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Flexibility, Stiffness, Springiness, Elasticity, Stress, and Strain in Knife Blades


The knife blade is substantially stiffer after hardening and tempering.
The knife blade is stiffer at higher hardness, and more flexible at lower hardness.
The knifemaker should understand and control this physical feature of the knife blade.
Many people don't understand this simple physical aspect.

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The Issue
  1. A knifemaker wants to build a fillet knife. He wants it very flexible, with the most movement against the least force—springy. He knows he must achieve a balance between hardness, toughness, and wear resistance, and yet, he wants it as springy as possible. How does he heat treat the blade to achieve the maximum springiness, or elasticity?
  2. A tactical knife client needs high stiffness in his blade. The blade must be extremely tough, yet remain as rigid as possible in order to support the point while the highest possible thrust force is applied. How does the knifemaker insure the highest possible stiffness?
The elasticity of steel varies depending on the alloy content, the geometry, and the heat treatment and condition (annealed, hardened, tempered, normalized, etc.).
The elastic nature of steel is largely misunderstood or misrepresented.

A knife blade is a curious thing—it's expected to be made strong, wear resistant, and often corrosion resistant. It's also expected that a blade has some kind of stiffness, or flexibility, depending on the geometry, design, and intended use. When a knifemaker designs a knife, it's very important that he has understanding and proven long-term familiarity with the physical aspects of the steel blade, in order to make a useful, durable, and well-performing knife.

When I make a knife blade in high alloy steel, I cut out the blade, surface grind the blade to a pre-determined thickness, drill all the necessary holes, and, if it's a full-tang knife blade, I taper the tangs. I then accomplish the grinds (mostly hollow but some flat grinds on very thin blades) and profile the edges. I then filework, and/or engrave the blade if desired. It is then ready for my heat treat. You can see these various steps on my "Where's My Knife, Jay?" page and get an idea how this is done on my Shop and Studio Pages One and Two.

Before I heat treat my blade, I hold it my hand and press sideways on the blade point with my thumb. This I do because I want to feel the geometry of the thickness of the point. I know it sounds a bit non-scientific, but when you've made literally thousands of knife blades, in all different styles and patterns (450 of my patterns here with links to over 800 photos of my knives), you develop an intuitive feel for the knife blade geometry, and a sensitivity for feeling deflection and force that is not a measurable thing. It is more of an experiential technique, based on observation, and one of the reasons that a lot of clients have come to expect an extremely well-balanced knife from me. When I do this slight manipulative assessment, I can tell whether the blade point is going to be too thick, too thin, too wide, underground, overground, or the geometry of the point needs improving. I'll make any substantial adjustments then, expecting what the outcome will be after heat treatment.

After heat treatment, hardening and tempering, I instinctively do the same manual deflection practice. I call it a practice and not a test, since a test would suggest a readable scalable numerical result (more on actual testing below). When I do this, I can feel that the blade is substantially stiffer, more resistant to sideways deflection after hardening and tempering. To me, it is remarkably stiffer, and this would make sense, since a completely different crystalline structure and allotrope set is established by heat treating and processing of the steel.

So imagine my surprise when I read and hear, over and over, that the stiffness of steel is fixed, that it never changes, no matter its condition or hardness! According to this belief, I couldn't possibly feel any difference, since the only two things effecting the stiffness of the blade are the steel's element (alloy) content and the blade geometry! According to this persistent belief, no matter how a blade or any other piece of steel is heat treated, it always has the same flexibility.

This is simply untrue.

Knifemakers and Colossal Confusion

The lie: "All knife blades have the same flexibility, no matter how hard they are."

Using the word "lie" might sound too harsh, but this mistaken concept is so common that it's clearly shocking to see it repeated, over and again, by people who should know a lot more about steel. This is the real problem. Knifemakers who claim to know what they are doing are clearly uneducated, inexperienced, and underdeveloped in their field, yet their mistaken opinions about the physics of steel properties are somehow held to be true, when they are clearly, provably false.

Knifemakers—particularly on discussion forums—continue to perpetuate this ridiculous myth. No doubt they've read it or heard it somewhere, and actually believe that a knife blade that is hardened and tempered to 60C Rockwell has the same flexibility as one that's been hardened and tempered to 55C Rockwell. They continue this error and mistaken concept, insisting to new and novice makers that they are correct when they are astoundingly, shockingly, embarrassingly wrong! Sadly, these new makers skulk away with mistaken beliefs, and this is disgraceful.

Knifemakers believing this myth have even argued with me over the phone, claiming they are right, merely because some forum moderator or anonymous metallurgist has told them the same lie. They insist, over and over again, that all steel has the same flexibility, no matter how it's hardened and tempered, and the only thing that changes the flexibility of a knife blade is the thickness and shape (cross sectional geometry) and steel type. There are guys even calling themselves machinists and perpetuating this false belief.

This stubborn concept is in flatly wrong and clearly untrue, and it's provable with simple testing. Yet the falsehood persists not only among knifemakers but also among some engineers, machinists, and metallurgists that don't have any real world experience with this physical characteristic.

What in the world is this all about?

By the time you finish reading this page, you'll understand how this concept is flawed, the origin of the confusion surrounding it, and understand how you can physically prove the truth to yourself if you are the experimental type.

The truth is, flexibility in steel can be changed, depending on how it is heat treated, hardened and tempered. Read on; if you have the slightest interest in this, you deserve to know the truth.

Page Topics

The steel knife blade is substantially stiffer, more resistant to sideways deflection after hardening and tempering.

The knife blade is stiffer at higher hardness, and more flexible at lower hardness.

The knifemaker should understand and control this physical feature of the blade.


Translated:

First of all I apologize for the language in which I write but I would like, if possible, that the idea I express should contain as much as possible of what I feel and think.

I have read attentively a clarification that makes on your page about your experiences, studies and no less valuable concepts of what your career has shown in what you do and your retractors. It is not my custom to messianize people but I consider an act of infinite justice the recognition not only of excellence but also of humility and desire to contribute to the teaching that you offer and promote.

Throughout history it has been shown that it is always easier to disqualify and destroy (whenever possible) than to learn through effort and perseverance and that, far from achieving it with you, produces the opposite effect and exposes the false and the mediocre. Honestly, I do not think about the badness of these people but about the incapacity and the consequent mediocrity.

For more than ten years I have followed your work and your progress with attention; I think I have mentioned sometime as I admire the family union that you have and the remarkable atmosphere that is breathed in your study-workshop. Although your creations of knives and blades in general are a technological and beautiful spectacle, there are other related activities that also deserve recognition and admiration such as leather, stone, casting, photography, creation, design and construction of machines and tools and the impeccability and usefulness of your website ... and many more logically.

I have thanked you before but I do not find it redundant to repeat my recognition of what you have achieved with great sacrifice and dedication in all these decades.

Receive my extensive greetings of course to your family ...

Lic. Juan Herbut G.


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Important Concepts

Most knifemakers who insist that elasticity in blades is independent of hardness believe this because someone told them it was so, or because they read the basic theory that the modulus of elasticity is fixed in isotropic, uniform, crystalline structures. They discount the dramatic changes of the crystalline structure of heat treated steels.

In order to understand this issue, I'll cover a few concepts about materials, so you can get a grounded and basic idea of how they interrelate.

Elasticity, stiffness, and the Modulus of Elasticity are important concepts to the designer, the engineer, and the machinist. It starts at the atomic level. Metals have metallic bonding, that is, the atoms that comprise the structure of the crystalline form of metals have very strong bonds between them, yet the electrons in the outer shells can move freely among themselves. This forms a sort of cloud or sea of electrons in the metal, and because the electrons can move, metals can conduct electricity as the electrons move around. The crystalline structure has a basic, fixed form, that in pure metals, is highly regular.

It takes a certain, definable force to displace these atoms from each other, or to pull them away from each other or to push them closer to each other. You can force the knife blade to deflect by putting your thumb on the side of the tip and pushing. Since this is not changing the physical characteristics or molecular or atomic structure of the steel, it is attributed to stretching out the interatomic spacing on one side of the blade, while compressing the interatomic spacing on the other. The force is removed and the blade then returns to its neutral position. It's easy to visualize if you consider that a crystal metallic form is a block comprised of a bunch of springs, in a regular, spaced arrangement in all three dimensions. When you pull, push, bend, or stretch these crystals, the metallic bonds distort in a very regular way. They can be pulled, and then when the pressure is off, they return to their stable positions. I emphasize stable because all materials have forces imposed on them at all times, even if it's just gravity, air pressure, or minimal loads created by their own geometry.

Because the bonds are atomic, and because they are chemically fixed, it is assumed that they are always the same. This is where the Modulus of Elasticity comes in. What it defines is how metals spring, or how stiff they are. The word modulus means a "constant factor or ratio." So, if one takes the word at its core, it is a very fixed and rigid number or ratio. The modulus of elasticity is a ratio. The ratio is stress to strain, or stress divided by strain.

Stress is the Load per Unit Area, or the amount of force put on a certain area of the material, and it's measured (in our terms) in KSI (thousands of pounds per square inch) or MSI (millions of pounds per square inch. There are other measurement methods—MPa, or megapascals and GPa or gigapascals. The easy thing to remember is that stress is measured in PSI (pounds per square inch).

Strain is the amount of stretch under load per unit length. Strain is simply a change in length or dimension. Simple enough!

The Modulus of Elasticity comes from the linear portion of a stress-strain curve. It's also called "Young's Modulus of Elasticity" for the 18th-century English physician and physicist Thomas Young who developed the idea. This part of the curve is where the Modulus of Elasticity is derived. The modulus is the pressure (in PSI) divided by the strain (change in length) so is represented in PSI. Since the numbers are big, steel is typically represented in thousands of psi, or KSI. It's also represented in millions of psi, or MSI. In SI units, it's represented in pascals, or gigapascals. We'll stick with KSI since I am here in the United States.

The modulus of elasticity does not refer to the area of the stress-strain curve where the material is permanently bent (strain hardening, stretching) or breaks (fracture); it only refers to the linear (straight) part of the curve. In the graphic below, it's the straight, diagonal line where the strain-stress ratio (triangle) is shown.

Simple enough. For steel, the Modulus of Elasticity is a ratio, used to describe elasticity or stiffness of a particular material, measured in KSI or MSI, or thousands or millions of pounds per square inch.

Generalized stress-strain curve
Plastic vs. Elastic

Sometimes, scientists and metallurgists insist that what is changed in heat treating and processing in steel is a plastic property, and not the elastic property. They may claim that steel allotropic conversion of crystalline structure creating martensite, for instance, only affects the plastic property of steel while the elastic properties, being based on atomic arrangement, remain the same.

This is an error. The plastic properties of metal are clearly defined.

  • Elastic deformation happens when force is applied to the metal, and when the force is removed, the metal returns to its original dimension and position.
  • Plastic deformation happens when force is applied to the metal, and it does not return to its original dimension and position.

The two are completely different properties. Simply put, in elastic deformation, the metal springs back; in plastic deformation, the metal is bent or permanently deformed. In a knife blade, elastic deformation is okay, but plastic deformation is permanent and a ruined knife blade.

Elasticity or Ductility

Another common error I've seen in discussions is confusing ductility with elasticity. In an effort to explain why there appears to be a difference in flexibility after heat treatment, some people claim that it's not a change in elasticity, but a change in ductility that accounts for the difference. This is wrong.

Ductility is a completely different property and in a very basic sense, it's the ability for a metal to be stretched into a wire or hammered into a thin sheet. I go into depth about ductility at this bookmark on my Blades page. Ductility is a plastic deformation property, so happens when steel is permanently deformed. Elasticity is simply the measure of movement when forced—strain when stressed—without permanent deformation. Elasticity is a definite, measurable property and it is not ductility, which is a plastic deformation property.

Temperature Critical!

Please note that the modulus of elasticity in steels is highly temperature critical; the modulus changes dramatically at elevated temperatures. On this page, and in referring to knife blades, please note that all determination and discussion is at room temperature, since knife blades are used typically at this temperature.

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How Elasticity is Measured

You might think that elastic movement in steel is strictly measured, but this is rarely the case. In most cases, standard ratios are employed. These are long-established numbers referred to over and over again, in a generalized way in steels. In other words, the modulus of elasticity is seldom measured at all!

Not often needed

This is the first limitation. There are great devices for measuring this, so one wonders why so little actual measurement takes place. This is because not many engineers, metallurgists, or machinists are concerned with the elasticity of steels. They are usually much more concerned with the yield strength, ultimate strength, and fracture strength of steels. Since the actual elasticity is fairly uniform, it's not usually measured, but only established by formula, which, in most applications, is close enough. In industrial uses, and in engineering applications, the modulus of elasticity is not as important as yield strength. Consider that in a structure, a bit of flexibility is expected, but when the steel moves enough to permanently deform (bend) you have much more important issues! So, standardization and generalization of elasticity is accepted.

Limitations of the Measurement
(Applicable to High Alloy Steels)

Below is a list of ways that the actual measurement of the modulus of elasticity is limited and thus, rarely used in high alloy steels. This applies specifically to knifemaking, where I know of no one who is actually measuring the elasticity of heat treated steels—except for me (see below)!

  1. Actual testing is not usually accomplished; standards are typically used. When actual force measurement for Young's Modulus of Elasticity is done, static testing can be performed. While there are several physical types of test (tensile, torsion, or bending), it's usually a tensile test. This is done by stretching the steel and measuring the length at which it stretches, compared to its original length, depending on the force. An extremely strong frame holds a round rod of the material being tested, force pulling it lengthwise is applied, the force is measured and the change in length is measured. This is done over and over again to determine a graph plot of results; it's a very impractical, difficult process, and most steels vary only by a small amount. So standards have been accepted in place of actual, robust, and continuous testing. In engineering, a steel beam of a known steel has the same modulus, no matter what the application is, and, after all, the yield strength is more important.
  2. It's a linear test. The testing and definition of Young's Modulus of Elasticity refers to a linear elastic solid. This is like a long rubber band, or long piece of aluminum rod, or a long steel rod, or a long bar of plastic, brass, wood, or bronze. This is a linear test and that is the second limitation.
  3. The knife blade is not a linear object. When you bend a knife blade sideways, one side of the blade stretches, and the other side of the blade compresses. Pulling or stretching a rod is an entirely different physical action. A rod is pulled, and the only compressive forces are derived from the contraction of the rod explained in Poisson's ratio. I won't get into that, but you can look it up if you're interested. Basically, stretching a rod is not compressing it, but bending a knife blade sideways is compressing as well as stretching it.
  4. Bending tests can be performed, but are less common, because tensile tests give fairly uniform, related results, which are typically standardized.
  5. The measurement only applies to isotropic, uniform materials. While you might consider a knife blade isotropic and uniform, you must consider that it is rolled, drawn, poured, or sprayed (in the case of particle metal technology) into a billet or bar form, and the form has inherent alignment and orientation characteristics of internal structure that are not completely uniform.
  6. The crystalline arrangement and direction will determine the test results. Crystalline structures have definite orientations, and this is seldom discussed among knifemakers. The orientation of the structure has a substantial effect on the modulus of elasticity.
  7. When individual actual tests are required, there are several methods. An ultrasonic thickness gauge transducer transmits a sound through a thin gauge of the material, the thickness of the material is entered into the software, and a ratio is derived. This is called a wave propagation method. A resonant frequency method is also used, and a nano-indentation method can be used to determine the modulus of elasticity.
  8. Because steel is so incredibly strong and stiff, the modulus of elasticity is in tens of millions of pounds per square inch. So in a basic way, it's so high that it's not extremely critical in most larger applications of steel. In knife blades, most makers leave them very thick, so there simply is no elasticity or springiness to feel!

No knifemaker uses these tests, and rarely do machinists use them, since general standardized ratio is accepted. Simply put, knifemakers and knife manufacturers do not regularly test, plot, chart, and record the modulus of elasticity of various heat treated blades, and they simply accept a fixed number, which is 30 MSI.

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The Mistake

In a fixed, isotropic crystalline solid, the modulus of elasticity is independent of hardness.

When the crystalline allotropes are changed, so is the modulus of elasticity.

Transformation of steel by heat treating, hardening, and tempering changes the allotrope arrangement, volume, and ratios dramatically, thus changing the modulus of elasticity.

Because the modulus of elasticity is theoretically considered an inherent atomic property of metals, it is believed by some engineers, scientists, and metallurgists to be fixed. However, the crystalline allotropes of steel are not fixed. If you make a steel harder, by standard heat treating (hardening and tempering) it does not behave in the same manner as if left fully annealed. Also, a steel that is hardened and tempered to HRC 55 is dramatically different than a steel that is hardened and tempered to HRC 60. Any practical engineer or metallurgist realizes this, and so should every knifemaker.

Understandably, many of the scholars who believe the elastic modulus does not change depending on hardness and condition are not talking about steel transformation. They are writing and talking about heat treating that does not change the allotropes of the crystalline structure. They may be discussing other metals or ceramics, or even plastics: materials that do not have dramatic internal crystalline transformations like steel when heat treating. This concept of a fixed modulus does not apply to high alloy transformational steels, steels that form austenite, martensite, upper and lower bainites, carbides, and have substantial crystalline conversions.

Basic physics textbooks for high school and lower college level education do not generally discuss the relationship of the condition of allotropes and the modulus of elasticity. They start by explaining Hooke's law which is that deformation depends on the force applied. They give a basic idea that intermolecular bonds and arrangements of isotropic uniform solids are fixed, and for basic comprehension, this is adequate. In a fixed crystalline arrangement, the modulus of elasticity does not change. Steel does not have a fixed crystalline arrangement!

In one "educational" text, this statement is made: "heat treating does not effect modulus." One must carefully examine the context of the statement, and this can cause some confusion. To be accurate within the context of the text, what the writer was trying to convey is that variations in the modulus of elasticity are not controlled separate from heat treating. In other words, heat treating is done for a specific reason, for instance, to make a steel wear resistant at HRC58, and the modulus of elasticity cannot vary from what it is in any particular steel hardened and tempered for HRC58. This is simply badly worded technical writing.

In one failure analysis handbook, another contextual error is the statement, "In general, in most heat treated steels, the modulus of elasticity will vary little." This is true from the position of yield strength vs. modulus of elasticity. Understand that the yield strength may be in the tens of thousands of PSI, and the modulus of elasticity may be in the millions of PSI. Therefore, when compared in failure analysis, this is only a small variation, when compared to failure by yield! This is far different from flexibility of a thin piece of blade steel.

Another failure analysis contextual description can be easily misinterpreted. "Most sudden onset damage is primarily related to the basic geometry and modulus of elasticity (of the steel part), which is not a strong function of any heat treating process." When you read this, you might think that the modulus of elasticity is not a strong function of the heat treating process, and that is another badly worded technical sentence. What the sentence means is that in failure, basic geometry and elasticity together is the cause of sudden failure, and the two cannot be altered by the heat treating process in order to prevent failure. Badly designed geometry can cause failure, together with the elasticity, but you cannot heat treat for increased elasticity, when other factors (like yield strength, hardness, and wear resistance) must be the primary function of heat treating.

Often, from single crystal data, the elastic properties of poly-crystalline aggregates is often calculated by an averaging scheme, with certain assumptions. This is not a valid, accurate test, but an averaging, generalized calculation. Since the engineer is more concerned with tensile strength in the order of tens of thousands of pounds per square inch, the elastic modulus at millions of pounds per square inch is less of a concern. The modulus is then often generalized and not specifically measured.

Most discussions absolutely forget one of the most important factors of steel conversion properties—dislocations. Dislocations create profound changes in the properties of heat treated steels, and they are one of the main reasons steel is a valuable and tremendously useful material. The change in steel by heat treatment not only changes the crystalline structure, it changes dislocations dramatically. The movement of dislocations allows atoms in crystal planes to slip past one another at a much lower stress levels. Change the arrangement of the crystalline lattice and its associated dislocations, and the properties of the crystal change, including the modulus of elasticity.

Grain size and arrangement matters. For a dislocation to pass into another grain, it is very difficult if it is misaligned. In a basic illustration, the "knotted up" misalignment of martensite makes it more difficult for atoms in crystal planes to slip past one another. This explains the increase in the modulus of elasticity, and the much more dramatic increase in strength, particularly in plastic deformation.

Not all steels have dramatic and extreme crystalline changes. For instance, heat treating 304 stainless steel (austenitic high chromium, high nickel stainless steel) does not significantly change the steel's internal structure enough to warrant a change in elasticity. 304 can be only slightly hardened or softened by mechanical pressure, manipulation, heat and cooling, so a standard elastic modulus is perfectly accepted. This is not high alloy, high carbon tool steel.

Below, you will clearly see that scientists and researchers still argue this point, when it's easily demonstrable and proven. I'll reveal that below, also.

The mistake among knifemakers is more basic. Makers who have limited experience and low sensitivity to balance, force and stiffness requirements may only notice a dramatic difference in flexibility in thinner, smaller blades. They may not notice the difference between steel that is annealed and steel that has been hardened and tempered. They can't feel a difference, so they assume it must not exist. They read somewhere that Young's Modulus of Elasticity is fixed, so they defend the belief without ever actually testing it.

Simply put: most knifemakers who insist that elasticity in blades is independent of hardness believe this because someone told them it was so, or because they read the basic theory in beginning physics textbooks. The basic theory claims that the modulus of elasticity is fixed in isotropic, uniform, crystalline structures. They discount the dramatic changes of the crystalline structure of heat treated steels.

Another argument by undereducated knifemakers is that the only thing heat treating changes is the yield point. They go back and forth, confusing yield strength with elasticity, when the two are completely different. The truth is that both of these properties (the modulus of elasticity and the yield strength) change depending on treatment and the final temper of the steel. What also changes is the ultimate tensile strength, the corrosion resistance, the toughness, and a myriad of other properties, like the electrical conductivity and even the size of the steel! Heat treating and final temper changes everything! Yet, they want us to believe that the elasticity stays the same. No, it doesn't.

More crucially, another more disturbing revelation is that they are most likely failing in their heat treating process, and the allotropic changes are not dramatic or even noticeable. This is a much more serious concern, because it means that the overall treatment of the blade is incorrect, or at the least, suspect. There are a lot of badly heat treated steel knife blades out there, blades that are heat treated with torches or forges, blades that are quenched with snap temper, steels that are processed in large batches by heat treating companies and individuals that are more concerned with mass processing (and dollars) than with individually treated, premium processed blades. More about that on my Heat Treating and Cryogenic Processing of Knife Blade Steels page. If the maker heat treats his own blades and he does not notice a definite increase in stiffness after heat treating, he had better check his own process; it's not working correctly! More on colossal heat treating errors.

Below, I'll show you (and anyone who wishes to understand this) how to actually experience, see, and measure the dramatic differences in stiffness and elasticity of hardened and tempered steel depending on treatment.

When questioned if hardness changes the elasticity of steel:

"I believe it will change. Young's modulus has its origin in the nature of bonding including interatomic distances. In case of the heat treatment you have referred to that is quenching for hardening of steel it is martensitic transformation which leads to hardening. Martensitic transformation leads to trapping of carbon in the ferritic(martensitic) lattice and thus leads to larger interatomic separation as compared to diffusional transformation leading to formation of equilibrium ferrites. Therefore, there must be difference between Young's modulus of the steel in annealed condition (equilibrium ferrite) and hardened condition (martensite)."

"By how much? I have not seen a literature answering this. This difference is indeed of consequence when modeling mechanical behavior of a structure having annealed and hardened regions, like in case of weld joints. Unfortunately, this aspect has been neglected thus far and needs attention to improve accuracy of the computed results. In one of my experiments with the steel I work with I observed ~ 10% difference. However, it was a single experiment and I cannot publish this without having sufficient statistics. However, there is indeed a difference as suggested by the theoretical consideration as well as experimental observation, though the experimental observation needs to be reinforced with more experiments."

--Santosh Kumar, Bhabha Atomic Research Centre

Mr. Kumar makes a good point, in not seeing the literature answering this. Would it surprise him to know that the difference is much more than 10%?

Mistakes and lies about elasticity by knifemakers:
  • "The amount of force needed to flex steel doesn't change in different hardnesses; it's only about the geometry."
    This is absolutely untrue. The amount of force to produce a given deflection (stress to strain) varies considerably at different hardnesses given a fixed geometry. This factor is the modulus of elasticity and it varies greatly depending on the condition and hardness of the steel.
  • "Elastic modulus is controlled by the interatomic bonding forces and not microstructure; therefor it does not change"
    This is absolutely untrue. Junior high level physics textbooks present interatomic forces as the cause for basic elasticity as a means for young minds to understand forces. Crystallography is much more complex. The elastic modulus is a definable, measurable factor (a number), and not a simple concept (an idea). The crystalline structure of steel varies the elastic modulus and this is determined by actually measuring it, not just claiming that it's a fixed atomic force. By the way, the entire crystalline structure varies, as does the atomic, molecular arrangement of steel with varying conditions and allotropes.
  • "The elastic modulus only varies by a small percentage and is not relevant to knife blades."
    This is absolutely untrue. A difference of 5% to 20% or more of elasticity (or stiffness) in knife blades can be easily felt, and the control of the stiffness of a knife blade is absolutely the responsibility of the knifemaker, just like the hardness, the toughness, the steel choice, the finish, the corrosion resistance, and the handle, fittings, sheaths, and accessories. Why would a knifemaker tell a client the stiffness of his blade doesn't matter?
  • "Young's Modulus of Elasticity is basically the same for all steel, about 30,000,000 psi."
    This is absolutely untrue and laughably ridiculous. 30 MSI, or 30,000 KSI is a generalized modulus of elasticity for low alloy, structural steels. Steels vary tremendously by their type in all properties, including the modulus of elasticity. Note the chart below for common A36 structural steel, which varies from 30,000 KSI to over 90,000 KSI depending on its condition—and that's just one steel type! While a generalized figure of 30 MSI is accepted for most calculations, this is not the specific reality.

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The Truth

The truth is not so difficult to understand. If you have read my "Heat Treating and Cryogenic Processing of Knife Blade Steel" page, you'll realize that tremendous transformational changes occur not just in steels that have been heat treated, but also in steels that are finished at different hardnesses by changes in tempering.

One of the reasons I started making knives four decades ago was due to my interest in heat treating—that a piece of steel could be tremendously harder (or softer) than a piece of steel that was cut from the same bar. The difference in heat treating creates astounding changes, and these changes mostly occur while steel is in a solid state. Let's look at some simple manufacturing methods and data to get a deeper understanding of how elasticity, springiness, flexibility and the modulus changes depending on the material condition.

Spring Manufacturing

The professionals who manufacture springs have a real jump on the idea of elasticity. Sorry for the bad pun, but really, if you are one of the people who insists that a spring at 60 HRC has the same elasticity as a spring at 52 HRC, why would spring makers temper the springs back at all? Why not leave them at high hardness, since they will be less subject to wear? You might answer that high hardness means more brittle, and that the spring would break, and you would be correct.

Conversely, if the modulus of elasticity remains the same no matter the hardness, why not leave the springs fully annealed? That way they are not brittle, are very tough and unlikely to ever fracture. The truth is, annealed springs would lack elasticity! Springs are carefully hardened and tempered for a desired combination of elasticity, hardness, and toughness.

Springs are made in a variety of ways, and while most are hardened and tempered, some of them are work-hardened (strain-hardened). Work hardening is compressing and forcing the metal to have many interrupted dislocations. The more dislocations are pinned, tangled, and stopped, the stiffer the spring is! What? How can that be—when steel is supposed to have fixed elasticity independent of treatment?

It's common professional spring manufacturing practice to vary the hardness of springs by heat treatment, tempering, and strain-hardening to various degrees to attain the desirable "springiness" or elasticity of the steel. What is critically important is the crystalline arrangement and dislocations, which dramatically depending on the final temper!

Right there, the whole argument for fixed elasticity is erased. Just look at how springs are manufactured, and it will be clear that the combination of forming, heat treating, tempering, and working changes the spring to vary the elasticity. Elasticity of steels is not fixed at and changes with hardness.

Steel Manufacturers and Foundries

If Young's modulus of elasticity does not vary in any particular steel type, why is it that on nearly every comprehensive data sheet about every modern steel, there is often a chart detailing a range of modulus of elasticity that varies depending on the heat treatment method? Why do these numbers vary depending on the treatment? Why do knifemakers (particularly) ignore that variations in heat treatments produce substantially different elasticity in these steels, even when the manufacturer details this to the exact KSI or MPa? While it's sad that most "one-page" data sheets throw out the generalized 30MSI modulus, upon closer examination and inquiry, more detailed data exists, even though many steel foundries and suppliers do not include it.

Knifemakers will discuss grain irregularities to the angstrom (they have no idea, no electron microscope, but do this on forums continually), all the while ignoring what the steel foundry has actually charted on their more detailed steel data documents. Good grief, if the steel maker can tell you how to vary the modulus, are knifemakers calling them liars claiming the modulus doesn't change?

Metallurgical Studies

Here's a simple study, with a fairly common steel. This was presented in the Journal of Material Science and Engineering, published January 31, 2016, titled: "Analysis of Mechanical Behavior and Microstructural Characteristics Change of ASTM A-36 Steel Applying Various Heat Treatment" by Hasan MF, Department of Industrial Engineering and Management, Khulna University of Engineering and Technology in Bangladesh.

This is just one singular study; there are many like this, easily available for investigation on this vast knowledge base called the internet. It's interesting to note that this particular study is peer reviewed and frequently referenced by hundreds of metallurgical scholars, so this is not some transitory document.

The study details treatment of a common structural steel. This is not a high alloy steel, it's A36, a mild carbon structural steel. It's important to note that high carbon alloys will demonstrate even a wider range of changes. Note carefully the drastic, proven change in Young's Modulus depending on the condition and treatment of this common steel type in the column in red.

WHAT? I thought that the modulus never changes! And this is no small change! From the lowest value (annealed) to the highest value (hardened) is a variation of 304%! What? How is this even possible?

It's simple, really, it happens because of the differences in allotropes. From ferrite and cementite (pearlite) to austenite, to martensite, to ferrite/austenite/martensite/bainite combinations (with carbides): these are all drastic changes in the material, the crystalline structure, the arrangement, the density, the dislocations, and the overall properties. Even the final size of steel varies depending on the treatment, due to allotrope change!

Simply put, actual studies demonstrate a substantial change in the Young's Modulus and the elasticity of steel, depending on the heat treatment and condition! How could this be denied?

Mechanical Properties of A36 Steel
Heat Treatment Tensile Strength
MPa (KSI)
Hardness
(in BHN)
Yield Strength
MPa (KSI)
Young's Modulus
GPa (MSI)
Untreated 402.45 (58.37) 69.8 220.03 (31.91) 207.88 (30.15)
Annealed 389.34 (56.46) 62.15 212.54 (30.83) 302.32 (43.85)
Normalized 452.13 (65.57) 120.36 242.26 (35.14) 288.12 (41.77)
Hardened 734.32 (106.50) 293.4 278.11 (40.34) 632.47 (91.73)
Tempered 421.76 (61.17) 100.01 232.78 (33.76) 293.63 (42.59)

I don't know how much more clear this could be. Yet many knifemakers and even some engineers and metallurgists claim that Young's Modulus is fixed, independent of hardness and treatment. Wow.

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When questioned if hardness changes the elasticity of steel:

The Young modulus is generally weakly influenced by point and line defects. However, as mentioned by Santosh, it might change because of phase transformations. For instance, in the annealed state, the microstructure consists of alpha ferrite and cementite while the as-quenched microstructure may be fully martensitic. Because these different phases have different elastic properties, the young modulus may change during a heat treatment.

Serra Topal, Gazi University


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The Origin of the Confusion about Elasticity

The origin of this misplaced, incorrect, and persistent idea (that elasticity is fixed) is a bit obscure. There will be many arguments here; I'm sure I'll get plenty of hate mail for stating the simple fact that the springiness of steel changes depending on the heat treatment, hardness, and condition of the steel—even though it's easily proven.

To determine where this misunderstanding comes from is just conjecture, but I'll do my best to explain where I think it originates. If you disagree, please don't write me, because I'm not willing to carry on endless chatter about what is an easily provable physical property of steel that I've seen over and over again, on every knife I've made in the last 40 years. Write instead to the President, and insist that this physical property (variation in elasticity) is something you're sure doesn't exist, and force him to change all steel currently in use so that it will conform—

If you refer to most advanced physics textbooks, it quickly becomes clear that elasticity is not a simple property. In an effort for young minds to understand, beginning physics books at high school level and introductory college level display crystalline atomic forms as a stack or square of balls on springs. They explain that these springs represent interatomic forces, and by stretching them or compressing them, you get elasticity. Since the springs (atomic bonds) don't change, the springiness doesn't either.

The reality of crystalline arrangement—particularly of steel—is much more complex. Stress-strain relationships of every crystal type are very different, and various arrangements become tremendously complicated. Pick up an advanced materials properties text, and you'll find yourself trying to solve six simultaneous equations and determinants, just for a single cubic crystal. But wait, the crystal is tetragonal and it's bent, and it's not aligned with other crystals in the steel. Then there are all these complex carbides interfering with force and strain location. And then there are the dislocations knotted up and pinned every which way...

This is not easy to grasp, so basic beginning physics concepts are chosen because they are simple to understand. These rudimentary models are repeated, and the simplest idea, though incorrect, seems good enough for most people.

Another idea is often repeated. Some knifemakers claim that if there is a change in elasticity, it's so small that it doesn't make any difference. I've seen this idea pop up recently, as more and more logical people question the false idea that elasticity in steels is fixed and independent of hardness. They claim that the tiny difference in elasticity isn't enough to notice.

They probably get this idea from the scope of structural engineering. Truly, if an I-beam with an 8" thickness is used to build a skyscraper, you won't notice a change in elasticity in a 20 foot length. However, structural steel is usually a high strength-low alloy steel, and not a piece of tool steel. A knife is not a structural member; it's a thin, narrow and lightweight piece of hardened steel. You will notice a 10%-15% change in flexibility, particularly if the blade is properly, thinly ground. Of course, most beginning knifemakers make big, thick, wide, blocky blades and they won't notice the difference no matter how their blades are treated!

The reality is proven by actual testing. Knifemakers seldom test their products, and this is a real shame. Test next!

When questioned if hardness changes the elasticity of steel:

"Technically, young's modulus depends upon the inter-atomic force vs. displacement profile. Heat treatment, which does not change the lattice structure, actually should not affect the modulus. If there is a transformation to martensite or other phases, yes it should change. But a simple heat treatment with no phase change should not affect the elastic constants.

--Hariharan Krishnaswamy, Assistant Professor at Indian Institute of Technology, Madras

Read carefully Dr. Krishnaswamy's quote above. It's clear that when heat treatment does not change the lattice structure, there is no change in the modulus. However, steel has dramatic and significant crystalline lattice structural changes (phase changes) not only in hardening and tempering but also at different final tempers! Because the lattices (and phases) are changed, the elastic modulus changes. Simple enough!

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The Test (Prove it to Yourself!)
Elastic Deformation Test

Here is a very simple, clear, and logical test that can be performed with a minimum of equipment and instruments. This test will absolutely prove that the elasticity of steel changes depending on the hardness. If you don't believe it, please do not write me. Do this test yourself and you will be absolutely convinced of the facts.

I did the elastic deformation test with O1 high alloy tool steel (photos below). I chose O1 because it's readily available, and is a good and common steel for knife blades and cutting tools. The same test could be accomplished with other steels. I did the test in conventional heat treatment method, with no cryogenics, because I wanted it to be simple, and others to be able to do it without cryogenic equipment. This is a standard, conventional heat treatment. I'm assuming that if you are a knifemaker, you have an accurate furnace, a hardness tester, and accurate measuring apparatus (calipers, electronic contact centering tool, height gauge and some standard weights help). Precision is important. So is repeatability. I repeated the test three times with three different samples at two hardnesses to eliminate any error. In other words, I used multiple gauges (pieces) and repeated the test 18 times to eliminate any slight variables or discrepancy. The results are remarkably consistent.

  1. Start with standard, precision ground 1/8" (0.125") diameter drill rod of O1, fully annealed. This is common in MRO and steel supply companies, and is very accurate in size.
  2. Cut all pieces from the same piece of rod for uniformity. Cut six pieces about 6" long. Dress one end square, using a 90° table and disc grinder or similar method. Mark three of the rods and leave three others unmarked. Do this with a file mark near the end that is not squared off.
  3. Bundle the pieces together with stainless steel wire, keeping each separated. This can be done in a "ladder" fashion. This assures that all of the rods receive the same heat treatment, while being uniformly exposed to heat and quenching.
  4. Harden the bundle. You must use a furnace; a torch is not accurate enough. Follow standard conventional heat treatment hardening process from the manufacturer: heating to austenitizing temperature and quenching in pre-heated oil.
  5. Separate the bundle of hardened rods. You may wish to test them, to assure uniformity of hardness. Do this with a Rockwell hardness tester. They should all be within one point of each other. Mine did not vary even a single point.
  6. Temper the three marked rods at 60 HRC, and temper the three unmarked rods at 55 HRC. Use an accurate tempering oven, not a torch or home oven. You need precision. Don't bother with multiple tempers, a single simple tempering cycle will give clear results. Test the hardness of all of them for certainty.
  7. After tempering, you have your test pieces. These will be clamped horizontally, individually, in a uniform clamping vise. This is important. I used a cam-lock vise with a v-notch, which applies even, uniform pressure at the same point. A stop of some type is necessary, so that the exact length of rod extends from the vise jaws for every test. I used a 4" length extending past the vise, using an accurate caliper as a stop. Make sure the marks (notches or scribe marks) are on the end in the vise jaws, therefore they will not influence the test.
  8. Set up a plate or stand below the end of the rod or measure above a granite surface plate using a height gauge. See photos below for my setup. Accurately measure the distance from the base to the rod. In other words, measure how high the end of the rod is. For greatest accuracy, I used an electronic contact indicator and a height gauge. This means that when the gauge electronically contacts the rod, a measurement is taken. This prevents any variation of measurement from the gauge pressing on the rod and moving it. Log this measurement. Leave the rod in the vise for the next measurement.
  9. Fashion a hanger with an eye that slips over the 1/8" rod attached to an accurate weight. I used an 8 oz. standard from scale weight kit. Using a caliper or length gauge, place the weight exactly three inches beyond the top vise jaw. Make sure this measurement is accurate to one thousandth of an inch, using a caliper.
  10. Now measure the height of the rod with the electronic contact indicator. It will be lower, since the weight pulls it down. Log this measurement.

And that is the test!

Repeat it with all three rods at the two different hardnesses. Repeat it three times for each rod by taking the rod out of the vise, rotating it around its axis (not end to end) and placing it back in the vise. This assures that any variation in the grain structure of the rod will be eliminated (there was none in my test rods). This will assure consistency. Just make sure that you clamp the rod, get an unstressed height and then immediately measure with the weight (stressed). If your deflection (bending) varies more than two thousandths of an inch from previous measurements of the same rod and same deflection (with or without the weight), then repeat the test to improve your accuracy. You'll find that once you set it up, it's surprisingly consistent no matter how the rod is oriented about its axis in the vise. Using the logged measurements, calculate the difference in height of each rod with the weight and without.

Please click on thumbnail photos
Elastic deformation test of hardened and tempered O1, gauge neutral
Elastic Deformation Test, Neutral Stress
Elastic Deformation test of O1 hardened and tempered rod, detail of height measurment and electronic contact indicator
Elastic Deformation Test, measure, indicator details
Elastic Deformation test of O1 hardened and tempered rod, with 8 oz. displacement weight
Elastic Deformation Test, 8 oz. Stress

Here is what you will find. The rods that are harder (at 60 HRC) deflect less than the rods that are softer (at 55 HRC). With the same weight, in the same location, they are stiffer and deflect less. How much less? My experiment proved that it was between 13-13.5% Yes, the test varied less than half a percent with six samples and 18 tests.

Thirteen percent is a lot. You might not think so, but it is substantial. And this is with conventionally treated O1, not annealed vs. hardened, not cryogenically treated, not multiple tempered: simply conventional treatment. As one engineer told me, "13 percent doesn't seem much, but cut off 13 percent of your body (any part) and see how that changes things."

Okay, that's a bit dramatic; we're not talking about pruning; we're talking about flexibility. So imagine this: if a 6" long blade of a fillet or boning knife flexes 1.5", the change in heat treatment can mean an increase in flexibility to 1.75" at the same force. This may not seem like a lot, but to the knife user it is substantial. It will dramatically change the feel and the flex of the blade. Imagine what will happen if the temper is knocked back to 53 HRC or 50 HRC.

If the aim is to reduce the flexibility and increase stiffness, know that a blade that flexes 1/16" inch at the tip at a lower hardness may be stiff enough at higher hardness to have undetectable movement at the same force. And that is stiffer indeed!

When questioned if hardness changes the elasticity of steel:

"From a physical point of view, the Young modulus of a metal is linked to the second derivative of the atomic potential energy curve, so by the stiffness of the atomic bonding. Each atom or couple of atoms have its own stiffness. Then if you add to a steel solid solution atoms (for instance W) with a higher stiffer bonds, you will increase the Young modulus of your steel.

In addition, the presence of different phases (with different Young modulus) will change the modulus of your material and in a first approximation you may evaluate this change by the rule of relative amounts. Higher content of a stiff (high modulus) phase you have, higher will be the modulus of the material.

With this two ideas, you may consider that when doing a thermal treatment you are changing the amounts of solid solution atoms (which will precipitate), as well as the amount of precipitated phases. Consequently, depending on the involved atoms and phases the final result of your material (steel or other) will undergo a change of the Young modulus.

There is another last factor that you have to consider. Dislocations contribute to an easy deformation of the material and so they can start moving at low stresses and giving you a lower slope on the stress-strain curve. Be careful because strictly this is not a change of the modulus value, but a softening of your sample which exhibit a very low micro-yield point. However dislocations can also contribute to a decrease of the intrinsic modulus because around the core of dislocations there is an increase of the interatomic distances, which have associated a decrease of the stiffness of the atomic bonding and consequently of the modulus of the material at local scale. So if you have a strongly deformed material (high density of dislocations), you may have a slight decrease of the modulus, in spite that you could have a hardening of the material (increase of the yield point) by work-hardening. Pay attention because there are two different concepts.

Nevertheless, in most of cases, a high hardness is obtained because of the precipitation of hard and stiff phases, as well as because of blockage of dislocations by strong point defects interaction (usually weight atoms) and in those cases you will have also an increase of the modulus. If the value of the Young modulus is a critical parameter for you computation by FEA, I recommend you to ask some colleague to measure the real modulus of the samples by a vibrating resonant equipment. The resonance frequency of the sample will give you a more reliable value of the modulus than the stress-strain curve. I hope that my answer could be useful for you."

Jose San Juan, Materials Science, Condensed Matter Physics, Materials Physics Professor
Universidad del País Vasco / University of the Basque Country, Public university in Leioa, Spain

Dr. San Juan clearly explains the resultant change in elasticity or stiffness of steel at various hardness and tempers. Steel does change depending on the hardness and crystalline structure, and the only way to know how much is to measure it! Simply claiming the stiffness and elasticity is fixed in heat treated steels is incorrect.

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Conclusion

If you have read this far, you might realize what is presented on forums and discussion boards by well-meaning people may not be correct. There are some of them who, upon reading this will realize that they have been in error in claiming that the steel property of elasticity does not change depending on hardness or condition. There are some who will stubbornly disagree, and fiercely defend what they believe to be true. I've seen this all my career, and some people just refuse to learn or change.

If you question what you read here, I encourage you to begin testing yourself. It's very simple, logical and completely within the skill set of most knifemakers. Before you accept a premise, from me or anyone else, please consider their logic, their education, and their experience, and then try it out for yourself!

It's fun, it's clear, and your results will add to the understanding of steel properties in knife blades and we always appreciate more actual data!

At the very beginning of this page, I presented two scenarios and now I'll present the solutions.

  1. A knifemaker wants to build a fillet knife. He wants it very flexible, with the most movement against the least force—springy. He knows he must achieve a balance between hardness, toughness, and wear resistance, and yet, he wants it as springy as possible. How does he heat treat the blade to achieve the maximum springiness, or elasticity?
    Answer: after performing the optimum heat treating specified by the steel type, start with a mid-range temper, knowing that flexibility is important. Start with HRC 56 (for most hypereutectoid stainless steels) and see how the knife blade feels after final temper. If it steel feels stiff, it can be tempered again, at a higher temperature, to achieve a lower hardness. It does not hurt to temper steel over and over again until you get the feel of the blade that you desire. Of course, a lower temper cannot be raised without complete heat treating repeated, but you can continue to slowly lower the temper in steps. If HRC 55 is still stiff, shoot for 54, or 53. Just don't go too soft, or it will be springy and you'll lose too much wear resistance. Flex the blade and feel the blade.
  2. A tactical knife client needs high stiffness in his blade. The blade must be extremely tough, yet remain as rigid as possible in order to support the point while the highest possible thrust force is applied. How does the knifemaker insure the highest possible stiffness?
    Answer: Choose a hypereutectoid steel that is high in toughness, one with plenty of chromium and molybdenum or niobium. Harden using a premium process—cryogenic is best. Multiple temper for high hardness, and make sure that you leave plenty of thickness at the point geometry to support increased force. Handle the knife well (with strong bolsters and substantial handle material) and have a knowledgeable tactical knife user take it to the field and push the knife to its limits. If the point breaks, make another knife, lower the temper slightly. Don't sacrifice point geometry by making the edge and point thinner; it won't penetrate as well. Test and refine, test and refine.

Both of these scenarios I've had presented in my career, that's why I've cited them here.

Thanks for reading, and thanks for helping stop misconceptions, falsehoods, and wives' tales in our profession. My apologies to wives, everywhere!

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