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Mechanical Engineering
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Lecture 34 - Temperature and rate effects on polymers E FFECT OF TEMPERATURE ON ELASTIC MODULUS OF POLYMERS Below T g Above T g Thermoplastics Thermoplastics • Only secondary bonds between chains • No bonding between chains • Modulus dictated by energy • Modulus dictated by entropy • Large strains cause fracture • Large strains ⇒ permanent deformation • Modulus ≈ 1 GPa as chains slide over each other Thermosets Thermosets • Extensive covalent cross-links & secondary • Extensive covalent cross-links between bonds between chains chains. • Modulus dictated by energy • Modulus dictated primarily by energy • Large strains cause fracture • Large strains involve bond rupture and yielding (permanent deformation) Elastomers Elastomers • A few covalent cross-links & secondary • A few covalent cross-links bonds between chains • Modulus dictated by entropy • Large strains recovered elastically • Modulus dictated by energy because the few cross-links provide • Modulus ≈ 1 GPa memory of unstrained state. • Modulus increases with extent of cross linking, chain size and side groups 50 100 E FFECTS OF TIME ON D EFORMATION OF POLYMERS • Chain motion impeded by tangles ⇒ activation energy needs to be overcome • Molecules and atoms vibrate with a frequency ν ∴ Probability (/second) that obstacles to motion will be overcome =−Q/RT ) ME382 - 16/iv/14 1 Lecture 34 - Temperature and rate effects on polymers ∴ For a given stress: strain ↑ as hold time ↑ or as T ↑ • Both reversible and permanent deformation (creep) may have time- & temperature- dependence • This sort of model gives rise to hysteresis Time-dependent modulus increase T E t,T = σ/ε t,T ) Note that this definition incorporates any possible creep strain as well as real elastic strain Fixed σ and T - measure ε(t) ⇒ calculate E(t) • For a given stress can obtain same strain by t ↑ or T ↓ increase t • Stress-relaxation modulus for fixed applied strain and monitoring stress as function of time ME382 - 16/iv/14 2 Lecture 34 - Temperature and rate effects on polymers Empirical relationship between time and temperature (WLF equation) • Empirical shift factor given by Williams, Landel and Ferry (WLF) equation: 17.5(T1− Tg) log a T 52+ T 1 T g Example: Polypropylene E = 1.5 GPa at T = 293 K and t = 100 secs. If Tg= 253 K, what is loading time to give the same modulus at 30 °C? 17.5(293− 253 ) Shift 1: 20° C → T g log aT= = 7.61 52+ 293 − 253 Shift 2: 30° C → T : g log( T= 17.5(303−253 )= 8.58
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