Chapt. 7 Mechanics Properties of polymers 7.1 Basic physical quantities Stress, strain, modulus 7.2 Mechanics properties of rubber elasticity Theory of rubber elasticity 7.3 Fracture Mechanics of Brittle materials Griffith Theory 7.4 Fracture properties of polymer in glassy and crystalline state Yield(屈服), Craze(银纹, Fracture(断裂)
Chapt. 7 Mechanics Properties of Polymers 7.1 Basic physical quantities 7.3 Fracture Mechanics of Brittle Materials Stress, strain, modulus Theory of rubber elasticity 7.4 Fracture properties of polymer in glassy and crystalline state Yield(ቸᴽ), Craze(䬦㓩), Fracture(ᯝ㻲) 1 7.2 Mechanics properties of rubber elasticity Griffith Theory
Mechanical properties of polymer Bulk polymers combine elastic and viscous properties in both the fluid and the solid state. Therefore they are generally addressed as“ viscoelastic”(.弹)and,in fact, polymers are the main representatives of this special class of materials. Different fields of polymer application are concerned and they all need their own approaches: the properties under moderate loads, where deformations and velocities of viscous flow remain small the case of large reversible deformations realized in rubbers and the rheological properties of polymer melts at higher strain rates, both representing non-linear behavior and finally, of special importance for applications, yielding (h 服) and fracture(断裂)
Mechanical properties of polymer: Bulk polymers combine elastic and viscous properties in both the fluid and the solid state. Therefore, they are generally addressed as “viscoelastic” (㋈ᕩ) and, in fact, polymers are the main representatives of this special class of materials. ¾ Different fields of polymer application are concerned and they all need their own approaches: ¾ the properties under moderate loads, where deformations and velocities of viscous flow remain small ¾ the case of large reversible deformations realized in rubbers and the rheological properties of polymer melts at higher strain rates, both representing non-linear behavior ¾ and finally, of special importance for applications, yielding (ቸ ᴽ) and fracture (ᯝ㻲)DŽ 2
7.1 Stress strain and modulus ensue shear bulk F
7.1 Stress, strain and Modulus F F l0 l A0 T A0 F tensile shear bulk 3
Characterization of viscous flow 复杂流动方式的分解:三种最基本的流动变形)方式 a剪切流动(形变) shear viscosity n、b拉伸流动(形变) tensile viscosity n velocity gradient→ c.压缩流动(形变)- bulk viscosity for incompressible fluids nb)00
Characterization of viscous flow ༽ᵲ⍱ࣘᯩᔿⲴ࠶䀓˖й⿽ᴰสᵜⲴ⍱ࣘ)ਈᖒ)ᯩᔿ a.࠷࢚⍱ࣘ)ᖒਈ)-shear viscosity Ks b.ը⍱ࣘ)ᖒਈ)-tensile viscosity Kt c. 㕙⍱ࣘ)ᖒਈ)-bulk viscosity for incompresible fluids Kbof velocity gradient 2 dv dx 4
7.1 Stress strain and modulus tensile shear bulk F b F △F t-I A 2-1E tan≈0 B=o/4 e=oE Young's Modulus G=o/y Shear Modulus Bulk Modulus 5
7.1 Stress, strain and Modulus 0 tan s F A l l V J TT ' | ,N 0 0 0 1 t F A l l l V H O F F l0 l A0 T A0 F 0 , 0 ln t t l l F A dl l l l V H ³ G=Vs E=V /J t /H 0 b P V V V ' ' B=Vb /' tensile shear bulk Young’s Modulus Shear Modulus Bulk Modulus 5
isotropic ideal solids △ △Z v: Poisson ratio v= △m/mo △l/l E E=2(1+v)=3B(1-2v) Incompressible solids v=0.5 E=3G
isotropic ideal solids EG B 2 1 3 12 Q Q Q: Poisson ratio 'm 'l 0 0 / / m m t l l H Q H ' ' Incompressible solids Q=0.5 E=3G 6
anisotropic ideal solids Oxx=axExxtary ExytaxEx t a =ao o ta+ σ」=[a[] LE,=la, 'lo, generalized hook,'s law广义虎克定律)
anisotropic ideal solids ... xx xx xx xy xy xz xz V HHH aaa ij ij ij ª º ª ºª º V H a ¬ ¼ ¬ ¼¬ ¼ Vxx Vyy Vzz generalized hook’s law (ᒯѹ㱾ݻᇊᖻ) 7 ' ij ij ij ª º ª ºª º H V a ¬ ¼ ¬ ¼¬ ¼ ' ' ' ... xx xx xx xy xy xz xz HVVV aaa
Nonlinear behaviors of Materials Property Elongation at break Elongation Initial modulus Strength f△ 08= f△/V odE=lfal/Vo=W/Vo Work(功) of Unit volume
Nonlinear Behaviors of Materials Property 8 VH 0 0 f l A l ' 0 'f lV/ 0 V Hd fdl V / ³ ³ Work(࣏ (of Unit Volume 0 W V/ Initial modulus Strength
7.2 Rubber (Elastomers) and rubber Elasticity General properties of elastomers The individual polymer chains of elastomers are held together by weak termolecular bonding forces which allow rapid chain slippage when a moderate pulling force is employed. Cross-links, which are introduced during vulcanization(硫化), permit rapid 经 elongation of the principal sections, to a point where the chains are stretched to Typical applied-force elongation behavior of rubber their elastic limit. Any additional elongation causes primary bond breakage. The cross-links which are the boundaries for the principal sections, permit the rubber to“ remember” its original shape, Sulphur bridges Hard domain with邮啦 that is, the original orientation of the linking cis-1, 4- Structure of thermo povIoDrene particular chains. plastic elastomers
7.2 Rubber (Elastomers) and Rubber Elasticity ¾ General properties of elastomers ¾ The individual polymer chains of elastomers are held together by weak intermolecular bonding forces, which allow rapid chain slippage when a moderate pulling force is employed. ¾ Cross-links, which are introduced during vulcanization (⺛ॆ), permit rapid elongation of the principal sections, to a point where the chains are stretched to their elastic limit. Any additional elongation causes primary bond breakage. The cross-links, which are the boundaries for the principal sections, permit the rubber to “remember” its original shape, that is, the original orientation of the particular chains. Typical applied-forceelongation behavior of rubber Sulphur bridges linking cis-1,4- polyisoprene Structure of thermoplastic elastomers 9
8 旦 Vulcanized rubber Unvulcanized rubber 200 400 Elongation, o
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