Chapter 7 Mechanical behaviour of materials 7.1 Mechanical testing procedures The load-elongation curves for both polycrystalline 7.1.1 Introduction mild steel and copper are shown in Figures 7.1a and 7.Ib, The corresponding stress (load per unit area, Real crystals, however carefully prepared, contain P/A)versus strain( change in length per unit length, lattice imperfections which profoundly affect those dl/1) curves may be obtained knowing the dimensions properties sensitive to structure. Careful examination of the test piece. At low stresses the deformation is of the mechanical behaviour of materials can give elastic, reversible and obeys Hooke's law with stress information on the nature of these atomic defects. linearly proportional to strain The proportionality con- In some branches of industry the common mechan stant connecting stress and strain is known as the cal tests, such as tensile, hardness, impact, creep and elastic modulus and may be either (a)the elastic or fatigue tests, may be used, not to study the'defect Young's modulus, E, (b) the rigidity or shear modulus duced against a standard specification. Whatever its the strain is tensile, shear or hydrostatic compressive, purpose, the mechanical test is of importance in the respectively. soissons ratio v, the ratio of lateral con- development of both materials science and engineer- tractions to longitudinal extension in uniaxial tension It is different machines for performing the tests are in gen- are related according to eral use. This is because it is often necessary to know E E the effect of temperature and strain rate at different 2(1-2u) μ=2(1+) levels of stress depending on the material being tested. 3K+ Consequently, no attempt is made here to describe the (71) details of the various testing machines. The elements but for impure iron and low carbon steels the onset of plastic deformation is denoted by a sudden drop in 7.1.2 The tensile test load indicating both an upper and lower yield point. This yielding behaviour is characteristic of many met In a tensile test the ends of a test piece are fixed into als, particularly those with bcc structure containing grips, one of which is attached to the load-measuring small amounts of solute element(see Section 7. 4.6) evice on the tensile machine and the other to the For materials not showing a sharp yield point, a co straining device. The strain is usually applied by means ventional definition of the beginning of plastic filow of a motor-driven crosshead and the elongation of the 0. 1 %o proof stress, in which a line is drawn parallel the specimen is indicated by its relative movement The load necessary to cause this elongation may be Load relaxations are obtained only on'hard'beam obtained from the elastic deflection of either a beam olanyi-type machines where the beam deflection is small or proving ring, which may be measured by usil hydraulic, optical or electromechanical methods. The hich the load-measuring device is a soft spring, rapid load last method (where there is a change in the resistance variations are not recorded because the extension re too large, while in dead-loading machines no lo of strain gauges attached to the beam) is, of course, relaxations are possible. In these latter machines sudden easily adapted into a system for autographically record lding will show as merely an extension under constant ing the load-elongation curveChapter 7 Mechanical behaviour of materials 7.1 Mechanical testing procedures 7.1.1 Introduction Real crystals, however carefully prepared, contain lattice imperfections which profoundly affect those properties sensitive to structure. Careful examination of the mechanical behaviour of materials can give information on the nature of these atomic defects. In some branches of industry the common mechani￾cal tests, such as tensile, hardness, impact, creep and fatigue tests, may be used, not to study the 'defect state' but to check the quality of the product pro￾duced against a standard specification. Whatever its purpose, the mechanical test is of importance in the development of both materials science and engineer￾ing properties. It is inevitable that a large number of different machines for performing the tests are in gen￾eral use. This is because it is often necessary to know the effect of temperature and strain rate at different levels of stress depending on the material being tested. Consequently, no attempt is made here to describe the details of the various testing machines. The elements of the various tests are outlined below. 7.1.2 The tensile test In a tensile test the ends of a test piece are fixed into grips, one of which is attached to the load-measuring device on the tensile machine and the other to the straining device. The strain is usually applied by means of a motor-driven crosshead and the elongation of the specimen is indicated by its relative movement. The load necessary to cause this elongation may be obtained from the elastic deflection of either a beam or proving ring, which may be measured by using hydraulic, optical or electromechanical methods. The last method (where there is a change in the resistance of strain gauges attached to the beam) is, of course, easily adapted into a system for autographically record￾ing the load-elongation curve. The load-elongation curves for both polycrystalline mild steel and copper are shown in Figures 7.1a and 7.lb. The corresponding stress (load per unit area, P/A) versus strain (change in length per unit length, dl/l) curves may be obtained knowing the dimensions of the test piece. At low stresses the deformation is elastic, reversible and obeys Hooke's law with stress linearly proportional to strain. The proportionality con￾stant connecting stress and strain is known as the elastic modulus and may be either (a)the elastic or Young's modulus, E, (b) the rigidity or shear modulus /z, or (c) the bulk modulus K, depending on whether the strain is tensile, shear or hydrostatic compressive, respectively. Young's modulus, bulk modulus, shear modulus and Poisson's ratio v, the ratio of lateral con￾tractions to longitudinal extension in uniaxial tension, are related according to E E 9K/.t K= 2(1-2v)' /.t= 2(1+v)' E= 3K+/z (7.1) In general, the elastic limit is an ill-defined stress, but for impure iron and low carbon steels the onset of plastic deformation is denoted by a sudden drop in load indicating both an upper and lower yield point. 1 This yielding behaviour is characteristic of many met￾als, particularly those with bcc structure containing small amounts of solute element (see Section 7.4.6). For materials not showing a sharp yield point, a con￾ventional definition of the beginning of plastic flow is the 0.1% proof stress, in which a line is drawn parallel 1Load relaxations are obtained only on 'hard' beam Polanyi-type machines where the beam deflection is small over the working load range. With 'soft' machines, those in which the load-measuring device is a soft spring, rapid load variations are not recorded because the extensions required are too large, while in dead-loading machines no load relaxations are possible. In these latter machines sudden yielding will show as merely an extension under constant load