Viscoelastic Material Modelsmi@seu.edlu.cn
Viscoelastic Material Models
Outline·Introduction（引」言）·Creep compliance and relaxationmodulus（蠕变柔度与松弛刚度）·Retardedelasticity（滞／粘弹性）·Steady-state creep（稳态蠕变）·Elasticvs.viscoelasticmaterials（弹性与粘弹性材料）·Maxwellmaterials（Maxwell模型）·Kelvin-voigt materials（KV模型）·Pronyseriesrepresentation（Prony级数模型）·WLFtime/temperatureequivalence（WLF时间／温度相当）·Calibratingviscoelastic models（粘弹性模型校准）·More sophisticatedviscoelasticmodels（复杂粘弹性模型）·Generalizationto3D（向三维模型推广）·Responseto harmonic loading（周期载荷的响应）2
Outline • Introduction（引言） • Creep compliance and relaxation modulus（蠕变柔度与松弛刚 度） • Retarded elasticity（滞/粘弹性） • Steady-state creep（稳态蠕变） • Elastic vs. viscoelastic materials（弹性与粘弹性材料） • Maxwell materials（Maxwell模型） • Kelvin-voigt materials（KV模型） • Prony series representation（Prony级数模型） • WLF time/temperature equivalence（WLF时间/温度相当） • Calibrating viscoelastic models（粘弹性模型校准） • More sophisticated viscoelastic models（复杂粘弹性模型） • Generalization to 3D（向三维模型推广） • Response to harmonic loading（周期载荷的响应） 2
Introduction.Amorphouspolymersshowcomplextime-dependentbehaviorwhen subjectedtoahistoryofstressorstrain.Viscoelasticity theory was developed to approximate this behavior in polymersthat are subjected to modest strains (less than 0.5%): Polymers strongly resist volume changes at all temperatures. The bulk modulus iscomparabletothatofmetalsorcovalentlybondedsolidsThe shearresponse of a polymer is stronglytemperaturedependent.Shear modulus (N/m?)ViscoelasticGlassy109RubberyMelt105GlasstransitiontemperatureTTemperature3
• Amorphous polymers show complex time-dependent behavior when subjected to a history of stress or strain. • Viscoelasticity theory was developed to approximate this behavior in polymers that are subjected to modest strains (less than 0.5%). • Polymers strongly resist volume changes at all temperatures. The bulk modulus is comparable to that of metals or covalently bonded solids. • The shear response of a polymer is strongly temperature dependent. Introduction 3 Shear modulus (N/m2 )
Introduction· At temperatures near the glass transition, the shear modulus is strongly timedependent. The time dependent shear response can be measured by applying (1) astep load or (2) a harmonic (sinusoidal) load to the specimen.The time-dependent modulus of polymers is also temperature dependentReducing the temperature is qualitatively equivalent to increasing the strain rateMost amorphous polymers are isotropicShearmodulus (N/m?)ViscoelasticGlassyButyl109RubberyMelt105Glass transitiontemperatureTTemperature4
Introduction 4 Shear modulus (N/m2 ) • At temperatures near the glass transition, the shear modulus is strongly time dependent. The time dependent shear response can be measured by applying (1) a step load or (2) a harmonic (sinusoidal) load to the specimen. • The time-dependent modulus of polymers is also temperature dependent. Reducing the temperature is qualitatively equivalent to increasing the strain rate. • Most amorphous polymers are isotropic
Response to Step Loading8O? Creep compliance:the strain response toa unit constant stress30 Relaxation modulus:the stress response to aunit constant strain.. The results of such a test depend on the degree of cross-linking inthe polymer.. Heavily cross-linked materials show “retarded elastic" behavior.whereas un-cross-linked materials show steady-state creep5
• Creep compliance: the strain response to a unit constant stress • Relaxation modulus: the stress response to a unit constant strain. Response to Step Loading 5 • The results of such a test depend on the degree of cross-linking in the polymer. • Heavily cross-linked materials show “retarded elastic” behavior, whereas un-cross-linked materials show steady-state creep