An Overview of the Hardness Differential Required for Abrasion

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Giuseppe Pintaude
Keyword(s):  
Mechanical Behavior ◽  
Slip Line ◽  
Rigid Plastic ◽  
Line Field ◽  
Slip Line Field ◽  
Abrasive Particles ◽  
Field Modeling ◽  
Material Hardness ◽  
Worn Surface ◽  
Abrasive Hardness

This paper presents an overview of the hardness differential required for abrasion. Empirically, the abrasive must be at least 1.2 times harder than the worn surface if it is to produce a scratch. This value has been determined theoretically using slip-line field modeling, which assumes rigid-plastic mechanical behavior, an assumption that is inadequate for most abrasive particles. Two approaches using elastic-plastic models and three tribological pairs with similar ratios of abrasive hardness to worn material hardness were tested to gain an understanding of the hardness differential required for abrasion. The analysis showed that the ratios of the property of the abrasive to the property of the worn surface did not change with the model used when the mechanical behavior of the materials was similar. However, when the behavior of the materials was very dissimilar—as is often the case in abrasive processes—the ratios varied greatly depending on the model used, showing that there is a need for models to describe the hardness differential required for abrasion.

Slip Line Field Analysis of a Simple Plane Strain Closed-Die Forging

1989 ◽  
Vol 203 (2) ◽  
pp. 91-99
Author(s):  
M V Srinivas ◽  
P Alva ◽  
S K Biswas
Keyword(s):  
Velocity Field ◽  
Plane Strain ◽  
Slip Line ◽  
Field Analysis ◽  
Line Field ◽  
Slip Line Field ◽  
Die Forging ◽  
Closed Die Forging ◽  
Cavity Filling ◽  
Single Cavity

A slip line field is proposed for symmetrical single-cavity closed-die forging by rough dies. A compatible velocity field is shown to exist. Experiments were conducted using lead workpiece and rough dies. Experimentally observed flow and load were used to validate the proposed slip line field. The slip line field was used to simulate the process in the computer with the objective of studying the influence of flash geometry on cavity filling.

The Relation Between the Friction of Lubricated Rough Surfaces and Apparent Normal Pressure

1989 ◽  
Vol 111 (2) ◽  
pp. 260-264 ◽  
Author(s):  
P. Lacey ◽  
A. A. Torrance ◽  
J. A. Fitzpatrick
Keyword(s):  
Surface Roughness ◽  
Friction Coefficient ◽  
Boundary Lubrication ◽  
Slip Line ◽  
Field Model ◽  
Rough Surfaces ◽  
Normal Pressure ◽  
Line Field ◽  
Slip Line Field ◽  
Asperity Contacts

Most previous studies of boundary lubrication have ignored the contribution of surface roughness to friction. However, recent work by Moalic et al. (1987) has shown that when asperity contacts can be modelled by a slip line field, there is a precise relation between the friction coefficient and the asperity slope. Here, it is shown that there is also a relation between the friction coefficient and the normal pressure for rough surfaces which can be predicted from a development of the slip line field model.

Plane-Strain Problems

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Plastic Flow ◽  
Slip Line ◽  
Field Analysis ◽  
Valuable Insight ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Nonsteady State ◽  
Plane Plastic

This chapter is concerned with the formulations and solutions for plane plastic flow. In plane plastic flow, velocities of all points occur in planes parallel to a certain plane, say the (x, y) plane, and are independent of the distance from that plane. The Cartesian components of the velocity vector u are ux(x, y), uy(x, y), and uz = 0. For analyzing the deformation of rigid-perfectly plastic and rate-insensitive materials, a mathematically sound slip-line field theory was established (see the books on metal forming listed in Chap. 1). The solution techniques have been well developed, and the collection of slip-line solutions now available is large. Although these slip-line solutions provide valuable insight into deformation modes and forming loads, slip-line field analysis becomes unwieldy for nonsteady-state problems where the field has to be updated as deformation proceeds to account for changes in material boundaries. Furthermore, the neglect of work-hardening, strain-rate, and temperature effects is inappropriate for certain types of problems. Many investigators, notably Oxley and his co-workers, have attempted to account for some of these effects in the construction of slip-line fields. However, by so doing, the problem becomes analytically difficult, and recourse is made to experimental determination of velocity fields, similarly to the visioplasticity method. Some of this work is summarized in Reference [2]. The applications of the finite-element method are particularly effective to the problems for which the slip-line solutions are difficult to obtain. The finite-element formulation specific to plane flow is recapitulated here.

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