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Toughness is defined as ability of material to absorb energy when deforming before fracture. Materials with high ductility and strength will have high toughness.

What is meant by ability of material to absorb energy? What kind of energy is absorbed?

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    $\begingroup$ This question is a duplicate of one posted here. Perhaps it is an exam or homework question. $\endgroup$ Aug 3 at 11:45
  • $\begingroup$ @mart I did research, but wasn't able to find an answer on how to connect material ability to absorb energy with its strength and ductility. $\endgroup$ Aug 3 at 12:06
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Usually the method to measure the toughness is either the Charpy or Izod Test. They are very similar and the main difference are the boundary condition of each one (Charpy fixed both ends, Izod: vertical cantilever).

The setup is the following (and the differences) are presented below.

enter image description here

Figure : Charpy and Izod impact testing (source Green-mechanic)

As you can see the setup is very simple. A swing is raised to height $h_0$ and then its left to drop. As it drops the potential energy converts to kinetic energy.

At the moment of impact, some of that energy is imparted to breaking the specimen and as a result the mass will only be raised up to point $h_1$.

Then the fracture toughness is the difference in potential energy ($mg\Delta h$) that was absorbed in breaking the bonds of the material.

  • A tough material will create a larger $\Delta h$
  • less tough material will create a lesser $\Delta h$

UPDATE - Force displacement - strain enery

This is for answering to the comment by Dario. From what I read I think you understand that the area beneath the Force vs Displacement diagram is the work. Below is a figure which compares the two diagrams (Force vs. Displacement and Stress vs strain).

enter image description here

Figure : Force vs displacement and Stress vs Strain (source SE)

AS you can see the shape is exactly the same (see discussion in this question for more details) because:

$$ \sigma = \frac{F}{A} \qquad \epsilon = \frac{\delta L}{L}$$

where:

  • $L$ is the length
  • $A$ is the crosssection.

If you multiply $ \sigma\cdot \epsilon$ you get:

$$ \sigma\cdot \epsilon= \frac{F}{A} \frac{\delta L}{L}$$ $$ \sigma\cdot \epsilon= \frac{F\cdot \delta L}{A\cdot L} $$

However, as you already know:

  • $F\cdot \delta L = W$ ( where W is the work)
  • $A\cdot L $ is the volume (assuming a constant cross-section its easier to envisage otherwise you need to do the integral)

so, the area under the stress-strain curve is equal to the work over the volume:

$$ \sigma\cdot \epsilon= \frac{W}{V} $$

This ratio of $\frac{W}{V}$ is known as (average) strain energy, and its units are $\frac{Joule}{m^3}= MPa$. Essentially (and with a few simplifications to avoid the use of $\nabla$ etc) this is the energy which is absorbed before breaking per unit volume.

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  • $\begingroup$ Yes, this is a method of measuring toughness which I do know. However, it didn't answer question I asked. When material is deformed, work is done to deform it and material absorbs that energy. More ductile material is, more energy it can absorb. However, what about strength? How can we connect strength with ability to absorb energy? $\endgroup$ Aug 3 at 11:56
  • $\begingroup$ @DarioMirić I updated the answer. Hopefully, I understood your question, and replied it in a meaningful manner). $\endgroup$
    – NMech
    Aug 3 at 12:12
  • $\begingroup$ @DarioMirić Metal with higher strength usually is stiffer and brittle than the lower strength counterpart. $\endgroup$
    – r13
    Aug 3 at 13:50
  • $\begingroup$ Thank you. I think I've got it. It is important to know that to deform material, work needs to be done which material absorbs. For example in uniaxial tensile test, work is done by outer tension force of the machine acting on the material sample. If material is strong, it requires a lot of force to break it which increases work done or energy absorbed. If material is ductile, it requires a lot of deformation to break it which increases displacement of the sample from starting point. $\endgroup$ Aug 3 at 14:35
  • $\begingroup$ Nobody who knows what they are doing uses Izod. $\endgroup$ Aug 3 at 15:04
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You make a common mistake; toughness of steel is toughness: not ductility or strength. Charpy is a cheap, easy way to get an estimate of toughness. I generally used it myself , what you really want is K1c, but that is expensive to measure and, ironically can't be measured in very tough steels. The Wikipedia entry for LEFM ( linear elastic fracture mechanics) is very good ; I suggest reading that instead trying to transcribe it here.

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