Linear viscoelastic materials contact mechanics

The contact mechanics of linear viscoelastic materials is less developed than for elastic materials. In particular, the effects of adhesion have not been systematically explored. After a brief discussion of time scales, this section first considers the case of no adhesion. Then the modifications due to adhesion are discussed. 

Recently introduced instruments from TA Instruments include the DMA Q800 analyser [4, 5]. The instrument can be used for the testing of mechanical properties of a broad range of viscoelastic materials at temperatures ranging from -150 °C to 600 °C. The DMA Q800 is claimed to provide unmatched performance in stress-strain control and measurement. It uses a proprietary non-contact linear motor to provide precise stress control, and optical encoder technology for unmatched sensitivity and resolution in strain deflection. 

It has recently become common to use the JKR theory (Johnson, Kendall Roberts, 1971) to extract the surface and inteifacial energies of polymeric materials from adhesion tests with micro-probe instruments such as the Surface Force Apparatus and the Atomic Force Microscope. However the JKR theory strictly applies only to perfectly elastic solids. The paper will review progress in extending the JKR theory to the contact mechanics and adhesion of linear viscoelastic spheres. The observed effects of adhesion hysteresis and rate-dependent adhesion are predicted by the extended eory. 

The purpose of this chapter has been to give a description of some of the most useful contact mechanics expressions as they relate to studies of adhesion. The primary assumption regarding the properties of the materials themselves is that a linear constitutive model is obeyed throughout the strained region, with the possible exception of a relatively small cohesive zone at the contact edge. Many of the results obtained for simple linear elastic behavior are analytic. Linear viscoelasticity can be handled as well, although in this case numerical approaches... 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

---