18 CHAPTER 1 TENSILE RESPONSE OF MATERIALS TABLE 1.5 Selected Strain-Hardening in-Hardening Coeficient, n Brass 035-0,4 030.35 Aluminum 0150.25 fact that this relationship is only an empirical approximation. (When a nonlinear log- log plot does result for a given material, the strain-hardening coefficient is often defined at a particular strain value. ) In general, n increases with decreasing strength level and with decreasing mobility of certain dislocations in the crystalline lattice More will be said about this material property in Chapter 3 1.2.2.1 Strength Levels in Materials It has become common practice to define several strength levels that characterize the materials tensile response. The proportional limit is that stress level below which SS IS to straIn Eq. 1-7. The elastic limit defines level below which the deformation strains are fully reversible. In most engineering materials, these two quantities are essentially equal. However, it is possible for a metal to exhibit nonlinear but elastic behavior. For example, very high-strength fila mentary particles often called whiskers--can exhibit elastic strains in excess of 2% In this range of very large elastic strains, the modulus of elasticity reveals its weak dependence on strain-something that is completely obscured when strains are very small. For example, note that dF/dx in Fig. 1.2b decreases with increasing distance of particle separation. As such, Hooke's law(Eq. 1-7) represents an empirical rela- tionship, albeit a good one at small strains. Consequently, the elastic limit is approx- imately equal to the proportional limit and may be slightly higher in some cases. elated to the onset of irreversible plastic deformation This quantity is amaury A much more important material property is the yield strength--a stress lev define, since the point where plastic fow begins will depend on the sensitivity of the displacement transducer. The more sensitive the gage, the lower the stress level where plastic fow is found. In recent years, special capacitance strain gages have been used to measure strains in the range of 10-6. In fact, a number of studies dealing with the mechanical behavior of materials in the microstrain region have been undertaken as a result of this breakthrough in instrumentation. These investigations have shown, for example, that plastic deformation-the irreversible movement of dislocations occurs at stress levels many times lower than the conventionally determined engineering yield strength To arrive at a uniformly accepted method for determination of the yield strength, therefore, a standard test procedure(ASTM Standard E 8-69) has been adopted. The yield-strength value is obtained in the following manner: (1)Determine the engineering stress-strain curve, such as the one shown in Fig. 1.6:(2)construct a line parallel to the elastic portion of the o-f curve but offset from the origin by a certain amount(the generally accepted offset is 0.002 or 0. 2% strain); and(3)define
1. 2 STRESS-STRAIN CURVES 19 curve. Tensile yield strength is defined at intersection of stress-strain curve and 0. 2% offset line. Points A, B, C, D, and E are the arbitrary stress levels discussed in 02% yield strength at the intersection of the a-e curve and the offset line. As cited ve, this value is usually defined as the 0. 2% offset yield strength. The ultimate tensile strength is defined as the maximum load divided by the initial cross-sectional area, while the true fracture stress is the load at fracture divided by the final cross- sectional area with correction made for any localized deformation(necking) in the inal fracture region(see Section 1. 2. 2. 2). A compilation of tensile properties for a number of engineering materials is given in Tables 1. 6 and 1.7. 1.2.2.2 Plastic Instability and Necking The true and engineering stress-strain plots from a tensile test reveal basic differences, as shown in Fig. 1.5. While the engineering curve reaches a maximum at maximum load and decreases thereafter to fracture, the true curve rises continually to failure The inflection in the engineering curve is due to the onset of localized plastic fow and the manner in which engineering stress is defined. To understand this, consider for a moment the following sequence of events. when the stress reaches a critical level, plastic deformation will occur at the weakest part of the test sample, somewhere along the gage length. This local extension under tensile loading will cause a simul- taneous area constriction so that the true local stress is higher at this location than anywhere else along the gage length. Consequently, all additional deformation would be expected to concentrate in this most highly stressed region. Such is the case in an ideally plastic material. For all other materials, however, this localized plastic defor mation strain hardens the material, thereby making it more resistant to further damage At this point, the applied stress must be increased to produce additional plastic deformation at the second weakest position along the gage length. Here again the material strain hardens and the process continues. On a macroscopic scale, the gage length extends uniformly in concert with a uniform reduction in cross-sectional area. Computerized data bases for material properties are presently being standardized [(e.g, see J. G. Kaufman, Stand. News ASTM 15(3),38(1987)
TABLE 1. 6a Tensile Properties for Selected Engineering materials Yield Tensile Elongation Strength Strength in 5-cm Treatment (MPa Steel Alloys As-rolled 61 +T②205°℃) 340 1150 (650C) 1365 6 ealed plate 310 316 Annealed bar 515 515 43I AFC-77 835-2140 026 32-74 PH 15-7Mo 95-1515 Ti-5A1-25S Annealed Ti-6A1-4V Ti-13V-11Cr-3Al t age Magnesium Alloys Extruded bar 185-195290295 215-260295315 46 17 7178 T6 Plastics 5-75 ly(tetra 1448100450 Nylon 66 polycarbonate Low density 2150800 41-54 50-1000 20
TABLE 1. 6b Tensile Properties for Selected Engineering materials Strength Material reatment Gage(%) 1080 1340 Q+T(400°F 11 35 14 4340 800vF 213 (1200F) Annealed plate 35 310 45 95 Annealed bar AFC-77 81-233 121310 10-26 32-74 PH 15-7Mo 55-210 130-220 2-35 Titanium Alloys i-8A1-1Mo-1V Ti-6Al-4V Ti-13V-11Cr-3A1 Solution age AZ31B Annealed 15-18 27-28 4243 4346 131 2024 T6,-T65 21 35 23 7075 Plastics ABS Medium impact 00450 Poly (vinylidene 5.1-7 Nylon 66 w density 69 Databook 1974, Metal Progress(mid-June 1974)
22 CHAPTER 1 TENSILE RESPONSE OF MATERIALS TABLE 1.7 Strength Properties of Selected Ceramics Flexural Strength Strength Elasticity Material MMPa〔ks)] Pa (ksi)] MPa (ksi]GPa(10°ps Alumina(85% dense) Alumina(99.8% dense) 2760(400) 205(30) 385(56 Alumina silicate 62(9) Partially stabilized 1860(270) +9%o MgO 24(35) Guide to Engineering Materials, Vol. 1(1), ASM, Metals Park, OH, 1986, pp. 16, 64, 6 (Recall that plastic deformation is a constant-volume process. )With increasing load, a point is reached where the strain-hardening capacity of the material is exhausted and the nth local area contraction is no longer balanced by a corresponding increase in material strength. At this maximum load, further plastic deformation is localized the necked region, since the stress increases continually with areal contraction even though the applied load is decreasing as a result of elastic unloading in the test bar outside the necked area. Eventually the neck will fail. Since engineering stress is based on Ao, the decreasing load on the sample after the neck has formed will result in the computation of a decreasing stress. By comparison, the decreasing load value is more than offset by the decrease in instantaneous cross-sectional area such that the true stress continues to rise to failure even after the onset of necking 1.2.2.3 Strain Distribution in Tensile Specimen total strain distribution along the in Fig. 1.7 for various levels as indicated on the engineering stress-strain on of elongation along the gage ler specimen, researchers occasionally report both the total strain,ls-loMo or In(/lo), and the uniform strain, which is related local neckin urve C in Fig. 1.7). It should be emphasized t test result will depend on the gage length of the test bar From Fig. 1.7, it is clear that as the gage length decreases, the elongation involved in the necking process become increasingly more dominant. Consequently, total strain values will increase the shorter the gage length. For this reason both specimen size and total strain data should be reported. ASTM has standardized specimen dimensions to minimize variability in test data resulting from such geometrical considerations. As noted in Table 1.8, the gage length to diameter ratio is standardized to a value of about 4 1.2.2.4 Extent of Uniform Strain From the standpoint of material usage in an engineering component, it is desirable to maximize the extent of uniform elongation prior to the onset of localized necking.It may be shown that the amount of uniform strain is related to the magnitude of the strain-harde