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67 comments

  1. Hi Matthew, I bought a wedding ring made of tungsten carbide. Is there some test I can perform, that I can use to determine the material used as a binder (cobalt, nickel, or something else)?

  2. Did you try using a magnet, I think it would be sensible to exclude the possibility that you have a steel with a tunsgten carbide coating. A good non destructive technique might be to measure the density. That would involve measuring the weight and the volume, it is also possible to do it by weighing in air and suspended in a liquid (e.g. water). In a full lab there is equipment to measure the composition, for example X-ray spectrometer or scanning electron microscope fitted with similar device. Those devices involve exciting the atoms with a beam and then measuring what characteristic X-rays are emitted.

  3. Thanks for the response! I did try using a magnet, and the ring didn’t respond.

    I haven’t tried measuring density, because I assumed that the relatively low proportion of the binder material, plus the fact that I don’t know the exact proportion, would make it difficult to tell which binder was used from the density. But I will give it a shot, at least to confirm the ring is actually tungsten carbide. I think it is, though, since it feels pretty heavy in the hand.

    My chief concern is that the cobalt binder leaves the ring more susceptible to corrosion, and I’ve read stories about them turning fingers green over time. It’s my understanding that the nickel binder is superior for jewelry applications.

    I assume X-ray spectrometry is prohibitively expensive for my needs 🙂 (but maybe not?). I wound up ordering a cobalt spot test kit designed to detect cobalt as an allergen by producing a visible chemical reaction when a test solution is applied with a swab (it changes color). I have no idea whether this will work, but it was the only “home” option I could find after quite a bit of digging.

  4. Hi Mathew,
    Lot of works in literature (Tomita and Okabayashi) pointed out that after a certain heat treatment, steel with mixture of lower bainite and martensite for a certain volume fraction of lower bainite shows greater strength than Martensite. Will that happen in every steel or this has something to do with steel chemical composition.

  5. Hi Rohith, I was hoping to have time to give a better answer… Tomita and Okabayashi reported results for 4340 steel, Fe-0.25Si-0.-01P-0.009-0.75Mn-1.79Ni-0.82Cr-0.2Mo wt%. Improvement in strength is due to partitioning of carbon into the residual austenite and a composite effect of having bainite and martensite together (according to Young and Bhadeshia MST 1994). Strength improvement is not completely general but easy to achieve, it depends on strength contribution from the bainite (transformation temperature) and the martensite which forms will always be stronger than martensite in the bulk (and then you have additional term). Examples were strength could be lowered by a mixture are (1) if the bainite forms at much higher temperature than the martensite, or (2) if martensite formation is suppressed resulting in large fraction of austenite. Therefore, an optimum strength can be achieved with mixture of bainite and martensite in many cases, including carbide free steels.

    • Thanks a lot for the nice explanation Mathew. I have another simple doubt, unfortunately I don’t get proper answer for this through my search.

      How to calculate the molar volume of Austenite phase. ?.

  6. Hi Mathew,
    I have a very simple question: why adding Mn,Cr,Mo,Ni (except Co) hardenability improves?
    Thank you in advance.

  7. Hardenability (ability to transform to martensite at lower temperature) depends on transformation kinetics of the various phases during cooling from the austenite phase field. Effect of alloying elements which improve hardenability is by delaying the pearlite or other transformations that occur at higher temperature range. Usually by lowering thermodynamic driving force.

    • Thank you very much for the answer, but I can’t figure out why pearlite transformation (for instance) is delayed….looking to a CCT it seems that all these elements stabilize austenite even if they contract the gamma field in phase diagrams.

      • Seems like you understand to me. Effect on nucleation and diffusion during growth may also be important. Austenite grain size is also important for hardenability.

  8. I know CR-Mo-W-V steel is available as castings; would you know if this is also available as an alloy in bar form (e.g.,”readymade” ) ?

  9. Hi there. I am designing a unique telescopic baton and wanted to know what metal would best balance cracking and bending resistance against weight over fairly prolonged use. Ideally a lighter metal as this isn’t designed to be a club lol.

    • Steel would be best obviously. Aluminium alloys might be an option. What you are talking about is optimisation of a tube. Stiffness and cracking resistance depend on diameter of the tube, also wall thickness and material properties. One way to decide is to write an equation to describe which material you should choose, a merit index. If you look at bike design you can see it’s possible to make good tubes with lots of materials. Most economic choice also depends on volume you will make and resources available to you.

  10. Hi. Our product http://www.givengohockey.com uses high strength low alloy sheet steel 10ga A1011 Gr 50 teeth to prevent it from moving on the ice when a puck hits it. The teeth are strong but not strong enough because they can still be bent if the unit is accidentally bumped into the boards. Is there an even stronger HSLA 10ga steel we can use or can what we are using be heat treated to make then even stronger? the material must be able to be welded onto a carbon steel frame as well. The teeth are sharp and 1/8 in thin so they are able to pierce the ice and keep the unit in place. There is a picture on our website under the gallery tab. Any help would be greatly appreciated! Thanks!

    • A saw there are two classes of A1011 Gr 50, with carbon content 0.15 and 0.25, those seem very different beasts to me. There is also similar classes of Gr 55.

      Advantage of HSLA steels is the toughness and weldability… not really strength. That makes them very forgiving. Since you fabricate by welding maybe it’s best to look at other ways of avoiding the teeth being damaged, like larger teeth, a retracting cover, or moving position of handles, etc.

      Give-N-Go Hocky Passing Aid

      It’s possible to get much stronger steels, but you need to see what the limits are to the welding equipment and procedures you have available. Attaching a separate part which is just teeth might be an idea (slot in or bolt on), then that can be replaced if damaged, and rest of construction can be made from usual low/medium carbon steel.

  11. What platings can be used to plate gold to provide hardness (besides nickel due to allergen reasons)? Are there any plating options that are clear in color?

    Thank you!

    • Maybe very thin oxide could be clear?

      Glass ceramic or pottery glazings I expect are harder if you can apply them without crazing. Maybe a glue like epoxy.

      Is this for jewelry? I wonder if surface hardness can be increased by deformation, peening or shot peening. You can use a lower carat gold which is alloyed producing a harder surface or you could alloy with platinum which preserves the carat but which is more costly.

      Titanium nitride films are used on steels to produce a wear resistant surface and have a gold colour.

      • Thank you for your response!

        This is for jewelry. I am looking for the hardest base metal possible while staying in the realm of precious metals, and the look of the end result doesn’t matter because it will be coated a different color. Its a good idea to alloy gold with something stronger like platinum — is it possible to alloy gold with something even stronger like titanium, tungsten, or steel?

    • Haha, heavy, not particularly toxic, possibly can be made very strong at high temperatures also utilising intermetallic phase which are known to exist in Au-Ti system. Only a matter of time till someone tries to make this as a high entropy alloy or checks to see if it is a high temperature super conductor.

  12. I’m interested in determining if it’s possible to create magnetic iron filings that are gold in color. They can be as fine as filings but the coarseness of glitter would be acceptable. Is there a process that would produce this result, whether plating the iron before filing (would the plating still be apparent) or employing a chemical process? Any thoughts on if this can be done, and if so, can it be done economically?

    • I’ve seen before a toy which had steel sheet pressed into cresent shapes and had silver and gold coating, although dont know what the coating was. For gold coating boron nitride coating is gold and hard wearing (as used on drill bits etc). Iron pyrite is also magnetic, but I don’t know the implications of using it as a powder.

  13. Alkali in iron ore, above 0.1 is not desired for blast furnace as they affect the life of the refractories/lining. At present, some iron ores possess high Na and K (>0.1). These ores are being mixed with other ores to sweeten the effect of Alkali and minimise its detrimental effect in the blast furnace. We need a process, other than physical beneficiation, which can either remove the alkali or the neutralize the effect of alkali during sinter making itself

    • What form are the Na and K in? I guess not water soluble? Can the ores be heated in furnace with alkali lining before being transferred to blast furnace? Can it be mixed with coke before charging? Can the Na and K be removed to make useful product to pay for removal?

      These are speculative questions but I do not usually work on making liquid metal.

  14. We received Inconel X750 2.00 dia. and had the material heat treated per ASTM B637 for N07750 Type 1.

    The material passed the room temperature tensile test (attached) but failed to reach the minimum time required for the stress rupture test on two occasions (also attached).

    Do you have any advice on why the material failed stress rupture or suggestions on what we can do to insure it passes the next time we heat treat the material?

  15. I would like to cast some simple shapes in bismuth. I’ve been thinking about making the molds out of thin copper sheet. Does pure (99.99%) molten bismuth wet copper? I’d like to be able to get the piece out of the mold.

  16. What material would be best to use as a heat shield on refractory in a natural gas fired fire tube boiler? What minimum thickness to start with?

  17. I’m trying to determine the chloride composition limit for material that is being used for pump stages. At what composition of chlorides in the process fluid is niresist type 1 likely to fail and we should switch over to duplex ss? And how does the amount of oxygen in the fluid affect this as well?
    Thanks

    • Corrosion prevention often becomes complicated, geometry and operation will effect compositions of liquid in contact with the steel. Choice of material should also depend on application and inspection regime. There are also different grades of Ni resist that can be considered before considering SS.

    • This amount of P is still very low [in comparison to solubility], the datasheet I saw for that alloy also has a much higher level of P possible in case of being produced by continuous casting (on the same datasheet with the same listed mechanical properties[although different heat treatments could be specified to ensure consistent properties]).

      I think the main concern should be why the production has gone out of specification, maybe it’s due to another problem in manufacture.

  18. Mathew, We are currently using a weldcote R60 for a patented invention we have. We need this to be about 4 times stronger for our application. To get a better idea of what we are doing, please go to http://www.aksalmonbear.com and watch our video. This will show you exactly what we are doing. The R60 works great when we apply 2 springs. When we apply 4 springs is where we a running into a problem with the R60, it will start to bend after a certain amount of hits it takes. We have been told we need more carbon in this rod. R60 contains 0.15 percent carbon. Is there something out there that you know of that would work better for us? Thank you for your time. Regards, Rex

    • Dear Rex, it is possible in to have weld metal be 4 times stronger than R60. R60 grade produces strength approximately 60 ksi (413 MPa) so 240 ksi (1650 MPa) which is below the maximum strength of steels that are available. However, this is still quite an exotic target strength for weld metal and I’m not sure it’s simple to achieve with off the shelf products. For example if you see the review “Low transformation temperature weld filler for tensile residual stresses reduction” by S. W. Ooi, J.E. Garnham and T. I. Ramjaun, published in materials and design 2014 available here: https://www.phase-trans.msm.cam.ac.uk/2013/review_Ooi_MD_2014.pdf you can see that the weld strengths maxed out at 1200 MPa. Although if you consider the low carbon contents of the filler that may give you hope. The true difficulty is not of course in achieving a high strength, but that strength with sufficient toughness and/or fatigue / corrosion resistance given the processing conditions (cleanliness, transient heat profile). From the design of your lever it looks like quite a high load would be concentrated on the weld, if you can change the position you might lower the load more easily than changing the welding conditions, for example rotate the join between the base and the plate with hole/pivot to be along the length of the base plate. e.g more like this https://goo.gl/images/q6Pab6

      Increasing the width of the part welded on to the base plate to increase the distance from the welds to the fulcrum might also lower the loads experienced by the weld.

      I don’t think there is a easy weld metal substitution that can be made.

  19. Is grade 5 titanium heat treated stronger in tensile strength and impact strength than any other steel alloys? Or is there a super steel class that is better in those areas?

  20. Is grade 5 titanium heat treated stronger in tensile strength and impact strength than any other steel alloys? Or is there a super steel class that is better in those areas?

    • Yes there are steel (and Titanium) alloys with superior strength levels. I think many people dont realise that steels can routinely be produced with strength above 2GPa, a problem here is the many steel alloys referred to as ‘high strength’ wheras they may just be a high strength variant of a particular alloy.

      One difficulty in giving a full answer is the different data reported on company datasheets. For example I wasnt able to quickly find the KIC toughness of grade 5 quoted along with strength level, or Charpy impact of 300M steel I used as example steel.

      Grade 5 commonly used titanium alloy. Typical strength around 1000 MPa and 24J Charpy impact. Density of 4.42 g/cm^3. (commercial datasheets)

      300M steel. Stength 1980 MPa, KIC fracture toughness 66-77 MPa.m^0.5. (commercial datasheet). Density 7.84 g/cm^3.

      Specific stength  (MPa/g/cm^3)
       1,000÷4.42
      =226

       1,980÷7.78
      =255

  21. Hello,

    I have absolutely no knowledge of the fascinating science of metallurgy. I however am a student in history. Im more particularily trying to establish the authenticity of an ancient story in which there is mention of a large wall made of iron and copper.

    The building of that ancient wall, it is said, was done in sections by firstly building a giant mould in the desired location, inside which smaller moulds would be placed;

    Firstly, molted iron is extracted from a blast furnace, then poured in the smaller sections, second and while iron is still hot (probably close to melting point), molten copper is poured on top after which the smaller mould is removed and the process repeated, until finally creating a wall, made of merged iron blocks, that were copper coated to provide some kind of protection against corrosion.

    The description might seem very primitive or incomplete, what i need to know is whether it is possible for a metal wall to be assembled using that method (or something technically close to it) and also another crucial point; is it possible or would it have been possible for ancient people to copper coat iron by pouring molten copper over very hot iron blocks? Would the copper adhere and stick to the hot iron surface?

    Thanks!

  22. Hi Greg, since the melting point of iron is above that of copper it would be possible to make such a structure.

    The melting point of elemental iron (100% Fe) is 1539’C, the product of reduction with carbon has a lower melting point, also known as iron, a mixture if iron and carbon with a melting point of 1147’C. The melting point of copper is 1084’C. Pouring hot copper onto the iron would be similar to pouring jelly mixture onto chocolate. If you overheat the copper, then the iron would dissolve depending on the total temperature. Just pouring hot copper onto cold iron would make a weld of sorts. I would expect there to be some technique to doing this part effectively which the authors might report if they have used this method.

    A modern technique to do this would be to form a protective barrier on steel by electroplating method, where first copper and then chrome is used to coat a product to confer corrosion resistance. This would probably be the best solution using modern technologies, for a given price, unless some particular combination of properties are required (like high heat transfer or electrical conductivity that can be provided by copper). In ancient times iron would be more expensive than copper, but these days copper is far more expensive than pig iron.

    Metal matrix composites exist today made of copper and iron. A structure can be made from iron powders and pressed together (probably heated too) such than a structure with a network of pores is formed, then molten copper can be infiltrated into the structure. Copper-infiltrated iron parts produced in this way may be suitable for applications requiring good resistance to shock loading and good fatigue strength accompanied by resistance to wear. Example applications would be; A clutch hub, A printing press paper gripper, An automatic transmission part. Where copper infiltrant used has 5% iron and 5% manganese by weight.

    A problem with knowing what the ancients meant by this story is that at that time not a lot was known about the nature of the chemical elements. Its likely that if they report a technique that was known at the time, the story could be corrupted, or not recorded in a way we can decipher today, for example the story might just refer to using two different types of metal which has been translated as iron and copper. Identifying a site of construction, or where the ores came from would help to determine the efficacy of such a construction.

    Do you have an original source for the story? I think it is in the Bible, Torah and Quoran.

  23. If mild steel is welded using a consumable electrode, will the hardness values in the welded area be different from the hardness values obtained in the base metal? If yes,why? Will the filler metal also contribute?

    • Yes there will be a hardness profile across the weld, and there is a range of welding consumables to match particular cases (base metal composition and thickness / type of weld.

      The weld filler is made of carefully controlled composition, also is reacting and filler has a flux (slag forming as in metal casting) to control reactions, or special welding procedures control the atmosphere around the weld (inert gases, vacuum etc).

      Usually the filler metal is chosen so that the weld metal is of lower hardness (higher toughness) than the base metal. Otherwise if the weld was harder and less tough, it can be viewed as a defect / stress concentrator.

      Along the weld, the base metal is heated to various temperatures (Heat affected zone) and may have higher hardess or lower toughness than the base metal.

      Generally there is more scope to control the microstructure of the base metal (more control of processing). In the welding process it’s unavoidable that the base metal near the weld will undergo different thermal processing at different distances from the weld, despite the high level of process control. Control of welding process, for example chose of filler, process conditions, post and prior welding temperature control of weld area are used to mitigate differences often.

      Mild steel covers a range of compositions with carbon over quite large range 0.05–0.25% carbon, having relatively low strength and ease of deformation. Imagine the metal nearest the weld with low thickness plate, and fast welding speed. A zone closest to weld will be heated up to austenite phase field and rapidly cool, giving possibility to transform to high hardness microstructure. A zone further away from weld will be heated up to a temperature just below austenite phase field, this zone will be severely tempered, carbides will coarsen potentially leading to decrease in toughness. Further away zones will be less severely tempered, which shouldn’t usually lead to a problem other than small decrease in strength, and beyond that we are back to the base metal.

      Strength of filler metal can be chosen to be higher or lower than the base metal on cooling, and a volume of base metal is melted and exchange atoms through diffusion.

      Size of these zones depends on welding procedure.

      • Hardness and strength are two different properties. Hardness is the ability to withstand deformation (usually measured by change in dimension on application of a load with an indenter), strength the ability to withstand a load (stress at which a deformation occurs e.g. to a certain plastic strain or to failure).

      • Does the precipitation of carbon always occur on the welded area of mild steel immediately after welding (using a consumable electrode)? If yes what causes it? How does it affect the microstructure of the welded area and its hardness?

      • It’s not clear what you mean by precipitation of carbon. Also what is welded area? Weld metal, HAZ etc (as I tried to explain above, weld contains many areas).

        Carbon is more soluble in austenite at higher temperatures (in liquid metal too). At lower temperatures carbon in solution is more likely to want to precipitate as carbides (e.g. Fe3C, for example in pearlite, or as carbides in tempered martensite or bainite). To what extent this occurs, and what the result us depends on all the conditions. For example in the region of weld which is heated to below the temperature needed to form austenite, the carbides will coarsen rather than simply dissolve.

        For specific case you can probably find better information from the welding consumable manufacturer.

        If you mean in the weld metal, what happens depends on the cooling rate and composition of the filler after mixing with the base metal. Usually the filler would have very low carbon content and carbon would precipitate on cooling as carbides (pearlite + ferrite, widmanstatten ferrite, bainite, etc). Even martensite that forms in low carbon can be at higher temperature e.g. 500^C so that autotempering occurs on cooling.

      • Can a material with 0% elongation and 0% area reduction after tensile test have a yield strength?

      • Please how is that possible? With 0% elongation and 0% area reduction there is no change in length,width and thickness (initial length=final length and initial cross sectional area=final cross sectional area) so how is that possible?

      • You could measure 0% elongation if you have 0.49% elongation and you round down to 0%. You could have a very small amount of yielding, e.g. a usual definition if 0.2% strain. So here amount of precision specified is important for your question.

        After load is removed all the elastic portion is recovered, so in a strong/brittle material this if often the approximate case. If no yielding is observed, the standard thing to do, is to take the yield strength to be equal to the UTS (check relevant standards/procedures).

        Also aboute the special case of the material contracts in tensile direction and expands in transverse direction on loading, then you could have negative strain and negative area reduction.

  24. do any one have a simulation for the microstructure change during austenite to bainite phase transformation as a function of time or temp.?

    • I like to use the mucg program for calculation of TTT diagram, this gives start time for transformation. If you are working on specific alloy you can compare your results and see from mucg program how different alloying will effect result.

      A simple model can be made if you make assumption about the size of bainite plate and the time for nucleation. e.g. “Kinetics of the bainite transformation”, Hiroshi Matsuda and Harshad K. D. H. Bhadeshia, Proceedings of Royal Society A, 2004. https://doi.org/10.1098/rspa.2003.1225

      For considering multiple transformations which may be necessary for design of steel in many cases you can see also the PhD thesis of Javen Chen “Modelling of Simultaneous Transformations in Steels”, University of Cambridge, 2009

      Click to access Thesis_Jiawen.pdf

  25. My question concerns 6463-T6 aluminum used as a sampling “cell” for analysis of water and ethanol vapor mixtures in both wet and dry gas variations. I have a basic grasp of our problem so please bear with me. As I understand it, the aluminum oxide covering our cells surface is being or has been previously damaged and thus causing, for lack of a better term, micro-abrasions of its surface. This allows water vapor to “attach” to the cells surface material which affects our testing process.

    We have looked at methods of cleaning the cells so to essentially allow the surface to re-oxidize with a cleaner, better surface. Different types of acid baths, boiling the cells in vinegar and rinsing thoroughly and so forth.

    Currently, we are discussing and trying to learn how the metal surfaces pH value can affect the quality or this aluminum oxidation and thus maybe determine a better cleaning method to achieve the desired results. I am currently trying to learn all I can about this type of aluminum, the oxidation process, methods to measure the metals
    pH value (so we can make the surface a neutral pH…I think) and how to devise a suitable cleaning method.

    Any insight you could provide to focus us into the right direction would be appreciated. Testing methods, procedures, ways to measure the metal surfaces pH value, which acids or bases might work best, if at all, etc…. I need to build a working knowledge of how this issue affects our product and maybe contribute viable testing protocols.

    If you have questions, please be very detailed and specific with them so I can provide useful answers while also learning more about this issue.

    • Hi Randy,

      This might be a good place to start:

      Jenny Linder, Masters Thesis, KTH Stockholm, 2012.
      “Alcoholate corrosion of aluminium in ethanol blends — the effects of water content, surface treatments, temperature, time and pressure.”

      Click to access FULLTEXT01.pdf

      Abstract As it becomes more important to replace fossil fuels with alternative fuels, biofuels like ethanol are becoming more commercially used. The increased use of ethanol brings good influences such as lower impact on the environment.However, the use of ethanol can also bring negative effects regarding corrosion of metals.In the automotive industry aluminium has been seen affected bya novel very aggressive corrosion phenomenon, alcoholate corrosion.This master thesis investigation hasin vestigated the effect of a few parameters of importance for alcoholate corrosion; water, temperature, time and pressure. The aluminium alloys AA6063 and A380 have been investigated and the capacity of five different surface treatments of AA6063 has been tested to observe if they inhibit the effect of alcoholate corrosion.Throughout the experiments the water dependence of alcoholate corrosion has showed to be of large importance for the corrosion process.An increase in water content will postpone the start of alcoholate corrosion or prevent corrosion to occur. A correlation between temperature and time has been observed. Higher temperatures results in a shorter time period of exposure before alcoholate corrosion occurs,and vice versa. The effect of different pressures was investigated and showed no effect on alcoholate corrosion when using pressurisation with the inert nitrogen gas.All surface treatments revealed a capacity to protectthe aluminium alloyagainst alcoholate corrosionto different extent. The electroless nickel plating seemedto prevent alcoholate corrosion while the Keronite coating seemed more sensitive to this form of corrosion.

  26. I have a question about normal rusting on 316 steel. We have a structure under a year old that has 316 handrails throughout, and less than a year in the handrail appear to have pretty uniform surface rust. To our knowledge nobody has used steel wool or anything strange on the rails, they’ve seen roughly about 6 months of use and one winters worth of exposure (these rails are close to an entrance that is de-iced regularly). Can you tell me if this is normal rusting that would just need an annual cleaning? Also, what could be causing this?

    Photos below:

    https://photos.app.goo.gl/2QWpW8C17Wm5VjVz6

    https://photos.app.goo.gl/ZNWoHWRk1wQQrNhV7

    https://photos.app.goo.gl/42mb5cdUYxKHeoJ28

    • Hi Laura, did you find a reason for this? I know that stainless steel can sometimes corrode against expectations from the name. I’m wondering if there is anything like a source of salt around near the steel, pidgeons/ seagulls nesting above (chickens?), maritime environment or any other source of corrosive particles landing on the stairs. Also is there any source of galvanic voltage accelerating the corrosion, for example an electrical circuit with the other metals in the staircase. Another environment when stainless steel can corrode would be sitting water. I’ve seen corrosion of stainless steel can occur when it’s exposed to deionised water. Possibly sitting rain water could be problematic.

      If the tubes have been fabricated by welding, susceptibility to corrosion can be caused by formation of carbides in the stainless steel. Therefore inadequate control of processing temperatures during production, or post welding could be a source. I don’t see sign of welds in your images but perhaps the seam runs along the bottom of the rails or has been de-burred.

  27. hi

    what steels are these?

    a) 0.26C, 3.11Cr, 1.98 Mn, 0.01Ni, 0.50Mo
    b) 0.25C, 3.01Cr, 0.08Mn, 2.00Ni, 0.51Mo
    c) 0.29C, 2.97Cr, 2.10Mn, – –

    are they some “historic” compositions? i wonder what they might compare to.

    regards

  28. What’s the difference ADI(Austempered ductile iron) and bainite (steel)? Are there any microstructure differences? I’m confused about this. Ausferritic, bainitic steel, bainitic ferrite….bla bla bla.

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