Viscoelasticity Defined Range of Material Behavior Solid Like ----------Liguid Like Ideal Solid ----Most Materials -----ldeal Fluid Purely Elastic ----Viscoelastic -----Purely Viscous Viscoelasticity Having both viscous and elastic properties
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
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 mathematical theory of linear viscoelasticity is based on a "superposition principle".This implies that the response (e.g.strain)at any time is directly proportional to the value of the initiating signal (e.g.stress).So,for example,doubling the stress will double the strain.In the linear theory of viscoelas- ticity,the differential equations are linear.Also,the coefficients of the time differentials are constant.These constants are material parameters,such as viscosity coefficient and rigidity modulus,and they are not allowed to change with changes in variables such as strain or strain rate.Further,the time derivatives are ordinary partial derivatives.This restriction has the consequence that the linear theory is applicable only to small changes in the variables
D。=where D。.is the Deborah number 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
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 T De
Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" Deborah Number [De]=t/T Relaxation time T is short [ T is long [24
Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" T is short [< 1s] T is long [24 hours] Deborah Number [De] = / Relaxation time
STORAGE&LOSS OF VISCOELASTIC MATERIAL SUPER BALL LOSS TENNIS BALL STORAGE
STORAGE & LOSS OF VISCOELASTIC MATERIAL SUPER BALL TENNIS BALL X STORAGE LOSS
Response for Classical Extremes Spring Purely Elastic Dashpo p Purely Viscous Response Response Hookean Solid Newtonian Liquid o ny 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
Response for Classical Extremes Purely Elastic Response Hookean Solid s = G 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 Dashpo t Purely Viscous Response Newtonian Liquid s =
y瓢-对 where where % iscalled x=% the relaxation time Maxwell Kelvin-Voigt J-Ta i is called the complaince
s 1 G t where G is called the relaxation time s G 1 e t where = G J s is called the complaince
Mechanical analogs of viscoelastic liquids o Gy o=ny Maxwell Kelvin-Voigt Burgers The Maxwell,Kelvin-Voigt and Burgers models
s s 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 angleδ and response is measured
Dynamic Mechanical Testing Deformation Response Phase angle –An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. –The material response (strain or stress) is measured. –The phase angle , or phase shift, between the deformation and response is measured