CHAPTER 6 MECHANICAL PROPERTIES(1) by hcj

VIEWS: 1 PAGES: 59

									Special Assignment

qAdd figures/graphics to all slides

qUse bullets instead of short sentences

qFor the 15’ presentations use fonts 18 or bigger;
however, for the 50’, font sizes 10, 12, 14 are fine. You
may use 16 or 18 for titles.

qAdd your summary slide

qGraphics should help to explain the topic
     CHAPTER 7:
MECHANICAL PROPERTIES
        CHAPTER 7:
   MECHANICAL PROPERTIES
                            Stress
ISSUES TO ADDRESS...        Strain
                            Elasticity
• Stress and strain
                            Strength
                            Tensile
• Elastic behavior          Elongation
                            Ductile
• Plastic behavior          Fracture
                            Tension
• Toughness and ductility   Flexural
                            Plasticity
• Ceramic Materials
           7.2 STRESS & STRAIN
• Tensile stress, s:               • Shear stress, t:




                       Stress has units:
                       N/m2 or lb/in2

                                                        4
                                          Stress (s) for tension and
                                          compression



                                           Strain (e) for tension and
                                           compression
                Compressive load
 Tensile load

                                               Shear stress




Shear strain      Torsional deformation
g = tan q         angle of twist, f
 7.2 COMMON STATES OF STRESS
• Simple tension: cable




                                    Ski lift   (photo courtesy P.M. Anderson)
• Simple shear: drive shaft




                              Note: t = M/Ac
                                                                      5
    OTHER COMMON STRESS STATES
• Simple compression:




                                   (photo courtesy P.M. Anderson)



                                   Note: compressive
                                   structure member
  (photo courtesy P.M. Anderson)   (s < 0 here).



                                                                6
  OTHER COMMON STRESS STATES
• Bi-axial tension:   • Hydrostatic compression:




Pressurized tank                        (photo courtesy
(photo courtesy                         P.M. Anderson)
P.M. Anderson)




                             s h< 0

                                                  7
          ENGINEERING STRAIN
• Tensile strain:     • Lateral strain:




• Shear strain:


                       Strain is always
                       dimensionless.



                                          8
    7.2 STRESS-STRAIN TESTING
• Typical tensile specimen                     • Typical tensile
                                                  test machine
         Adapted from Fig. 6.2,
          Callister 6e.




            • Other types of tests:            Adapted from Fig. 6.3, Callister 6e.
                                               (Fig. 6.3 is taken from H.W. Hayden,
               --compression: brittle          W.G. Moffatt, and J. Wulff, The
                                               Structure and Properties of
                 materials (e.g., concrete)    Materials, Vol. III, Mechanical
               --torsion: cylindrical tubes,   Behavior, p. 2, John Wiley and Sons,
                                               New York, 1965.)
                 shafts.                                                       9
Normal and shear stresses on an arbitrary plane

Stress is a function of the orientation

On plane p-p’ the stress is not pure tensile

There are two components
Tensile or normal stress s’ (normal to the pp’ plane)
Shear stress t’ (parallel to the pp’ plane)
       ELASTIC DEFORMATIONS
       7.3 Stress-strain behavior
• Modulus of Elasticity, E:
 (also known as Young's modulus)

• Hooke's Law:
       s=Ee
• Poisson's ratio, n:


 metals: n ~ 0.33
 ceramics: ~0.25
 polymers: ~0.40
  Units:
  E: [GPa] or [psi]
  n: dimensionless
                                    10
    PROPERTIES FROM BONDING: E
  • Elastic modulus, E




Energy ~ curvature at ro

         E is larger if Eo is larger.




                                        11
c07f08
c07tf01
7.4 ANESLATICITY

Assumed:
Time-independent elastic deformation
Applied stress produces instantaneous elastic strain
Remains constant while elasticity stress is applied
At release of load, strain is recovered

In real life:
Time-dependent elastic strain component: Anelasticity
Time-dependent microscopic and atomistic processes
For metals is small
Significant for polymeric materials: Viscoelastic behavior
7.5 ELASTIC PROPERTIES OF MATERIALS

                        Poisson’s ratio
                        n = -ex/ez = -ey/ez


                     For isotropic materials
             YOUNG’S MODULI:
               COMPARISON
                  Graphite
         Metals                     Composites
                  Ceramics Polymers
         Alloys                       /fibers
                  Semicond




E(GPa)

                                                 Based on data in Table B2,
                                                 Callister 6e.
                                                 Composite data based on
                                                 reinforced epoxy with 60 vol%
                                                 of aligned
                                                 carbon (CFRE),
                                                 aramid (AFRE), or
                                                 glass (GFRE)
                                                 fibers.




                                                                          13
II. MECHANICAL BEHAVIOR—METALS
   II. ELASTIC DEFORMATION
     1. Initial       2. Small load   3. Unload




Elastic means reversible!



                                           2
II. PLASTIC (PERMANENT) DEFORMATION
                         (at lower temperatures, T < Tmelt/3)

• Simple tension test:




                                                         15
II. PLASTIC DEFORMATION (METALS)
      1. Initial   2. Small load   3. Unload




  Plastic means permanent!


                                               3
           7.6 Tensile properties
• YIELD STRENGTH, sy
Stress at which noticeable plastic deformation has
   occurred.
                           when ep = 0.002




                                                     16
7.6 YIELD STRENGTH: COMPARISON




                     Room T values
                    Based on data in Table B4,
                    Callister 6e.
                    a = annealed
                    hr = hot rolled
                    ag = aged
                    cd = cold drawn
                    cw = cold worked
                    qt = quenched & tempered




                                          17
      7.6 TENSILE STRENGTH, TS
Maximum possible engineering stress in tension


                                            Adapted from Fig. 6.11,
                                            Callister 6e.




• Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are
 aligned and about to break.
                                                            18
7.6 TENSILE STRENGTH:
     COMPARISON




                Room T values
                Based on data in Table B4,
                Callister 6e.
                a = annealed
                hr = hot rolled
                ag = aged
                cd = cold drawn
                cw = cold worked
                qt = quenched & tempered
                AFRE, GFRE, & CFRE =
                aramid, glass, & carbon
                fiber-reinforced epoxy
                composites, with 60 vol%
                fibers.
                                      19
                             7.6 DUCTILITY, %EL
                               Degree of plastic deformation at fracture
                              Brittle, when very little plastic deformation


   • Plastic tensile strain at failure:




   Adapted from Fig. 6.13,
   Callister 6e.



ductility as percent reduction
in area
   • Note: %AR and %EL are often comparable.
     --Reason: crystal slip does not change material volume.
     --%AR > %EL possible if internal voids form in neck.
                                                                              20
c07tf02
Stress-strain of iron at several temperatures




                  c07f14
RESILIENCE
Capacity to absorb energy when deformed elastically and then upon
unloadign, to have this energy recovered

Modulus of Resilience




For a linear elastic region:
                  7.6 TOUGHNESS
• Ability to absorb energy up to fracture




  Usually ductile materials are tougher than brittle ones
  Areas below the curves
                                                            21
        7.7 True stress & strain
Decline in stress necessary to continue deformation past M
Looks like metal become weaker
Actually, it is increasing in strength
Cross sectional area decreases rapidly within the neck region
Reduction in the load-bearing capacity of the specimen
Stress should consider deformation
          7.7 True stress & strain
HARDENING: An increase in sy due to plastic deformation.




• Curve fit to the stress-strain response:

                                   n = hardening exponent
                                   n = 0.15 (some steels)
                                   n = 0.5 (some copper)
                                                       22
c07tf04
7.8 Elastic Recovery After Plastic Deformation
7.9 Compressive, Shear, and
Torsional Deformation

Similar to tensile counterpart

No maximum for compression

Necking does not occur

Mode of fracture different from that of
tension
III. MECHANICAL BEHAVIOR—CERAMICS
Limited applicability, catastrophic fracture in a brittle
manner, little energy absorption

7.10 FLEXURAL STRENGTH
Tensile tests are difficult
     difficult to prepare geometry
     easy to fracture
     ceramics fail at 0.1% strain
     bending stress
     rod specimen is used
     three of four point loading technique
     flexure test
               7.10 MEASURING STRENGTH
• Flexural strength= modulus of rupture
= fracture strength = bend strength




          • Type values:

 Si nitride   700-1000 300
 Si carbide    550-860 430
 Al oxide      275-550 390
 glass (soda)    69     69
Data from Table 12.5, Callister 6e.
7.11 Elastic Behavior (for
ceramics)

Similar to tensile test for metals

Linear stress-strain

Moduli of elasticity for
ceramics are slightly higher
than for metals

No plastic deformation prior
to fracture
          7.12 INFLUENCE OF POROSITY ON THE
          MECHANICAL PROPERTIES OF CERAMICS
                                   Powder as precursor
          Aluminum oxide           Compaction to desire shape
          E = Eo(1 – 1.9P + 0.9P2) Pores or voids elimination
                                   incomplete
                                   Residual porosity remains
                                   Deleterious influence on
                                   elasticity and strength
                                   Volume fraction porosity P

Eo = modulus of elasticity of
the non porous material                     Aluminum oxide
-Pores reduce the area
-Pores are stress concentrators
                                            sfs = soe    -nP

-tensile stress doubles in an
isolated spherical pore
IV MECHANICAL BEHAVIOR—POLYMERS

7.13 STRESS—STRAIN BEHAVIOR

                                                      Stress-strain curves
                                                      adapted from Fig.
                                                      15.1, Callister 6e.
                                                      Inset figures along
                                                      elastomer curve
                                                      (green) adapted from
                                                      Fig. 15.14, Callister
                                                      6e. (Fig. 15.14 is from
                                                      Z.D. Jastrzebski, The
                                                      Nature and Properties
                                                      of Engineering
                                                      Materials, 3rd ed.,
                                                      John Wiley and Sons,
                                                      1987.)




 • Compare to responses of other polymers:
   --brittle response (aligned, cross linked & networked case)
   --plastic response (semi-crystalline case)
7.13 T & STRAIN RATE: THERMOPLASTICS
 • Decreasing T...
  --increases E
  --increases TS
  --decreases %EL




                     • Increasing
                         strain rate...
                       --same effects
                         as decreasing T.
                                            26
7.14 Macroscopic Deformation




       Semicrystaline polymer




                  c07f25
            7.15 Viscoelasticity Deformation


Amorphous polymer:
Glass at low T
Viscous liquid at higher T
Small deformation at low T may be elastic
Hooke’s law
Rubbery solid at intermediate T
A combination of glass and viscous/liquid
Viscoelasticity
Elastic deformation is instantaneous
Upon release, deformation is totally recovered
   7.15 Viscoelasticity Deformation


                           Totally elastic

Load




                               Viscous


Viscoelastic


                 c07f26
Relaxation Modulus for viscoelastic
polymers:




                       Amorphous polystyrene
                       A viscoelastic polymer
                         Polystyrene configurations




                      Almost totally crystalline isotactic




                         Lightly crosslinked atactic

Viscoelastic creep
Creep modulus Ec(t)
                         amorphous
V. Hardness & Other Mechanical Property Considerations

7.16 Hardness

Measure of material resistance to localized plastic deformation
Early tests: Mohs scale 1 for talc and 10 for diamond

Depth or size of an indentation

Tests:
         Mohs Hardness
         Rockwell Hardness
         Brinell Hardness
         Knoop & Vickers Microindentation Hardness
c07tf05
c07tf06a
c07tf06b
Hardness Conversion
Correlation between Hardness and Tensile Strength


Tensile strength and Hardness
measure metal resistance to plastic
deformation

For example:

TS(Mpa) = 3.45 × HB

or

TS(psi) = 500 × HB
7.17 Hardness of Ceramic Materials




               c07tf07
7.18 Tear Strength & Hardness of Polymers


 Thin films in packaging
 Tear Strength: Energy required to tear apart a cut specimen of a
 standard geometry
VI. Property Variability and Design/Safety Factors
7.19 Variability of Material Properties: Average and
   standard deviation
    7.20 DESIGN/SAFETY FACTORS
• Design uncertainties mean we do not push the limit.
• Factor of safety, N           Often N is
                                     between
                                     1.2 and 4


• Ex: Calculate a diameter, d, to ensure that yield does
  not occur in the 1045 carbon steel rod below. Use a
  factor of safety of 5.




                 5


                  d = 47.5 mm                              29
                  SUMMARY
• Stress and strain: These are size-independent
   measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
   shows a linear relation between stress and strain.
   To minimize deformation, select a material with a
   large elastic modulus (E or G).
• Plastic behavior: This permanent deformation
   behavior occurs when the tensile (or compressive)
   uniaxial stress reaches sy.
• Toughness: The energy needed to break a unit
   volume of material.
• Ductility: The plastic strain at failure.


                                                        30

								
To top