Viscoelastic loading

The mechanical behavior of plastics on time-dependent applied loading can cause different important effects on materials viscoelasticity. Loads applied for short times and at normal rates (Chapter 2) causes material response that is essentially elastic in character. However, under sustained load plastics, particularly TPs, tend to creep, a factor that is included in the design analysis. 

In the case of viscoelastic loaded QCM two approaches have been followed one methodology is to treat the device as an acoustic transmission line with one driven piezo-electric quartz layer and one or more surface mechanical load (TLM) [50, 51]. A simpler approach is to use a lumped-element model (LEM) that represents mechanical inter-actions by their equivalent electrical BVD circuit components [52, 53]. 

When the summit height PDF is exponential within the contact region z > d, all four of the above integrals can be evaluated explicitly (Question 3). We note that in reality, polyurethane is viscoelastic, loads are usually high enough so that at least some asperities are plastically deformed, and observed... 

After the immobihsation of control and active receptors, the resultant sensor chip can then be stored for future use, or used directly after receptor immobihsation. hi a typical RAP assay (Fig. 3) at t = 0 s, buffer was contacted with the receptor via the microfluidic device. At t = 60 s a solution of analyte (in this case mouse IgG) in the rimning buffer was passed over the active surface (rabbit anti-mouse-Fc) and the control surface (mouse IgG). As the analyte boimd to the active receptor, the additional mass and viscoelastic load on the resonator resulted in a change in the resonance signal (depicted here as a negative change in series resonance). 

Viscoelastic loading The impact of viscoelastic materials on the electromechanical properties of a TSM resonator can be best described by the acoustic load concept. Adding a viscoelastic film with a sufficiently small shear modulus to the quartz crystal results in an additional frequency shift as expected for a thin rigid layer if the environment is air, or a decrease in frequency shift as expected from eqn [1] if the layer is adsorbed in liquid. The so-called extra mass effect occurring in air can be expressed by a plus sign in eqn [5] ... 

A rather new and very exciting application of TSM resonators is the detection and characterization of pro- and eukaryotic cells, as the technique provides information of the viscous and viscoelastic load on the surface. Most piezosensors used for the detection of bacteria in solution are based on an antigen-antibody reaction, in which the bacterium binds to the corresponding surface confined antibody and thus can be monitored. In most cases, a linear relation between the bacterial cell number and frequency shift is fovmd enabling one to calibrate the system for the bacterial cell numbers. However, whole cells do not always form complete layers on the surface they have dimensions extending that of the acoustic... 

Weihnacht M, Bruenig R, Schmidt H (2007) 5D-3 more accurate simulation of quartz crystal microbalance (QCM) response to viscoelastic loading. In Ultrasonics symposium, IEEE, New York, NY (USA), pp 377-380... 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

Eracture mechanics concepts can also be appHed to fatigue crack growth under a constant static load, but in this case the material behavior is nonlinear and time-dependent (29,30). Slow, stable crack growth data can be presented in terms of the crack growth rate per unit of time against the appHed R or J, if the nonlinearity is not too great. Eor extensive nonlinearity a viscoelastic analysis can become very complex (11) and a number of schemes based on the time rate of change of/have been proposed (31,32). 

International Rubber Hardness. The International mbber hardness test (ASTM D1415) (2) for elastomers is similar to the Rockwell test ia that the measured property is the difference ia penetration of a standard steel ball between minor and major loads. The viscoelastic properties of elastomers require that a load appHcation time, usually 30 seconds, be a part of the test procedure. The hardness number is read directly on a scale of 0 to 100 upon return to the minor load. International mbber hardness numbers are often considered equivalent to Durometer hardness numbers but differences ia iadenters, loads, and test time preclude such a relationship. 

Figure 16 (145). For an elastic material (Fig. 16a), the resulting strain is instantaneous and constant until the stress is removed, at which time the material recovers and the strain immediately drops back to 2ero. In the case of the viscous fluid (Fig. 16b), the strain increases linearly with time. When the load is removed, the strain does not recover but remains constant. Deformation is permanent. The response of the viscoelastic material (Fig. 16c) draws from both kinds of behavior. An initial instantaneous (elastic) strain is followed by a time-dependent strain. When the stress is removed, the initial strain recovery is elastic, but full recovery is delayed to longer times by the viscous component.

Penetration—Indentation. Penetration and indentation tests have long been used to characterize viscoelastic materials such as asphalt, mbber, plastics, and coatings. The basic test consists of pressing an indentor of prescribed geometry against the test surface. Most instmments have an indenting tip, eg, cone, needle, or hemisphere, attached to a short rod that is held vertically. The load is controlled at some constant value, and the time of indentation is specified the size or depth of the indentation is measured. Instmments have been built which allow loads as low as 10 N with penetration depths less than mm. The entire experiment is carried out in the vacuum chamber of a scanning electron microscope with which the penetration is monitored (248). 

Contact mechanics, in the classical sense, describes the behavior of solids in contact under the action of an external load. The first studies in the area of contact mechanics date back to the seminal publication "On the contact of elastic solids of Heinrich Hertz in 1882 [ 1 ]. The original Hertz theory was applied to frictionless non-adhering surfaces of perfectly elastic solids. Lee and Radok [2], Graham [3], and Yang [4] developed the theories of contact mechanics of viscoelastic solids. None of these treatments, however, accounted for the role of interfacial adhesive interactions. 

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

Fig. 20. The JKR represenUilion of loading experimental and modified data for a viscoelastic adhesive contact. Each set of points corresponds to a compression step in which the load P and contact radius a decreases and increases with time, respectively. LHS refers to the term on the left hand side of Eq. 61. It represents the equivalent of r/ in elastic JKR plot after being weighed by the viscoelastic factor (38. ...

Throughout this chapter the viscoelastic behaviour of plastics has been described and it has been shown that deformations are dependent on such factors as the time under load and the temperature. Therefore, when structural components are to be designed using plastics, it must be remembered that the classical equations which are available for the design of springs, beams, plates, cylinders, etc., have all been derived under the assumptions that... 

The obvious question is Ts there an optimum design for the corrugations Unfortunately the answer is No because if one wishes to increase transverse stiffness then the obvious thing to do is to increase D up to the point where buckling problems start to be a concern. Usually this is when D/h = 10, for short-term loading and less than this for long term loading because of the decrease in modulus of viscoelastic materials. 

The simplest theoretical model proposed to predict the strain response to a complex stress history is the Boltzmann Superposition Principle. Basically this principle proposes that for a linear viscoelastic material, the strain response to a complex loading history is simply the algebraic sum of the strains due to each step in load. Implied in this principle is the idea that the behaviour of a plastic is a function of its entire loading history. There are two situations to consider. 

The ramp of pressure to about 3 GPa observed in shock-loaded fused quartz has been used very effectively in acceleration-pulse loading studies of viscoelastic responses of polymers by Schuler and co-workers. The loading rates obtained at various thicknesses of fused quartz have been accurately characterized and data are summarized in Fig. 3.6. At higher peak pressures there are no precise standard materials to produce ramp loadings, but materials such as the ceramic pyroceram have been effectively employed. (See the description of the piezoelectric polymer in Chap. 5.)... 

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