This brief introductory chapter outlines the broad coverage of the book and its intended contribution in the context of other available sources. It is recognized that there are many excellent books covering the “mechanics of materials,” often with a strong bias towards metals, but relatively few that are focused strongly on testing procedures designed to reveal details about how they deform plastically. There are in fact many subtleties concerning metal plasticity and the information about it obtainable via various types of test. No attempt is made in this chapter to convey any of these, but the scene is set in terms of outlining the absolute basics of elastic and plastic deformation.

Hardness test procedures of various types have been in use for many decades. They are usually quick and easy to carry out, the equipment required is relatively simple and cheap, and there are portable machines that allow in situ measurements to be made on components in service. The volume being tested is relatively small, so it’s possible to map the hardness number across surfaces, exploring local variations, and to obtain values from thin surface layers and coatings. The main problem with hardness is that it’s not a well-defined property. The value obtained during testing of a given sample is different for different types of test, and also for the same test with different conditions. Identical hardness numbers can be obtained from materials exhibiting a wide range of yielding and work hardening characteristics. The reasons for this are well established. There have been many attempts to extract meaningful plasticity parameters, particularly the yield stress, from hardness numbers, but these are mostly based on neglect of work hardening. In practice, materials that exhibit no work hardening at all are rare and indeed quantification of the work hardening behavior of a metal is a central objective of plasticity testing. The status of hardness testing is thus one of being a technique that is convenient and widely used, but the results obtained from it should be regarded as no better than semi-quantitative. There are procedures and protocols in which they are accorded a higher significance than this, but this is an unsound approach.

Testing in (uniaxial) compression is sometimes an attractive alternative to tensile testing. Specimens can be simpler in shape and smaller, since there is no gripping requirement. The key question is whether corresponding information can be obtained. In general, it can, but there is sometimes a perception that at least some materials behave differently under compression – i.e. that there is tensile-compressive asymmetry in their response. In fact, this is largely a myth: at least in the majority of cases, the underlying plasticity response is symmetrical (and indeed the von Mises (deviatoric) stress, which is normally taken to be the determinant of the response, is identical in the two cases). However, there are important caveats to append to this statement. For example, if the material response is indeed dependent on the hydrostatic component of the stress, as it might be for porous materials and for those in which a phase transformation occurs during loading, then asymmetry is possible. Also, while the underlying plasticity response is usually the same, the compressive stress–strain curve is often affected by friction between sample and platen (leading to barreling). Conversely, the necking that is likely to affect the tensile curve cannot occur in compression, although some kind of buckling or shearing instability is possible. It’s also important to distinguish the concept of tension/compression asymmetry from that of the Bauschinger effect (a sample pre-loaded in tension exhibiting a different response if then loaded in compression).

Mechanical testing on a very fine scale, particularly indentation, has become extremely popular. Sophisticated equipment has been developed, often with accompanying software that facilitates the extraction of properties such as stiffness, hardness and other plasticity parameters. The region being tested can be very small – down to sub-micron dimensions. However, strong caveats should be noted concerning such measurements, particularly relating to plasticity. Some of these concern various potential sources of error, such as the effects of surface roughness, oxide films, uncertainty about the precise geometry of the indenter tip etc. Moreover, even if these can be largely eliminated, extraneous effects tend to arise when (plastically) deforming a small region that is constrained by surrounding (elastic) material. They are often grouped together under the heading of “size effects,” with a clear tendency observed for material to appear harder as the scale of the testing is reduced. Various explanations for this have been put forward, some based on dislocation characteristics, but understanding is incomplete and compensating for them in a systematic way does not appear to be viable. A similar level of uncertainty surrounds the outcome of fine scale uniaxial compression testing, although the conditions, and the sources of error, are rather different from those during nanoindentation. Despite the attractions of these techniques, and the extensive work done with them, they are thus of limited use for the extraction of meaningful mechanical properties (related to plasticity).

Comprehensive treatment of metal plasticity requires an understanding of the fundamental nature of stresses and strains. A stress can be understood at a basic level as a force per unit area on which it acts, while a strain is an extension divided by an original length. However, the limitations of these definitions rapidly become clear when considering anything other than very simple loading situations. Analysis of various practical situations can in fact be rigorously implemented without becoming embroiled in mathematical complexity, most commonly via usage of commercial (finite element) numerical modeling packages. However, there are various issues involved in such treatments, which need to be appreciated by practitioners if outcomes are to be understood in detail. This chapter covers the necessary fundamentals, relating to stresses and strains, and to their relationship during elastic (reversible) deformation. How this relationship becomes modified when the material undergoes plastic (permanent) deformation is covered in the following chapter.

The uniaxial tensile test is the most commonly used mechanical testing procedure, and indeed it is in very widespread use. However, while it is simple in principle, there are several practical challenges, as well as a number of points to be noted when examining outcomes. For example, there is the issue of converting between nominal (“engineering”) and true values of the stress and strain. While many stress–strain curves are presented, and often interpreted, only as nominal data, it is the true relationship that accurately reflects the mechanical response of the sample. Furthermore, conversion between nominal and true values is straightforward only while the stress and strain fields within the gauge length of the sample are uniform. This uniformity is lost as soon as the sample starts to deform in an inhomogeneous way within the gauge length, which most commonly takes the form of “necking.” After the onset of necking, which may be quite difficult to detect and could occur at an early stage, useful interpretation of the stress–strain curve becomes difficult. However, FEM modeling does allow various insights into the behavior in this regime, with potential for revealing information (about the fracture event) that is otherwise inaccessible. There are also several important points relating to the way that the strain is measured during a test.

The capacity of metals to undergo large plastic strains (without fracturing) is one of their most important characteristics. It allows them to be formed into complex shapes. It also means that a component under mechanical load is likely to experience some (local) plasticity, rather than starting to crack or exhibit other kinds of damage that could impair its function. Metals are in general superior to other types of material in this respect. This has been known for millennia, but the reasons behind it, and the mechanisms involved in metal plasticity, only started to become clear less than a century ago and have been understood in real depth for just a few decades. Central to this understanding is the atomic scale structure of dislocations, and the ways in which they can move so as to cause plastic deformation, although there are also several other plasticity mechanisms that can be activated under certain circumstances. These are described in this chapter, together with information about how they tend to be affected by the metal microstructure. This term encompasses a complex range of features, including crystal structure, grain size, texture, alloying additions, impurities, phase constitution etc.

Various loading geometries can be used for mechanical testing aimed at plasticity characterization. The simplest involve uniform stress states of uniaxial tension or compression, while the other common configuration is indentation, which creates complex and changing (2-D or 3-D) stress fields that are not amenable to simple analysis. These tests are covered in earlier chapters. However, other types of geometry can be employed, which may offer certain advantages. For example, bending or torsion of beams can be convenient experimentally and, while the associated stress fields are not uniform, they are relatively simple and may be suitable for analytical treatment. In fact, beam bending, in particular, offers potential for obtaining material properties via iterative FEM, in a similar way to indentation plastometry. Other geometries, such as those involving hollow tubes, may be relevant to particular types of application and expected (plastic) failure modes (such as buckling). There are also various tests involving temporal effects. Prolonged application of constant, uniform stress, leading to creep deformation, is covered in Chapter 5. However, again with a view to specific applications, the applied load may be cycled with a certain frequency, rather than being held constant or increased monotonically. While such (fatigue) testing is sometimes focused on propagation of well-defined cracks, there is also interest in progressive damage that essentially arises from plastic deformation. Finally, some types of test are designed to create high strain rates, under which plasticity often takes place rather differently (because, as outlined in Chapter 3, the mechanisms involved exhibit a time dependence). This chapter covers all of these testing variants.

The handling of stress and strain during elastic deformation is covered in the preceding chapter. However, the situation becomes more complex after the onset of plastic deformation. Whereas elastic straining essentially occurs just via changes in interatomic spacing, the mechanisms involved in plastic (permanent) deformation are far from simple. These mechanisms are described in some detail in the next chapter. The current chapter is based, as is the previous one, on treating the material as a homogeneous continuum, albeit one that may be anisotropic (i.e. exhibit different responses in different directions). Much of the coverage concerns conditions for the onset of plasticity (often described as “yielding”) and subsequent rises in applied stress that are required for further plastic straining (“work hardening”). Two yielding criteria are in common use and these are described. The work-hardening behavior is often quantified using empirical constitutive laws and two of the most prominent of these are also outlined. This chapter also covers the representation of temporal effects – both the changes in stress–strain characteristics that occur when high strain rates are imposed and the progressive straining that can take place over long periods under constant stress, which is often termed “creep.”

Indentation plastometry is now emerging as a potentially valuable addition to the range of testing techniques in widespread use. In many ways, it incorporates an amalgamation of the convenience and ease of usage offered by hardness testing with the more rigorous and meaningful outcomes expected of tensile testing. The indentation procedure itself is very similar to that of hardness testing, except that the loads required are higher than those used in most types of hardness test. The major difference is that the experimental data extracted are much more comprehensive, either in the form of a load–displacement plot or as a residual indent profile (with the latter offering several advantages). However, these experimental data only become useful if they can be processed so as to obtain a (true) stress–strain relationship, which can in turn be used to predict the (nominal) stress–strain curve of a conventional tensile test, including the strength (UTS) and the post-necking and rupture characteristics. This can only be done in a reliable way via iterative FEM simulation of the indentation process, but commercial packages in which this capability is integrated with a test facility are now becoming available.