General Maxwell Model For stress relaxation relaxation time spectrum(松弛时间谱) E(1)=∑Ee H(=f(G E(1=H(G)e"'dInt E(=f()e"dr II 6 罗 ngle T log T+ A MWe>>L
General Maxwell Model / i t i i E t Ee W ¦ / 0 t Et f e dW W W f ³ For stress relaxation relaxation time spectrum (ᶮᕋᰦ䰤䉡) Ht f W W Mw: III>II>>I / ln t Et H e dW W W f f ³ single W polymer 21
Viscosity relaxation modulus E(0=Eet 7=,E E(1)=∑Ee" E(dt=eeltdt=Eh"dt=Et,=n n=∑=∑.E()h=∑E()t eliot n(T)=E(T, 1)
Viscosity & Relaxation Modulus 22 / i t i i E t Ee W ¦ K W i ii E / i t E t Ee i i W / / 00 0 i i t t E t dt Ee dt E e dt E i i i ii i W W W K ff f ³³ ³ 00 0 ii i ii i K K E t dt E t dt E t dt ff f ¦¦ ¦ ³³ ³ 0 K T E T t dt , f ³
General Voigt model For creep retardation time spectrum(推迟时间谱) D()=L()(1-e"lnr For creep recovery D2(()=L()e"d InT For dynamic mechanics Eo E General maxwell Model E ∑ 1+o2r 1+ or aT General Voigt Model E.(1+02r E Oτ
General Voigt Model For creep retardation time spectrum (᧘䘏ᰦ䰤䉡) 2 2 22 22 * 1 1 i i ii i i i i E E E i Z W ZW ZW ZW ¦ ¦ / 1 1 1 ln t Dt L e d W W W f f ³ For dynamic mechanics 22 22 1 * 1 1 i i i ii ii D i E E ZW ZW ZW ¦ ¦ or General Maxwell Model General Voigt Model For creep recovery / 2 2 ln t Dt L e dW W W f f ³ 23
iscosity Modulus Relaxation Time Solid Elasticity (short) Liquid Viscosity (long) o=Ea σ=m7(dad) Viscoelasticity of Polymer TFni E i-th movement mode Modulus vs relaxation Time E(T,1)=∑E(7)e E(T, 1)=H(T, r)e"dInt Viscosity Vs Modulus relaxation time spectrum 1. oscillatory shear E To n"(7,o) E(T,) n'(T,o 2. static shear E(T, tdt
Viscosity & Modulus & Relaxation Time 24 ' " , , E T T Z K Z Z " ' , , E T T Z K Z Z 0 K T E T t dt , f ³ 1. oscillatory shear 2. static shear / , ln , t ETt e d H T W W W f f ³ Modulus vs Relaxation Time Viscosity vs Modulus Wi =Ki /Ei i-th movement mode / , i t i i ETt E T e W ¦ relaxation time spectrum Viscoelasticity of Polymer Solid Elasticity(short) Liquid Viscosity(long) V = EH V = K(dHdt)
5.2 Viscous Flow of polymers > The rheological properties(流变性质)of polymers is extremely important for polymer processing Rheology: The study of the deformation and flow of matter Strain Stress Velocity
5.2 Viscous Flow of Polymers ¾The rheological properties (⍱ਈᙗ䍘) of polymers is extremely important for polymer processing Stress Strain Velocity Rheology: The study of the deformation and flow of matter. 25