INTRODUCTION

This chapter will examine the application of FE metalforming techniques to a wide range of industrially-relevant processes.

The main reasons for conducting computer simulations of metalforming processes are to:

1. reduce development lead times by minimising the number of experimental trials required (get closer to ‘right first time’)

2. reduce development costs, particularly those incurred by the manufacture of expensive dies for experimental trials

Both of these considerations result in increased industrial competitiveness and flexibility through the ability to introduce new products quickly and cheaply.

Estimates vary of the proportion of forged parts in the UK that have axi-symmetric geometries, but this figure probably lies somewhere in the region of 60 to 70%. The development of tooling for axi-symmetric parts does not present anywhere near the difficulties that are associated with the design of dies for non-symmetric components, but even so, computer simulation can significantly speed up the design process for axi-symmetric parts. The savings in time and money will be even greater when non-symmetric parts are to be formed.

The program listed in this appendix was designed principally for demonstration purposes and to form an introduction to non-linear FE plasticity analyses. In order to simplify the approach, only constant-strain triangular elements have been used. The program is sufficiently flexible, however, to be able to deal with plane-stress, plane-strain and axi-symmetric examples.

The data contained within the sub-program FILDATA are specifically for sticking-friction axi-symmetric upsetting. It should be a simple matter to change the appropriate entries to tackle different problems. Comment statements are used liberally throughout the program in order to try and explain what is happening at each stage. The programs could have been written in a more condensed and efficient form, but the format given here was chosen deliberately to allow the reader and potential user to follow the program structure and operation as easily as possible.

© Copyright 1990 University of Birmingham.

Permission to use, copy, modify and distribute this software for any purpose and without fee is hereby granted, provided that the above copyright notice appears in all copies and that both that copyright and this permission notice appear in supporting documentation. The University of Birmingham makes no representations about the suitability of this software for any purpose. The University of Birmingham, the Cambridge University Press and the employees of both organisations disclaim liability for any loss or damage caused through its use.

INTRODUCTION

The first applications of the FEM were concerned with structural problems, and so it is not surprising that when the FEM began to be applied to the modelling of plastic deformation, this was viewed simply as an extension of non-linear elastic behaviour, with the elastic stress/strain matrix in the FE formulation replaced by an appropriate plastic one, as described in Chapter 3. When the amounts of plastic deformation and material displacement are small, this is a valid approach and is often used in the study of plastic failure of structures such as pressure vessels. The small-strain technique also has the advantage of being easily understood, thus providing a good introduction to the principles and underlying FE plasticity, and of being easily incorporated into available elastic FE programs.

As the examples in the previous chapter show, the small-strain approach can give good approximations to the overall pattern of deformation in certain simple forming processes. However, this technique cannot accurately predict the values of important workpiece parameters, such as the components of strain and stress, particularly if the metalforming process involves appreciable material rotation. This is due partly to the nature of elastic–plastic deformation, for which correct definitions of stress and strain increment must be chosen, and partly to the large total and incremental strains involved in metalforming, which require special numerical techniques for their evaluation.

This chapter re-examines the FEM in the light of these considerations in order to derive a formulation that is able to model large-strain elastic–plastic deformation.

INTRODUCTION

The methods described in Chapters 1 and 2 are generally applicable though the discussion so far has been related largely to linear elastic problems. In these problems the [D] matrix does not change during deformation and the changes in the [B] matrix due to the changes in nodal co-ordinates are small.

In plastic deformation, and especially in metalforming, the strains may be very large. A change of 30–40% in diameter of a drawn wire or height of a forging, for example, can often be required. In extrusion the strains may be much greater still, reaching logarithmic strains of 5 or more. This introduces very severe local distortion and we shall consider the problems involved later, in Chapters 5 and 6.

Even when the deformation involves only a small amount of plastic strain, the yield stress will change in a non-linear manner. The metal deforms elastically at first with essentially constant values of Young's Modulus and Poisson's Ratio, but as soon as the stress reaches the yield value, plastic deformation occurs with a much lower effective modulus. The yield stress itself increases with strain due to work hardening, and stress is no longer proportional to strain, but is related to the strain increment and, at least for hot working, also to the strain rate.

In this chapter, we shall consider only isothermal plastic deformation at temperatures such as the normal ambient, well below the range of hot working.

Introduction

The hardness and chemical stability of ceramics should make them ideal materials for tribo-elements that have to function under severe wear and high temperature conditions. Unfortunately, large variations in both friction and wear resistance can occur when ceramics are slid against themselves, or against a metal counterface, in the unlubricated condition. These variations have tended to prevent the widespread use of ceramics in tribo-systems. However, the recent interest in developing the ceramic diesel has tended to bring about an increase in fundamental research into the tribological properties of ceramic/ceramic and ceramic/metal tribo-systems, some of which looks very promising.

Some of the earliest work on the tribology of ceramics was carried out by Seal (1958) on diamond. Other materials include ionic crystals (Steijn, 1963), sapphire (Steijn, 1961), silicon carbide (Miyoshi and Buckley, 1979a), boron nitride (Buckley, 1978), manganese zinc-ferrite (Miyoshi and Buckley, 1981b), titanium (Nutt and Ruff, 1983), silicon nitride (Dalal, Chiu and Rabinowicz, 1975) and many other materials too numerous to mention. Since we are mainly interested in the application of physical analytical techniques to ceramic tribology, we will be very selective and discuss silicon nitride, silicon carbide and sapphire tribo-systems. Other systems may be more relevant to the reader's interest, but at least we know that various physical analytical techniques have been applied to tribo-systems with these materials as tribo-elements.

Introduction

The publication of the definitive paper by Lim and Ashby (1987) was probably the most important step towards providing tribologists with an easily applied method for estimating the type of wear mechanism most likely to occur for a given set of conditions. It is clear that mild-oxidational wear and severe-oxidational wear are very widespread in the wear mechanism map for steel (see Figure 1.5). It seems that oxidational wear is one of those areas of tribological endeavour most likely to receive an increasing amount of attention, especially in view of the interest in developing tribo-systems which can function effectively (without conventional lubrication) in high temperature environments, for example the ceramic diesel engine.

We have already discussed the oxidational theory of wear in some detail (in Section 1.4.4). In Section 6.1.4, we described how heat flow analysis in conjunction with the oxidational wear theory can be used to obtain information about temperatures (Tc) occurring at the real areas of contact, the number N of asperity contacts within those real arcs of contact and the thickness ξ of the oxide film formed at the real areas of contact. In Section 6.2.3 it was shown how proportional analysis (by X-ray diffraction) of the wear debris produced in the oxidational wear of steels, led to independent estimates of the contact temperature.

Thermal aspects of sliding

Introduction

There have been many attempts to measure the temperature of the interfaces of sliding surfaces, both by direct and indirect measurements. Early direct measurements tended to involve the dynamic thermocouple, for example Shore (1925), Herbert (1926) and Furey (1964). Such measurements tend to be restrictive as regards the choice of sliding material combinations. They are also insensitive to the very rapid transients that occur during sliding. More recent direct measurements involve the use of optical photography through the transparent member of a sliding pair (Quinn and Winer, 1985) or the use of an infra-red detector (Meinders, Wilcock and Winer, 1984). We will describe both types of measurements in more detail in later sub-sections. The indirect measurements of surface temperature have tended to be a mixture of theory and experiment, for example see Ling and Pu (1964) and Archard (1959). Occasionally, temperature-dependent transitions in tribo-element phases have been used to give an indirect indication of the temperatures of sliding, for example see Quinn (1968), a paper in which the proportions of the various iron oxides in the wear debris were used to estimate the most probable temperature of formation of those oxides. We will describe the X-ray analysis of wear debris in a later sub-section (Section 6.2).

The analysis of extreme-pressure lubricant films formed in the presence of typical disulphide additives

Introduction

In this section of our chapter on the analysis of lubricant films, we will be concerned with the use of physical methods of analysis to investigate the mechanisms whereby some selected disulphides provide protection under conditions of sliding which would otherwise have resulted in the breakdown or seizure of the tribo-system if the disulphides were not present as ‘extreme-pressure’ additives in the lubricant. There are, in fact, two types of extreme-pressure additives, one that prevents catastrophic failure when a tribo-system is suddenly subjected to unexpectedly high loads (such an additive is truly called an ‘extreme-pressure’ additive), and another that reduces the wear to an ‘acceptable’ level in a system designed to work close to the limits of lubrication, for example a hypoid gear system. We call the latter type of lubricant additive an ‘anti-wear’ additive, for obvious reasons. Some tribologists suggest we should drop the word ‘pressure’ in the generic word for the whole family of lubricant additives and merely call them ‘extreme-temperature’ additives. As we shall see, the temperature between the wearing interfaces is indeed an important factor in the mechanisms whereby extreme-pressure lubricant additives provide protection of those interfaces from the incidence of severe way.