Mechanical behavior

11.6 Mechanical behavior

11.6.1 Deformation

At a basic level, the mechanical behavior of polymers may be compared directly with that of metals, in that stress–strain properties, modulus, tensile strength, elongation, etc. are measured. The broad classification of polymers into thermoplastics, thermosets and elastomers gives rise to distinctly different stress–strain curves, as shown in Figure 11.10. While these curves are somewhat similar to brittle, ductile and superplastic metals, polymer materials are neither as strong nor as stiff as metals.

The glass transition temperature T g is an important parameter in defining the mechanical properties, which are extremely sensitive to changes of temperature within the vicinity of room temperature. Table 11.2 gives the mechanical characteristics of some of the common polymers.

The slope of the stress–strain curve increases with increasing strain rate, and decreasing temperature has a similar effect. Modulus is particularly dependent on temperature and usually divided into three regions, namely rigid, leathery and rubbery, as shown in Figure 11.11. Increasing the molecular weight tends to increase the rubbery region, while an increase of crystallinity raises the melting point and thus the modulus of the rubbery region.

With reference to Figure 11.12, during the elastic deformation of a semicrystalline polymer, it is mostly the chain molecules which elongate. This is followed by an upper yield point, when a small

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Stress (MPa) 20 x

Figure 11.10 Stress–strain behavior of brittle (A), plastic (B) and elastomeric (C) polymers. Table 11.2 Mechanical properties of some polymers.

Elong % Density

Strength MPa at break Mgm −3 Polyethylene (LDPE)

modulus GPa

0.95 Polyvinyl chloride (PVC)

3.2 42 46 60 1.3 Polypropylene (PP)

0.9 Polystyrene (PS)

2.8 50 50 2 1.0 Polycarbonate (PC)

1.2 Polytetrafluoroethylene (PTFE)

48 10 1.35 (Bakelite) Polymethacrylate

m 8 Leathery

(b) Figure 11.11 Temperature dependence of tensile modulus (a) and time dependence of relaxation

(a)

modulus (b) in thermoplastic polymeric solid ( from Hertzberg, 1989; by permission of John Wiley and Sons).

neck forms and locally strengthens as the chains align (curve B in Figure 11.10). A lower yield point follows when the deformed region spreads along the tensile gauge length. During plastic deformation the amorphous regions between the lamellae stretch as they attempt to align with the tensile axis, following which the lamella regions attempt to reorient themselves. With increasing deformation,

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Figure 11.12 Structural change in a semicrystalline polymer during tensile elongation (after Schultz, 1974).

more and more lamella regions become aligned with the stress axis until after a significant deformation the polymer is highly oriented. The lamellae are broken down into smaller ‘blocks’, making up microfibrils, as shown in Figure 11.12. The individual blocks retain their chain-folding structure and are linked together by the molecules from the unfolding of the original lamellae. With this process the spherulite structure undergoes a considerable shape change and is very much broken up by extensive deformation. Nevertheless, annealing of the polymer close to the melting point tends to recover some of the original structure.

11.6.2 Viscoelasticity

Under certain conditions most polymers will behave in a viscoelastic manner when stressed and to exhibit both viscous (i.e. time-dependent) and elastic (instantaneous) strain characteristics. Vis- coelastic behavior is dependent on time and temperature, and may be studied using a stress relaxation technique when a specimen is strained in tension to a predetermined, relatively low, level, as shown in Figure 11.13. The stress necessary to maintain the strain ε o is found to decrease with time, due to molecular relaxation processes, and the relaxation modulus E t at a time t is given by

E t =σ t /ε o . The variation of log E t with time is shown in Figure 11.11b and is similar to the tensile elastic modulus

versus temperature curve (Figure 11.11a). When the stress level is maintained constant, viscoelastic creep takes place. The results are dis- played, as for metals, in a strain versus time plot. The creep rate is temperature dependent and increases sharply as the temperature approaches T g . The effects of viscoelasticity can also be easily demon- strated in a nanoindentation test during unloading (Section 4.8.4). During slow unloading from the peak load (Figure 11.14), even though the load is reducing the indenter may still keep sinking further into the polymer, resulting in a ‘nose’-shaped unloading curve. The viscous strain component always increases as long as a positive load is acting, and so if it dominates over the elastic component, the overall strain will still be increasing even though the load is reducing. However, at a high unloading rate, the viscous component may become a lot stiffer than the elastic component, so that the overall response may become very elastic.

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Tensile stress e o

Tensile strain e

Figure 11.13 Stress relaxation at constant strain.

Loading rate: 800 mN min ⫺ 1

Holding time at peak load: 2 s

120 Load (mN) 100 80 60

Displacement (nm) Unloading rate ⫽ 10 mN min ⫺ 1

Unloading rate ⫽ 500 mN min ⫺ 1

Figure 11.14 Nanoindentation load–displacement curves of polypropylene at different unloading rates at room temperature. At a small unloading rate, the unloading curve becomes

nose shaped, with a negative apparent unloading stiffness (Tang and Ngan, 2003).

11.6.3 Fracture

Overall, the fracture toughness of polymers is quite low (K c ∼ 1 MN m −3/2 ), because of their low modulus. However, thermoplastic polymers exhibit both brittle and ductile modes of fracture and can display a brittle–ductile transition. Lowering temperature, increase of strain rate, sharp notches, etc. all favor brittle behavior. Brittle amorphous polymers are characterized by crazing, which can form at

a stress much lower than yield stress. Crazes are narrow zones of highly deformed polymer containing microvoids ∼10–20 nm separated by bridges 10–40 nm in diameter of oriented molecular chains. They are usually formed in glassy polymers (PMMA, PS) but may occur in semicrystalline polymers such as PP. With increasing stress, microvoids grow and coalesce to resemble a crack. The craze differs from the final crack in that it can still support some load across the craze (Figure 11.15). Crazes are easily visible even to the naked eye and may be induced by chemical agents and stress. The stress for crazing is temperature dependent and as mobility increases so the stress for crazing decreases. Chemical agents increase the susceptibility and the resultant fracture is termed environment stress cracking (ESC), with amorphous polymers being more susceptible than semicrystalline polymers.

Although not a proper crack, crazing can cause leakage if the specific polymer is used for pipes.

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Intact fibril

Broken fibril

Figure 11.15 Schematic structure of a craze.

Stress amplitude (MP 10 3 10 5 10 7

Cycles to failure

Figure 11.16 Schematic fatigue curves for: (i) PS, (ii) PMMA, (iii) PP and (iv) PE.

Temperature (°C) 0 ⫺ 200 ⫺ 100

1s ⫺ 1 Brittle fracture

10 ⫺ 6 s ⫺ 1 Cold

10 ⫺ 3 Crazing and

10 shear yielding 1 Decomposition

drawing

Strength (MPa)

E 0 PMMA ⫽ 8.57 GPa

Normalized strength (strength

Viscous

Contours of strain rate T g ⫺ ⫽ 378 k 5 10 ⫺ 6 s ⫺ 1 flow 1s ⫺ 10 1 ⫺ 1 0 0.4 0.8 1.2 1.6 10

Normalized temperature (T/T g )

Figure 11.17 Deformation map for PMMA showing deformation regions as a function of normalized stress versus normalized temperature ( from Ashby and Jones, 1986).

The craze can become a proper crack and propagate as a result of the stress concentration at the tip. Polymers like the epoxy resins have very low toughness values because the cross-linking prevents the flow of material at the tip to blunt the crack.

The fatigue strength of most polymers shows the same features as metals when the stress amplitude is plotted against cycles to failure (Figure 11.16). Fatigue occurs at low stress levels relative to the yield strength. Polyethylene has relatively poor fatigue properties compared to polypropylene and polyester (PET). Using the concept of deformation maps, Ashby has shown it is possible to portray the strength–temperature characteristics of polymers (Figure 11.17).

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