One concept that can be difficult to understand intuitively is that the hardness or strength of steel does not change its stiffness. Meaning, “flexing” steel without permanently bending it is not changed by its hardness. I have heard many people swear up and down that they can tell a difference, so I found a great Youtube video that illustrates this [1]:
I promise he is not using any tricks here; despite the difference in hardness, placing identical weights on the end of each leads to the same degree of flexing. I will explain some more about what is going on here. When it comes to flexing, or bending without “permanently” bending, it is controlled by “elastic modulus” also called “Young’s modulus” which is a measure of the materials stiffness. Why isn’t stiffness and hardness correlated? I’m glad you asked.
Elastic Modulus
When we flex the steel, we are stretching or compressing the atomic bonds between atoms, as illustrated by springs in this image [2]:
When you pull the set of atoms in tension then you stretch the bonds, and when compressing them you compress the bonds. Steel is polycrystalline, or made up of many grains of different crystallographic orientations, meaning that the planes of atoms are randomly oriented throughout, so there isn’t any real directionality in the bulk material in terms of modulus because of the orientation of the atoms, as illustrated by this simple schematic [3]:
So the end result in our bulk material is that the elastic modulus is controlled by the strength of these bonds. Since steel is primarily iron it is controlled by the strength of the iron-iron bonds. The strength of those bonds does not change with heat treatment, and changes by only small amounts when other elements are added (such as with chromium additions for a stainless steel).
When the cantilever in the video is being bent then the top surface is in tension and the bottom surface is in compression [4]:
Since the Youtube video uses a simple rectangular cantilever beam, it is relatively easy to derive the equations for the degree of deflection as well as the stresses at the surface of the sample:
The amount of deflection is calculated by the equation shown in the figure, where you can see that it is divided by the thickness cubed, so the thickness is a major contributor to limiting the amount of deflection.
There is zero stress at the very center of the sample and the maximum tensile and compression stresses are at either side of the sample as shown on the schematic. The stress at the surface is given by the equation in the figure, where you can see that the surface stress is divided by the thickness squared. So though thicker samples resist deflection, there is also a much greater stress at the surface.
Since the top surface is in pure tension we can describe the behavior in that location with a tensile test, where a piece of steel is pulled in tension typically until it breaks, such as is illustrated here [5]:
In a tensile test if you stay in the modulus region of the material, the behavior is completely linear, pulling the material causes it to elongate, and removing the load causes it to return to its original length. The slope of the line is equal to the Elastic Modulus. Applying more load leads to more elongation:
In the video he mentions that the two different samples bend the same amount because they have a similar cross section. The stress, σ, shown in the earlier figure demonstrates the importance of cross section. The load, width, thickness, and Modulus are all the same so the samples have the same degree of deflection despite the difference in hardness. Therefore, for a given material because its modulus is fixed, the greatest controlling factor for resistance to flexing is the cross section and particularly the thickness.
In the video he then bends the “soft” sample to the degree that it is permanently bent. Bending the “hard” sample to the same degree doesn’t permanently bend it but it springs back to its original position. As he mentions this is because of the difference in “yield point” between the two materials. The yield stress of the material is a measure of its strength and does typically change with hardness, though ultimate tensile stress typically best correlates with hardness. The yield point or yield stress can be seen in this stress-strain curve of a tensile test [6]:
There is a transition in behavior at the yield point where it is no longer controlled by the bonds between the atoms. What the transition in behavior is from I will cover in a future post. When materials have different strength levels the elastic modulus remains the same and but the yield stress can change greatly [7]:
When the yield stress is exceeded then “plastic deformation” occurs where the steel will remain permanently bent. In terms of a stress-strain curve, unloading will not lead to a return to zero, but retains some amount of deformation, or displacement [8]:
Though as you can see, during unloading and reloading the material still follows the elastic modulus. When reloaded the yield stress is higher than it was originally, however, as the material has been strengthened somewhat during the initial plastic deformation, this is the same mechanism by which cold rolling strengthens steel.
Summary
Both materials in the video bent the same degree with a given load because they had the same cross sectional area and elastic modulus; the hardness does not affect these two parameters. The elastic modulus is controlled by the strength of the iron-iron bonds, which does not change with heat treatment, strength, or hardness. In the video with the soft steel, the yield stress was exceeded by further bending, the material was work hardened, and it was permanently bent. With the hard steel, its yield stress was much higher so it could accommodate much more bending before reaching the point of permanent deformation.
Examples in Knives
Fillet Knives
Fillet knives are sometimes shown off for their flexibility by flexing them 90 degrees. The reason they are so flexible is due to the thin geometry, since as described above the deflection for a given load is inversely proportional to the thickness cubed. The stress on the blade is also lower due to the stress being inversely proportional to the thickness squared. Sometimes knifemakers will state that they heat treat them to a lower hardness to ensure flexibility. As described in this article that is a misunderstanding of the steel behavior. The flexing is purely within the elastic behavior of the steel and if anything the maker must ensure sufficient hardness so that the yield stress is not exceeded during flexing.
ABS 90 Degree Bend Test
As part of the ABS performance tests the maker must bend his or her knife 90 degrees [9]. The knife must also be able to chop through a 2×4 so some thickness to th blade is necessary to withstand chopping and to provide some weight during chopping. So the smith must balance the thickness necessary for chopping with the advantage a thinner blade gives in the 90 degree bend test. Because the thickness necessary would lead to exceeding the yield stress during a 90 degree bend they instead intentionally make the spine soft either through differential hardening or tempering back the spine. That leads to a low yield stress but also much higher ductility so the knife can accommodate much more strain during the bending [10]:
So after the 90 degree test it can be clearly seen that the knife has been bent and does not return to straight due to the bending past the yield point [11]:
Brass Rod Test
A test sometimes performed by knifemakers is the “brass rod test” where the maker holds th knife at a 45 degree angle and presses the edge against the rod to cause the edge to deflect by some amount. First and foremost this a test to get a feel for how much the edge will deflect under a given load, which is highly thickness dependent, as discussed in this article. The hardness does not change the degree to which the edge deflects. The test is also claimed to be good for determining if a blade is too soft or too brittle. In practice it requires a relatively soft knife to permanently bend in this test with typical geometry knife edges, but if the knife was too soft then the yield point would be exceeded and the edge would be plastically deformed. If the knife was brittle then the edge would chip, as very brittle materials barely deform at all prior to cracking as shown in the figure comparing the “brittle” and “ductile” materials in a tensile test; however, the steel would have to be very brittle. Therefore, the test may give some limited information on if the steel is much too soft or much too hard but a hardness test would tell much more. It is more useful for getting a feel for how much the edge may flex based on its geometry.
[1] https://www.youtube.com/watch?v=SIFfY-MS3yA
[2] https://www.tf.uni-kiel.de/matwis/amat/iss/kap_4/backbone/r4_1_3.html
[3] http://www.tpub.com/doematerialsci/materialscience5.htm
[4] https://pocketdentistry.com/2-mechanics-and-mechanical-testing-of-orthodontic-materials/
[5] http://www.totalmateria.com/page.aspx?ID=CheckArticle&site=kts&NM=351
[6] https://www.rolledalloys.com/technical-resources/blog/how-to-measure-tensile-strength-elastic-modulus-and-ductility
[7] http://www.metalpass.com/metaldoc/steels/StructureSteelQA_files/
[8] https://www.quora.com/How-does-cold-working-affect-stress-strain-curve
[9] http://www.americanbladesmith.com/uploads/file/Testing/JS%20Test%20FINAL%204-24-2010.pdf
[10] https://www.doitpoms.ac.uk/tlplib/BD6/yield.php
[11] https://m.youtube.com/watch?v=Sfs2114aTnw
Really been enjoying these. Keep up the good work! It’s so nice to see some actual metallurgy instead of the half-voodoo that you sometimes read.
Thanks!
Hello Larrin,
fan of your work and articles since you started, first seeing them in Spyderco Forums and Bladeforums
I was reading again this article because I remembered an article from Jay Fisher whose line of thinking seems to be contrary to the evidence shown here, and explains that in his website.
http://www.jayfisher.com/Elasticity_Stiffness_Stress_Strain_Knife_Blades.htm
Is me that I’m interpreting it wrong or does his article contradict the information here?
I am genuinely curious and puzzled by this fact. Thanks for your thorough research and helping us nerds out
Not all information on the internet is accurate. Even from experienced knifemakers. 🙂
Thank you Larrin, I thought so
I am really learning a lot from your articles, and can finally satisfy my steel nerd cravings and curiosity. Keep up the excellent work!
The fact that Young’s modulus of steel remains more or less unchanged is well known to me through my engineering education. That’s why I was very surprised to find that hardened steel has a very different ‘ping’ sound compared to soft steel as demonstrated by Kippington on KKF (can’t find his video of it now). I figure sound is a function of geometry, stiffness, density and hysteresis. Since stiffness and mass are more or less constant, and he kept the geometry the same as well I figure there may be some meaningful difference in the vibration energy absorbent (damping) properties of hardened versus unhardened steel. Not because the static behavior of two materials are identical it necessarily always follows the dynamic properties are as well. Which for me makes the question whether or not a trained person can feel a difference in feedback once again unanswered.
thanks for this interesting piece, BUT:
diagrams from [7] and [10] seem to directly contradict each other?
can you clarify why, at first, the elastic modulus is not affected by differences in hardness (commonly achieved through heat treatment), and then later it DOES change through heat treatment?
The second is a comparison between two different materials (ductile and brittle) which have two different modulus values.
Thank you for writing all of these wonderful articles! As much as it is enlightening to know more, I feel like I’m just starting to understand how deep a pond I jumped into…
There is one thought that I can’t seem to shake, where there is a somewhat common situation in knifemaking where the steel might actually flex differently after heat treat, in contrast to the steel tests described in this article.
Assuming that the elastic modulus stays roughly the same for the steel, it would take more energy, and a higher force, to stretch a hypothetical ideal spring (F=-kx) from 0 to 1 cm when compared to 2 to 3 cm, even though the difference between start and end points is the same for both stretches.
I have seen that this pre-stretching is effective in many places, such as when rebar is pre-stressed when setting blocks of concrete, to apply the rebar’s tensile strength to the concrete without having unsightly cracks. A prince rupert’s drop is also significantly stronger than normal glass, and it seems to be formed by a somewhat similar thermal shock to quenched steel. So, it seems the internal stresses can make a big difference in the final product.
I have also heard machinists talk about the challenges of milling cold-rolled steel plate. Apparently, cutting through the outer “skin” of the metal on one side will cause it to bend like a potato chip.
Warped blades from heat-treat unfortunately seem to happen very often, and many people will advise doing a “snap temper” on as-quenched 1095 blades. Apparently, thicker pieces might break, even if they are just sitting on a bench overnight. The steel seems to effectively stress-relieve after tempering, but directly out of the quench, I’m thinking that the internal stresses might change the properties in interesting ways.
With all of these examples in mind, I am wondering—just how much might the internal stresses from heat treat affect steel blades? Is it possible that certain techniques can make stiffer blades out of the same geometry, or is it just making the blade more brittle? Would higher stresses from the quench also indicate conversion of martensite, corresponding to changes in audible “ringing” sound? So many questions… maybe food for more thought.