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for this question: "What is the difference between strength, hardness and toughness in materials?" i have searched and have found these following definitions

Strength refers to resistance to deformation, and also to a large elastic range. In the Elastic region of the stress-strain relationship, the relationship is described by a linear function, such that σ = E ϵ, where σ is the stress, E is the Elastic modulus, and ϵ is the strain.

Toughness is the resistance to failure or crack propagation. It is somewhat related to strength. Very strong materials will have low toughness, i.e. low tolerance for flaws or defects, i.e. incipient cracks.

Reference https://www.physicsforums.com/threads/difference-between-toughness-and-strength.67220/

i don't understand those definitions. Aren't deformation and failure one? Are toughness, strength and hardness both the ability to resist external forces?

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Strength = Ability of a material to withstand an applied load. There are several different measures of strength. Two common measures are the ability to withstand a load without plastic deformation (yield strength) or without failure (ultimate strength). In the sketch below, Material 1 has higher strength than Material 2. It can carry more load both before deforming plastically and before failing.

Toughness = Ability of a material to absorb energy without fracture. In a stress-strain curve, the area under the curve is often considered a measure of toughness. In the sketch below, Material 2 has higher toughness than Material 1. (I should have drawn them to be more obviously different, but let’s say the area under the Material 2 curve is greater than the area under the Material 1 curve.) So, Material 2 may have a lower strength than Material 1 but it is able to absorb more total energy before failure.

Hardness = ability of a material to resist plastic deformation.

Note that the sketch reflects two hypothetical (imaginary) material curves. Many other stress-strain curve profiles are possible. Also note that the description of toughness presented here is based on general material toughness, which is only one way to assess toughness. There is also impact toughness, notch toughness, and fracture toughness (the NDT resource center offers an introductory discussion of each) but these quantitative toughness measures are outside my personal experience so I won’t attempt to comment on them.

stress strain curve

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  • $\begingroup$ I'll add that strength and toughness can be different depending on direction or plane of loading. Some materials are stronger in compression than tension (concrete). Hardness is usually measured at the surface by trying to make a scratch or indent with another material (a harder rock is able to scratch a softer rock) $\endgroup$
    – EMiller
    Feb 12, 2019 at 20:09
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    $\begingroup$ I want to know how you made that sweet chart. $\endgroup$
    – geekly
    Feb 13, 2019 at 12:51
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    $\begingroup$ @geekly it’s drawn using an iPad pro, apple pencil, and the Autodesk Sketchbook app $\endgroup$
    – CableStay
    Feb 13, 2019 at 12:58
  • $\begingroup$ To learn more about toughness look at LEFM in Wikipedia ( linear elastic fracture mechanics ). The original reference is incorrect ; Very high strength materials may also have high toughness. $\endgroup$
    – blacksmith37
    Feb 13, 2019 at 17:00
  • $\begingroup$ @blacksmith37 The sketch wasn’t saying anything about absolute values of toughness or intending to suggest higher strength materials always have lower toughness relative to lower strength materials. It was merely intended to be a hypothetical illustration. It shows two possible (imaginary) material curves. Of course many other stress-strain curves are possible. I may edit the answer to include that clarification. $\endgroup$
    – CableStay
    Feb 13, 2019 at 17:59
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Hardness is the measure of a material resistance to scratching, like it's hard to drill a hole into, or hard to sand. Or diamond that can cut many surfaces but is hard to cut.

Toughness is the ability of material to resist cracking or breaking under stress.

Strength is the ability of material to withstand great tension or compression or other forces. Like a steel cable that can support great tension.

This properties overlap at certain functionalities.

I have added a diagram that clarifies this more.

digram

And this is link to the site to the site.

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  • Strength = Stress required to produce failure. It is often used to determine how much force an object can take without breaking, but there are many measures of strength.
  • Hardness = Force / Area. The larger the area produced by a given force, the lower the hardness. It can be correlated to, but is not the same as strength.
  • Toughness = Energy required to form a crack. Ceramics have low toughness because cracks form easily.
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