Mechanical Properties

Chapter 4c

Heat Distortion Temperature • The maximum temperature at which a polymer can be used in rigid material applications is called the softening or heat distortion temperature (HDT).

• • A typical test (plastic sheeting) involves application of a static load, and heating at a rate of 2 o C per min. The HDT is defined as the temperature at which the elongation becomes 2%.

• • • • • • • • A: Rigid poly(vinyl chloride) 50 psi load.

B: Low-density poly(ethylene) 50 psi load.

C: Poly(styrene-

co

-acrylonitrile) 25 psi load.

D: Cellulose acetate (Plasticized) 25 psi load.

• • • • Transient Testing: Resilience of Cured Elastomers Resilience tests reflect the ability of an elastomeric compound to store and return energy at a given frequency and temperature.

• • • • • • • Change of rebound resilience (h/ho) with temperature T for: 1.

cis

-poly(isoprene); 2. poly(isobutylene); 3. poly(chloroprene); 4. poly(methyl methacrylate).

Types of Polymers

Polymer Family Tree Thermoplastics Will reform when melted Thermosets/Elastomers Will not reform Not Cross-Linked 90% of market Cross-linked 10% of market Polyethylene 33% Vinyls 16% Polypropylene 15% PMMA ABS Nylon Polycarbonate Saturated Polyester PEEK Polyurethane Some are thermosets as well.

PVC Epoxy Melamine Formaldehyde Phenolic Polyester (unsaturated) Polyimide Polyurethane Some are thermoplastic as well.

Silicone Urea Formaldehyde

Ballpark Comparisons

Tensile strengths

Polymers: ~ 10 - 100 MPa Metals: 100’s - 1000’s MPa

Elongation

Polymers: up to 1000 % in some cases Metals: < 100%

Moduli (Elastic or Young’s)

Polymers: ~ 10 MPa - 4 GPa Metals: ~ 50 - 400 GPa

Amorphous v Crystalline Polymers Thermo-mechanical properties

Thermal Expansion

If a part is to be produced within a close dimensional tolerance, careful consideration of thermal expansion/contraction must be made.

Parts are produced in the melt state, and solidify to amorphous or semi-crystalline states.

Changes in density must be taken into account when designing the mold.

Thermal Expansion

Stress Strain Studies

Anatomy of a Stress Strain Graph  /strain Elongation = 100% x   Initial slope is the Young’s Modulus (E’ or sometimes G) TS = tensile strength  y = yield strength Toughness = Energy required to break (area under curve)

Compression and Shear vs. Tensile Tests Stress-strain curves are very dependent on the test method. A modulus determined under compression is generally higher than one derived from a tensile experiment, as shown below for polystyrene.

Tensile testing is most sensitive to material flaws and microscopic cracks.

Compression tests tend to be characteristic of the polymer, while tension tests are more characteristic of sample flaws.

Note also that flexural and shear test modes are commonly employed.

Stress Strain Graphs

Chains in neck align along elongation direction: strengthening

 

Elongation by extension of neck

Beyond “B”, the yield strength, deformations are plastic

Ductility & Elongation (E L ) E L E L < 5% Brittle > 5% Ductile Thermosets = strong & brittle Not Ductile Thermolastics = depends on T

Cold Drawing above the Tg

TENSILE RESPONSE: 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) 25

High entropy

Elastomer Molecules

Low entropy Low energy High energy Model of long elastomer molecules, with low degree of cross-linking: (a) unstretched, and (b) under tensile stress.

YOUNG’S MODULI: COMPARISON

1200 1000 800 600 400

E(GPa)

200 100 80 60 40

Metals Alloys Graphite Ceramics Semicond Polymers

Diamond Tungsten Molybdenum Steel, Ni Platinum Cu alloys Zinc, Ti Si carbide Al oxide Si nitride <111> Si crystal <100> Glass-soda Concrete 109 Pa 20 Graphite 10 8 6 4 Polyester PET PS PC 2 1 0.8

0.6

0.4

0.2

PTFE LDPE

Composites /fibers

Carbon fibers only CFRE(|| fibers)* Aramid fibers only AFRE(|| fibers)* Glass fibers only GFRE(|| fibers)* GFRE* CFRE* GFRE( fibers)* CFRE( fibers)* AFRE( fibers)* Epoxy only

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.

Wood( grain)

13



Linear Elasticity: Possion Effect

• Hooke's Law :



= E



• Poisson's ratio,

 :   

width strain axial strain

  

w

/

w

 l / l   

L



metals:



~ 0.33

ceramics: ~0.25

polymers: ~0.40

Units: E: [GPa] or [psi]



: dimensionless Why does



have minus sign?

Poisson Ratio

• Poisson Ratio has a range –1

  

1/2 Look at extremes • No change in aspect ratio:

    

w

/ /

w

  1 

w

/

w

  /

• Volume ( V = AL )



Hence,



V = (L



A+A



L) = 0. So,



V =0.



A

/

A

 

L

/

L

In terms of width, A = w 2 , then



A/A = 2 w



w/w 2 = 2



w/w = –



L/L.

Hence,

   

w

/

w

 /   (  1   / / )  1/2

Incompressible solid.

Water (almost).



Poisson Ratio: materials specific Metals: Ir W 0.26

Solid Argon: 0.25

Ni 0.29

Covalent Solids: Ionic Solids: Si 0.27

MgO 0.19

Silica Glass: 0.20

Cu 0.31

Ge 0.28

Al 0.34

Al 2 O 0.23

3 Ag 0.34

TiC 0.19 Au 0.38

generic value ~ 1/3 generic value ~ 1/4 Polymers: Network (Bakelite) 0.49

Elastomer: Chain (PE) 0.40

Hard Rubber (Ebonite) 0.39 (Natural) 0.49

0.42

Example: Poisson Effect Tensile stress is applied along cylindrical brass rod ( 10 mm diameter). Poisson ratio is



= 0.34

and E = 97 GPa .

• Determine load needed for 2.5x10

–3 if the deformation is entirely elastic?

mm change in diameter Width strain: (note reduction



x =



d/d = – (2.5x10

–3 in diameter) mm)/(10 mm) = –2.5x10

–4 Axial strain:



z = –



x /



Given Poisson ratio = –(–2.5x10

–4 )/0.34 = +7.35x10

–4 Axial Stress:



z = E



z = (97x10 3 MPa)(7.35x10

–4 ) = 71.3 MPa.

Required Load: F =



z A 0 = (71.3 MPa)



( 5 mm ) 2 = 5600 N.

Negtive poisson’s ratio

• foams

Lakes, R. S., "No contractile obligations", Nature, 1992, 358, 713-714.

Compression Radial n = -1.24

Axial n = 0

Anisotropic Materials 1) Compaction of UHMWPE powder 2) Sintering 3) Extrusion

• Mechanical properties are sensitive to temperature FIGURE 10.9 Effect of temperature on the stress-strain curve for cellulose acetate, a thermoplastic. Note the large drop in strength and increase in ductility with a relatively small increase in temperature.

Source

: After T.S. Carswell and H.K. Nason. 2008.

Manufacturing Processes for Engineering Materials, 5th ed.

Kalpakjian • Schmid Prentice Hall,

Poly(methyl methacrylate)

Ceramics Metals Polymers Strain •Lower elastic modulus, yield and ultimate properties •Greater post-yield deformability •Greater failure strain

Polymers: Thermal Properties • In the liquid/melt state enough thermal energy for random motion (Brownian motion) of chains • Motions decrease as the melt is cooled • Motion ceases at “glass transition temperature” • Polymer hard and glassy below T g , rubbery above T g

Polymers: Thermal Properties

T g T m semicrystalline crosslinked Temperature linear amorphous

Polymers: Thermal Properties

decreasing temperature or increasing crystallinity

Strain

• Properties depend on amount of cross-linking Increasing cross-linking Figure 8.13 M. P. Groover, “Fundamentals of Modern Manufacturing 3/e” John Wiley, 2007