GENG2004 - Lecture 6

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GENG2004 - Lecture 5
Measuring Mechanical Properties - Slides

Measuring Mechanical Properties

• @ Review: Elastic Properties of Materials

  

• ! Slides explain how these constants are found through experiments

Experimental Measurement

Material constants are obtained through testing:

• Tensile/compression test → $E,\text{upnu}$
• Shear/torsion test → $G$
• Hydrostatic compression → $K$

As an engineer, it is important that we understand how these properties are obtained, as in the future if you are using a new material, you will need to be able to determine its properties through experimentation.

Skills you will need as an engineer:

• Designing experiments intentionally
• Keeping them simple (1 variable ideally)
• Knowing all your variables:
  • Independent variables
  • Dependent variables
  • Controlled variables

Static and Dynamic Loading Conditions

• Static loading $-$ slow, constant application of load
• Dynamic loading $-$ very fast application of load
  • Time which the sample is loaded is comparable with time of elastic wave propagating through the sample
    • Size is known
    • Wave propagating velocities are known
• ! Materials behave differently depending on loading speed

Characteristic Points of Stress-Strain Curve

Recap: Understanding Deformation Behaviour & Mechanical Properties

• True stress $-$ actual cross-sectional area of sample used to find stress
  • Shrinks during loading, more physically accurate
• Nominal stress $-$ initial cross-sectional area of sample used
  • Used in solving problems

Through deformation of most material, the true stress will shrink as necking occurs; you can observe this in photographs in the slides

• OA $-$ linear elastic region
  • Straight (linear) line
  • Stress $\propto$ strain
  • This is the area where Hooke’s Law applies
    • Slope of OA is the Young’s Modulus
    • Past this point, equations fail

Point A $-$ proportional limit

• Beyond A, proportionality between stress and strain no longer exists

• AB $-$ non-linear region (elastic → plastic transition)

  • Curve bends
  • Material starts behaving differently internally
  • Some part still elastic, some part permanently deformed

Point B $-$ Yield Point

• The corresponding value of stress is known as yield stress

• Yield stress = yield strength → we do not want to exceed this point

• BC $-$ perfectly plastic region (yielding)

  • Strain increases, stress stays constant
  • Material is deforming without extra load

• CD $-$ strain hardening

  • Stress increases again
  • Crystalline structure changes
  • Increased resistance of material to further deformation

Point D $-$ Ultimate stress

• Maximum stress reached → known as ultimate strength
• Further stretching → results in failure at point E or E’
  • Necking occurs reducing area significantly
• Fracture point is known as failure stress

In real engineering design, we must ensure:
${\sigma }_{working}<{\sigma }_{yield}$
This is to avoid permanent deformation

As engineers, we can use the curve in order to choose an appropriate material depending on the circumstance:

• The curve indicates both strength (yield stress) and stiffness (slope)

Offset Method

• Some materials have no clear yield point
  • However, they have initial linear region
• An arbitrary yield stress may be determined using the offset method

Method:

1. Take linear elastic slope
2. Shift it right by a small strain:
   $ϵ=0.002(0.2\%)$
3. Where new line intersects the curve → offset yield stress

Elastic vs Plastic Behaviour

• Elastic limit is the max stress a material can withstand without experiencing permanent deformation
  • Elastic limit usually same or slightly above proportional limit
• Plasticity $-$ ability of a material to undergo permanent deformation
  • Plastic flow occurs when large deformations occur in a ductile material loaded into the plastic region
  • Material structure permanently changes

Non-linear Behaviour

• Stress-strain curve depends on the material

  

Creep

• Stress/strain also depends on time
  • Recap: ENSC1004 - Creep
• Strain increases overtime under constant stress

Relaxation $-$ decrease in stress over time under constant strain

Fatigue

• Fatigue is failure due to repeated loading cycles
  • Material can fail at stresses much lower than ultimate stress
  • Shown using a $\text{upsigma}$-N curve: stress vs # of cycles
    
• Endurance limit is the stress for which failures do not occur
  • Even for indefinitely large number of loading cycles
• Recap: Failure by Fatigue

Materials such as aluminium and copper have no endurance limit meaning they will always fail eventually

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GENG2004 - Lecture 7