Materials Characterization

1
Materials Characterization
2
Learning Objectives

• Identify compressive and tensile forces
• Identify brittle and ductile characteristics
• Calculate the moment of inertia
• Calculate the modulus of elasticity

3
Elasticity

• When a material returns to its original shape
  after removing a stress
• Example rubber bands

4
Elastic Material Properties
Unstressed Wire
Apply Small Stress
Remove Stress and Material Returns to Original
Dimensions
5
Inelastic Material Properties
Bottle Undergoing Compressive Stress
Unstressed Bottle
Inelastic Response
6
Compression

• Applied stress that squeezes the material
• Example compressive stresses can crush an
  aluminum can

7
Compression Example
Unstressed Sponge
Sponge in Compression
8
Compressive Failure

• This paper tube was crushed, leaving an
  accordion-like failure

9
Tension

• Applied stress that stretches a material
• Example tensile stresses will cause a rubber
  band to stretch

10
Tension Example

• Steel cables supporting I-Beams are in tension.

11
Tensile Failure

• Frayed rope
• Most strands already failed
• Prior to catastrophic fail

12
Tensile Failure

• This magnesium test bar is tensile strained until
  fracture
• Machine characterizes the elastic response
• Data verifies manufacturing process control

13
Force Directions

• AXIAL an applied force along the length or axis
  of a material
• TRANSVERSE an applied force that causes bending
  or deflection

14
Force Direction Examples
Transverse Stress on the Horizontal Aluminum Rod
Axial Stress on the Vertical Post
15
Graphical Representation

• Force vs. Deflection in the elastic region

16
Yield Stress

• The stress point where a member cannot take any
  more loading without failure or large amounts of
  deformation.

17
Ductile Response

• Beyond the yield stress point, the material
  responds in a non-linear fashion with lots of
  deformation with little applied force
• Example metal beams

18
Ductile Example
Unstressed Coat Hangar
After Applied Transverse Stress Beyond the Yield
Stress Point
19
Brittle Response

• Just beyond the yield stress point, the material
  immediately fails
• Example plastics and wood

20
Brittle Example
Unstressed Stick
Brittle Failure After Applied Stress Beyond the
Yield Stress Point
21
Brittle and Ductile Response Graphs

22
Moment of Inertia

• Quantifies the resistance to bending or buckling
• Function of the cross-sectional area
• Formulas can be found in literature
• Units are in length4 (in4 or mm4)
• Symbol I

23
Moment of Inertia forCommon Cross Sections

• Rectangle with height h and length b
• I (in4 or mm4)
• Circle with radius r
• I (in4 or mm4)

h
? ?
bh3
____
? b ?
12
? 2r ?
p r4
____
4
24
Modulus of Elasticity

• Quantifies a materials resistance to deformation
• Constant for a material, independent of the
  materials shape.
• Units are in force / area. (PSI or N/m2)
• Symbol E

25
Flexural Rigidity

• Quantifies the stiffness of a material
• Higher flexural rigidity stiffer material
• Product of the Modulus of Elasticity times the
  Moment of Inertia (EI)

26
Calculating the Modulus of Elasticity
48EI
_______

• Slope
• Measure L
• Calculate I
• Solve for E

L3

Slope is 1.342 lb/in
27
Acknowledgements

• Many terms and the laboratory are based a paper
  titled A Simple Beam Test Motivating High
  School Teachers to Develop Pre-Engineering
  Curricula, by Eric E. Matsumoto, John R.
  Johnson, Edward E. Dammel, and S.K. Ramesh of
  California State University, Sacramento.