On Friction of Ploughing by Rigid Asperities in the Presence of Straining—Upper Bound Method

Abstract

Upper bound applications traditionally assume that a rigid/perfectly-plastic material moves by rigid blocks, creating discontinuities of velocity at the interfaces between the blocks. In the present version, the elements (blocks) are plastically deformable and there are no velocity discontinuities between adjacent sides. Since this modification incorporates major features of finite element representation employing arbitrary cells, it allows the use of many parameters for minimization, thus achieving high accuracy. On the other hand, it retains the advantage of upper bound techniques in that the incremental procedure for loading is not necessary, and the results for steady processes are obtained directly. Some energy statements for combined loading are derived and a technique for calculating the ploughing force is presented. Examples for a single fully embedded rigid pyramid and a periodic array of asperities ploughing through the rigid/perfectly plastic material in the presence of subsurface straining are given. The friction factor decreased as the rate of subsurface straining increased, as the pyramid angle of the asperities increased, and as the distance between asperities increased.