CHAPTER 6: MECHANICAL PROPERTIES. ISSUES TO ADDRESS. • Stress and strain : What are they and why are they used instead of load and deformation?. • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?. - PowerPoint PPT Presentation
1 1 ISSUES TO ADDRESS... • Stress and strain: What are they and why are they used instead of load and deformation? • Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? • Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? 1 • Toughness and ductility: What are they and how do we measure them? CHAPTER 6: CHAPTER 6: MECHANICAL PROPERTIES MECHANICAL PROPERTIES
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ISSUES TO ADDRESS...• Stress and strain: What are they and why are they used instead of load and deformation?
• Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?
• Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation?
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• Toughness and ductility: What are they and how do we measure them?
Chapter 6: Mechanical Properties of MetalsChapter 6: Mechanical Properties of Metals6.1 Introduction6.1 Introduction
Why Study the Mechanical Properties of Metals ?Why Study the Mechanical Properties of Metals ?
It is important for engineers to understand It is important for engineers to understand – How the various mechanical properties are measured, andHow the various mechanical properties are measured, and– What these properties representWhat these properties represent
The role of structural engineers is to determine stresses and stress The role of structural engineers is to determine stresses and stress distributions within members that are subjected to well-defined loadsdistributions within members that are subjected to well-defined loads– By experimental testingBy experimental testing– Theoretical and mathematical stress analysis.Theoretical and mathematical stress analysis.
Design structures/components using predetermined materials such that Design structures/components using predetermined materials such that unacceptable levels of deformation and/or failure will not occur.unacceptable levels of deformation and/or failure will not occur.
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6.2 Concepts of 6.2 Concepts of Stress and StrainStress and Strain
Static loadStatic load changes changes relatively slowly with relatively slowly with time time
Applied uniformlyApplied uniformly over a cross-section or over a cross-section or surface of a member.surface of a member.
6.2 Concepts of Stress and Strain (Contd.)6.2 Concepts of Stress and Strain (Contd.)
TENSION TESTTENSION TEST
Most common mechanical stress-strain testMost common mechanical stress-strain test
Used to ascertain several mechanical properties that are important in designUsed to ascertain several mechanical properties that are important in design
A specimen is deformed, usually to fracture, with a gradually increasing A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of the specimen.tensile load that is applied uniaxially along the long axis of the specimen.
A A standard specimenstandard specimen is shown in Figure 6-2. is shown in Figure 6-2.
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6.2 Concepts of Stress and Strain (Contd.)6.2 Concepts of Stress and Strain (Contd.)
The specimen is mounted by its ends The specimen is mounted by its ends into the holding grips of the testing into the holding grips of the testing apparatus (Figure 6-3).apparatus (Figure 6-3).
Tensile testing machineTensile testing machine– To elongate the specimen at a To elongate the specimen at a
constant rateconstant rate– To continuously and To continuously and
simultaneously measure the simultaneously measure the instantaneous load and the instantaneous load and the resulting extensionresulting extension
– Load using load cellLoad using load cell– Extension using extensometerExtension using extensometer
Takes few minutes and is destructive.Takes few minutes and is destructive.
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6.2 Concepts of Stress and Strain (Contd.)6.2 Concepts of Stress and Strain (Contd.)
Engineering StressEngineering Stress ( () = Instantaneous applied ) = Instantaneous applied load (load (FF) / Original Area () / Original Area (AoAo))
COMPRESSION TESTSCOMPRESSION TESTS Similar to tensile test, compressive loadSimilar to tensile test, compressive load Sign convention, compressive force is taken negative Sign convention, compressive force is taken negative
stress negative stress negative Since lSince lo o > l> lii , negative strain , negative strain
0A
F
00
0
l
l
l
lli
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6.2 Concepts of Stress and Strain (Contd.)6.2 Concepts of Stress and Strain (Contd.)
SHEAR AND TORSIONAL TESTSSHEAR AND TORSIONAL TESTS
Shear stressShear stress : : = F / A= F / Aoo
• F: F: Load or force imposed Load or force imposed parallel to the upper and parallel to the upper and lower faces lower faces
• AAoo:: shear or parallel area shear or parallel area
Shear strainShear strain ( () is defined as the ) is defined as the tangent of the strain angle tangent of the strain angle ..
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6.2 Concepts of Stress and Strain (Contd.)6.2 Concepts of Stress and Strain (Contd.)
GEOMETRIC CONSIDERATIONS OF GEOMETRIC CONSIDERATIONS OF THE STRESS STATETHE STRESS STATE
Stress is a function of orientations of the Stress is a function of orientations of the planesplanes
– Follow same loading and Follow same loading and unloading pathunloading path
Linear elastic deformationLinear elastic deformation Hooke’s LawHooke’s Law
– Modulus of elasticity or Modulus of elasticity or Young’s Modulus Young’s Modulus stiffness or a material’s stiffness or a material’s resistance to elastic resistance to elastic deformationdeformation E
On an atomic scale, macroscopic On an atomic scale, macroscopic elastic strain is manifested as elastic strain is manifested as small changes in the interatomic small changes in the interatomic spacing and the stretching of spacing and the stretching of interatomic bonds.interatomic bonds.
E is a measure of the resistance E is a measure of the resistance to separation of adjacent atomsto separation of adjacent atoms
Modulus is proportional to the Modulus is proportional to the slope of the interatomic force-slope of the interatomic force-separation curve (Fig 2.8a) at separation curve (Fig 2.8a) at equilibrium spacingequilibrium spacing
With increasing With increasing temperature, the modulus temperature, the modulus of elasticity diminishesof elasticity diminishes
Shear stress and strain Shear stress and strain are proportional to each are proportional to each other:other:
Shear modulus or Shear modulus or modulus of rigidity modulus of rigidity ( Table 6.1)( Table 6.1)
G
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6.4 Anelasticity6.4 Anelasticity Up to this point, it is Up to this point, it is assumedassumed that that
– Elastic deformation is time-independentElastic deformation is time-independent
– An applied stress produces an instantaneous elastic strainAn applied stress produces an instantaneous elastic strain
– Strain remains constant over the period of time the stress is maintainedStrain remains constant over the period of time the stress is maintained
– Upon release of the load, strain is totally recovered (immediately returns Upon release of the load, strain is totally recovered (immediately returns to zero)to zero)
In most engineering materials, there will also exist a In most engineering materials, there will also exist a time-dependent elastic time-dependent elastic strainstrain component , i.e. component , i.e.
– elastic deformation will continue after stress applicationelastic deformation will continue after stress application
– Upon load release some finite time is required for complete recoveryUpon load release some finite time is required for complete recovery
– Loading and unloading path are differentLoading and unloading path are different
For metalsFor metals, the anelastic component is normally small and neglected., the anelastic component is normally small and neglected. For some polymersFor some polymers, it is significant and known as , it is significant and known as viscoelastic behaviorviscoelastic behavior
(Sec. 16.7)(Sec. 16.7)
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6.5 Elastic Properties of Materials6.5 Elastic Properties of Materials
Poisson’s ratioPoisson’s ratio
E = 2G(1 + E = 2G(1 + ))
Example 6.1Example 6.1 Example 6.2Example 6.2
z
y
z
x
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PLASTIC DEFORMATIONPLASTIC DEFORMATION
For most metals, For most metals, elastic deformationelastic deformation persists only to persists only to strains of about 0.005strains of about 0.005
Plastic deformationPlastic deformation– Stress not proportional to strain (Hooke’s law cease to Stress not proportional to strain (Hooke’s law cease to
be valid)be valid)– PermanentPermanent– NonrecoverableNonrecoverable– Non-conservativeNon-conservative
TransitionTransition from elastic to plastic deformation from elastic to plastic deformation– Gradual for most metalsGradual for most metals– Some curvature results at the onset of plastic Some curvature results at the onset of plastic
Plastic deformation (Contd.)Plastic deformation (Contd.) From as atomic perspectiveFrom as atomic perspective
– Plastic deformation corresponds to the Plastic deformation corresponds to the breaking of bondsbreaking of bonds with with original atom neighborsoriginal atom neighbors
– Reforming bondsReforming bonds with new neighbors with new neighbors
– Large number of atoms and molecules Large number of atoms and molecules movemove relative to one relative to one anotheranother
– Upon removal of stress, they Upon removal of stress, they do not returndo not return to their original to their original positionposition
Mechanism of plastic deformationMechanism of plastic deformation::
– Crystalline SolidsCrystalline Solids::
» accomplished by a process called slipaccomplished by a process called slip
» Involves the motion of dislocations (Sec 7.2)Involves the motion of dislocations (Sec 7.2)
– Non-crystalline solidsNon-crystalline solids (as well liquids) (as well liquids)
» Occurs by a viscous flow mechanism (Sec 13.9)Occurs by a viscous flow mechanism (Sec 13.9)
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• Stress at which noticeable plastic deformation has occurred.
when p = 0.002 tensile stress,
engineering strain,
y
p = 0.002
YIELD STRENGTH, YIELD STRENGTH, yy
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6.6 Tensile Properties6.6 Tensile Properties
YIELDING and YIELD STRESSYIELDING and YIELD STRESS
In most cases, the position of yield In most cases, the position of yield point may not be determined point may not be determined precisely.precisely.
Established conventionEstablished convention: a straight : a straight line is constructed parallel to the line is constructed parallel to the elastic portion at some specified elastic portion at some specified strain offsetstrain offset, usually 0.002 (0.2%) , usually 0.002 (0.2%) Fig. 6.10a Fig. 6.10a corresponding corresponding intersection point gives intersection point gives yield yield strengthstrength..
Some steels and other materials exhibit the behavior as shown in Fig 6.10bSome steels and other materials exhibit the behavior as shown in Fig 6.10b
– The yield strength is taken as the The yield strength is taken as the average stressaverage stress that is associate with the that is associate with the lower yield pointlower yield point..
Magnitude of yield strengthMagnitude of yield strength is a measure of its resistance to plastic is a measure of its resistance to plastic deformationdeformation
– RangeRange from 35 MPa to 1400 MPa from 35 MPa to 1400 MPa
– 35 MPa for 35 MPa for low-strength aluminumlow-strength aluminum
– 1400 MPa for 1400 MPa for high-strength steelhigh-strength steel
TensileTensile strength TS (MPa or psi) strength TS (MPa or psi) is the stress at the maximum on is the stress at the maximum on the engineering stress-strain curvethe engineering stress-strain curve
All deformation up to this point is All deformation up to this point is uniformuniform..
Onset of Onset of neckingnecking at this stress at at this stress at some point some point all subsequent all subsequent deformation at this neck.deformation at this neck.
Range: 50 - 3000 MPaRange: 50 - 3000 MPa50 MPa for aluminum50 MPa for aluminum3000 MPa for high strength steel 3000 MPa for high strength steel
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• Plastic tensile strain at failure:
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Engineering tensile strain,
Engineering tensile stress,
smaller %EL (brittle if %EL<5%)
larger %EL (ductile if %EL>5%)
• Another ductility measure: %AR
Ao A fAo
x100
• Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck.
Lo LfAo Af
%EL
L f LoLo
x100
Adapted from Fig. 6.13, Callister 6e.
DUCTILITY, %ELDUCTILITY, %EL
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Effect of TemperatureEffect of Temperature As with modulus of elasticity (E), the magnitudes of both As with modulus of elasticity (E), the magnitudes of both
yield and tensile strengths yield and tensile strengths declinedecline with increasing with increasing temperaturetemperature
Ductility usually Ductility usually increasesincreases with temperature with temperature Figure shown stress-strain behavior of iron Figure shown stress-strain behavior of iron
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RESILIENCERESILIENCE
ResilienceResilience is the capacity of a material is the capacity of a material to to absorb energyabsorb energy when it is deformed when it is deformed elasticallyelastically and then, upon unloading, and then, upon unloading, to have this energy recovered.to have this energy recovered.
Modulus of resilience (Ur)Modulus of resilience (Ur)
– Associated propertyAssociated property
– Area under the engineering stress-Area under the engineering stress-strain curvestrain curve
– Strain energy per unit volumeStrain energy per unit volume required to stress from an unloaded required to stress from an unloaded state to yieldingstate to yielding
Mathematically,Mathematically,E
dU yyyr 22
12
0
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• Energy to break a unit volume of material• Approximate by the area under the stress-strain curve.
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smaller toughness- unreinforced polymers
Engineering tensile strain,
Engineering tensile stress,
smaller toughness (ceramics)
larger toughness (metals, PMCs)
TOUGHNESSTOUGHNESS
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TOUGHNESSTOUGHNESS A measure of the ability of a material to absorb energy up to A measure of the ability of a material to absorb energy up to
fracture.fracture.
Specimen geometry and the manner of load application are Specimen geometry and the manner of load application are important in toughness determination:important in toughness determination:
– Notch toughness: dynamic (high strain rate) loading, specimen Notch toughness: dynamic (high strain rate) loading, specimen with notch (or point of stress concentration) (Sec 8.6)with notch (or point of stress concentration) (Sec 8.6)
– Fracture toughness: property indicative of a materials resistance Fracture toughness: property indicative of a materials resistance to fracture when crack is present (Sec 8.5)to fracture when crack is present (Sec 8.5)
For static (low strain rate) condition, modulus of toughness is equal For static (low strain rate) condition, modulus of toughness is equal to the total area under the stress-strain curve (up to fracture ):to the total area under the stress-strain curve (up to fracture ):
For Ductile Material :For Ductile Material : For Brittle Material:For Brittle Material:
fuyfuTU %)2.0(2
1fuTU
3
2
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6.7 True Stress and Strain6.7 True Stress and Strain
Engineering stress-strain curve Engineering stress-strain curve beyond maximum point (M) seems to beyond maximum point (M) seems to indicate that the material is becoming indicate that the material is becoming weaker.weaker.– Not true, rather it becomes Not true, rather it becomes
stronger.stronger. Since cross-sectional area is Since cross-sectional area is
decreasing at the neck decreasing at the neck reduces reduces load bearing capacity of the materialload bearing capacity of the material
True stress:True stress: Actual or current or Actual or current or instantaneous force divided by the instantaneous force divided by the instantaneous cross-sectional area.instantaneous cross-sectional area.
True Strain:True Strain: Change in length per Change in length per unit instantaneous lengthunit instantaneous length
iT A
F
00lAlA ii
ii
i
l
l i
iT D
D
A
A
l
l
l
dli
00
0
ln2lnln0
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6.7 True Stress and Strain (Contd.)6.7 True Stress and Strain (Contd.)
Relation between two Relation between two definitionsdefinitions
Above equations are valid Above equations are valid only to the onset of necking; only to the onset of necking; beyond this point true stress beyond this point true stress and strain should be and strain should be computed from actual load, computed from actual load, area and gauge length.area and gauge length.
Schematic comparison in Schematic comparison in Figure 6.16Figure 6.16
– Corrected takes into Corrected takes into account complex stress account complex stress state with in neck region.state with in neck region.
)1(
)1ln(
T
T
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6.7 True Stress and Strain (Contd.)6.7 True Stress and Strain (Contd.)
For some metals and alloys, the true stress-For some metals and alloys, the true stress-strain curve is approximated asstrain curve is approximated as
Parameter Parameter nn– strain-hardening exponentstrain-hardening exponent– A value less than unityA value less than unity– Slope on log-log plotSlope on log-log plot
Parameter Parameter KK– Known as strength coefficientKnown as strength coefficient– True stress at unit true strainTrue stress at unit true strain
nTT K
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6.8 Elastic Recovery During Plastic Deformation6.8 Elastic Recovery During Plastic Deformation
Upon release of load, some Upon release of load, some fraction of total strain is fraction of total strain is recovered as elastic strainrecovered as elastic strain
During unloading, straight During unloading, straight path parallel to elastic path parallel to elastic loadingloading
ReloadingReloading– Yielding at new yield Yielding at new yield
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