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