Mechanical Behavior mostly Ceramics, Glasses and Polymers

Chapter 6: Part 2Dr. R. Lindeke

• Room T behavior is usually elastic, with brittle failure.• 3-Point Bend Testing is often used. -- tensile tests are difficult for brittle materials!

Adapted from Fig. 12.32, Callister 7e.

Measuring Elastic Modulus

FL/2 L/2

= midpoint deflection

cross section

R

b

d

rect. circ.

F

linear-elastic behavior

• Determine elastic modulus according to:

x

d

F

dslope =

E =F

d

L3

4bd 3=

F

d

L3

12pR 4

rect. cross

section

circ.cross

section

• 3-point bend test to measure room T strength.

Adapted from Fig. 12.32, Callister 7e.

Measuring StrengthF

L/2 L/2

= midpoint deflection

cross section

R

b

d

rect. circ.

location of max tension

• Flexural strength: • Typ. values:

Data from Table 12.5, Callister 7e.

rect.

s fs =1.5Ff L

bd 2

=Ff L

pR3Si nitrideSi carbideAl oxideglass (soda)

250-1000100-820275-700

69

30434539369

Material sfs (MPa) E(GPa)

xF

Ff

dfsd

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!)

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!

Mechanical Properties

• i.e. stress-strain behavior of polymers

brittle polymer

plasticelastomer

FS of polymer ca. 10% that of metals

Strains – deformations > 1000% possible (for metals, maximum strain ca. 100% or less)

elastic modulus – less than metal

Adapted from Fig. 15.1, Callister 7e.

Tensile Response: Brittle & Plastic

brittle failure

plastic failure

s (MPa)

e

x

x

crystalline regions

slide

fibrillar structure

near failure

crystalline regions align

onset of necking

Initial

Near Failure

semi-crystalline

case

aligned,cross-linkedcase

networkedcase

amorphousregions

elongate

unload/reload

Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along plastic response curve adapted from Figs. 15.12 & 15.13, Callister 7e. (Figs. 15.12 & 15.13 are from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)

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 stretching direction -- decreases ductility (%EL)• Annealing after drawing... -- decreases alignment -- reverses effects of drawing.• Comparable to cold working in metals!

Adapted from Fig. 15.13, Callister 7e. (Fig. 15.13 is from J.M. Schultz, Polymer Materials Science, Prentice-Hall, Inc., 1974, pp. 500-501.)

• Compare to responses of other polymers: -- brittle response (aligned, crosslinked & networked polymer) -- plastic response (semi-crystalline polymers)

Stress-strain curves adapted from Fig. 15.1, Callister 7e. Inset figures along elastomer curve (green) adapted from Fig. 15.15, Callister 7e. (Fig. 15.15 is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.)

Tensile Response: Elastomer Case

s (MPa)

e

initial: amorphous chains are kinked, cross-linked.

x

final: chainsare straight,

stillcross-linked

elastomer

Deformation is reversible!

brittle failure

plastic failurex

x

• 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. 15.19, Callister 7e. (Fig. 15.19 is from F.W. Billmeyer, Jr., Textbook of Polymer Science, 3rd ed., John Wiley and Sons, Inc., 1984.)

Thermoplastics vs. Thermosets

Callister, Fig. 16.9

T

Molecular weight

Tg

Tmmobile liquid

viscous liquid

rubber

tough plastic

partially crystalline solid

crystalline solid

• Decreasing T... -- increases E -- increases TS -- decreases %EL

• Increasing strain rate... -- same effects as decreasing T.

Adapted from Fig. 15.3, Callister 7e. (Fig. 15.3 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.)

T and Strain Rate: Thermoplastics

20

40

60

80

00 0.1 0.2 0.3

4°C

20°C

40°C

60°Cto 1.3

s (MPa)

e

Data for the semicrystalline polymer: PMMA (Plexiglas)

Melting vs. Glass Transition Temp.

What factors affect Tm and Tg?

• Both Tm and Tg increase with increasing chain stiffness

• Chain stiffness increased by1. Bulky sidegroups2. Polar groups or sidegroups3. Double bonds or aromatic

chain groups

• Regularity (tacticity) – affects Tm only

Adapted from Fig. 15.18, Callister 7e.

Figure 6.40 Typical thermal-expansion measurement of an inorganic glass or an organic polymer indicates a glass transition temperature, Tg, and a softening temperature, Ts .

• Stress relaxation test:-- strain to eo and hold.-- observe decrease in stress with time.

or

ttE

)(

)(

• Relaxation modulus: • Sample Tg(C) values:PE (low density)PE (high density)PVCPSPC

- 110- 90+ 87+100+150

Selected values from Table 15.2, Callister 7e.

Time Dependent Deformation

time

strain

tensile testeo

s(t)

• Data: Large drop in Er

for T > Tg. (amorphouspolystyrene)

Adapted from Fig. 15.7, Callister 7e. (Fig. 15.7 is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.)

103

101

10-1

10-3

105

60 100 140 180

rigid solid (small relax)

transition region

T(°C)Tg

Er (10s) in MPa

viscous liquid (large relax)

Figure 6.41 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).

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

Figure 6.43 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).

Figure 6.44 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.

Figure 6.45 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.

Figure 6.46 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.

Figure 6.47 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.]

Figure 6.48 Increased cross-linking of a thermoplastic polymer produces increased rigidity of the material.

Figure 6.49 The modulus of elasticity versus temperature plot of an elastomer has a pronounced rubbery region.

Figure 6.50 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.

Figure 6.51 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 6.50. 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.

Figure 6.52 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.)