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

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. 12.32, 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

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. 12.32, 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) 250-1000 100-820 275-700 69 304 345 393 Material (MPa) E(GPa) x F Ff d

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 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)

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. 15.12 & 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 -- 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.)

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. 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.) 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)

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. 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.)

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. 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.)

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. 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 .

Time Dependent Deformation • Stress relaxation test: • Data: Large drop in Er for T > Tg. (amorphous polystyrene) 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.) 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.

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 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.)