There is one thing about Young's modulus that I find unexpected and confusing.

When certain solid materials, pure metal, steel or an alloy of a certain composition, gets strengthened by cold working or by heat treating, the Young's modulus stays exactly the same as before even though the yield strength of that material gets doubled, and the elongation gets reduced by an order of magnitude.

Take maraging steel 350 for example. Annealed yield strength = 830 MPa ... Annealed elongation = 18% ... Annealed Young's modulus = 190 GPa

Aged yield strength = 2300 MPa ... Aged elongation = 4% ... Aged Young modulus = 190 GPa

This seems crazy to me. Strength triples and elongation is reduced to less than a quarter, yet the Young's modulus doesn't change one bit? I don't understand.

If the definition of Young's modulus is the ratio between stress and strain, when steel after aging gets 300% stronger, and that strength is achieved at 20% elongation, how could the Young's modulus possibly not get massively changed too?


It's important to distinguish between two very different regimes when considering the stress-strain behavior of metals: (1) The elastic regime and (2) the plastically deforming regime. When relatively small stresses are applied to metals, they tend to behave elastically. If you apply a stress it bends a little, and if you then remove the stress it goes back to its original position. Elastic properties of metals depend on the elemental composition of the metal, but they tend to be insensitive to the microstructural details of the metal. Things like dislocations (produced by work hardening a metal) or fine precipitates (which can be produced by age hardening the metal) don't affect the elastic properties of metals like the Young's modulus much since they tend to be a relatively small volume fraction of the overall volume of the metal.

So the question is really why do these microstructural details become so important when the metal starts to plastically strain? When the stress on a metal becomes large enough to plastically stain it, we enter into a very different regime in which the material is undergoing large deformation which is enabled by the movement of dislocations through it. When this starts to happen, then all those little microstructural details in the metal such as grain boundaries, pre-existing dislocations, and fine precipitates become very important because they all act to block the smooth flow of dislocations through the metal. As a result, more stress has to be applied to the metal in order to overcome the dislocation barriers and make the metal plastically flow. That's why work-hardening and precipitation hardening (i.e., "age hardening") are so effective at increasing the yield strength, which is a measure of the stress required in order to make the metal plastically deform.

Bottom Line:

Elastic Properties (e.g., Young's modulus, Bulk modulus, Poisson's ratio) depend on the elemental composition of a metal but are insensitive to the microstructural details of a metal.

Plastic Properties (e.g., Yield strength, tensile strength, elongation at maximum yield) are sensitive to the microstructural details of a metal (e.g., grain boundaries, pre-existing dislocation bundles, fine precipitates) because these microstructural features can block the movement of dislocations through a metal which enable the metal to plastically deform.

  • $\begingroup$ While I found your answer full of good information,pardon my noobiness but I still dont understand it.I feel your answer have good stuff in it,just not exactly on topic,or the kind I need to understand it,or maybe I am just stupid.Same Young modulus value means for given stress,the material will strain exactly same,that seems impossible to me when the aged alloy is much stronger,how can something stronger deflect or bend exactly same amount as weaker alloy for same force applied,especially considering the stronger alloy have much smaller elongation before break. $\endgroup$ Mar 23 '18 at 5:35
  • $\begingroup$ @wavscientist Young's modulus is about the bonds between neighboring atoms. With an elastic strain, all bonds in that direction are proportionally longer or shorter. $\endgroup$
    – user137289
    Mar 23 '18 at 6:39
  • $\begingroup$ @wavscientist - The Young's modulus is an elastic property. It is only meant to describe the stress response of a material for relatively small stresses. When you talk of the (yield) strength of an aged alloy, you are talking about the behavior of the material in an entirely different (and higher) stress regime. The yield strength is a measure of the amount of stress that a material can withstand before it starts to show significant plastic strain. $\endgroup$
    – user93237
    Mar 23 '18 at 6:53
  • $\begingroup$ Isnt Yield strenght at the end of elastic region? I know its upper extreme,its on the edge,but its in that linear elastic region,the small stress region as you call it.... Pieter what do you mean all bonds are proportionaly shorter? Isnt yield strenght and aging about bonds between atoms too? $\endgroup$ Mar 23 '18 at 7:54
  • $\begingroup$ @wavscientist - No, the yield strength is not "in" the linear elastic region. Rather, it marks the boundary between elastic behavior and plastic behavior. $\endgroup$
    – user93237
    Mar 23 '18 at 16:48

Here’s a diagram relating pre and post aging performance:

pre vs post aging pre vs post aging performance

For that material, you can see how yield point elongation decreases while the slope of the linear part (modulus) doesn’t change much.

  • $\begingroup$ Does thar graph say that for given stress,the strain is same for both unaged and aged material when its within elastic range of the unaged material? $\endgroup$ Mar 23 '18 at 4:57
  • 1
    $\begingroup$ @wavscientist yes, it does. That linear section is the part where Young’s modulus is meaningful. That’s why it’s basically the same. $\endgroup$ Mar 23 '18 at 18:47

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