1. Mechanical Behavior mostly Ceramics, Glasses and Polymers
Chapter 6: Part 2
Dr. R. Lindeke

2. Measuring Elastic Modulus
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing is often used.
-- tensile tests are difficult for brittle materials! F
L/2
 = midpoint
deflection
cross section R b d
rect.
circ.
Adapted from Fig , Callister 7e.
• Determine elastic modulus according to: x d F
slope = E = L 3 4 bd 12 p R
rect.
cross
section
circ. F
linear-elastic behavior

3. Measuring Strength s = 1.5Ff L bd 2 Ff L pR3 x F F
• 3-point bend test to measure room T strength. F
L/2
 = midpoint
deflection
cross section R b d
rect.
circ.
location of max tension
Adapted from Fig , Callister 7e.
• Flexural strength:
• Typ. values:
Data from Table 12.5, Callister 7e.
rect. s fs =
1.5Ff L
bd 2
Ff L
pR3
Si nitride
Si carbide
Al oxide
glass (soda) 69
304
345
393
Material
(MPa) E(GPa) x F Ff d

4. Mechanical Issues:
Properties are significantly dependent on processing – and as it relates to the level of Porosity:
E = E0(1-1.9P+0.9P2) – where P is a fraction ‘porosity’
fs = 0e-nP -- 0 & n are empirical values and functions of porosity
Because the very unpredictable nature of ceramic defects, we do not simply add a factor of safety for tensile loading
We may add compressive surface loads
We often choose to avoid tensile loading at all – most ceramic loading of any significance is compressive (consider buildings, dams, brigdes and roads!)

5. Figure 6.15 Stress (σm) at the tip of a Griffith crack.
Where the so called Griffith cracks are introduced into the ceramic or glass materials during processing
The crack tip “stress concentration” m can be very high since the “radius” of the crack tip () can be on the order of ionic diameters!

6. Mechanical Properties
i.e. stress-strain behavior of polymers
brittle polymer
FS of polymer ca. 10% that of metals
plastic
elastomer
elastic modulus – less than metal
Adapted from Fig. 15.1, Callister 7e.
Strains – deformations > 1000% possible (for metals, maximum strain ca. 100% or less)

7. Tensile Response: Brittle & Plastic
(MPa)
fibrillar structure
near
failure
Initial
Near Failure x
brittle failure
onset of
crystalline
regions align
necking
plastic failure x
crystalline
regions
slide
amorphous
regions
elongate
aligned,
cross-
linked
case
networked
unload/reload e
semi-
crystalline
case
Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along plastic response curve adapted from Figs & 15.13, Callister 7e. (Figs & are from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp )

8. Predeformation by Drawing
• Drawing…(ex: monofilament fishline)
-- stretches the polymer prior to use
-- aligns chains in the stretching direction
• Results of drawing:
-- increases the elastic modulus (E) in the
stretching direction
-- increases the tensile strength (TS) in the
-- decreases ductility (%EL)
• Annealing after drawing...
-- decreases alignment
-- reverses effects of drawing.
• Comparable to cold working in metals!
Adapted from Fig , Callister 7e. (Fig is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp )

9. Tensile Response: Elastomer Case
(MPa)
final: chains
are straight,
still
cross-linked x
brittle failure
Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along elastomer curve (green) adapted from Fig , Callister 7e. (Fig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)
plastic failure x x
elastomer
initial: amorphous chains are
kinked, cross-linked.
Deformation
is reversible! e
• Compare to responses of other polymers:
-- brittle response (aligned, crosslinked & networked polymer)
-- plastic response (semi-crystalline polymers)

10. Thermoplastics vs. Thermosets
Callister,
Fig. 16.9 T
Molecular weight Tg Tm
mobile
liquid
viscous
rubber
tough
plastic
partially
crystalline
solid
• Thermoplastics:
-- little crosslinking
-- ductile
-- soften w/heating
-- polyethylene
polypropylene
polycarbonate
polystyrene
• Thermosets:
-- large crosslinking
(10 to 50% of mers)
-- hard and brittle
-- do NOT soften w/heating
-- vulcanized rubber, epoxies,
polyester resin, phenolic resin
Adapted from Fig , Callister 7e. (Fig is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.)

11. T and Strain Rate: Thermoplastics
(MPa)
• Decreasing T...
-- increases E
-- increases TS
-- decreases %EL
• Increasing
strain rate...
-- same effects
as decreasing T. 20 4 6 8
Data for the
4°C
semicrystalline
polymer: PMMA
20°C
(Plexiglas)
40°C
to 1.3
60°C e
0.1
0.2
0.3
Adapted from Fig. 15.3, Callister 7e. (Fig is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.)

12. Melting vs. Glass Transition Temp.
What factors affect Tm and Tg?
Both Tm and Tg increase with increasing chain stiffness
Chain stiffness increased by
Bulky sidegroups
Polar groups or sidegroups
Double bonds or aromatic chain groups
Regularity (tacticity) – affects Tm only
Adapted from Fig , Callister 7e.

13. Figure Typical thermal-expansion measurement of an inorganic glass or an organic polymer indicates a glass transition temperature, Tg, and a softening temperature, Ts .

14. Time Dependent Deformation
• Stress relaxation test:
• Data: Large drop in Er
for T > Tg.
(amorphous
polystyrene)
Adapted from Fig. 15.7, Callister 7e. (Fig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) 10 3 1 -1 -3 5 60
100
140
180
rigid solid
(small relax)
transition
region
T(°C) Tg
Er (10s)
in MPa
viscous liquid
(large relax)
-- strain to eo and hold.
-- observe decrease in
stress with time.
time
strain
tensile test eo
s(t)
• Relaxation modulus:
• Sample Tg(C) values:
PE (low density)
PE (high density)
PVC PS PC
- 110
- 90
+ 87
+100
+150
Selected values from Table 15.2, Callister 7e.

15. Figure Upon heating, a crystal undergoes modest thermal expansion up to its melting point (Tm), at which a sharp increase in specific volume occurs. Upon further heating, the liquid undergoes a greater thermal expansion. Slow cooling of the liquid would allow crystallization abruptly at Tm and a retracing of the melting plot. Rapid cooling of the liquid can suppress crystallization producing a supercooled liquid. In the vicinity of the glass transition temperature (Tg), gradual solidification occurs. A true glass is a rigid solid with thermal expansion similar to the crystal, but an atomic-scale structure similar to the liquid (see Figure 4.21).

16. Figure 6.42 Illustration of terms used to define viscosity, η, in Equation 6.19.

17. Figure Viscosity of a typical soda–lime–silica glass from room temperature to 1,500°C. Above the glass transition temperature (~450°C in this case), the viscosity decreases in the Arrhenius fashion (see Equation 6.20).

18. Figure Thermal and stress profiles occurring during the production of tempered glass. The high breaking strength of this product is due to the residual compressive stress at the material surfaces.

19. Figure Modulus of elasticity as a function of temperature for a typical thermoplastic polymer with 50% crystallinity. There are four distinct regions of viscoelastic behavior: (1) rigid, (2) leathery, (3) rubbery, and (4) viscous.

20. Figure 6. 46 In comparison with the plot of Figure 6
Figure In comparison with the plot of Figure 6.45, the behavior of the completely amorphous and completely crystalline thermoplastics falls below and above that for the 50% crystalline material. The completely crystalline material is similar to a metal or ceramic in remaining rigid up to its melting point.

21. Figure Cross-linking produces a network structure by the formation of primary bonds between adjacent linear molecules. The classic example shown here is the vulcanization of rubber. Sulfur atoms form primary bonds with adjacent polyisoprene mers, which is possible because the polyisoprene chain molecule still contains double bonds after polymerization. [It should be noted that sulfur atoms can themselves bond together to form a molecule chain. Sometimes, cross-linking occurs by an (S)n chain, where n > 1.]

22. Figure Increased cross-linking of a thermoplastic polymer produces increased rigidity of the material.

23. Figure The modulus of elasticity versus temperature plot of an elastomer has a pronounced rubbery region.

24. Figure Schematic illustration of the uncoiling of (a) an initially coiled linear molecule under (b) the effect of an external stress. This illustration indicates the molecular-scale mechanism for the stress versus strain behavior of an elastomer, as shown in Figure 6.51.

25. Figure The stress–strain curve for an elastomer is an example of nonlinear elasticity. The initial low-modulus (i.e., low-slope) region corresponds to the uncoiling of molecules (overcoming weak, secondary bonds), as illustrated by Figure The high-modulus region corresponds to elongation of extended molecules (stretching primary, covalent bonds), as shown by Figure 6.50b. Elastomeric deformation exhibits hysteresis; that is, the plots during loading and unloading do not coincide.

26. Figure Modulus of elasticity versus temperature for a variety of common polymers. The dynamic elastic modulus in this case was measured in a torsional pendulum (a shear mode). The DTUL is the deflection temperature under load, the load being 264 psi. This parameter is frequently associated with the glass transition temperature.
(From Modern Plastics Encyclopedia, 1981–82, Vol. 58, No. 10A, McGraw-Hill Book Company, New York, October 1981.)