lecture02 slides me382 uofm

8/11/2019 Lecture02 Slides ME382 UofM

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ME 382

Lecture 02

Suggested Reading:

A&J-1: 8 (not 8.8); 11.4


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3 Important Terms for Mechanical Design

Stiffness

Strength

Toughness

How arethese

different?


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Tensile test to measure mechanical properties

lo

P

P

cross sectionalarea Ao

1. Measure length and area

2. Pull specimen

Measure load, P

Measure extension, !

But, this curve depends on your choice of specimen .


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Engineering (nominal) stress and strain

Engineering (nominal) stress: !n = P /Ao

(Aois original cross sectional area)

Engineering (nominal) strain: "n = #/ lo(lois original length)


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Nominal stress-strain curve for a ductile metal

Nominal stress (MPa)

Nominal strain

X

neckingbegins

(ultimate)

tensile strength

yield strength(yield stress)

(onset of plasticity)

yield begins

linear elastic deformation

(slope =modulus)

plastic deformation

(movement of dislocations)

fracture


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Other mechanical properties

Measures of ductility:Percent elongation:

Reduction in area:

100!lf - l0

l0

Energy absorption: U= Pd"#

Energy

per unit volume:u = "nd#n$(area under stress strain curve)

(J)

(Jm-3)

100!A

0- A

break

A0

100!10mm- 5mm

5mm=100%

100!10mm- 7mm

7mm= 42.9%

100!10mm

2- 5mm

2

10mm2

= 50%

100!10mm

2- 7mm

2

10mm2

= 30%


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Unloading

Permanent deformation after yield

Note - not the

same slope for

1&2 unless its atrue stress-true

strain curve.

Why?


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True Stress and True Strain

After yield, memoryof original shape is lost

$nominal stress and strain may be meaningless

True strain: d"= dl

l

lis current length

True stress: "=P

AAis current area

"="n1+ #

n

( )

"= ln 1+ "

n( )

(if volume is conserved)


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Work hardening (strain hardening) results in an increase inyield strength - cold work

Often described by power-lawhardening: "= H#n

True stress / true strain tensile curve


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Experimental data for a 5754 aluminum alloy

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

5754 Aluminum alloy

Truestress(M

Pa)

True strain

"= H#n


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1

10

100

1000

0.001 0.01 0.1

5754 Aluminum alloy

Truestress(MP

a)

True strain

!= 367 "0.238~ ~

Determining the strain-hardening parameters

!! = H!!n

ln !! = n ln!!+ lnH


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0

50

100

150

200

250

0 0.02 0.04 0.06 0.08 0.1

5754 Aluminum alloy

Truestress(MP

a)

True strain

power law

experimental data

Comparison of power-law with experimental results

Pretty good!


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There are other forms of uniaxial stress-strain curves.

lecture02 slides me382 uofm

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