Partial slip contact of a rigid pin and a linear viscoelastic plate. (1st December 2016) - Dayalan, Satish Kumar; Sundaram, Narayan K.
Abstract: This paper analyzes partial slip contact problems in the theory of linear viscoelasticity under a wide variety of loading conditions, including cyclic (fretting) loads, using a semi-analytical method. Such problems arise in applications like metal-polymer contacts in orthopedic implants. By using viscoelastic analogues of Green's functions, the governing equations for viscoelastic partial-slip contact are formulated as a pair of coupled Singular Integral Equations (SIEs) for a conforming (pin-plate) geometry. The formulation is entirely in the time-domain, avoiding Laplace transforms. Both Coulomb and hysteretic effects are considered, and arbitrary load histories, including bidirectional pin loads and remote plate stresses, are allowed. Moreover, the contact patch is allowed to advance and recede with no restrictions. Viscoelasticity necessitates the application of the stick-zone boundary condition in convolved form, and also introduces additional convolved gap terms in the governing equations, which are not present in the elastic case. Transient as well as steady-state contact tractions are studied under monotonic ramp-hold, unload-reload, cyclic bidirectional (fretting) and remote plate loading for a three-element solid. The contact size, stick-zone size, indenter approach, Coulomb energy dissipation and surface hoop stresses are tracked during fretting. Viscoelastic fretting contacts differ from their elastic counterparts in notable ways. While they shakedown just like their elastic counterparts, the number of cycles to attain shakedown states is strongly dependent on the ratio of the load cycle time to the relaxation time. Steady-state cyclic bulk hysteretic energy dissipation typically dominates the cyclic Coulomb dissipation, with a more pronounced difference at slower load cycling. However, despite this, it is essential to include Coulomb friction to obtain accurate contact stresses. Moreover, while viscoelastic steady-state tractions agree very well with the elastic tractions using the steady-state shear modulus in load-hold analyses, viscoelastic fretting tractions in shakedown differ considerably from their elastic counterparts. Additionally, an approximate elastic analysis misidentifies the edge of contact by as many as 7 degrees in fretting, showing the importance of viscoelastic contact analysis. The SIE method is not restricted to simple viscoelastic networks and is tested on a 12-element solid with very long time scales. In such cases, the material is effectively always in a transient state, with no steady edge-of-contact. This has implications for fretting crack nucleation.