458 Mechanics of Materials 2 §11.1 一Low cycle fotigue+十 High cycle fotigue Cotfin-Monson slope 0.5 其 Bosquin slope。0I2 企1o5 cycles Log cycles to failure Fig.11.16.Relationship between total strain and cycles to failure in low and high cycle fatigue. cycles.Therefore,it can be said that up to this figure fatigue performance is a function of the material's ductility,whilst for cycles in excess of this,life is a function of the strength of the material. 11.1.7.Combating fatigue When selecting a material for use under fatigue conditions it may be better to select one which shows a fatigue limit,e.g.steel,rather than one which exhibits an endurance limit, e.g.aluminium.This has the advantage of enabling the designer to design for an infinite life provided that the working stresses are kept to a suitably low level,whereas if the latter material is selected then design must be based upon a finite life. In general,for most steels,the fatigue limit is about 0.5 of the tensile strength,there- fore,by selecting a high-strength material the allowable working stresses may be increased. Figure 11.17. Alloy steel (apnilldwo Ploin corbon steel Copper ond aluminium Cast iron Log N, Fig.11.17.Relative performance of various materials under fatigue conditions
458 Mechanics of Materials 2 $11.1 a P e E e + - 0 t + o w J Low cycle fatigue- Hiqh cycle fotique - I I 0 12 105 CN~L Lag cycles to failure Fig. 11.16. Relationship between total strain and cycles to failure in low and high cycle fatigue. cycles. Therefore, it can be said that up to this figure fatigue performance is a function of the material’s ductility, whilst for cycles in excess of this, life is a function of the strength of the material. I1 .I .7. Combating fatigue When selecting a material for use under fatigue conditions it may be better to select one which shows a fatigue limit, e.g. steel, rather than one which exhibits an endurance limit, e.g. aluminium. This has the advantage of enabling the designer to design for an infinite life provided that the working stresses are kept to a suitably low level, whereas if the latter material is selected then design must be based upon a finite life. In general, for most steels, the fatigue limit is about 0.5 of the tensile strength, therefore, by selecting a high-strength material the allowable working stresses may be increased. Figure 11.17. LOO N, Fig. 11.17. Relative performance of various materials under fatigue conditions
§11.1 Fatigue,Creep and Fracture 459 Following on the above,any process that increases tensile strength should raise the fatigue limit and one possible method of accomplishing this with steels is to carry out heat treatment. The general effect of heat treatment on a particular steel is shown in Fig.11.18. W.Q ond tempered ot 200C (90) W.Q and tempered at 400.C Annealed Log N Fig.11.18.Effect of heat treatment upon the fatigue limit of steel. Sharp changes in cross-section will severely reduce the fatigue limit (see $10.3.4),and therefore generous radii can be used to advantage in design.Likewise,surface finish will also have a marked effect and it must be borne in mind that fatigue data obtained in laboratory tests are often based upon highly polished,notch-free,samples whilst in practice the component is likely to have a machined surface and many section changes.The sensitivity of a material to notches tends to increase with increase in tensile strength and decrease with increase in plasticity,thus,in design situations,a compromise between these opposing factors must be reached. Figure 11.19 shows the fatigue limits of typical steels in service expressed as a percentage of the fatigue limits obtained for the same steels in the laboratory and it will be noticed that Highly polished,notch free peuIDiqo iWIl Machined,notch free 80 Mochined with sharp notch 60 Hot rolled,scaled surface 40 20 Tensile strength of material Fig.11.19.Effect of surface conditions on the fatigue strength of materials
$11.1 Fatigue, Creep and Fracture 459 Following on the above, any process that increases tensile strength should raise the fatigue limit and one possible method of accomplishing this with steels is to carry out heat treatment. The general effect of heat treatment on a particular steel is shown in Fig. 11.18. ~ LOP N, Fig. 11.18. Effect of heat treatment upon the fatigue limit of steel. Sharp changes in cross-section will severely reduce the fatigue limit (see Q 10.3.4), and therefore generous radii can be used to advantage in design. Likewise, surface finish will also have a marked effect and it must be borne in mind that fatigue data obtained in laboratory tests are often based upon .highly polished, notch-free, samples whilst in practice the component is likely to have a machined surface and many section changes. The sensitivity of a material to notches tends to increase with increase in tensile strength and decrease with increase in plasticity, thus, in design situations, a compromise between these opposing factors must be reached. Figure 1 1.19 shows the fatigue limits of typical steels in service expressed as a percentage of the fatigue limits obtained for the same steels in the laboratory and it will be noticed that Highly polished, notch free loo I Tensile strengrh of moterial Fig. 11.19. Effect of surface conditions on the fatigue strength of materials
460 Mechanics of Materials 2 §11.1 the fatigue limit of a low-strength steel is not affected to the same extent as the high- strength steel.i.e.the former is less notch-sensitive (another factor to be taken account of when looking at the relative cost of the basic material).However,it must be pointed out that it may be poor economy to overspecify surface finish,particularly where stress levels are relatively low. Because fatigue cracks generally initiate at the surface of a component under tensile stress conditions,certain processes,both chemical and mechanical,which introduce residual surface compressive stresses may be utilised to improve fatigue properties(see $10.2).However,the extent of the improvement is difficult to assess quantitatively at this juncture of time.Among the chemical treatments,the two most commonly employed are carburising and nitriding which bring about an expansion of the lattice at the metal surface by the introduction of carbon and nitrogen atoms respectively.Figure 11.20 shows the effect upon fatigue limit. Nitrided steel Nitrided.and polished Shot peened steel SS9540 As mochined Cycles to failure IN,) Fig.11.20.Effect of processes which introduce surface residual stresses upon the fatigue strength of a steel. The most popular mechanical method of improving fatigue limits is shot peening,the surface of the material being subjected to bombardment by small pellets or shot of suitable material.In this manner,compressive residual stresses are induced but only to a limited depth, roughly 0.25 mm.Other mechanical methods involve improving fatigue properties around holes by pushing through balls which are slightly over-sized-a process called"ballising," and the use of balls or a roller to cold work shoulders on fillets-a process called "rolling". 11.1.8.Slip bands and fatigue The onset of fatigue is usually characterised by the appearance on the surface of the specimen of slip bands which,after about 5%of the fatigue life,become permanent and cannot be removed by electropolishing.With increase in the number of load cycles these bands deepen until eventually a crack is formed. Using electron microscopical techniques Forsyth(1)observed extrusions and intrusions from well-defined slip bands and Cottrell()proposed a theory of cross-slip or slip on alternate slip planes whereby,during the tensile half of the stress cycle,slip occurs on each plane in turn to produce two surface steps which on the compressive half of the cycle are
460 Mechanics of Materials 2 $11.1 the fatigue limit of a low-strength steel is not affected to the same extent as the highstrength steel. i.e. the former is less notch-sensitive (another factor to be taken account of when looking at the relative cost of the basic material). However, it must be pointed out that it may be poor economy to overspecify surface finish, particularly where stress levels are relatively low. Because fatigue cracks generally initiate at the surface of a component under tensile stress conditions, certain processes, both chemical and mechanical, which introduce residual surface compressive stresses may be utilised to improve fatigue properties (see $ 10.2). However, the extent of the improvement is difficult to assess quantitatively at this juncture of time. Among the chemical treatments, the two most commonly employed are carburising and nitriding which bring about an expansion of the lattice at the metal surface by the introduction of carbon and nitrogen atoms respectively. Figure 11.20 shows the effect upon fatigue limit. Nitrided and polished As mochined I Cycles to failure (N,) Fig. 11.20. Effect of processes which introduce surface residual stresses upon the fatigue strength of a steel. The most popular mechanical method of improving fatigue limits is shot peening, the surface of the material being subjected to bombardment by small pellets or shot of suitable material. In this manner, compressive residual stresses are induced but only to a limited depth, roughly 0.25 mm. Other mechanical methods involve improving fatigue properties around holes by pushing through balls which are slightly over-sized - a process called “bullising,” and the use of balls or a roller to cold work shoulders on fillets - a process called “rolling”. 11 .I .8. Slip bands and fatigue The onset of fatigue is usually characterised by the appearance on the surface of the specimen of slip bands which, after about 5% of the fatigue life, become permanent and cannot be removed by electropolishing. With increase in the number of load cycles these bands deepen until eventually a crack is formed. Using electron microscopical techniques Forsyth‘”) observed extrusions and intrusions from well-defined slip bands and Cottrell(“) proposed a theory of cross-slip or slip on alternate slip planes whereby, during the tensile half of the stress cycle, slip occurs on each plane in turn to produce two surface steps which on the compressive half of the cycle are
§11.1 Fatigue,Creep and Fracture 461 converted into an intrusion and an extrusion (see Fig.11.21).Although an intrusion is only very small,being approximately 1 um deep,it nevertheless can act as a stress raiser and initiate the formation of a true fatigue crack. Fig.11.21.Diagrammatic representation of the formation of intrusions and extrusions. Fatigue endurance is commonly divided into two periods:(i)the"crack initiation"period; (ii)the "crack growth"or "propagation"period.It is now accepted that the fatigue crack is initiated by the deepening of the slip band grooves by dislocation movement into crevices and finally cracks,but this makes it very difficult to distinguish between crack initiation and crack propagation and therefore a division of the fatigue based upon mode of crack growth is often more convenient. Initially the cracks will form in the surface grains and develop along the active slip plane as mentioned briefly above.These cracks are likely to be aligned with the direction of maximum shear within the component,i.e.at 45 to the maximum tensile stress.This is often referred to as Stage growth and is favoured by zero mean stress and low cyclic stress conditions. Stage ll Stage I Slip planes Fig.11.22.Stage I and II fatigue crack propagation
911.1 Fatigue, Creep and Fracture 46 1 converted into an intrusion and an extrusion (see Fig. 1 1.2 1). Although an intrusion is only very small, being approximately 1 pm deep, it nevertheless can act as a stress raiser and initiate the formation of a true fatigue crack. Fig. 11.2 1. Diagrammatic representation of the formation of intrusions and extrusions. Fatigue endurance is commonly divided into two periods: (i) the “crack initiation” period; (ii) the “crack growth” or “propagation” period. It is now accepted that the fatigue crack is initiated by the deepening of the slip band grooves by dislocation movement into crevices and finally cracks, but this makes it very difficult to distinguish between crack initiation and crack propagation and therefore a division of the fatigue based upon mode of crack growth is often more convenient. Initially the cracks will form in the surface grains and develop along the active slip plane as mentioned briefly above. These cracks are likely to be aligned with the direction of maximum shear within the component, Le. at 45” to the maximum tensile stress. This is often referred to as Stage I growth and is favoured by zero mean stress and low cyclic stress conditions. Stage I \‘ \ Slip planes \\ \ d Fig. 11.22. Stage I and I1 fatigue crack propagation
462 Mechanics of Materials 2 §11.2 At some point,usually when the crack encounters a grain boundary.Stage I is replaced by Stage I/growth in which the crack is normal to the maximum principal tensile stress. This stage is favoured by a tensile mean stress and high cyclic stress conditions.Close examination of the fractured surface shows that over that part associated with Stage II,there are a large number of fine lines called"striations",each line being produced by one fatigue cycle and by measuring the distance between a certain number of striations the fatigue crack growth rate can be calculated. Once the fatigue crack has reached some critical length such that the energy for further growth can be obtained from the elastic energy of the surrounding metal,catastrophic failure takes place.This final fracture area is rougher than the fatigue growth area and in mild steel is frequently crystalline in appearance.Sometimes it may show evidence of plastic deformation before final separation occurred.Further discussion of fatigue crack growth is introduced in $11.3.7. 11.2.Creep Introduction Creep is the time-dependent deformation which accompanies the application of stress to a material.At room temperatures,apart from the low-melting-point metals such as lead,most metallic materials show only very small creep rates which can be ignored.With increase in temperature,however,the creep rate also increases and above approximately 0.4 Tm, where Tm is the melting point on the Kelvin scale,creep becomes very significant.In high-temperature engineering situations related to gas turbine engines,furnaces and steam turbines,etc.,deformation caused by creep can be very significant and must be taken into account. 11.2.1.The creep test The creep test is usually carried out at a constant temperature and under constant load conditions rather than at constant stress conditions.This is acceptable because it is more representative of service conditions.A typical creep testing machine is shown in Fig.11.23. Each end of the specimen is screwed into the specimen holder which is made of a creep- resisting alloy and thermocouples and accurate extensometers are fixed to the specimen in order to measure temperature and strain.The electric furnace is then lowered into place and when all is ready and the specimen is at the desired temperature,the load is applied by adding weights to the lower arm and readings are taken at periodic intervals of extension against time.It is important that accurate control of temperature is possible and to facilitate this the equipment is often housed in a temperature-controlled room. The results from the creep test are plotted in graphical form to produce a typical curve as shown in Fig.11.24.After the initial extension OA which is produced as soon as the test load is applied,and which is not part of the creep process proper(but which nevertheless should not be ignored),the curve can be divided into three stages.In the first or primary stage AB,the movement of dislocations is very rapid,any barriers to movement caused by work-hardening being overcome by the recovery processes,albeit at a decreasing rate. Thus the initial creep strain rate is high but it rapidly decreases to a constant value.In the
462 Mechanics of Materials 2 511.2 At some point, usually when the crack encounters a grain boundary. Stage I is replaced by Stage ZZ growth in which the crack is normal to the maximum principal tensile stress. This stage is favoured by a tensile mean stress and high cyclic stress conditions. Close examination of the fractured surface shows that over that part associated with Stage 11, there are a large number of fine lines called “striations”, each line being produced by one fatigue cycle and by measuring the distance between a certain number of striations the fatigue crack growth rate can be calculated. Once the fatigue crack has reached some critical length such that the energy for further growth can be obtained from the elastic energy of the surrounding metal, catastrophic failure takes place. This final fracture area is rougher than the fatigue growth area and in mild steel is frequently crystalline in appearance. Sometimes it may show evidence of plastic deformation before final separation occurred. Further discussion of fatigue crack growth is introduced in 5 1 1.3.7. 11.2. Creep Introduction Creep is the time-dependent deformation which accompanies the application of stress to a material. At room temperatures, apart from the low-melting-point metals such as lead, most metallic materials show only very small creep rates which can be ignored. With increase in temperature, however, the creep rate also increases and above approximately 0.4 T,, where T, is the melting point on the Kelvin scale, creep becomes very significant. In high-temperature engineering situations related to gas turbine engines, furnaces and steam turbines, etc., deformation caused by creep can be very significant and must be taken into account. I I .2 .l. The creep test The creep test is usually carried out at a constant temperature and under constant load conditions rather than at constant stress conditions. This is acceptable because it is more representative of service conditions. A typical creep testing machine is shown in Fig. 11.23. Each end of the specimen is screwed into the specimen holder which is made of a creepresisting alloy and thermocouples and accurate extensometers are fixed to the specimen in order to measure temperature and strain. The electric furnace is then lowered into place and when all is ready and the specimen is at the desired temperature, the load is applied by adding weights to the lower arm and readings are taken at periodic intervals of extension against time. It is important that accurate control of temperature is possible and to facilitate this the equipment is often housed in a temperature-controlled room. The results from the creep test are plotted in graphical form to produce a typical curve as shown in Fig. 11.24. After the initial extension OA which is produced as soon as the test load is applied, and which is not part of the creep process proper (but which nevertheless should not be ignored), the curve can be divided into three stages. In the first or primary stage AB, the movement of dislocations is very rapid, any barriers to movement caused by work-hardening being overcome by the recovery processes, albeit at a decreasing rate. Thus the initial creep strain rate is high but it rapidly decreases to a constant value. In the