Viscoelasticity and dynamic mechanical testing

1 1 AN004AN004 Viscoelasticity and dynamic mechanical testing A. Franck, TA Instruments GermanyKeywords: dynamic mechanical testing , Viscoelasticity , Hookean body, Newtonian fluid, relaxation time, ,VISCOELASTICITYMost materials are not purely viscous and oftenshow significant elastic behavior. Such materials arereferred to as viscoelastic materials and the keyparameter, the time determines whether viscous orelastic behavior in a slow deformation or flow processthe viscous behavior dominates, whereas in a shorttime process the material behaves predominatelyelastic. Whether a process is fast or slow dependson a characteristic internal material material will be perceived as a viscous liquidif the material time is very short in comparison tothe time of the deformation process.

2 For example,the material time of water is about 10-10 s and anydeformation process must seem very long comparedto that value. If on the other hand the material timeis long, it will be seen as an elastic solid, glasswhich has a material time in the range of hundredsof relationship between experiment or processtime and material time is given by a dimensionlessnumber, the Deborah number De (or Weissenbergnumber) and is defined as the ratio of material toprocess time. If a rheological experiment is fasterthan the relaxation process, the material will appearelastic (high De number), otherwise the viscous partwill dominate (low De number). Measurements inthe elastic region provide information about thematerials internal structure, molecular orphysical (morphology) structure; in the viscousregion information about the flow behavior,important for processing extrusion, mixing,pumping, leveling, etc.

3 Is MODELS TO DESCRIBEVISCOELASTICITYV iscoelastic materials can exhibit both viscousand elastic behavior. They can therefore be seen asa combination of both ideal types of materials:purely viscous fluids and ideally elastic flow properties of a purely viscous materialcan be determined in a simple flow experiment. IfF GkxF==orxF GkxF==orx &==orDvFF, v &==orDvFF, vthe material deforms at a constant rate the appliedconstant stress is constant and described by a simplerelationship known as Newton s law. Such liquidsare known as Newtonian fluids, and the materialconstant is referred to as Newtonian viscosity. Thedeformation for Newtonian fluids is of this type are characterized by a dashpotmodel (Figure 1a).

4 With the viscosity (1)For an elastic solid material ( , a steel springor crosslinked rubber) a simple linear relationshipexists between the stress and the strain. The materialFigure 1a: The Dashpot model describes purely viscousfluidFigure 1b: The Spring model describes an ideally elasticbodydtd = 2 AN004deforms instantaneously when subjected to a suddenstress and the strain will remain constant until thestress is removed. There is no loss of energy andthe solid will return to its original shape (thedeformation is fully reversible).The materialconstant is the modulus of the material. The equationrelating the stress and the strain is known as Hooke slaw. Materials of this type are repre-sented by aspring (Figure 1b).

5 G = with the sear modulus G (2)The Newtonian and Hookean laws represent twoextremes. Most materials however show somecharacteristics of both elastic and viscous behaviorand can be described by combining spring(s) anddashpot(s) parallel or in series. These mechanicalmodels do not represent the actual structure of amaterial but provide a physical framework todescribe the general behavior of viscoelastic simplest models are the Maxwell and the Maxwell model is a spring and dashpotassembled in series (figure 2). In this model, theapplied stress is the same for each element, the strainis additive. If a constant strain (relaxation ex-periment) is applied to this model, the stressincreases instantly to a maximum value determinedby the elastic modulus of the spring and then relaxesexponentially to zero.

6 How fast the stress relaxes isgiven by the relaxation time t= dtGds +=+= stress = s = dshear rate + . = .Ginitially take the entire load and the model deformsat maximum rate. As the deformation increases, thespring contribution to the total stress increases andthe deformation rate exponentially slows down tozero (deformation reaches its maximum value). Atthis point the spring supports the total stress appliedto the model. How fast the deformation reaches themaximum is given by the retardation time =G/ . + G dtds =+=strain = s = dThe Kelvin Model consists of a spring anddashpot in parallel (figure 3). The strain for thismodel is the same for both elements whereas thestress is additive.

7 If a constant stress is applied(retardation or creep experiment), the dashpot willFigure 2: The Maxwell model combines the spring anddashpot in seriesDYNAMIC mechanical TESTINGIn an oscillatory measurement the material issubjected to a sinusoidal stress or strain and thestrain or stress response is measured (figure 4). Thedynamic mechanical analysis (DMA) analyzes bothelastic and viscous material response simul-taneously. In this type of experiment, a motor is usedto either apply a sinusoidal strain or stress to amaterial (in tension, bending, or shear) and theresulting stress is measured with a force transduceror the resulting strain is measured with a rheological material behavior can bemeasured as a function of time, temperature, strainor stress amplitude and frequency.

8 The resultsFigure 3: The Kelvin model combines a spring and dashpotin parellelstrainstress stresstime strainFigure 4: Stress and Strain signals during an oscillationexperiment3 AN004obtained provide information about the samplestructural properties such as MW, MWD, con-centration, crosslinking density for polymers orparticle/domain size, shape, interface properties, multiphase fluids. This information is importantin product development (formulation) to predictproduct performance and processing behavior ofnew or modified general rheological behavior in an oscillationexperiment can be described with the Maxwellmodel. At the application of a sinusoidal stress, thespring will expand instantaneously.

9 The dashpothowever retards the deformation of the overallsystem. Therefore, a phase shift d between strainand stress is found as shown in the figure 4 The phase shift would be zero for an elasticmaterial, as the spring follows the stress directly. Ifthe material consisted of a dashpot only, the stressfollows the strain rate directly and the phase shiftbecomes 90o for the strain. For a viscoelasticmaterial the phase shift for the strain is between 0oand phase shift d is a measure of the amount ofelasticity present in a sample. A material is equallyelastic and viscous if the phase shift is 45o or tan = frequency of this event is characteristic for amaterial and therefore an ideal description of thematerial time ( mat=1/( (tan =1)).)

10 A series of material parameters can be calculatedfrom the measured strain and stress. If theexperiment has been performed in shear (plate-plateor cone-plate geometry) then the shear modulus (G)is obtained. Tensile and bending tests measure thetensile modulus (E). In an oscillatory experiment,the phase shift is used to separate the measured stressinto a component in phase and to determine theelastic or storage modulus (G or E ) of a material,defined as the ratio of the elastic (in-phase) stressto strain. The storage modulus relates to thematerial s ability to store energy , the loss modulus (G or E ) of a materialis the ratio of the viscous (out of phase) componentto the stress, and is related to the material s abilityto dissipate stress through figure 5 shows the frequency dependenceof G and G as the result of an oscillatory shearmeasurement for a high viscosity viscoelasticsilicone oil.