Transcript Class 1.2 CIVE 2110 Material prop ductile

Class #1.2
Civil Engineering Materials – CIVE 2110
Strength of Materials
Mechanical Properties
of Materials
Fall 2010
Dr. Gupta
Dr. Pickett
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Stress and Strain
Mechanical Properties of Materials
- used to develop relationships between
Stress and Strain.
- determined Experimentally.
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Experimental Determination
of Mechanical Properties of
Materials
Stress and Strain experiments:
A standard specimen of the Material:
- Pulled in Uniaxial Tension.
- Diameter = 0.5 in.
- Gauge Length = 2.0 in.
Or
- a strain gauge is placed
parallel to long axis of specimen
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P
Stress-Strain Diagrams
Conventional Stress-Strain Diagram :
Normal Stress calculated using
ORIGINAL cross sectional area, AO.
Called Engineering Stress.
P  Load

AO
P
Even though cross section decreases, necks down.
Assumes stress is CONSTANT over cross section.
Normal Strain calculated using

  L  LO
LO
ORIGINAL length, LO.
Assumes strain is CONSTANT over cross section
P
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P
Stress-Strain Diagrams
TRUE Stress-Strain Diagram :
Normal Stress calculated using
ACTUAL cross sectional area, Ai, at any instant.
Called TRUE Stress.
P
Because cross section decreases, necks down.
P  Load

Ai
Normal Strain calculated using
ACTUAL length, Li , at any instant.

  L  Li
Li
P
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Stress-Strain Diagram – Ductile Material
Conventional (Engineering)
and TRUE
Stress-Strain diagrams
Differ only in regions of LARGE strain .
P  Load

AO

  L  LO
LO

  L  Li
Li
σ (KSI)
P  Load

Ai
ε (μ in./in.)
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Stress-Strain Diagram – Ductile Material
σ (KSI)
Engineering Stress-Strain diagrams:
- Label the axes.
- REGIONS:
- Elastic – region where specimen will return to
original size & shape
after loading & unloading
- Plastic - region where specimen will NOT return
to original size &
shape after
loading & unloading
- Yielding – region where
specimen will continue
to elongate with little
or no increase in load
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ε (μ in./in.)
Stress-Strain Diagram – Ductile Material
σ (KSI)
Engineering Stress-Strain diagrams:
- REGIONS:
- Strain Hardening – region where specimen will elongate
only with increasing load, and the
cross sectional area will decrease
uniformly over entire specimen gauge length
- Necking - region where
specimen cross sectional
area will decrease in a
localized spot, and
load carrying capacity
will decrease,
uncontrollably
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ε (μ in./in.)
Stress-Strain Diagram – Ductile Material

E

σ (KSI)
Engineering Stress-Strain diagrams:
- POINTS:
- Proportional Limit, σPL – highest stress at which
Stress and Strain
are linearly proportional, via E
- Modulus of Elasticity (Young’s Modulus) –
the slope of the
Stress-Strain curve in the
Linear-Elastic region,
slope up to σPL
(ESTEEL=29x106 psi)
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ε (μ in./in.)
Stress-Strain Diagram – Ductile Material
- Hooke’s Law
  E


σ (KSI)
Engineering Stress-Strain diagrams:
- POINTS:
- Modulus of Elasticity (Young’s Modulus)
the slope of the
E
Stress-Strain curve in the
Linear-Elastic region,
slope up to the
Proportional Limit
(ESTEEL=29x106 psi)
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ε (μ in./in.)
Stress-Strain Diagram – Ductile Material
σ (KSI)
Engineering Stress-Strain diagrams:
- POINTS:
- Modulus of Elasticity
(Young’s Modulus) =
the slope of the
Stress-Strain curve in the
Linear-Elastic region
- alloy content affects
- Proportional Limit
- not Modulus of Elasticity
(ESTEEL=29x106 psi)

E
 Stiffness

ε (μ in./in.)
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Stress-Strain Diagram – Ductile Material
σ (KSI)
Engineering Stress-Strain diagrams:
- POINTS:
- Elastic Limit, σEL – highest stress at which the specimen
will return to original size and shape
after loading and unloading
(Steel, very close to Proportional Limit)
- Yield Point, σY – stress
at which specimen
will have permanent
(plastic) deformation
after loading & unloading,
specimen will elongate
with LITTLE or NO load
increase
(Steel, very close to
Proportional Limit)
ε (μ in./in.)
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Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
- POINTS:
- Ultimate Stress, σU – highest stress on the specimen
σ (KSI)
- Fracture Stress, σF – stress at which specimen breaks
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ε (μ in./in.)
Stress-Strain Diagram – Ductile Material
Engineering Stress-Strain diagrams:
σ (KSI)
- DUCTILE vs. BRITTLE Behavior:
- Ductile behavior – specimen exhibits significant
permanent (plastic) deformation
before failure,
(good, gives warning before failure)
- Brittle behavior –
specimen exhibits
little or no
permanent (plastic)
deformation
before failure,
(bad, no warning before
failure)
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ε (μ in./in.)
Some Ductile materials have
distinct Yield Point and
large yielding region:
- alloys such as;
steel, brass,
- elements such as;
Molybdenum, Zinc
σ (KSI)
Engineering Stress-Strain Diagram – Ductile
ε (μ in./in.)
Some Ductile materials have
no distinct Yield Point:
- Such as; Aluminum
- need to define a YIELD STRENGTH
- Stress at 0.2% strain
- draw a line from ε = 2000x10-6 = 0.002 = 0.2%
- parallel to the linear elastic portion of curve
- σYS = stress at intersection of parallel line with curve
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ε (μ in./in.)
Engineering Stress-Strain Diagram – Brittle
Brittle materials exhibit
LITTLE or NO permanent deformation
BEFORE failure (BAD).
σ (KSI)
Examples:
- Gray Cast Iron
- Concrete
- Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building
ε (μ in./in.)
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Brittle - Concrete
Concrete
- Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building
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Brittle - Concrete
Concrete
- Low Tensile Strength
- High Compression Strength
- No failure warning (Tension or Compression)
- BAD
- need to get people
- off bridge
- out of building
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Ductility
DUCTILITY can be measured by:
σ (KSI)
- Percent Elongation:
L fracture  Loriginal
% Elongation
Loriginal
ε (μ in./in.)
- Percent Reduction of Area:
% Re duction_ of _ Area 
A fracture  Aoriginal
Aoriginal
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Strain Hardening & Hysteresis
The slope of the UNLOADING curve will be
the SAME SLOPE, E, as the LOADING curve.
σ (KSI)
If a specimen is loaded past σEL,
Then unloaded,
Some deformation will be removed,
Some deformation will remain.
ε (μ in./in.)
If specimen is loaded again,
The slope of the re-load curve will be E.
A higher σY will be reached because of
STRAIN HARDENING.
Original Yield Point
But there will be a smaller plastic region
Remaining,
So DUCTILITY will be less.
Yield Point after
Strain Hardening
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Strain Hardening & Hysteresis
Some energy will be
LOST or USED or DISSIPATED
In the LOAD and UNLOAD processes.
Energy dissipated is a function of the
area inside the LOAD-UNLOAD curves,
called HYSTERESIS loops.
Mechanical hysteresis devices are used to
Reduce EARTHQUAKE forces on structures.
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Hysteresis Devices
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Hysteresis Devices
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Stress
-Strain
Diagrams
Example:
Problem 3-4
Hibbeler 7th edition,
pg. 102
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Stress
-Strain
Diagrams
Example:
Problem 3-4
Hibbeler 7th edition,
pg. 102
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