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As far as I understand they both relate to the amount of deformation based on a given amount of stress.

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Materials are usually put into a basket of either being ductile or brittle. Brittle materials usually don't experience plastic deformation whilst ductile materials do. Some materials might then be described as more ductile than others based on some measures and stress conditions like you described. Stiffness is a global phenomenon, and it's a measure of how much deformation (could be non plastic) a material experiences under stress.

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  • $\begingroup$ So if a material is brittle its probably gonna break before being deformed, and if a material is ductile then it will probably deform before breaking? $\endgroup$ Jan 9 at 17:32
  • $\begingroup$ Yeah in really broad terms. Brittle materials undergo usually something called elastic deformation before breaking. Elastic deformation means the material goes back to it's previous shape when load is removed. $\endgroup$ Jan 9 at 17:34
  • $\begingroup$ So if I dropped a cup, which is brittle, out of my window, this would be elastic deformation? Wouldn't it simply shatter into pieces? $\endgroup$ Jan 9 at 17:38
  • $\begingroup$ Yes, some of the kinetic energy would first turn into strain before it breaks. $\endgroup$ Jan 9 at 17:43
  • $\begingroup$ You also risk injuring someone. $\endgroup$ Jan 9 at 17:43
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Stiff and flexible are opposing qualitative metrics in the elastic regime. Under an applied stress, a stiff material will deform less than a flexible material. When the stress is released, both will return to their origin point (no deformation).

Ductile and brittle are opposing behaviors in the failure regime after the elastic behavior has occurred. Under an applied stress, a ductile material will deform permanently while a brittle material will break. Both modes are failure. The transition for ductile materials is the yield stress. The transition for perfectly brittle materials is the failure stress. A second mode of breaking called fracture is not identical to brittle failure. Fracture occurs due to macroscopic flaws in the material.

Here are general examples for the qualifications of elastic behavior (flexible to stiff) versus plastic (failure) behavior (ductile to brittle) across the various classes of materials by chemistry.

  • Metals - flexible to stiff, ductile to brittle
  • Ceramics - stiff, brittle
  • Semiconductors - stiff, brittle
  • Thermosets - stiff, brittle
  • Thermoplastics - flexible to stiff, highly ductile to brittle
  • Elastomers - highly flexible, brittle

As you see, we cannot simply put materials in one basket or another using only the two terms stiff and ductile. The two terms are not opposites in the same way, they are qualitative metrics for behavior in two different regimes (elastic or reversible versus plastic or irreversible).

Finally, elasticity (flexible or stiff) is quantified by the Young's modulus $E$, measured as the stress to cause a specific strain (relative change in length), while ductility is quantified by the relative deformation in the material at breaking after removing the elastic deformation length. For change in length $L$, with final and initial at transition, we write $(L_f - L_o)/L_o$. A material will higher ductility will have a greater relative change in length at the point that it breaks. A material with zero ductility is perfectly brittle but may still have deformed elastically (been flexible). A rubber band is the best example of this case.

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Ductility specifically refers to the condition of yielding (i.e. permanent deformation). Whereas stiffness does not necessarily refer to yield and may refer to elastic deformation.

Something that is stiff may either shatter or yield when sufficiently deformed. What determines whether it yields or shatters is its ductility, or lackthereof.

Gum for example is very ductile, but not stiff at all.

Steel, brass, bronze, and aluminum are stiffer and ductile (though not as ductile as gum).

Carbon fiber and glass is even stiffer, but not ductile at all.

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  • $\begingroup$ Well said! Thank you so much! $\endgroup$ Jan 9 at 22:53
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Picture the stress-strain curve.

Ductility refers to how wide the range of strain, just after the elastic portion. I.e., where you can deform the material without breaking it. Ductility is unequivocally a material property.

Stiffness, at least when talking about the material (without introducing the geometry of the object) is I think synonymous with elastic modulus, i.e. the slope of the elastic portion of the curve.

We also use stiffness when talking about objects, for instance stiffness of a spring, or stiffness of a truss. The qualitative idea in the stress-strain curve then becomes a graph of load vs displacement.

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