Viscoelasticity Defined Range of Material Behavior Solid Like-Liquid Like Ideal Solid----Most Materials-----/dea/Fluid Purely Elastic-Viscoelastic----Purely Viscous Viscoelasticity:Having both viscous and elastic properties Linear Viscoelasticity .The word viscoelastic means the simultaneous existence of viscous and elastic properties in a material. .It is not unreasonable to assume that all real materials are viscoelastic. .The response of a material to an experiment depends on the time-scale of the experiment in relation to a natural time of the material. .Initially,the restoring force increases linearly with the distance that any deformation takes the material away from its rest state,but eventually non-linearities will be encountered. The meaning and consequences of linearity The development of the mathem 1
1 Range of Material Behavior Solid Like ---------- Liquid Like Ideal Solid ----- Most Materials ----- Ideal Fluid Purely Elastic ----- Viscoelastic ----- Purely Viscous Viscoelasticity Defined Viscoelasticity : Having both viscous and elastic properties Linear Viscoelasticity •The word viscoelastic means the simultaneous existence of viscous and elastic properties in a material. •It is not unreasonable to assume that all real materials are viscoelastic. •The response of a material to an experiment depends on the time-scale of the experiment in relation to a natural time of the material. •Initially, the restoring force increases linearly with the distance that any deformation takes the material away from its rest state, but eventually non-linearities will be encountered
D.where D.is the Deborah number r is the characteristic or relaxation time associate with the material,and T is a characteristic time of the deformation process High Deborah numbers correspond to solids and Low Deborah numbers correspond to liquids Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of"Silly Putty" Deborah Number [De]=t/T Relaxation time Tis short[k1s】 T is long [24 hours] STORAGE LOSS OF VISCOELASTIC MATERIAL ◆SUPER BALL LOSS TENNIS BALL STORAGE 2
2 Low Deborah numbers correspond to liquids High Deborah numbers correspond to solids and T is a characteristic time of the deformation process is the characteristic or relaxation time associate with the material, and where D is the Deborah number e τ τ T De = Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" T is short [< 1s] T is long [24 hours] Deborah Number [De] = τ / Τ Relaxation time STORAGE & LOSS OF VISCOELASTIC MATERIAL SUPER BALL TENNIS BALL X STORAGE LOSS
Response for Classical Extremes Spring Purely Elastic Dashpot Purely Viscous Response Response Hookean Solid Newtonian Liquid o=Gy o=nt In the case of the classical extremes,all that matters is the values of stress,strain,strain rate.The response is independent of the loading. 为 where where is called b the relaxation time Maxwell Kelvin-Voigt = is called the complaince Mechanical analogs of viscoelastic liquids o=GY 0=71 Maxwell Kelvin-Voigt Burgers The Maxwell,Kelvin-Voigl and Burgers models. 3
3 Response for Classical Extremes Purely Elastic Response Hookean Solid σ = Gγ In the case of the classical extremes, all that matters is the values of stress, strain, strain rate. The response is independent of the loading. Spring Dashpot Purely Viscous Response Newtonian Liquid σ = ηγ. γ = σ 1 G + t η ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ where η G is called the relaxation time γ = σ G 1− e −t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ where τ =η G J = γ σ is called the complaince σ ηγ σ γ = & = G Mechanical analogs of viscoelastic liquids
Dynamic Mechanical Testing -An oscillatory (sinusoidal) Deformation deformation (stress or strain) is applied to a sample. -The material response Response (strain or stress)is measured The phase angleδ，or phase shift,between the deformation Phase angle and response is measured. Given y=。sinot For Solids: For Liquids: o=Gy=Gy。sin ot dy=n dt a-mi-nd d (y。sino) 0=7@Y。c0s0M Dynamic Mechanical Testing Response for Classical Extremes Purely Elastic Purely Viscous Response Response (Hookean Solid) (Newtonian Liquid) 8=0° 8=90° Str Strain 4
4 Dynamic Mechanical Testing Deformation Response Phase angle δ –An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. –The material response (strain or stress) is measured. –The phase angle δ, or phase shift, between the deformation and response is measured. t t dt d dt d G G t For t Given o o o σ ηω γ ω η γ ω γ σ γ γ ω σ ηγ η γ γ ω cos sin ( sin ) Solids: For Liquids: sin = o = = = = = = & Dynamic Mechanical Testing Response for Classical Extremes Stress Strain δ = 0° δ = 90° Purely Elastic Response (Hookean Solid) Purely Viscous Response (Newtonian Liquid) Stress Strain
Dynamic Mechanical Testing Viscoelastic Material Response Phase angle 0°<8<90 Strain Stress G*1=Yo Complex Parameters their Components G*=G'+iG" Complex Storage Loss Modulus Modulus Modulus G★ Real Root Imaginary Root G tan 8 =G"/G' Dairy Products ·Fluid Milk Cultured Dairy Products cottage cheese cheese yogurt sour cream etc. Ice Cream 5
5 Dynamic Mechanical Testing Viscoelastic Material Response Phase angle 0° < δ < 90° Strain Stress |G*| = σο/γο γο σο Complex Parameters & their Components G* G' G" tan δ = G"/G' G* = G' + iG" Complex Modulus Storage Modulus Loss Modulus Real Root Imaginary Root δ Dairy Products • Fluid Milk • Cultured Dairy Products cottage cheese cheese yogurt sour cream etc. • Ice Cream