force; -III. Application to brittle fracture systems of CoSi2 single crystals (III). Theory and experiments completely agree.
  • asked a question related to Fracture Mechanics
Question
2 answers
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.
Relevant answer
Answer
Progress is achieved with respect to previous description:
1) The crack extension force G, per unit length of the crack front, is now available in analytical form
2) G value now includes the contribution of gravitational forces due to the earth.
Please refer to “BRITTLE CRACKS IN A THREE-DIMENSIONAL ELASTIC HALF-SPACE UNDER THE RECTILINEAR CONTACT PRESSURE OF A CYLINDER: INTRODUCING GRAVITATIONAL FORCES”.
  • asked a question related to Fracture Mechanics
Question
3 answers
Cross-slip, twinning and fracture are major deformation modes adopted by loaded materials. It appears sound that these apparently different deformation mechanisms can be analysed on the equal manner!
Relevant answer
Answer
Cross-slip, twinning, and fracture systems under applied loadings receive the same mathematical theory using continuous distributions of elliptical dislocations in the framework of linear elasticity. Essentially the theory provides a quantity G that is a ratio, defined as the decrease ΔE of the total energy of the system divided by the corresponding change ΔS of the surface of the dislocation distribution, after incremental infinitesimal time dt: G= -ΔE/ΔS. In fracture G is the energy release rate or crack-extension force per unit length of the crack-front. Stationary configurations under which d<G> = 0 are those observed experimentally. <G> is the value of G averaged over all the spatial positions on the defect front. Please refer to the following works for details: Conoidal crack with elliptic bases, within cubic crystals, under arbitrarily applied loadings-I. Dislocation, crack-tip stress, and crack extension force; -II, III, and IV: Application to systems of twinning in copper (II), fracture in CoSi2 (III), and cross-slip in copper (IV). Theory and experiments completely agree.
  • asked a question related to Fracture Mechanics
Question
10 answers
Can we restrict the vertical and horizontal displacement in two directions for the lower semicircular in bottom hole of CT specimen and apply incremental displacement in the upper semicircular in top hole?
Or is it done some other way?
Relevant answer
Answer
If I consider the problem domain to be the entire CT specimen. What will be the boundary conditions? In that case do I have to restrict the Uy in the middle portion along the direction of crack?
  • asked a question related to Fracture Mechanics
Question
2 answers
Hello all,
I need to pre-crack a steel specimen with the following dimensions.
W = 25mm, an = 6mm, B = 5mm
How do I identify the force required for the pre-crack initiation?
Relevant answer
Answer
Thank you for your reply!
I will try it out and get back to you.
  • asked a question related to Fracture Mechanics
Question
3 answers
2024 3rd International Conference on Materials Engineering and Applied Mechanics (ICMEAAE 2024) will be held from March 15 to 17, 2024 in Changsha, China.
ICMEAAE 2024 provides an enabling platform for Materials Engineering and Applied Mechanics experts to exchange new ideas and present research results. This conference also promotes the establishment of business or research relations among global partners for future collaboration. We hope that this conference could make a significant contribution to the update of knowledge about this latest scientific field.
ICMEAAE 2024 warmly invite you to participate in and look forward to seeing you in Changsha, China.
---Call For Papers---
The topics of interest include, but are not limited to:
1. Materials
- Materials Science and Engineering
- Nanomaterials
- New Energy Materials
......
2. Applied Mechanics
- Vibration Science
- Elasticity
- Particle mechanics
......
All accepted full papers will be published in the conference proceedings and will be submitted to EI Compendex / Scopus for indexing.
Important Dates:
Full Paper Submission Date: February 23, 2024
Registration Deadline: March 1, 2024
Final Paper Submission Date: March 8, 2024
Conference Dates: March 15-17, 2024
For More Details please visit:
Relevant answer
Answer
Dear Sarabjeet KaurFor more details please visit the conference website:
  • asked a question related to Fracture Mechanics
Question
3 answers
Who know about conferences on fracture mechanics in 2024 ?
Relevant answer
Answer
Thanks a lot Dr. Al-Mukhtar. I have looked information about this conference. Have you take apart in this conference?
A. M. Al-Mukhtar
  • asked a question related to Fracture Mechanics
Question
2 answers
The motivation comes from the following common observation. Blocks of stone with large dimensions (say of the order of three meters or larger) can be easily fractured into two pieces. First, cylindrical holes are introduced at top surface using drills. Second, fracture is initiated from the holes with the help of sledgehammers and wedges. Without any additional action, the crack will move with time downward other very large distance and separate the block of stone into two parts. The fracture surface is perfectly flat. What is the reason?
Relevant answer
Answer
Phenomena such as the Al Naslaa Rock, Active cracks in Yosemite National Park find explanation from gravitational forces.
  • asked a question related to Fracture Mechanics
Question
1 answer
Under dominant mode I loading, planar cracks have been observed to move from zero velocity v= 0; for a certain value v= v1, these turn into non-planar crack configurations. An explanation is offered below.
Relevant answer
Answer
We refer to the work “NON-PLANAR CRACKS IN UNIFORM MOTION UNDER GENERAL LOADING” by ANONGBA (2020):
When the velocity v of planar cracks increases toward the terminal velocity ve = 0.52 ct (ct, the velocity of transverse sound wave), moving non-planar crack configurations have been found (0.33 ct < v < 0.55 ct, approximately) with average crack extension force < G > much larger than those of planar cracks. This indicates that non-planar cracks may be associated with larger decrease of the energy of the system on change of crack configuration. Hence, the starter planar crack transforms itself into a non-planar configuration to maintain higher speed motion during its evolution in steady motion.
  • asked a question related to Fracture Mechanics
Question
6 answers
Hello Researchers,
To conduct fracture toughness tests for pipeline material how do you machine specimen using pipelines with small thicknesses (ex 7mm)?
According to ASTM E399, how do you satisfy the ligament length condition with a smaller specimen?
Thank you
  • asked a question related to Fracture Mechanics
Question
1 answer
I see a lot of equations work very well without Pi then it is needed to use Pi in fracture machines.
Relevant answer
Answer
Pi (π) is not specifically used in fracture mechanics equations as a fundamental constant like it is in geometry or trigonometry. However, it may appear in some fracture mechanics equations due to the inherent geometry and mathematics involved in describing cracks and crack growth.
  • asked a question related to Fracture Mechanics
Question
2 answers
Fatigue fracture surfaces of broken high strength materials exhibit rough conoidal cracks at the vertex of which are located inclusions or heterogeneities
Experimental: The observations refer to Sakai et al. (2002), Abdesselam et al. (2018), Stinville et al. (2018) ... These cracks have been named “fish-eye marks” by two former authors and their formations have been divided into three stages: (i) formation of the characteristic area as a fine granular area (FGA); (ii) crack propagation to form the fish-eye (i.e. according to us “rough conoidal crack”); (iii) rapid crack propagation to cause the catastrophic fracture.
Relevant answer
Answer
With this work at hand (i.e. "ROUGH CONOIDAL CRACK GROWING UNIFORMLY UNDER GENERAL LOADING"), it becomes possible to follow the evolution (propagation) of highest complexity cracks that nucleate from defects (such as heterogeneities, inclusions ...) located inside materials. The provided G (the crack extension force per unit length of the crack front) is function of highest number of variables and parameters.
  • asked a question related to Fracture Mechanics
Question
2 answers
This subject is important because evidence of conoidal rough cracks is observed experimentally on various macrographs of broken specimens, under fatigue for instance. Our recent works (see below in answers) provides associated physical quantities.
Relevant answer
Answer
Again with this work at hand, it becomes possible to follow the evolution (propagation) of highest complexity cracks that nucleate from defects (such as heterogeneities, inclusions ...) located inside materials. The provided G (the crack extension force per unit length of the crack front) is function of highest number of variables and parameters.
  • asked a question related to Fracture Mechanics
Question
1 answer
YES! THIS HAS BEEN SHOWN IN “PLANAR CRACKS IN UNIFORM MOTION UNDER MODE I AND II LOADINGS” (ANONGBA 2020).
Earlier works have suggested that crack speeds v could not exceed Rayleigh wave velocity, in the subsonic velocity regime (v< ct transverse sound wave velocity).
Relevant answer
Answer
YES! THIS HAS BEEN SHOWN IN “PLANAR CRACKS IN UNIFORM MOTION UNDER MODE I AND II LOADINGS” (ANONGBA 2020).
THIS IS WITHIN THE THEORY OF LINEAR ELASTICITY!!!
In mode I loading and in the subsonic velocity regime (v < ct, the velocity of transverse sound wave), G (I) increases continuously with v from the value in the static case G(I)0 (v = 0) to a maximum G(I)max = 1.32 G(I)0 at v = v (e) =0.52ct; then, G (I) decreases rapidly to zero when v tends to ct. In agreement with experiments, the value v (e) corresponding to the maximum of the crack extension force is identified to the terminal tensile crack velocity, observed in the fracture of brittle materials. No reference is made to the Rayleigh wave velocity cR. In the transonic speed regime (ct < v < cl), the crack characteristic functions are identical in form with those of the subsonic regime. However, for v < ct√2, we show that the faces of the crack, separated under load before the extension of the crack, close under motion; this indicates that the crack movement is hindered. for v > ct√2, the motion of the crack is possible. In mode II loading and in the subsonic regime (v < ct), G (II) increases continuously with v (when v < cR) from the value in the static case G(II)0(v = 0); when v approaches cR, G (II) increases very rapidly. Above cR (cR < v < ct), the relative displacement of the faces of the crack, formed under load before crack motion, closes in motion; this indicates that crack motion is impeded. The velocity of uniformly moving cracks is limited by the Rayleigh wave velocity. In the intermediate speed regime (ct < v < cl), the crack characteristic functions are similar in form to those below cR. The mouvement of the crack is possible.
  • asked a question related to Fracture Mechanics
Question
1 answer
This question deserves to be posed and clarified. It is at this price that we will be able to consider an improvement involving analyses including new concepts. The answer to this question is given below.
Relevant answer
Answer
YES, FRACTURE MECHANICS IS BEAUTIFULLY COMPLETED. It has been suggested and demonstrated that a crack in an elastic loaded solid in the framework of linear elasticity may be viewed as a continuous distribution of infinitesimal dislocations (For a review, see Bilby and Eshelby, 1968). These authors provide an expression for G, the crack extension force per unit length of the crack front (or energy release rate), for steady motion. G is sum of terms that are products of stresses and values of the relative displacement of the faces of the crack at the tip of the crack. We find in recent works (Anongba, 2021 and 2022) that for a dislocation in the form of an arbitrary closed loop, there exists only one singularity in the dislocation stress fields. This singularity is of the Cauchy type: i.e., 1 / │r - r0│; r the position in the medium and r0 the position on the dislocation where G is evaluated. These are terms involving that singularity which contribute a non-zero value to G. All the other additional terms in the dislocation stress fields are bounded and contribute nothing. In this sense, we may say that Fracture Mechanics is completed.
  • asked a question related to Fracture Mechanics
Question
2 answers
Hello everyone,
I am currently investigating the phenomenon known as the Indentation Size Effect (ISE) using the Finite Element Method (FEM). My research involves conducting indentation tests through simulation using ABAQUS.
Here are some specifications of the model:
  • It is a 2D axisymmetric model.
  • The indenter is represented as a rigid body and possesses a semi-angle of 70.3°.
  • The specimen material is assumed to be homogeneous and isotropic, characterized by an ideal elastoplastic model.
  • Mesh is refined near the indenter tip to capture stress concentration accurately.
  • Contact Interaction: Surface-to-surface contact, Tangential behaviour - Frictionless, Normal behaviour - Hard Contact.
I have conducted simulations at various depths, ranging from 500 nm to 5000 nm. To determine the hardness, I have employed the Oliver-Pharr Method. According to the concept of ISE, the hardness should decrease as the indentation depth or load increases. However, in my results, I have observed that the hardness remains almost constant regardless of the depth. Consequently, I am unable to observe the anticipated trend associated with the Indentation Size Effect in my findings.
For your convenience, I have attached the .cae file and the hardness vs indentation depth plot.
I would greatly appreciate any assistance or insights you can provide to help me address this issue.
Thank you all in advance.
Relevant answer
Answer
Your work on Indentation Size Effect (ISE) using Finite Element Method (FEM) in ABAQUS sounds intriguing and challenging. The phenomenon of ISE that you are observing (or rather, not observing) could potentially be attributed to several factors.
To simulate the ISE using FEM in ABAQUS, you should consider the following:
  1. Material Hardening: In many indentation studies, it has been seen that classical elastoplastic constitutive laws, such as the von Mises yield criterion, fail to reproduce the ISE due to strain gradient hardening not being accounted for. The ISE typically becomes observable in materials with strain gradient plasticity. It might be beneficial to incorporate strain gradient plasticity into your model.
  2. Model Scale: The length scale of the model might be affecting your simulation results. If the scale is not in the nanometer range, you may not see ISE.
  3. Mesh Sensitivity: It seems you've already refined your mesh near the indenter tip, which is a good step. However, it's still worth rechecking your mesh sensitivity. If the mesh isn't fine enough, it might not be able to capture the material behaviour accurately.
  4. Contact Interaction: Check the contact definitions again. Problems in the definition of contacts, such as contact stiffness and overclosure, can lead to abnormal results.
  5. Indentation Load: Be aware of the possibility that the load you are applying might be too high. Plastic deformation might be the dominant deformation mode if the load is too large, and you may not observe ISE.
  6. Influence of Material Model Parameters: Check whether the material model parameters are accurate. Wrong input parameters can greatly affect the simulation results.
Remember that the simulation of ISE using FEM is a complex task due to the involvement of various scale-dependent phenomena. It might take several iterations of refining and validating your model to get it right finally. Good luck with your research!
The Indentation Size Effect (ISE) is a phenomenon observed in materials science where the hardness of a material appears to increase as the size of the indentation (or, equivalently, the load of the indenter) decreases. In other words, smaller indentations result in higher hardness values. This trend contradicts the classical definition of hardness, which is expected to be a constant material property, independent of the indenter size or load.
The ISE is often explained by the strain gradient plasticity theory, which accounts for the influence of the geometrically necessary dislocations on the deformation behaviour of the material. This theory suggests that the plastic deformation beneath the indenter is not uniform but instead exhibits a gradient, with higher strain (and thus, higher dislocation density and hardness) near the surface, and lower strain deeper in the material.
Consequently, when you conduct indentation tests at varying depths or loads, you should observe that the hardness decreases as the indentation depth or the load increases. This decrease should follow a specific trend, often modelled by Meyer's law or the proportional specimen resistance (PSR) model.
However, remember that the ISE might not be observable in all materials or under all conditions. Factors such as the type of material, the nature of the indenter, the scale of the test, and the specific methodology can all influence whether and to what extent the ISE is observed.
  • asked a question related to Fracture Mechanics
Question
1 answer
Dear researchers,
I am currently researching the issue of fracture in thin steel plates containing holes. Some scholars have already conducted static tensile fracture tests on plates with holes [1], and the test model is shown in the attachment. I have derived the stress distribution field under static tensile conditions. However, in my practical applications, the specimen is subjected to high loading rates, where the tensile force approximates an impulse force. Therefore, the static results can only serve as a reference. I would like to further investigate the fracture mechanisms in the transient tensile behavior of the steel plate, including the influence of the distribution of cracks near the hole and hole geometry on the results. It would be ideal to obtain theoretical solutions. Could you provide me with some suggestions or references regarding the research direction? Thank you for your attention.
[1] Wang W and Jiang L 2011 Fracture Mode of High Strength Steel Thin Plates with Elliptical Hole. In: 2011 Fourth International Conference on Information and Computing, pp 338-41
Relevant answer
Answer
Hi
Experimental and numerical methods can be used to investigate transient fracture mechanisms and crack distribution in thin steel plates with holes under high loading.
In the experimental method, it is possible to check the mechanical behavior of the steel plate under high loading by using tensile and bending tests. These tests can help identify weak points and fractures in the steel plate.
In the numerical method, finite element modeling software can be used to simulate the mechanical behavior of steel plates under high loading. These simulations can help us identify transient failure mechanisms and crack distribution in perforated steel plates under high loading.
In both experimental and numerical methods, equipment such as electron microscopes and digital imaging tools can be used to investigate transient failure mechanisms and crack distribution. By using these tools, it is possible to identify weak points and fractures in steel plates more precisely.
On the other hand, to investigate transient failure mechanisms and crack distribution in steel plates with holes, the necessary precautions must be taken in terms of safety and hygiene. For example, safety clothing and masks must be used, and safety devices must also be used to perform tests.
  • asked a question related to Fracture Mechanics
Question
9 answers
I am currently deriving the stress intensity factor for a crack at the edge of a circular hole in a plate. The integral form of the stress intensity factor is as follows:
I would like to inquire if there are any innovative approaches or potential combinations with emerging theoretical methods for solving this equation. Could you please provide some insights on this matter? Alternatively, are there any recommended reference books and papers on this topic?
Thank you for your time and attention.
Relevant answer
Answer
Hello, you can solve the problem using finite element software such as Abaqus. The two mentioned books recommended by friends are also good guides. You can also use other books on fracture mechanics.
I hope I have been able to help you.
  • asked a question related to Fracture Mechanics
Question
48 answers
In fracture mechanics, the obsolete principle of stress intensity factor K (SIF) is still used, even though it has a limited validity and questionable interpretation.
What experience do you have and what is your opinion?
Relevant answer
Answer
Rhys:
This is a question that has been raised for half a century or more - I can remember Keith Miller, when I was a graduate student, opining that delta-K could not be used to describe fatigue-crack growth - nevertheless fracture mechanics is still successfully used today. As long as one is properly aware of the basis and limitations of governing parameters such as K and J, I still believe that they have a powerful application. However, this is not always the case when they are used and accordingly fracture mechanics has become one of the most abused form of mechanics.
If you think that this approach should be dismissed though because of its "limited validity and questionable interpretation", could I respectively ask what you would recommend as a replacement?
cheers Rob
  • asked a question related to Fracture Mechanics
Question
1 answer
This subject is very important because evidence of circular cracks is observed experimentally on various macrographs of broken specimens, under fatigue for instance. Our recent work (see below in answers) provides associated physical quantities.
Relevant answer
Answer
A corresponding work (Anongba, 2021) is intitled ʺ Elliptical crack under general loading: dislocation, crack-tip stress, and crack extension forceʺ. The various physical quantities displayed there depend implicitly on time t through the dependence on time of the circular crack radius R ≡ vt (v= constant). We take ar = a1 / a2 = 1 where aiare the semiaxes of the elliptical crack; R = a1.
P.N.B. ANONGBA, Elliptical crack under arbitrarily applied loadings: dislocation, crack-tip stress and crack extension force, Rev. Ivoir. Sci. Technol., 38 (2021) 388 – 409; see also, http://dx.doi.org/10.13140/RG.2.2.27048.29446
  • asked a question related to Fracture Mechanics
Question
2 answers
Abaqus provides the option to define the mode mix ratio based on energy or traction. The traction-based mixed mode response ( Mode I/II problem) where pure Mode I and II traction separation relation is already defined in the input file. Is the Abaqus interpolates for the intermediate mode mix ratios?
Relevant answer
Answer
Thanks Kaushik
I was looking for the same in Abaqus documentation. It would be a great help, if you can share the link or refer the section in Abaqus documentation (if you have acces to).
Regards
Sailendu
  • asked a question related to Fracture Mechanics
Question
2 answers
My research mate Fernando Coelho came up with this excellent terminology regarding a novel publication about using mechanical pull-off testing for failure pattern analysis for adhesives. This is already standardized via ISO 10365.
However, it is important to note that even 40 years ago, Hutchinson and Sue (1992) already applied fracture analysis tests correctly to address this issue - and not pull-off tests.
What do you think about this issue?
Is it correct to use simple pull-off testing for fracture analysis?
Let me know in the comments below!
PS: You can also watch the disussion flowing on LinkedIN
Relevant answer
Answer
The variation in analysis is so great that just about any model will work. The question (problem) is applying to say an acceptance tests with documented uncertainty for the values determined.
  • asked a question related to Fracture Mechanics
Question
1 answer
In fracture mechanics, there are several test specimen, such as the C(T) specimen, and when assessing the crack growth behoavior, to determine the threshold stress intensity factor, a precrack is needed prior to perform the crack propagation test?
Relevant answer
Answer
Fracture mechanics is a branch of solid mechanics. It analyzes a solid body with a sharp crack, i.e., a mathematical sharp crack tip with zero radius. The stress in the brittle material at the crack tip is infinite theoretically. A machined notch has a well defined corner radius and the notch tip is not sharp enough to be a crack tip. Even use standard EDM, the notch radius would be about 0.15mm. You need to create a natural, sharp crack in CT specimen to get valid fracture toughness. Refer to ASTM E1820 for test procedure.
  • asked a question related to Fracture Mechanics
Question
3 answers
In fracture mechanics, the principle of linear-elastic strain energy release rate GIc is still widespreadly applied, even though it has a limited validity and questionable interpretation.
What experience do you have and what is your opinion?
Relevant answer
Answer
In the oil & gas industry, Fracture Mechanics principles have been successfully applied in the "Engineering critical Analysis" and "Fitness for service assessment" of pressure vessels, pipeline and others made from steel. There are two industry standards: API 579 and BS7910. None of them uses GIc. For fracture toughness, we use J-integral and CTOD.
  • asked a question related to Fracture Mechanics
Question
2 answers
The ʺstress intensity factorsʺ concept is known from Irwin (1948, 1957) who linked these to the energy release rate (crack extension force per unit length of the crack front) in the case of a crack in a two-dimensional crack analysis. In practice (to be used in three dimensions), the crack is viewed planar (Ox1x3) with a straight front running indefinitely in the x3-direction, perpendicular to the crack propagation x1-direction. In this situation, the utility of the stress intensity factor is apparent. For an arbitrary crack front in three dimensions, please see what follows.
Relevant answer
Answer
The GIc method is already outdated by non linear plastic principles such as GF.
  • asked a question related to Fracture Mechanics
Question
4 answers
Could you please tell me what is according to you the best conference on Fracture Mechanics to attend? Especially for surface hardened steel materials used in aeronautics applications ? Thanks for your help ;)
Relevant answer
Answer
Dear Jean-Baptiste Libot, I agree with the Adam Niesłony replay. I would like to point out that it is important also the continuity to participation in the conference to create a group of scientists on specific themes.
Regards.
  • asked a question related to Fracture Mechanics
Question
7 answers
Hello researchers,
If a cyclic load is used for fatigue crack growth testing, why does it require pre-crack with a cyclic load?
Isn't it the same thing?
Relevant answer
Answer
The straightforward answer is to create a natural crack, which eliminates the notch effect.
  • asked a question related to Fracture Mechanics
Question
1 answer
Hello everyone,
I want to investigate the debonding behavior of the matrix-particle interface in a particulate composite with spherical particles in a two-dimensional matrix, using the Abaqus Dynamic Explicit solver.
I used General Contact (Explicit), with cohesive behavior and Johnson -cook damage formulation. However, stress concentration is occurred at matrix, and the stress is not transferred to the particles. Also, interface perpendicular to force direction is deboned very early. I think my interface definition is not correct, any help would be highly appreciated.
Relevant answer
Answer
To define debonding at the matrix-particle interface using the cohesive surface method in Abaqus, you can follow these steps:
  1. Create a surface or surfaces in your model that represent the interface between the matrix and the particles. These surfaces should be associated with the matrix material.
  2. In the Abaqus/CAE interface, go to the "Material" tab and select "Cohesive Surface" from the "Material Type" dropdown menu.
  3. Define the cohesive surface properties, such as the normal and tangential stiffness, normal and tangential strength, and debonding energy. These values should be determined based on the material properties of the matrix and the particles and the desired debonding behavior.
  4. Assign the cohesive surface material to the interface surfaces in your model.
  5. Run the simulation and monitor the debonding behavior at the matrix-particle interface. You may need to adjust the cohesive surface properties and re-run the simulation if the debonding behavior is not as desired.
Keep in mind that the cohesive surface method is just one approach to modeling debonding in particulate composites. Other methods, such as the cohesive element method, may also be used depending on the specific needs of your simulation.
  • asked a question related to Fracture Mechanics
Question
12 answers
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
Relevant answer
Answer
In my opinion, Franc3D is the best.
  • asked a question related to Fracture Mechanics
Question
2 answers
In the paper "Predicting thermally induced edge-crack initiation using finite fracture mechanics" by S. Dölling, et al. in Eng.Frac.Mech. 252 (2021) 107808, which is discussed on the iMechanica platform as ESIS blog paper #35, I find that what I would call a two-parameter fracture criterion is presented as a "finite fracture mechanics" methodology. The two parameters are the energy release rate and a stress criterion. This is a sub-group of the large variety of two-parameter criteria, I find the denotation "finite fracture mechanics" somewhat cryptic.
Nevertheless, I accept it as it is, but I have a question regarding the physical background of the method: As I understand it the fracture processes are not modeled. Considering this, how is it possible to know if the autonomy of these processes is preserved by the two-parameter criterion? Not always I assume, but when?
Disclaimer: I could have used the comment opportunity that iMechanica offers, but this is only for members. After having had my membership application rejected several times, it was suggested I use this platform instead.
Sophie B. Lange
Relevant answer
Answer
Dear Sophie,
I find your question really interesting, I hope my answer here will help you clarify a bit your doubts.
1. Yes, FFM is a two-parameter fracture criterion. In fact, Dölling & co-authors refer to the foundational paper of Leguillon ( ) on two-parameter (stress+energy) fracture criterion.
2. Yes, fracture processes are not modeled. Why? Because it's hard to do it. In terms of energy balance, the fracture problem involves external energy transferred macroscopically to the specimen that is dissipated by microscopic mechanisms at or very close to the crack tip. Thus, it is an inherently multi-scale problem. But we want to model it while staying in the realm of continuum (macroscopic) mechanics. Models like the cohesive zone model (cohesive elements) or phase field fracture mechanics try to model these dissipation mechanisms through internal variables and/or material properties, which have proven to be quite difficult to measure. In FFM, we simply assume that we can model the end result of these processes (i.e. macroscopic fracture) with a two-parameter macroscopic criterion. So, can you say something about these microscopic dissipative processes? Not really, as we are not modeling them. We assume that we can predict the end result by neglecting their exact physics and using a "correct" macroscopic criterion.
3. So, why the "Finite" in FFM? Well, it is so-called in comparison with what came before, i.e. Linear Elastic Fracture Mechanics (LEFM). Now, it is the latter name that is deceiving. The name LEFM is more historical than mathematical. Historically, first came elasticity, and upon the results of the theory of elasticity people like Irwin, Griffith, Westergaard built the foundations of what became Fracture Mechanics (FM). It was thus called LEFM. But if you look at the mathematical formulation of the fracture criteria proposed, it should be more properly called Infinitesimal Fracture Mechanics (IFM?). Why? Because the properties governing fracture (Stress Intensity Factors, Energy Release Rate, mode ratio, etc...) are evaluated in the limit r-->0 with r the radial distance from the crack tip, i.e. infinitesimally. In contrast, FFM starts from the assumption that fracture propagation is characterized by a finite length scale. Thus the properties governing fracture should not be evaluated infinitesimally, but at a finite "characteristic" distance from the crack tip. Thus the "finite" in FFM. How do you determine this characteristic distance? This is actually the problem in FFM, as the characteristic length is the main link between macroscopic criterion and microscopic dissipative processes. Usually, some calibration with experiments is needed to find a fitting value.
I hope it helps.
Best,
Luca
  • asked a question related to Fracture Mechanics
Question
3 answers
Currently I am modelling a timber beam with bolted connection using Abaqus CAE. I'm using displacement control as loading in my analysis. In order to get a good load-displacement curve (elastic and plastic region) for my result, I need to define plasticity and damage properties for my wood material. I also want to see the failure mode (damage zone) of the connection. Can anyone help me to solve this problem? Thank you.
Relevant answer
Answer
Here is the latest published Modelling Guide for Timber Structures developed by more than 100 global experts: https://web.fpinnovations.ca/modelling/. Chaper 4.1 discusses the constitute models for wood-based products and key modelling considerations.
  • asked a question related to Fracture Mechanics
Question
8 answers
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
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
23 answers
I'd like some opinions. What are the major challenges in fatigue and fracture mechanics?
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
4 answers
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?
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
4 answers
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?
Relevant answer
Answer
  • asked a question related to Fracture Mechanics
Question
15 answers
  • 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 ?
Relevant answer
Answer
  • asked a question related to Fracture Mechanics
Question
3 answers
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
Relevant answer
Answer
Dear Izaz,
Read these articles, it may help you in your research.
Good luck.
  • asked a question related to Fracture Mechanics
Question
4 answers
Can I be assisted with guidelines to linear elastic fracture mechanics in timbers?
Relevant answer
  • asked a question related to Fracture Mechanics
Question
9 answers
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?
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
5 answers
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?
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
5 answers
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).
  • asked a question related to Fracture Mechanics
Question
4 answers
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?
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
8 answers
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
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
9 answers
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
Relevant answer
Answer
Here it is. Good luck
  • asked a question related to Fracture Mechanics
Question
8 answers
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
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
3 answers
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
Relevant answer
Answer
I would probably use Abaqus. It will be easier when you implement the characteristics of your material model (user defined material or element).
  • asked a question related to Fracture Mechanics
Question
2 answers
How to define quarter-point element at the crack front, in a Static Structural analysis with a 3D CAD model in Ansys Workbench? Is there an APDL command that can be used in WB do to so?
Relevant answer
Answer
On my research thesis, I used Ansys Workbench but at entry level only. Some researcher are discussing your issue too. Sometimes in Ansys you have to use some techniques to solve the issue. because it is not "straightforward software". It is like doing research, putting other people answer together and solving puzzles... then see if you can find your answer (Up)
By the way, maybe this link of website below is useful for you.
  • asked a question related to Fracture Mechanics
Question
2 answers
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?
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
8 answers
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.
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
1 answer
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
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
5 answers
Does a single-valued description exist for isotropic materials?
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
5 answers
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.
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
7 answers
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.
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
5 answers
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
Relevant answer
Answer
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.
  • asked a question related to Fracture Mechanics
Question
5 answers
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.
Relevant answer
Answer
Thanks sir.
  • asked a question related to Fracture Mechanics
Question
5 answers
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.
Relevant answer
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
  • asked a question related to Fracture Mechanics
Question
6 answers
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?
Relevant answer
Answer
  • asked a question related to Fracture Mechanics
Question
3 answers
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,
Relevant answer
Answer
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!
  • asked a question related to Fracture Mechanics
Question
1 answer
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
Relevant answer
Answer
If you wish to use FRANC3D : write to me on nls@dhioresearch.com
  • asked a question related to Fracture Mechanics
Question
1 answer
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?
Relevant answer
Answer
  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.
  • asked a question related to Fracture Mechanics
Question
15 answers
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.
Relevant answer
Answer
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
  • asked a question related to Fracture Mechanics
Question
4 answers
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!
Relevant answer
Answer
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