Ductility - Science topic

Hi Ravi,

(No need to call me sir).

Yes, you really only need to concentrate on the value of ductility at each temperature in terms of strain. This should be compared to the level of strain in the material as it cools. If the applied strain is greater than the ductility, the material will tear.

Best wishes,

Simon

The issue likely arises from incorrect material parameters (e.g., yield stress too high), insufficient mesh refinement in the impact zone, overly high mass scaling (causing unrealistic dynamics), or improper contact settings (e.g., inadequate stiffness or alignment). Verify material plasticity parameters, refine the mesh, reduce mass scaling, and ensure contact interactions are correctly defined.

There is no simple linear relationship between elongation percentage and dimple size during ductile failure, but some general trends can be observed:

3- Dimple size distribution is often asymmetric, with many small dimples and fewer large ones, complicating the analysis

4- As elongation increases, dimples tend to become more elongated rather than simply larger

The DBTT of low carbon steel is influenced by both the carbon content and the presence of alloying elements or impurities. Elements like manganese and nickel can lower the DBTT and improve toughness, while higher levels of carbon, phosphorus, sulfur, and oxygen tend to raise it, making the steel more brittle at lower temperatures. The following studies may be helpful: https://doi.org/10.1007/s11223-019-00075-8; https://doi.org/10.3390/ma14071634; https://doi.org/10.1007/s12540-021-01053-z; The effect of chemical composition on the DBTT in low-carbon steel alloys plays a decisive role in determining the microstructure of the material. Generally, low-carbon steels exhibit a ferrite-pearlite microstructure, and refining the grain size can lower the DBTT, thereby improving impact toughness. For instance, a finer grain structure significantly enhances resistance to brittleness. This phenomenon can be explained by the Hall-Petch relationship, which states that as grain size decreases, the material's yield strength increases, and the fracture stress rises accordingly. Additionally, the inclusion of elements like aluminum or manganese in the chemical composition of low-carbon steels also affects the DBTT. For example, an increase in manganese content enhances the ductility of the steel, lowering the transition temperature. The addition of aluminum can further reduce the DBTT in ferritic structures, improving the material's thermal resilience. These factors can be optimized according to the steel's intended applications and required strength characteristics.

The PEEQ values for monotonic and cyclic loading will undoubtedly differ. In cyclic loading, plastic strain accumulation is generally higher, as it depends largely on the number of cycles endured and the specific loading protocol. In contrast, for monotonic loading, PEEQ may be relatively lower, since the specimen isn't subjected to reversed loading. This could explain why your numerical model shows premature failure compared to the experimental data. For more insights into PEEQ (at fracture) variation under different stress states in mild steel subjected to monotonic loading, you may refer to our article: https://doi.org/10.1016/j.engfracmech.2023.109638.

CYS remains virtually unchanged when small surface cracks appear in the material, whereas YS can decrease several times.

Hello,

- Regarding strength, we have two different cases depending on the grain size:

1- Hall-Petch Relationship: This relationship states that as the grain size decreases, the strength and hardness of the metal increase. This is because grain boundaries act as barriers to dislocation motion, making it harder for the material to deform.

2- Inverse Hall-Petch Breakdown: At extremely small grain sizes (typically below 10-15 nm), the strengthening effect can reverse. This is due to mechanisms like grain boundary sliding becoming more prominent, leading to softening.

- Concerning ductility, nanocrystalline metals can become more brittle because there are fewer dislocations within the grains to allow for plastic deformation.

- To make a balance between strength and ductility, having a bimodal grain size distribution could be a solution, with both small (for example, 10-20 nm) and slightly larger grains (more than 100 nm up to 1-2 µm). This can improve ductility while maintaining high strength. The very small grains contribute significantly to the strength of the material due to the Hall-Petch effect while the slightly larger grains enhance ductility by providing pathways for dislocation movement and accommodating more plastic deformation without leading to premature failure.

Hope this helps.

FYI

Your explicit simulation will give you the dynamic response. If you simulate a quasi-static process in a severly reduced time(and thus a much higher loading rate), it's quite possible that you delay or prevent buckling phenomena.

I'd recommend running the simulation with a linear elastic material and check if you will eventually see some buckling. If nothing happens, try to apply the load more slowly (or reduce the mass scaling, if you used that).

Thanks to all for your valuable comments

Risheng Pei

Not sure which alpha version you are using:

For alpha-8:

import damask

g = damask.GeomGrid.load('Polycrystal.vti')'

g.initial_conditions['phi'] = 1.0 # assuming none of the points are damaged (pristine material), you can obviously change that.

g.save('Polycrystal.vti')

For alpha-7:

import damask

g = damask.Grid.load('Polycrystal.vti')'

g.initial_conditions['phi'] = 1.0 # assuming none of the points are damaged (pristine material), you can obviously change that.

g.save('Polycrystal.vti')

Hope this helps!

I see two solutions: first you calculate a the results in ozlc2019 database for the ductile iron pipe only then a) either try to export, than import it to ecoinvent or b) create a spreadsheet where you can combine the results of the two calculations. By the way it is not recommended to use separate databases because they might have profound underlying modeling differences which makes the data incompatible. I rather try to remodel the pipe production process in ecoinvent than trying to import something ffrom another database to it...

Hi Shiyao,

I believe you need to use CREEP subroutine in which you can define the creep constitutive equations (depending on which creep model you want to use). You can also include creep damage equations in the subroutine.

I believe ABAQUS only accept one subroutine file, so creep and damage have to be in the same subroutine file.

Regards,

Wu

Hi, usually, this problem occurs when I switch on the wifi or internet connections. As I remember, some parameters of ipv6 should be changed.

The main problem is with ETABS algorithm which can not consider and draw bi-linear curve truly. Take your curve and use excel to draw bi-linear curve instead of drawing it in SAP or ETABS.

I do know what your purpose is.

I think if you could dip coat of pure Al on iron and then oxidate the Al coat to form Al2O3.

Dip coat of Al will not envole water, Cl, whic would lead to iron corrision.

This is a guess.

hi Md. Sohidul Islam

Here are the steps to check structural ductility and performance level according to FEMA 440 and ATC-40 using ETABs results for a G+15 building pushover analysis:

Run pushover analysis in ETABS up to the target displacement. Make sure to record base shear and roof displacement at each analysis step.

Plot the pushover curve of base shear vs roof displacement. From this curve, determine the yield and ultimate displacement (Δy and Δu).

Calculate ductility factor μ as Δu/Δy.

Check ductility requirements for seismic force-resisting systems according to FEMA 440 Table C2-3. Requirement is ductility factor μ ≥ 2 for Special Moment Frames.

Determine performance point as the intersection of demand curve with design spectrum. Note the spectral displacement SD1 and acceleration SA1.

Calculate post-yield stiffness degradation index Iγ using equation from FEMA 440.

Plot Iγ vs ductility factor μ on ATC-40 Figure 6.2-1 graph. Read off the expected performance level.

Cross check performance level does not exceed the Collapse Prevention (CP) level for Life Safety objective as per ATC-40 Section 6.4.1.

Tabulate results including pushover curves, μ, Iγ values and determined performance level for reporting.

If the top reinforcement is equal to bottom reinforcement then this will act as steel beam and this typical behaviour can be experienced

Dear Doctor James Lewis

The purpose of modern seismic regulation is to build structures that: a) In frequent earthquakes with a high probability of occurrence, nothing will happen, b) In earthquakes with a medium probability of occurrence, minor, repairable damage will occur, and c) In very strong earthquakes with a low probability of occurrence, no loss of life will occur. So we should not use the term "absolute" in seismic structures. We should use the term 'quality' structures which means applying at least the requirements of all modern regulations. The quality of construction and its safety is also a function of the economic situation of countries, among other factors. It is understandable that poor countries cannot be compared with countries where they have expensive modern seismic regulations. Conclusion... there is no absolute seismic planning today, and we should not refer to absolute seismic planning, but to quality planning. So there is a great need today to invent a more modern anti-seismic design that corresponds to absolute anti-seismic design, with lower construction costs.

Yeah,

Thank you for the answer Junxian Chen .

I fully agree with Dr. Punashri. Further, if some kind of minimum reinforcement (horzontal, and possibly verical as well) is added in the inill walls, they will perform much better. Lateral collapse of infill is avoided in this manner. These bars should be properly anchored in the columns

Professor William Callister wrote the famous book "Materials Science and Engineering: An Introduction".

Go to the chapter that discusses mechanical behavior of metals. You will find the answer there.

Long story short... elongation is about the change in length. Reduction in area is about the change in the cross-sectional area at the point of fracture.

The magnitudes of elongation and reduction in area will, in general, be different.

Best regards.

The stiffness degradation you intend to use from reference article can be employed in CDP of ABAQUS. You can refer to these articles to develop your own damage parameters from constitutive relations.

You can also refer to this article where they have used CDP for other similar type of material at nano-scale.

The maximum principal stress criterion is appropriate for brittle materials that fracture under tension or compression, such as ceramics or some composites. In this case, the maximum principal stress criterion is useful because it considers the state of stress in all three dimensions, and is sensitive to the orientation of the applied load. This criterion assumes that the material fails when the maximum principal stress reaches a critical value.

On the other hand, the maximum nominal stress criterion is appropriate for ductile materials that deform plastically before fracturing, such as most metals. In this case, the maximum nominal stress criterion is useful because it accounts for plastic deformation and the stress triaxiality effects. This criterion assumes that the material fails when the maximum nominal stress reaches a critical value. Advantages of using the maximum principal stress criterion include its sensitivity to the orientation of the applied load, and its suitability for brittle materials that fail under tension or compression. However, this criterion does not consider the effects of plastic deformation and is therefore not appropriate for ductile materials. Advantages of using the maximum nominal stress criterion include its ability to account for plastic deformation and the stress triaxiality effects, making it suitable for ductile materials. However, this criterion does not consider the orientation of the applied load, and may not be suitable for brittle materials that fracture under tension or compression. In general, the choice between using maximum principal stress and maximum nominal stress as the damage initiation criterion in ABAQUS should be based on the material behavior and the type of loading. For materials that exhibit both brittle and ductile behavior, it may be necessary to use a combination of these criteria to accurately model the material response.

Sorry. I am not an expert in that field.

There are several factors that can affect the material removal phenomenon during machining, and it may be difficult to pinpoint the specific cause of the issue you are experiencing without more information. Here are a few things you might consider:

I hope these suggestions are helpful. If you are still having difficulty achieving the desired material removal phenomenon, it may be helpful to seek the guidance of an expert in the field or to consult with the manufacturer of your cutting tool or machine.

If fracture stress exceeds yield strength, then the material has already deformed plastically (note that plastic strain at yield is 0.2% due to offset). Being on the right side of these curves implies defect(s) in the material should be below a size that does not cause premature fracture before yield strength is reached. I hope this helps.

Thank you very much Dr. Shashikant Kumar for a nice discussion

This is very intresting observations. What you defined as different fracture modes? There were static, quasi-static or dynamic loads?

U need 2 use Johnson Cook Damage model

ِِِِِِِDear Seyed Saeed Askariani ,I read your report. I think it is useful and I will definitely use your report after verifying my new job and I may ask some questions.

Best regard.

There are two ways to increase steel's strength at the expense of its ductility: cold working and hardening. Any steel can be cold worked, but hardening only works for steels with a carbon content above 0.3%.

Mohammadreza Arjmandi Did you figure out how to calculate those parameters?

i really want to know,,,

the yield strength is the minimum stress under which a material deforms permanently. in fsw as this is done on aluminium alloys or soft materials, where stress is very less and the material is ductile, therefore yield strength mean less and are not the properties which matter.

Yes, basically cutting relates to shear of the material. Higher the shear strength higher will be the difficulty to cut the material. e.g. Cast iron is easier to machine than steel, because CI is weak in shear where as steel has good shear strength.

Dear Yassine Hersi,

I hope this can help you:

step one:

Programming the user element by means of the "uel subroutine" in ABAQUS. You save the file "userfile.f".

step two:

In the input "jobfile.inp" you must identify the user elements, and define their properties, and degrees of freedom. For example:

*USER ELEMENT, TYPE=U1, NODES=3, COORDINATES=2, PROPERTIES=8, VARIABLES=60

1,2

*ELEMENT, TYPE=U1, ELSET=CZ

** PLACE HERE THE COHESIVE ELEMENTS

12360,1376,2923,1325

…….

*UEL PROPERTY, ELSET=CZ

1700,…..

Step three:

If abaqus subroutine is enabled in your computer, you run the uel subroutine in the command window writing this:

Abaqus job= jobfile user=namefile

Best regards

Susana

W: 164 1.7-2.1

Mo: 158 4.6

Ta: 62.8 5.4

Nb: 47.2 8.7

REF:Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory high-entropy alloy

The higher shear modulus values of W,Mo doesn't permit adjacent layers to slip thereby high CRSS(Critically Resolved Shear Stress) and low Peierls Stress inducing brittleness. While low shear modulus values, LOW CRSS(Critically Resolved Shear Stress) and high Peierls Stress of Ta,Nb permit easy shear or slip enabling ductility.

thanks & regards,

g.sudhakar

phd(materials engg),HCU.

That's a Very Good Question. Yes it's true that strength and ductility are generally vary inversely , in this particular context Cu is FCC and Zn is HCP. FCC has 12 slip systems while HCP has only 3 slip systems. The more the slip systems higher the ductility and vice versa. FCC metals are very ductile and HCP metals are brittle.

The anamoly lies in tradeoff between ductily and brittleness. While HCP is contributor to strength while FCC to ductility. While former has little influence,but latter has greater influence by which we observe elongation and strength increase in single phase alpha region. Beyond >35%,beta phase steps in the influence of HCP Zn is more predominating than FCC Cu by which elongation decreases and strength increases(alpha + beta) region. Beyond >45%,fully beta prime HCP. Both strength and ductility fall.

thanks & regards.

You need to be very careful with your selection because of extractables and leachables. It depends on your application (patient contact/long term vs short term). Maybe take a closer look at some of the USP Class VI or ISO 10993 rated Polyurethane based photopolymer resins but you might need to use a top down printer to reduce the need for supports depending on the length of the wire and overall geometry. These usually contain some degree of PEGDMA. Also be careful of what type of photointiator you are planning on using.

The end result after curing is typically a polymer with low molecule weight photolites left over that can migrate easily out of the polymer itself after curing and through skin, food packaging and other similar examples. A lot of work is being done to reduce extractables and leachables but applications such as long and or short term skin contact (intact skin vs rating for contact with mucosal membranes) has been successful if you look around at some offerings from some of the larger 3d printing names in the industry.

You may also find more information in this paper

Kindly see also the following very good RG link:

Yes, sure. Technologies of additively manufactured metals has varying success and complexity for different alloys. For example, for metals and alloys with high chemical activity and affinity for oxygen (aluminum, titanium, magnesium, zirconium, etc.), the production of products using these technologies is much more difficult than for metals with lower chemical activity (iron, copper, nickel, cobalt, molybdenum, etc.).

There are other features of 3D printing technologies for different alloys, for example, associated with subsequent heat treatment (porosity elimination by hot isostatic pressing, hardening, tempering, dispersion strengthening, normalization, etc.).

I completely agree with Jonathan David Parker and Mark Petkov . This question should interest the Project

Personally, I think that small punch tests should never replace the uniaxial test. Nevertheless, there would be a role for small punch tests when (1) material is limited and (2) the problem being investigated requires large strains.

The "large strain" issue is the key point to Jon's question.

Dear Hanlin, thank you for sharing this very interesting technical question with the RG community. I found a statement in a relevant literature reference that (citation): "Over the last decade, the concept of high entropy alloy (HEA) has attracted world-wide attention for the design of novel metallic materials." For more detailed information about these interesting and unusual materials please have a look at the following useful articles which might help answering your question:

This paper is freely accessible as public full text on RG, so that you can download it as pdf file.

Also potentially useful:

Understanding Phase Stability of Al-Co-Cr-Fe-Ni High Entropy Alloys

(please see attched pdf file)

Good luck with your work and best wishes!

Stress-strain curve from literature is only suitable for steels in a normalized state (tempered at approx. 800°C). As soon as you deform the steel for the first time, it is work hardened and the stress-strain curve changes. This means that after every further cold drawn without intermediate annealing there is a new stress-strain curve. Of course you won't find any such curves in literature.

Hi dear Megha Bhatt

Do you need 5 international reviewers to suggest them to the journal you are going to submit to?

The best way is to choose from the authors that you have referenced their papers in your article. And since you used Indian standards, it is better to select reviewers from your own country (who do not live in India currently).

Finally, bear in mind that usually, journals have their reviewers. If they can't find proper reviewers, they will opt from your suggested ones.

That is a good question.

Check the following references for general information:

Dear Sir Abdulaziz Albannai ,

Thank you for replying me.

This is Refrigerant aluminum tube. Pitting corrosion occur in the bend position.

we know that bend property depends on ductility of a materials. But maximum pitting corrosion occur in the bend position.

So have any relation pitting corrosion and ductility?

Dear Christi,

I just came across your very interesting technical question. I fully agree with the other expert RG members in that there is no single "perfect" FRP (= Fiber-Reinforced Polymer). The variety of known FRPs is just too large. For a highly instructive overview of this field please have a look at the following useful article:

This paper has been published Open Access, so that it is freely accessible as pdf file (see attachment).

A large number of other helpful references about this topic can also be found and accessed by searching the "Publications" section of RG. Simply search for the term "Fiber-Reinforced Polymer Composites" and then click on "Publications":

A large number useful articles about this topic have been posted by RG members, many of them even as public full texts.

I hope this helps. Good luck with your research work and best wishes!

Yes, the heat treatment in open atmosphere is an effective method for decrease carbon on surface graphitic cast iron

according to my published paper

Novel Approach for Using Ductile Iron as Substrate in Bimetallic Materials for Higher Interfacial Bonding Bearings

Hi,

You can mount a strain gauge on your part. Each set of measurements give you three values. Then the rest of the stress tensor components can be found using the equilibrium equations. When you have all the stress components, you would be able to calculate principal stresses.

Good luck

Farzad

Dear Diogo Cabrita

Please find the attached file.

Pls see our article where we made a comparative table showing different strengthening technique for URM with cost and strength effectiveness...further we proposed a bed-joint concept to overcome the de-bonding issues.

The main difference between the two loads lie in the prediction of their occurrence. While wind loads could be predicted with much accuracy(including the time of occurrence & intensity levels), unfortunately we have not yet developed any methodologies that enable prediction of time-specific or intensity specific occurrence of earthquakes at a site. Only probabilistic seismic hazard analyses (PSHA) are undertaken for better prediction of earthquake occurrence.

Secondly it is highly uneconomical and impractical to design a structure to remain elastic for a highly uncertain event such as earthquake. Therefore, the ductility of the structure is called for( by introducing R factor) while designing the structure for a much lower level of earthquake. Further it shall be noted that during earthquakes, structures are permitted to undergo different damage states depending on the return periods of the earthquake event.

Dear Jay Paresh Mehta many thanks for asking this very interesting technical question. Apparently large areas can be coated with tungsten disulfide by chemical vapor deposition but I really don't know how this is scalable and what the costs are:

In this context please also have a look at the following potentially useful articles which migth help you in your analysis:

and

All three articles have been posted by the authors as public full texts on RG, so they can bee freely downloaded as pdf files.

I'm afraid that these references will not provide a satisfactory answer to your question, but perhaps they contain some useful hints.

Good luck with your work and best wishes, Frank Edelmann

Dear Mohammad Farshbaf Ahmadipour,

The problem is known - the presence of a defect in the surface. This type of defect is typical in the following cases: - Presence of moisture in the mold; - poor adaptation of the vomit; - poor separation of air and gases from the mold; - lack of sufficient channels for removal of air and gases from the mold; - low hydrostatic pressure during casting; - low casting temperature unlikely but not switched off; - basket thinness of the metal due to loss of chemical elements or low casting temperature; and other. Nebivadase also turns off the temperature of the heated mold, it has a strong influence on the quality of the casting.

Melissa Semaan

Hope so this video may help you! Good Luck

Dear Lennard Euler thank you for your interesting technical question. Please have a look at the following potentially useful articles which might help you in your analysis:

1. Do Voids Initiate at Grain Boundaries During Ductile Rupture?

and

2. Recent Advances in EBSD Characterization of Metals

(Review article)

Please find attached both articles as pdf files.

Which hardness scale is much suitable for the CFRP/GFRP/KFRP Epoxy composites?

The standard heat treatment for this alloy appears to be aimed at increased creep resistance and elevated temperature service rather than conventional lower temperature tensile strength. • The standard heat treatment as utilized on the as received material has a high-temperature solution cycle aimed at setting the grain size and partially dissolving the prior particle boundaries. • Slow cooling is employed to allow large section sizes to be processed with reduced risk of quench cracking. • A slow or interrupted cooling rate through the gamma prime precipitation and growth range was used to set the large gamma-prime size and distribution. • The ageing cycle used for this material is believed to stabilize the gamma-prime and secondary carbide phases for optimum high-temperature performance.

Hi, my darling

This is a good question and certainly has a good answer, too. However, I do not know the answer, and I must think about that.

Seriously, What is different between this two ways of the cracking process?

Usually, the more compressive strength concrete has, the less its ductility becomes.

Within the elastic displacement phase all the energy of the earthquake is stored in the trunks of the beams and columns and returns in the opposite direction, like the spring. We have no failures in elasticity. When the displacement grows larger than the elastic limit we have inelastic displacement with leaks - cracks. To manage the inability of seismic designs to control the inevitable inelastic displacement, they built the Ductility mechanism. They are unable to control the deformation. This is the problem, and Ductility just manages it better. But it does not solve the problem of deformation which causes from failures to collapse of structures.

Seismic damping consists of different damping mechanisms. 1) The horizontal seismic damping (bearings) limit the acceleration of the ground to pass on the construction. 2) Ductility is also this mechanism of seismic damping, because with the small failures on the trunks of the beams that it allows to be made, it releases seismic energy. 3) Hydraulic systems create seismic damping by converting the kinetic energy of the earthquake into thermal energy through its liquids which are heated when compressed by the displacement of the piston. 4) Elasticity is the vestibule of inelasticity and it also consumes seismic energy because heat is produced in the steel molecules when it receives stresses. There are other seismic damping systems that each operate differently in different areas of the structure to provide basically less instantaneous high seismic intensities on the structure. When we talk about dynamics this is something else. It is not seismic damping. It is a force against another force The design method I suggest involves something completely new and that is that it receives power from an external factor (that of the soil) and transfers it to the structure to help the structure respond dynamically against seismic forces, in order to have a balance of forces and not failure. This external force factor can be used to increase the dynamics of structures. It is not a seismic damping mechanism. So some who try to compare bearings with the external factor dynamics offered by my patent are misplaced because they compare two different things that have nothing to do with each other. However, if we want to use the invention as a seismic damping mechanism before it acts dynamically, then we simply place a seismic damping mechanism on the patent mechanism which will resiliently resist seismic shifts by drawing the reaction force from the ground before the main mechanism of the patent action dynamically to stop the inelastic displacement of the construction. In the dynamics of structures we study the structures in dynamic stress as a consequence of seismic movement of the ground. What my method is studying is how it will help the dynamic response of structures in the dynamic equilibrium equation, using external dynamic response factors, with and without damping.

In SEM it is possible to distinguish ductile zone and calculate the percentage.

The traditional thinking is in stress limits and small deformations. The stretch-strain curve of elastomers becomes quite steep when approaching the limiting stretch. Therefore, the stress at rupture is less certain. But the limiting stretch is. Unfortunately you will hardly find tabulated values.

However, you can find some large deformation theories for limiting chain extensibility material models like the van der Waals rubber model. Then you can find that the square root of the trace of the left and right Cauchy Green tensor is limited to approx. 8.8. (The eigenvalues/proper values of this tensor are the squares of stretch.)

It is often stated that “Grain boundary strengthening has the advantage that the ductility of the material does not decrease with decreasing grain size and increasing strength.” (Rösler, Harders, Bäker, Mechanical Behavior of Engineering Materials). This is an exception to the generally observed inverse relation between strength and toughness.

In this context it is important to differentiate between toughness, which requires a pre-existing crack or notch and ductility, which is the ability of the material to plastically deform and is usually determined in a tensile test, e.g. by the fracture strain.

Fine-grained structures usually have smaller potential flaws, which increases the stress to fracture.

Grain boundaries can also act as barriers to crack propagation, the different crystallographic orientations cause the crack change direction, and cracks can be bridged in fibrous grain structures.

For fracture to occur in a tensile test of a semi-brittle material, slip bands have to nucleate at the yield stress, these have to nucleate micro-cracks, and these micro-cracks have to propagate.

Cottrell (A.H. Cottrell, Theory of brittle fracture in steel and similar metals, Trans. AIME 212 (1958) 192-203.) developed a model in which the stress for propagating a microcrack that was initiated at the intersection of two slip planes can be calculated to $\sigma_{f} \approx \frac{4 G \gamma_{m}}{k_{y}} d^{-1 / 2}$

with $\sigma_{f}=$ fracture stress $G=$ shear modulus $\gamma_{m}=$ plastic work done around a crack as it moves through the crystal $\begin{aligned} k_{y} &=\text { dislocation locking term from Hall-Petch relation \\ d &=\text { grain size } \end{aligned}$.

Which is similar to the Hall-Patch equation.

For more, see e.g. chap. 7.2.2. of Hertzberg, Vinci, Hertzberg, Deformation and Fracture Mechanics of Engineering Materials or p.325 of Haasen, Physical Metallurgy.

Hope this helps,

Erik

Please check the attached paper. The ductility demand is calculated in the paper.

Thank you Patlola

Madhusudhan

I have asked this question from ACI TECHNIQUE STAFF and they have answered:

yes as below:

Can you tell why NOT??

It goes without saying that the hard and brittle materials that are applied to a soft surface make the surface hard and brittle. If you hit this brittle surface, the metallic substrate under the layer is plastically deformed and the layer crumbles. However, it does not mean that this surface has to fail if the component is subjected to other loads. If you think that, for example, when the coated rod is elastically bent, the brittle layer always breaks before the metallic base material, then it is not always the case. In this case, not only the ductility of the layer, but also its strength and its modulus of elasticity play an important role. I know of cases where the steel substrate broke earlier than the brittle layer on its surface under cyclic alternating loads (in the elastic range). The "secret" lay in the layer's low modulus of elasticity. So, in other words, the word "brittle" doesn't always mean "bad".