materials characterization. learning objectives identify compressive and tensile forces identify...

Materials Characterization

Learning Objectives

• Identify compressive and tensile forces

• Identify brittle and ductile characteristics

• Calculate the moment of inertia

• Calculate the modulus of elasticity

Elasticity

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

• Example: rubber bands

Elastic Material Properties

Unstressed Wire

Apply Small Stress

Remove Stress and Material Returns to Original Dimensions

UnstressedBottle

Inelastic Material Properties

Bottle UndergoingCompressive

Stress

InelasticResponse

Compression

• Applied stress that squeezes the material

• Example: compressive stresses can crush an aluminum can

Compression Example

Unstressed Sponge Sponge in Compression

Compressive Failure

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

Tension

• Applied stress that stretches a material

• Example: tensile stresses will cause a rubber band to stretch

Tension Example

• Steel cables supporting I-Beams are in tension.

Tensile Failure

• Frayed rope

• Most strands already failed

• Prior to catastrophic fail

Tensile Failure

• This magnesium test bar is tensile strained until fracture

• Machine characterizes the elastic response • Data verifies manufacturing process control

Force Directions

• AXIAL: an applied force along the length or axis of a material

• TRANSVERSE: an applied force that causes bending or deflection

Force Direction Examples

Axial Stress on the Vertical Post

Transverse Stress on the Horizontal Aluminum Rod

Graphical Representation

• Force vs. Deflection in the elastic region

0

5

10

15

20

25

0 5 10 15 20

Deflection, y (in x 0.01)

Steel Beam Data

Linear Regression

Yield Stress

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

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

Ductile Example

Unstressed Coat Hangar

After Applied TransverseStress Beyond the Yield

Stress Point

Brittle Response

• Just beyond the yield stress point, the material immediately fails

• Example: plastics and wood

Brittle Example

Unstressed Stick

Brittle Failure After Applied Stress Beyond the Yield Stress Point

Brittle and Ductile Response Graphs

0

5

10

15

20

25

0 15 30 45 60

Deflection, y

Ductile Response

Brittle Response

Failure

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

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)

2r

b

12bh3

____

4____π r4

h

Modulus of Elasticity

• Quantifies a material’s resistance to deformation

• Constant for a material, independent of the material’s shape.

• Units are in force / area. (PSI or N/m2)

• Symbol: E

Flexural Rigidity

• Quantifies the stiffness of a material

• Higher flexural rigidity = stiffer material

• Product of the Modulus of Elasticity times the Moment of Inertia (E*I)

Calculating the Modulus of Elasticity

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

0

5

10

15

20

25

0 5 10 15 20

Deflection, y (in x 0.01)

Steel Beam Data

Linear Regression

_______48EIL3

Slope is 1.342 lb/in

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.