Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces

Abstract

Alexandrov, S; Mishuris, G. Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces. Journal of Engineering Mathematics. 2009, 65(2), 143-156The maximum-friction surface is a source of singular solution behaviour for several rate-independent plasticity models. Solutions based on conventional viscoplastic models do not show such behaviour. For a class of materials, there is a range of temperatures and/or strain rates where a necessity of the consideration of rate effects depends on the area of application of the final result. Hence, the same material under the same conditions can be represented by either rate-independent or rate-dependent models. In this case, a reasonable requirement is that viscous effects should not be very significant and, in particular, the qualitative behaviour of viscoplastic solutions should be similar to that of solutions based on rate-independent models. The present paper deals with this issue by means of the solution for simultaneous shearing and expansion of a hollow cylinder under plane-strain deformation. One of the goals of the paper is to show that there is a class of viscoplastic models satisfying the requirement formulated. The other goal is to find an asymptotic representation of the solution in the vicinity of the maximum-friction surface and compare it with the rigid perfectly plastic solution.Peer reviewe

Quasi-static axially symmetric viscoplastic flows near very rough walls

“…The inequality (46) and the previous result for d P 2 show that the singular solutions at sliding are only possible if d > 1. This result coincides with the particular semi-analytical solution given in [30].…”

“…The present study demonstrates how to choose the function Uðn eq Þ such that solutions at sliding become possible even if the wall is perfectly rough. It is worthy of note that no direct experiment can be used to distinguish viscoplastic models with and with no saturation stress [30]. However, the friction test on an aluminum alloy at elevated temperatures (conditions under which viscoplastic models are usually adopted) proposed and carried out in [33] clearly demonstrates that a narrow layer of intensive plastic deformation whose thickness is about 200 lm is generated near the friction surface.…”

“…Therefore, as |n xy | increases the magnitude of s xy eventually attains its maximum possible value r s = ffiffiffi 3 p . Using simple analytic examples such behavior of solutions has been demonstrated in [29,30]. Any further increase in jn xy j results in the regime of sliding independently of the friction law (otherwise, no solution exists).…”

“…Such representations can be then used in the extended finite element method [28] to overcome the aforementioned difficulty with the use of standard finite element techniques. In particular, it has been shown in [29,30] that solutions for viscoplastic models with a saturation stress may be singular near maximum friction surfaces. The meaning of the saturation stress is that the tensile stress in a hypothetical tensile test approaches its value as the corresponding strain rate approaches infinity.…”

A numerical method for determining the strain rate intensity factor under plane strain conditions

“…In particular, the double-shearing model [34] and the double slip and rotation model [35] of pressure-dependent plasticity have been considered in [4,36], respectively. A special model of viscoplasticity has been introduced and studied in [37]. The model of anisotropic plasticity presented in [38] has been considered in [5].…”