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DoITPoMS Teaching & Learning Packages Introduction to Mechanical Properties of Materials Plastic deformation: strength and ductility
Introduction to Mechanical Properties of Materials AimsBefore you startIntroductionTensile test: force and extensionStress, strain and Poisson's ratioElastic deformation: Hooke's law and stiffnessViscoelasticityPlastic deformation: strength and ductilitySlip: resolved shear stress and Schmid factor, Taylor factorHardness and work hardeningCreepFracture: toughnessDuctile-brittle transition temperatureSummaryQuestionsGoing further
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Plastic deformation: strength and ductility

nominal stress strain curve

Figure 10. A typical nominal stress and strain curve for ductile metal

Let’s come back to the stress-strain curve given by the tensile test and focus on the region beyond a certain stress limit, where the material cannot recover to its original shape. This onset stress limit for plastic deformation to occur is called the yield strength, \( \sigma_y \).

Sometimes the yield point is not well defined, so we will often measure the stress at which a certain amount of plastic deformation has occurred, called the offset yield strength. Proof stress is the point at which the material exhibits 0.2% of plastic deformation.

Strength is the property that measures a material’s ability to withstand plastic deformation.

Ultimate tensile strength (\( \sigma_u \) or UTS) is the maximum stress that a material can withstand while being stretched or pulled before breaking. \( \sigma_u \) indicates the onset of necking. See details in the Mechanical Testing of Metals TLP.

Failure stress or failure strength. \( \sigma_f \) is the stress at which the sample finally fails.

Ductility is a measure of the degree of plastic deformation that has been sustained at fracture. It can be expressed qualitatively as either percent elongation (%EL) or percent reduction in area (%RA).

\[ \%{\rm{EL}} = \frac{l_{\rm{f}} - l_{\rm{0}}}{l_{\rm{0}}} \times 100\% \]
\[ \%{\rm{RA}} = \frac{A_{\rm{0}} - A_{\rm{f}}}{A_{\rm{0}}} \times 100\% \]

Note the percentage elongation is identical to Strain to failure \( \varepsilon_\rm{f} \), i.e., the total strain of the sample at the point of final failure.

Therefore, to summarise, a tensile test allows us to measure the following mechanical properties:

  • Young’s modulus, \( E \)
  • Yield stress, \( \sigma_\rm{y} \)
  • Ultimate tensile strength, \( \sigma_\rm{u}\)
  • Failure strength, \( \sigma_\rm{f} \)
  • Ductility, as either percent elongation (%EL) or percent reduction in area (%RA)

The plastic behaviour of crystal materials is significantly determined by the linear microstructural defects known as dislocations. Dislocation motion along a crystallographic direction is called glide or slip. For an introduction to dislocation, see here.

Plastic deformation of metals most commonly occurs as a result of the glide of dislocations, driven by shear stresses.

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