Martin Materials for Engineering

3. Auflage 2006
ISBN: 978-1-84569-160-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 264 Seiten

This third edition of what has become a modern classic presents a lively overview of Materials Science which is ideal for students of Structural Engineering. It contains chapters on the structure of engineering materials, the determination of mechanical properties, metals and alloys, glasses and ceramics, organic polymeric materials and composite materials. It contains a section with thought-provoking questions as well as a series of useful appendices. Tabulated data in the body of the text, and the appendices, have been selected to increase the value of Materials for engineering as a permanent source of reference to readers throughout their professional lives. The second edition was awarded Choice's Outstanding Academic Title award in 2003. This third edition includes new information on emerging topics and updated reading lists.

John Martin is Emeritus Reader in Physical Metallurgy at the University of Oxford and a recipient of the Platinum Medal of the Institute of Materials, Minerals and Mining.

Autoren/Hrsg.

Martin, J.

Leseproben

2

Determination of mechanical properties

2.1 Introduction

Mechanical testing of engineering materials may be carried out for a number of reasons: The tests may simulate the service conditions of a material, so that the test results may be used to predict its service performance. Mechanical testing may also be conducted in order to provide engineering design data, as well as acceptability, the main purpose of which is to check whether the material meets the specification.

In the USA, the American Society for Testing Materials (ASTM) publish standard specifications and methods of testing which are updated every three years. In the UK, the British Standards Institution (BSI) publish an annual catalogue of all BSI Standards, and agreed European Standards (EN series). All of these organizations issue publications relating to the selection of test-pieces and the conducting of mechanical tests. We will consider a number of these tests in turn.

2.2 The tensile test

The tensile test is widely used for measuring the stiffness, strength and ductility of a material. The testing machine subjects the test-piece to an axial elongation and the resultant load on the specimen is measured. Depending on the nature of the product being tested, the specimen may be round or rectangular in cross-section, with the region between the grips usually being of reduced cross–section. The gauge length is marked in this region.

We will consider the response of a ductile metal as an illustration. The load–elongation data are normally converted to stress and strain:

Strain?=?Extension?of?gauge?length/Original?gauge?length

Figure 2.1 illustrates the behaviour at small strains. The linear part of the curve may correspond to easily measured elongations in some polymeric materials, but in metals the displacements are very small and usually require the use of an extensometer or resistance strain-gauge to measure them with sufficient accuracy.

2.1 Tensile test at small strains.

This part of the curve, described by Hooke’s Law, represents elastic behaviour. Its slope corresponds to Young’s modulus (E), which is given by the ratio of stress to strain. We have seen in Fig. 0.1, which plots Young’s modulus vs. density for engineering materials, that the value of Young’s modulus can vary by over three orders of magnitude for different materials with elastomers having values of the order 0.1 GPa and metals and ceramics having values of hundreds of gigapascals.

It is clearly important for design engineers to know the stress at which elastic behaviour ceases. The limit of proportionality is the highest stress that can be applied with Hooke’s Law being obeyed and the elastic limit is the maximum stress that can be applied without causing permanent extension to the specimen. Neither of these stresses will be found in reference books of properties of materials, however, since their experimental measurement is fraught with difficulty. The more sensitive the strain gauge employed in the experiment, the lower the limit of proportionality and the elastic limit will appear to be. Thus, as one changes from mechanical measurement of the strain with, say, a micrometer, to an optical lever device then to an electrical resistance strain gauge and, finally, to optical interferometry one would detect departure from elastic behaviour (as defined above) at progressively lower stresses, due to the presence of microstrains.

Departure from elasticity is therefore defined in an empirical way by means of a proof stress, the value of which is independent of the accuracy of the strain-measuring device. Having constructed a stress–strain curve as in Fig. 2.1, an arbitrary small strain is chosen, say 0.1 or 0.2%, and a line parallel to Young’s modulus is constructed at this strain. The point of intersection of this line with the stress–strain curve defines the 0.1 or 0.2% proof stress and values of this stress for different materials are available in books of reference, since they provide an empirical measure of the limit of elastic behaviour. In the USA this stress is known as the offset yield strength.

The Bauschinger Effect

If a metallic specimen is deformed plastically in tension up to a tensile stress of + st (Fig. 2.2) and is then subjected to a compressive strain (as indicated by the arrows in Fig. 2.2), it will first contract elastically and then, instead of yielding plastically in compression at a stress of –st as might have been expected, it is found that plastic compression starts at a lower stress (–sc) – a phenomenon known as the Bauschinger Effect (BE). The BE arises because, during the initial tensile plastic straining, internal stresses accumulate in the test-piece and oppose the applied strain. When the direction of straining is reversed these internal stresses now assist the applied strain, so that plastic yielding commences at a lower stress than that operating in tension.

2.2 Illustration of the Bauschinger Effect when the direction of straining is reversed as indicated by the arrowed dotted line.

The BE may be encountered in the measurement of the yield strength of some linepipe steels. Tensile specimens are cut from the finished pipe and these are cold flattened prior to testing. The measured yield strength in such specimens can be significantly lower than that obtained on the (undeformed) plate from which the pipeline is manufactured. This is because the pipe has suffered compressive strain during the unbending process, so the tensile yield stress is reduced by the BE. The plate material thus has to be supplied with extra strength to compensate for this apparent loss in yield strength.

2.2.1 The behaviour of metals at larger strains

Figure 2.3 illustrates the form of a typical load–elongation curve for a ductile metal: after the initial elastic region, the gauge length of the specimen becomes plastic so that, if the load is reduced to zero, the specimen will remain permanently deformed. The load required to produce continued plastic deformation increases with increasing elongation, i.e. the material work hardens.

2.3 Tensile test of a ductile metal.

The volume of the specimen remains constant during plastic deformation, so as the gauge length elongates its cross-sectional area is progressively reduced. At first, work hardening more than compensates for this reduction in area and the gauge length elongates uniformly. The rate of work hardening decreases with strain, however, and eventually a point is reached when there is an insufficient increase in load due to work hardening to compensate for the reduction in cross-section, so that all further plastic deformation will be concentrated in this region and the specimen will undergo necking, with a progressive fall in the load. The onset of necking is known as plastic instability, and during the remainder of the test the deformation becomes localized until fracture occurs.

2.2.2 The engineering stress–strain curve

The load–elongation curve of Fig. 2.3 may be converted into the engineering stress–strain curve as shown in Fig. 2.4 The engineering, or conventional, stress s is given by dividing the load (L) by the original cross-sectional area of the gauge length (Ao), and the strain (e) is as defined above, namely the extension of the gauge length (l – lo) divided by gauge length (lo).

2.4 Engineering stress–strain curve.

The maximum conventional stress in Fig. 2.3 known as the Ultimate Tensile Stress (UTS) is defined as:

=Lmax/Ao

and this property is widely quoted to identify the strength of materials.

The tensile test also provides a measure of ductility. If the fractured test-piece is reassembled, the final length (lf) and final cross-section (Af) of the gauge length may be measured and the ductility expressed either as the engineering strain at fracture:

f=(lf-lo)/lo,

or the reduction is cross-section at fracture, RA, where:

=(Ao-Af)/Ao

These quantities are usually expressed as percentages. Because much of the plastic deformation will be concentrated in the necked region of the gauge length, the value of ef will depend on the magnitude of the gauge length – the smaller the gauge length the greater the contribution to ef from the neck itself. The value of the gauge length should therefore be stated when recording the value of ef.

2.2.3 True stress–strain curve

The fall in the engineering stress after the UTS is achieved, due to the presence of the neck, does not reflect the change in strength of the metal itself, which continues to work harden to fracture. If the true stress, based on the actual cross-section (A) of the gauge length, is used, the stress–strain curve increases continuously to fracture, as indicated in Fig....