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CHAPTER 7: MECHANICAL PROPERTIES

ISSUES TO ADDRESS... Stress and strain Elastic behavior Plastic behavior Toughness and ductility Ceramic Materials Stress Strain Elasticity Strength Tensile Elongation Ductile Fracture Tension Flexural Plasticity

4 Tensile stress,  : Shear stress,  : Stress has units: N/m 2 or lb/in STRESS & STRAIN

Tensile load Compressive load Shear strain  = tan  Torsional deformation angle of twist,  Stress (  ) for tension and compression Strain (  ) for tension and compression Shear stress

5 Simple tension: cable Simple shear: drive shaft Note:  = M/A c Ski lift (photo courtesy P.M. Anderson) 7.2 COMMON STATES OF STRESS

6 Simple compression: Note: compressive structure member (  < 0 here). (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES

7 Bi-axial tension: Hydrostatic compression: Pressurized tank   < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) OTHER COMMON STRESS STATES

8 Tensile strain: Lateral strain: Shear strain: Strain is always dimensionless. ENGINEERING STRAIN

Typical tensile specimen 9 Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Typical tensile test machine Adapted from Fig. 6.2, Callister 6e. Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.) 7.2 STRESS-STRAIN TESTING

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  ’ (normal to the pp’ plane) Shear stress  ’ (parallel to the pp’ plane)

Modulus of Elasticity, E: (also known as Young's modulus) 10 Hooke's Law:  = E  Poisson's ratio, : metals: ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] : dimensionless ELASTIC DEFORMATIONS 7.3 Stress-strain behavior

11 Elastic modulus, E Energy ~ curvature at r o E is larger if E o is larger. PROPERTIES FROM BONDING: E

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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 = -  x /  z = -  y /  z For isotropic materials

13 Metals Alloys Graphite Ceramics Semicond Polymers Composites /fibers 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. YOUNG’S MODULI: COMPARISON

II. MECHANICAL BEHAVIOR—METALS

2 1. Initial2. Small load3. Unload Elastic means reversible! II. ELASTIC DEFORMATION

15 Simple tension test: (at lower temperatures, T < T melt /3) II. PLASTIC (PERMANENT) DEFORMATION

3 1. Initial2. Small load3. Unload Plastic means permanent! II. PLASTIC DEFORMATION (METALS)

16 YIELD STRENGTH,  y Stress at which noticeable plastic deformation has occurred. when  p = Tensile properties

17 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 7.6 YIELD STRENGTH: COMPARISON

18 Maximum possible engineering stress in tension Metals: occurs when noticeable necking starts. Ceramics: occurs when crack propagation starts. Polymers: occurs when polymer backbones are aligned and about to break. Adapted from Fig. 6.11, Callister 6e. 7.6 TENSILE STRENGTH, TS

19 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. 7.6 TENSILE STRENGTH: COMPARISON

Plastic tensile strain at failure: 20 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. Adapted from Fig. 6.13, Callister 6e. 7.6 DUCTILITY, %EL Degree of plastic deformation at fracture Brittle, when very little plastic deformation

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c07f14 Stress-strain of iron at several temperatures

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:

Ability to absorb energy up to fracture TOUGHNESS Usually ductile materials are tougher than brittle ones Areas below the curves

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

HARDENING: An increase in  y due to plastic deformation. 22 Curve fit to the stress-strain response: 7.7 True stress & strain n = hardening exponent n = 0.15 (some steels) n = 0.5 (some copper)

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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 Si carbide Al oxide glass (soda) 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 Compaction to desire shape 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 -Pores reduce the area -Pores are stress concentrators -tensile stress doubles in an isolated spherical pore Aluminum oxide E = Eo(1 – 1.9P + 0.9P 2 ) Aluminum oxide  fs =  o e -nP

Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig , Callister 6e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) IV MECHANICAL BEHAVIOR—POLYMERS 7.13 STRESS—STRAIN BEHAVIOR

26 Decreasing T... --increases E --increases TS --decreases %EL 7.13 T & STRAIN RATE: THERMOPLASTICS Increasing strain rate... --same effects as decreasing T.

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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

c07f Viscoelasticity Deformation Totally elastic Viscoelastic Viscous Load

Relaxation Modulus for viscoelastic polymers: Amorphous polystyrene A viscoelastic polymer

Polystyrene configurations amorphous Lightly crosslinked atactic Almost totally crystalline isotactic Viscoelastic creep Creep modulus E c (t)

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

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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

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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

Design uncertainties mean we do not push the limit. Factor of safety, N 29 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 DESIGN/SAFETY FACTORS d = 47.5 mm

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  y. 30 Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. SUMMARY