200 Modern Pl Metallurgy and Materials Engineering tension or compression, but all involve the same prin ciple of subjecting the material to constant cycles of stress. To express the characteristics of the stress sys tem, three properties are usually quoted: these include (I)the maximum range of stress, (2)the mean stress, and(3)the time period for the stress cycle. Four dif ferent arrangements of the stress cycle are shown in Figure 7. 4, but the reverse and the repeated cycle tests (e.g. push-pull")are the most common, since they are L。wr,Low the easiest to achieve in the laboratory. and to subject them to tests using a different rang of stress, S, on each group of specimens. The num Figure 7.3 Typical creep curves. ber of stress cycles, N, endured by each specimen at a given stress level is recorded and plotted, as shown occur at all stress levels, but the creep rate increase in Figure 7.5. This S-N diagram indicates that some with increasing stress at a given temperature. For the metals can withstand indefinitely the application of a accurate assessment of creep properties, it is clear that large number of stress reversals, provided the applied special attention must be given to the maintenance of limit. for certain ferrous materials when they are used surement of the small dimensional changes involved. in the absence of corrosive conditions the assumption This latter precaution is ne of a safe working range of stress seems justified, bu rials a rise in temperature by a few tens of degrees for non-ferrous materials and for steels when they are used in corrosive conditions a definite endurance limit shows the characteristics of a typical creep curve and cannot be defined. Fatigue is discussed in more detail following the instantaneous strain caused by the sud divided into three stages, usually termed primary or 7. 1.7 Testing of ceramics transient creep, second or steady-state creep and ter- Direct tensile testing of ceramics is not generally tiary or accelerating creep. The characteristics of the favoured, mainly because of the extreme sensitivity of creep curve often vary, however, and the tertiary stage ceramics to surface flaws. First, it is difficult to apply of creep may be advanced or retarded if the tempera- a truly uniaxial tensile stress: mounting the specimen ture and stress at which the test is carried out is high in the machine grips can seriously damage the surface or low respectively(see Figure 7.3, curves b and c). and any bending of the specimen during the test will Creep is discussed more in Section 7.9 cause premature failure. Second, suitable waisted spec- imens with the necessary fine and flawless finish are 7.1.6 Fatigue testing expensive to produce. It is therefore common practice to use bend tests for engineering ceramics and glasses The fatigue phenomenon is concerned with the prema - (They have long been used for other non-ductile mate- ture fracture of metals under repeatedly applied low rials such as concretes and grey cast iron. In the three- stresses, and is of importance in many branches of and four-point bend methods portrayed in Figure 7.6,a engineering (e.g. aircraft structures ). Several differ- beam specimen is placed between rollers and carefully ent types of testing machines have been constructed loaded at a constant strain rate. The fexural strength in which the stress is applied by bending, torsion, at failure, calculated from the standard formulae, is Figure 7.4 Alternative forms of stress cycling:(a)reversed;(b)alternating(mean stress zero),(c) fluctuating and200 Modern Physical Metallurgy and Materials Engineering s t c e~ u~ c/N,gh /', / i| Low r, Low d Ttrn~ Figure 7.3 Typical creep curves. occur at all stress levels, but the creep rate increase with increasing stress at a given temperature. For the accurate assessment of creep properties, it is clear that special attention must be given to the maintenance of the specimen at a constant temperature, and to the mea￾surement of the small dimensional changes involved. This latter precaution is necessary, since in many mate￾rials a rise in temperature by a few tens of degrees is sufficient to double the creep rate. Figure 7.3, curve a, shows the characteristics of a typical creep curve and following the instantaneous strain caused by the sud￾den application of the load, the creep process may be divided into three stages, usually termed primary or transient creep, second or steady-state creep and ter￾tiary or accelerating creep. The characteristics of the creep curve often vary, however, and the tertiary stage of creep may be advanced or retarded if the tempera￾ture and stress at which the test is carried out is high or low respectively (see Figure 7.3, curves b and c). Creep is discussed more fully in Section 7.9. 7.1.6 Fatigue testing The fatigue phenomenon is concerned with the prema￾ture fracture of metals under repeatedly applied low stresses, and is of importance in many branches of engineering (e.g. aircraft structures). Several differ￾ent types of testing machines have been constructed in which the stress is applied by bending, torsion, tension or compression, but all involve the same prin￾ciple of subjecting the material to constant cycles of stress. To express the characteristics of the stress sys￾tem, three properties are usually quoted: these include (1) the maximum range of stress, (2) the mean stress, and (3) the time period for the stress cycle. Four dif￾ferent arrangements of the stress cycle are shown in Figure 7.4, but the reverse and the repeated cycle tests (e.g. 'push-pull') are the most common, since they are the easiest to achieve in the laboratory. The standard method of studying fatigue is to pre￾pare a large number of specimens free from flaws, and to subject them to tests using a different range of stress, S, on each group of specimens. The num￾ber of stress cycles, N, endured by each specimen at a given stress level is recorded and plotted, as shown in Figure 7.5. This S-N diagram indicates that some metals can withstand indefinitely the application of a large number of stress reversals, provided the applied stress is below a limiting stress known as the endurance limit. For certain ferrous materials when they are used in the absence of corrosive conditions the assumption of a safe working range of stress seems justified, but for non-ferrous materials and for steels when they are used in corrosive conditions a definite endurance limit cannot be defined. Fatigue is discussed in more detail in Section 7.11. 7.1.7 Testing of ceramics Direct tensile testing of ceramics is not generally favoured, mainly because of the extreme sensitivity of ceramics to surface flaws. First, it is difficult to apply a truly uniaxial tensile stress: mounting the specimen in the machine grips can seriously damage the surface and any bending of the specimen during the test will cause premature failure. Second, suitable waisted spec￾imens with the necessary fine and flawless finish are expensive to produce. It is therefore common practice to use bend tests for engineering ceramics and glasses. (They have long been used for other non-ductile mate￾rials such as concretes and grey cast iron.) In the three￾and four-point bend methods portrayed in Figure 7.6, a beam specimen is placed between rollers and carefully loaded at a constant strain rate. The flexural strength at failure, calculated from the standard formulae, is (8) (b) (c) (d) Figure 7.4 Alternative forms of stress cycling: (a) reversed; (b) altet~ating (mean stress ~ zero), (c) fluctuating and (d) repeated