Mechanical Behavior of Materials - Science topic

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.

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.

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.

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”.

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.

Dear Varun:

Without prior exoerimental data on this particular steel, I would maintain that it is practically impossible to accurately predict the DBTT for any low carbon steel. The DBTT will depend on its composition of course, but also on its microstructure and prior heat treatment. The DBTT, however, is extremely sensitive to any small amounts of impurities, such as S and P. The best low carbon steels, with the lowest DBTT, invariably have very low content of these impurity elements (this is termed "aircraft quality" in many higher strength steels). My advice to you is to experimentally measure the DBTT using such simple tests as Charpy impact tests; relying on any predictions or estimates would be highly questionable.

ROR

Theoretically, it doesn't matter whether the specimen is rectangular or circular, But technically a problem may arise with circular specimens if you use knife edges on your transverse extensometer. The knives may bite into the specimen by an unpredictable depth, depending on radius. On flat surfaces their clamping force is distributed. It is not a coincidence that testing standards like ASTM E132 advise to use rectangular cross-section for measuring Poisson's ratio.

Also, it is beneficial to have specimens as wide as possible to increase gauge length of transverse measurement. At the same time it is not wise to increase greatly the overal cross-section, because that may require buying a new, testing machnie with bigger force limit ). Rectangular shape allows to vary with and thickness independently.

Phenomena such as the Al Naslaa Rock, Active cracks in Yosemite National Park find explanation from gravitational forces.

It turns out that thickening the material leads to new mechanisms of resistance/plasticity. A reasonable question arises here, but what is the minimum thickness for such a situation? It is clear that 0.5 < x < 1, but I would like to be more precise. Perhaps this is not one mechanism, but several.

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.

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.

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.

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.

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.

Cylinder Strength = Cube Strength * 0.8

The conversion factor of 0.8 is commonly used to convert between cube and cylinder strengths in the Australian construction industry. This factor takes into account the differences in the shape and size of cubes and cylinders used for testing concrete strength.

There are several methods used in the automotive industry to detect damage or cracks, depending on the type of material and the location of the potential damage. Here are a few examples:

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

The GIc method is already outdated by non linear plastic principles such as GF.

In my opinion, Franc3D is the best.

yes stacking fault energy does depend on strain rate and you will find many research article to support it.

We have released the implementation of a nonlocal GTN model for Abaqus/Standard (UMAT) and Abaqus/Explicit (VUMAT) at http://www.tu-freiberg.de/en/nonlocalGTN . It does not require an UEL but uses the analogy to the heat equation and is thus easy to use.

There is no single factor for all materials that reflects the influence of sample size on the result of strength measurement. It is quite natural that small specimens often show higher specific strength than large specimens, since statistically they have fewer structural defects. However, this difference in specific strength depends on many properties of the material, primarily on its deformability: the more plastic the material, the smaller the difference.

the grade of the steel is important in order to compromise properties.... but totally 24 hours is suitable

Dear Ghanbar

I agree with Aliasger. Beam elements can't be used for heat transfer and coupled temp-displacement coupled steps because they don't have a temperature degree of freedom. You must use solid, shell, or truss elements to do so.

¿Alguien conoce cómo cambiar el nombre ?

If you assume that the load frame always deforms elastically, and that your sample initially deforms elastically, then you can use the springs-in-series reciprocal addition relationship to correct for frame compliance based on the theoretical Young's modulus of your material and your initial sample dimensions. I have attached a MATLAB script that does this in an automated way. Please see the image attached, along with a sample dataset and the MATLAB script. A note - if you use an extensometer to measure strain on the sample, then you do not need to correct for compliance. For this reason, extensometers and digital image correlation are increasingly popular.

That is a good question.

Dear Vanda Nur Ilmi

It is suggested to read following papers:

Hi Ghanbar,

You can use the spring for your model.

thanks for your important question

Hi,

Your question takes me back many years, to a collaborative project on reheat cracking in the 1970s.

The test that might help you was developed by Martin Murphy and David Batte at the Charles Parsons turbine manufacturers. It was used in that project, where it is described as a notched-bend relaxation test. See this article:

The second reference in the article, Batte et al 1976, describes the test more fully. It was published by Allianz, the insurance company; I suggest you contact them for a copy.

The test jig comprised a stiff, hollow, rectangular frame in which a Charpy specimen could be loaded in 3-point bend. The inner surface of one long edge carried two ridges, the opposite side was drilled to hold a heavy bolt that pressed the third ridge against the specimen, opposite the notch. The specimen could be pre-stressed to a controlled amount by tightening the bolt. If the rig was made from exactly the same material as the test specimen, then it was self-compensating for thermal expansion.

Once loaded, the jig and specimen can be placed in the furnace / autoclave for a set time at temperature.

On removal, there are several options. First would be to carry out an impact test in the usual way; the properties can be compared with those of virgin material and of a specimen that had seen the same thermal history, but without load. Examinng the fracture surface would reveal the extent of any cracking during the thermal treatment, and metallography would reveal and quantify any associated cavitation.

Please let me know if this works! I'm afraid that after 40 years I have no drawing or photos, but I'm sure you can devise a jig like this.

It may be possible to produce something similar using a small punch specimen.

Two other articles which might help in interpretation are:

Best wishes

John

Dear Johannes Luft,

Since magnesium alloy retains its strength and elongation after annealing at high temperatures , hence its high innovative demand in production technology. Mostly magnesium alloy fine wire is applicable in couple of potentials areas such as;

1. Surgical as Tension band wiring

2. Biodegradable applications, such as suture materials

3. Medical devices (bioabsorbable medical devices)

4. Cardiology; coil stents- potential applications for magnesium alloys in cardiovascular medicine

5. Orthopedic applications

6. Degradable implants with ligatures for blood vessels

7. Motor paddle shifters

8. High purity Magnesium Wire with the highest possible density for use in semiconductor etc.

Hope information is helpful for you.

Ashish

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

I am searching the same problem.

I think this article will be useful.

It explain PCI 2010 material model and Power Formula model.

Has anyone stored the digitize.opk for Origin V.75 and earlier. It is not available anymore on the fileexchange site. Thanks!

Use high pressure water Descaler. Most of forgings and steel producers are using to remove scale from heated billets / slabs.

Water spray @ 200 bar is applied through flat jet nozzles. This reduces billet / slab temperature @ 5 to 10 degree, which is acceptable in these process.

Yes , I have used this in my thesis for modelling of composite

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

G(I)max=2*Gamma

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

I could recommend to pay attention to the Manoj Gupta works regarding Mg metal matrix composites design and investigation. Even about lightweight the Mg alloys.

Xiaoyao Xu You just need to go the input file and change the gamma there. You can also have control over the number of anisotropic invariants used for instance you want to use just one instead of two,whatever.

you can find sample records for Abaqus umat subroutine in:

I will address the general solution divergence issue in Comsol. You can try following steps to improve the convergence.

Use structural meshes where you think you are getting the error (or use everywhere), Play with adaptive mesh refinement in solver or adapt option inside mesh node ~ Use this everytime to fine your meshes

Use the Generalized Alpha rather than BDF with strict or intermediate time stepping ~ this improves the convergence in many cases for me

Play with the tolerances (relative and absolute both) ~ sometimes if I change from factor to manual absolute tolerance (with enough time-discretization) it works.

Get the Jacobian update on every iteration than minimum ~ very important for non-linear solvers

Increase the number of maximum iterations ~ good option if you are using very fine tolerances

Change from fully coupled to segregated solvers ~ if you have many integrated physics

Use assembly in geometry and play with source to destination mesh refinements ~ when you are defining BCs or ICs inside the domains

Change scaled values of variables to manual and use values of their respective maximums ~ very helpful at the start of simulation fails.

Regards

Noman

Maybe you can focus on the shape of the cavities.

Assume under uniaxial creep testing:

If the plastic hole growth takes control, then the cavities should be more like a standing needles which is perpendicular to the GB. Otherwise if the vacancy diffusion mechanism controls, the cavities should be like cracks that is parallel to the GB.

But to remember, when the constrained diffusional growth mechanism takes control, then the cavities growth rate actually depends on the slow creep deformation on the neighbourhoods matrix. However, the cavities look like the crack-type, since the vacancy diffusion contributes most of the growth but it is constrained by surrounding slow creep deformation rate. This is the most common type of creep cavitation.

Since the Young modulus is related to the bonding between the atoms of materials, generally, it doesn't change after heat treatment processes. However, if the nature of an atomic bonding is affected by the HT, via the crystallographic or phase transformations, the value of Young modulus may be changed. Anyway, the other elastic characteristics e.g. the yield stress or the modulus of resilience are certainly changed after the HT.

One reason could be

STATEV dimension from fortran(UMAT) file is higher than the Depvar dimension in material definition. For e.g., Depvar dimension in material definition is 2, then if you try to access the STATEV(3) in fortran "Illegal memory reference" pops up in during execution at integration point.

Dear Dhanraj Rajaraman

Please find the attached file.

I would rather plot Force (kN) VS. Displacement (mm) curve and calculate the area which essentially will give Energy (J). You can calculate Energy at any point of your curve. And do not try to go deeper than that.. keep the life simple, it will give a less probability to make a error/s (sometimes fatal).

HI,

I think, from FEMFAT Material Data! It is a nice way to get input parmeters for ANSYS Strain Life calculation.

Best regards, László

You should remove flash, surface irregularities and all areas of roughness.

I recommend this article, because it is simple and so perfect.

Consistent with the mechanistic arguments in the earlier replies one can say:

Mr. Kumar,

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

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

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

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

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

With regards,

Abhishek

dear Abdul Basit, the star-like squared pattern that you see results from the circular (!) face of the cylinder which you want to change into a more or less squared shape. If you dont want it, because it is related to made properties, you can change the material flow by designing the intermediate forming steps in a way to enhance the flow as much as possible towards the straight sides of the square first before puching the material into the corners. Regarding the distribution of material properties, it depends very much on the properties of the initial cylinder and the alloy grade and casting properties. You can improve on some of the material properties by forming but also causing problems. It is hard to say from the scratch. Is also a question of design and application.

By the way in open die forming you should generate a mostly perfect circle pattern until you work towards the squared shape, but the distance from the edges of the former circular face to the final squared side edges can be manufactured constant on all sides as well corners in this way.

Not yet. But Im planning to have one.

The article, "Evolution of Specimen Strain Rate in Split Hopkinson Bar Test," by H Shin and J-B Kim reports a method of validating the experimental result of the split Hopkinson bar. It cal also be used for the calibration of the instrument. The article can be downloaded at: https://doi.org/10.1177/0954406218813386

A recent paper by H. Shin and J.-B. Kim, "Evolution of Specimen Strain Rate in Split Hopkinson Bar" reports a method for verifying the experimental result of the split Hopkinson bar. It can be downloaded at: https://doi.org/10.1177/0954406218813386

Nadeem, can you share how to use UMATHT subroutine ?

I found the following video link very informative - although I assume there is bit of anomaly in the definition of anodic and cathodic current.

I am Aziz from Taiyuan university. I get terrible with doing Tensile strength simulation model of Inconel 718. Could you give me any help?

I want to know the Johnson cook damage (d1,d2,d3,d4,d5) of inconel 718.

Heating it in open air for various times will form oxygen layer of various thickness on the surface of Zr. O2 is very eager to get into the surface of Zr :). Than you can anneal the sample in furnace for penetration of O2 content. Though this is not a scientific way of doing it. You may get different results with different experiments.

Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material. Many non-brittle metals with a reasonably high melting point as well as several polymers can be strengthened in this fashion. Alloys not amenable to heat treatment, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at low temperatures, such as indium, however others can only be strengthened via work hardening, such as pure copper and aluminum.

Work hardening may be desirable or undesirable depending on the context. An example of undesirable work hardening is during machining when early passes of a cutter inadvertently work-harden the workpiece surface, causing damage to the cutter during the later passes. Certain alloys are more prone to this than others; superalloys such as Inconel require machining strategies that take it into account. An example of desirable work hardening is that which occurs in metalworking processes that intentionally induce plastic deformation to exact a shape change. These processes are known as cold working or cold forming processes. They are characterized by shaping the workpiece at a temperature below its recrystallization temperature, usually at ambient temperature. Cold forming techniques are usually classified into four major groups: squeezing, bending, drawing, and shearing. Applications include the heading of bolts and cap screws and the finishing of cold rolled steel. In cold forming, metal is formed at high speed and high pressure using tool steel or carbide dies. The cold working of the metal increases the hardness, yield strength, and tensile strength

Dear Andrey Leonov ,

I think the load of indentation, you have used, was not high enough to induce the radial cracks at all corners of indenter's impression. I recommend you to increase the load and repeat the test for 3 or 4 times. In my opinion, you can not rely on only one indentation as well as on the length of only one crack instead of four cracks.

Dear Manish,

There was a mistake in my last pdf.Please see the revised pdf.

The loss tangent is omega*mu/E. (omega : radial frequency(rad/sec), mu : viscosity(Pa*s), E: Young's modulus (Pa))

Sincerely ,

Ryuzo Horiguchi (Kao Corporation)

Hello

you can read this link

http://abaqus.software.polimi.it/v6.13/books/usb/default.htm?startat=pt05ch23s02abm20.html

Existence of upper and lower yield points is typical for alloyed steels. The reason for that is so called "solute drag", namely: solute atoms' preference to displace in the vicinity of the dislocations (due to an interaction of their stress fields with those of around dislocation core). Thus, when an external stress applied to a sample reaches the vicinity of a yield stress of the material, initially existing dislocations, surrounded (caught) by solute (impurity) atoms, need to additional stress to come off them. This "additional" stress developed onto the loaded sample, is seen as a "higher" yield point. When the majority of dislocations overcome their interaction to solute atoms, the yield point "fall" to its "lower" level. This mechanism works both for interstitial and substitutional solid solutions.

Regarding superalloys, their phase formation should be discussed in details for each specific case separately. For example, for multi-principle alloys (like high-entropy alloys), no "solute" atoms may be defined and then they normally do not demonstrate higher and lower yield points. For intermelallic hardened superalloys, the majority of alloying elements form inermetallide phases, so no "free"solute" atoms exist and then these materials also have no higher and lower yield points.

Thanks to both of you. I shall try these methods.

-bharat

The basic assumption of RVE modeling is that the overall geometry is obtained by an infinite repetition of the RVE in all allowed (depending on specific BCs) directions. You need to tile (fill) the 2D (3D) space by infinitely repeating the RVE without gaps.

Thus, the RVE shape does not need to be regular per se, but it must be such that, when repeated infinite times, it fills the space without gaps. The simplest such geometries are the square, the rectangle and the hexagon. More are available, with different degrees of regularity (a term that should be better specified, we are using it with a quite vague meaning), and one has to look into the research on tessellations. It would be interesting to study how different patterns affect the calculated mechanical behavior. However, you cannot use arbitrary "irregular" shapes or even purely random geometries. It is not compatible with the homogenization method's assumptions.

Furthermore, geometries and size of RVE do affect the mechanical homogenized behavior, especially for composites (and any material with structure at multiple scales). The RVE should in theory be independent of geometry, but in practice you need to investigate which configuration is best to model the homogenized material.

Yes, this is simplest feature and should be available with any software. Please search in the manual for how to define. I have no experience with these two software.

The above answer does not seem satisfactory. Indeed, strain hardening, which is due to an increase of the dislocation, will occur whatever the loading direction is (i.e. tension or compression).

In my opinion, the most likely explanation for this asymmetry is the impact of processing. Indeed, during the fabrication of your alloy, a significant amount of plastic deformation has been used for forming (e.g. extrusion, rolling). Because this plastic deformation result in strain hardening, the yield surface of your alloy has significantly been altered by processing. Strain hardening is usually directional (i.e. kinematic hardening), which means that the evolution of the yield strength is direction dependent. The consequence is that, because of processing-induced hardening, the compression and tensile yield strength are different.

An excellent online industry-based resource is that from Ovako.

Online software has been developed by:

I believe that combining the excellent previous scientifc work of Kirkaldy reported by JMatPro might allow most of us to build his/her own software for quite "general" steels.

Many years ago ( I believe 2008) we built "3d mensionnal" curves of TTT/CCT curves, they were good looking but seems no-one have been using seriously them to date for practical issues..

So a more recenta nd serious option is:

or directly here (for researchgate users):

Please refer to the following books:

1. Geopolymer, Green Chemistry and Sustainable Development Solutions by Joseph Davidovits . Please refer to page 136. You can find the book at google book.

2. Concrete Construction Engineering Handbook by Edward G. Nawy . Please refer to page 26-10. You can find the book at google book.

Hope this will help.

There are several possible sources for the experimental-simulation mismatch, which seem to me more likely than a mismatch in the tension and compression behavior of Al 1100 H14, which I expect to be rather small, if it exists at all.

1.) Modelling the specimen undergoing indentation, geometry and boundary conditions:

The size of the simulation box (halfspace) should be sufficiently large both in width and depth directions to properly reflect the elastic effects.

If the halfspace is sufficiently large in lateral direction, the chosen boundary conditions (free or fixed) at the lateral boundaries do no longer play a significant role for the microindentation results. You can check that simply by comparing the results for different conditions.

If the simulation box size in depth direction is chosen too small, the (structural) stiffness of the indented halfspace will be larger than the real one, such that plastic yielding commences at an earlier stage of indentation.

2.) Finite element modeling:

In order to avoid artificial stiffening effects („locking“) it is recommended to use rather hexahedral/brick-type solid elements than tetrahedral ones, better quadratic shape functions (e.g. C3D20) than linear ones.

A sufficiently fine resolution not only of the indentation volume but also of its surroundings is crucial – you mentioned the measurement of mesh refinement in that region.

Hint: For the existing isotropy you can exploit symmetry and reduce the indented halfspace e.g. to one fourth, or even less, of course. (You could even exploit rotational symmetry.) Then a mucher finer discretization can be invested for the same costs compared to the full model.

- Modeling frictional contact comes on top of that, I would start out with a rigid indenter, zero friction.

3.) Material model.

The choice of isotropic elastoplasticity at finite strains seems to me adequate for that material and the deformation regime (large plastic deformations in the indentation zone).

Accurate material parameters in agreement with the experiments, i.e. yield stress and the hardening behavior. The hardening behavior will strongly influence the behavior of pile-up (low strain hardening rates) or sink-in (for large hardening rates).

Hope there is something helpful in it, good luck and have a great day ahead!