• Engineering Stress:
  • $S = \frac{F}{A_o}$
    • Units: Pa, psi, etc.
    • $F$ = applied force
    • $A_o$ = original cross-sectional area of sample
• Engineering Strain:
  • $e=\frac{\delta L}{L_o}$
    • Unitless (expressed as percent change)
    • $\delta L$ = change in length of sample
    • $L_o$ = original length of sample
• Loading mechanisms:
  1. Tensile loading
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  2. Compressing loading
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  3. Shearing
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• Poisson’s ratio- the relationship between lateral and longitudinal strain
  • $\nu = -\frac{e_{lateral}}{e_{longitudinal}}$
  • ~0.3 for metals, 0.5 during plastic deformation
  • Means that there is no volume change in a sample since lateral strain is offset by longitudinal strain
  • Negative Poisson’s ratio- only in man-made materials

We rely upon mechanical testing to determine mechanical properties of materials.

• Methods of mechanical testing:

1. Measure load and deformation (tension, compression, or shear)
   1. Simplest method; not possible for brittle materials (e.g. glasses, ceramics)
2. Bending- 3 point, 4 point
   1. For brittle materials
3. Hardness- macro, micro, nano
   1. Measures resistance to plastic deformation
4. Scratch
5. Impact (high strain rate)
6. Cyclic stress (fatigue)
   1. Note: 99% of materials fail under cyclical loading
7. Fracture toughness
8. Extended time stress and strain (stress relaxation and creep)
9. Dynamic loading (viscoelastic properties of polymers)
10. Wafer curvature- stress in thin films
    1. E.g. used on glass in a phone screen

Stress and Strain

• Tensile Test
  • A dog-bone shaped sample is gripped by a moveable crosshead.
  • As the crosshead moves upward, it applies an upward force on the sample, and this induces stress and strain on the sample.
  • The change in distance between two dots on the sample can be tracked to calculate strain. The applied force, which can be determined from a load cell, along with the original cross-sectional area of the sample, can be used to calculate stress.

Terminology from Stress-Strain:

• Young’s modulus/modulus of elasticity (E)- the slope of the linear region of tensile stress-strain diagram; units of GPa
  • Usually the same in tension and compression for metals but is different in tension and compression for ceramics.