- Several precautions must be observed in the proper use of the Rockwell scales.. - Readings taken on the sides of cylinders or spheres should be corrected for the curvature of the surface. - The hardness numbers for all the Rockwell scales are an inverse measure of the depth of the indentation. - Each division on the dial gauge of the Rockwell machine corresponds to an 80 x 10 6 in depth of penetration. - A good example of this is the case of the effect of cold work on the hardness of a fully annealed brass. - The Brinell hardness H 8 is the hardness number obtained by dividing the load that is applied to a spherical indenter by the surface area of the spherical indentation produced. - is then withdrawn from the machine and the operator measures the diameter of the indentation by means of a millimeter scale etched on the eyepiece of a special Brinell microscope. - The denominator in this equation is the spherical area of the indentation.. - The Brinell hardness number of a given material increases as the applied load is increased, the increase being somewhat proportional to the strain-hardening rate of the material. - The Meyer hardness H M is the hardness number obtained by dividing the load applied to a spherical indenter by the projected area of the indentation. - The difference between these two hardness scales is simply the area that is divided into the applied load—the projected area being used for the Meyer hardness and the spherical surface area for the Brinell hardness. - Both are based on the diameter of the indentation. - The units of the Meyer hardness are also kilograms per square millimeter, and hardness is calculated from the equation. - The values of the strain-hardening exponent for a variety of materials are available in many handbooks. - Nevertheless, this approximate relationship between the strain- hardening and the strain-strengthening exponents can be very useful in the practical evaluation of the mechanical properties of a material.. - The diamond-pyramid hardness H p , or the Vickers hardness H v , as it is frequently called, is the hardness number obtained by dividing the load applied to a square- based pyramid indenter by the surface area of the indentation. - The indentation at the surface of the workpiece is square-shaped. - The diamond pyramid hardness number is determined by measuring the length of the two diagonals of the indentation and using the average value in the equation. - d = diagonal of the indentation, mm a = face angle of the pyramid, 136°. - In order to be geometrically similar, the angle subtended by the indentation must be constant regardless of the depth of the indentation. - It is believed that if geo- metrically similar deformations are produced, the material being tested is stressed to the same amount regardless of the depth of the penetration. - ber regardless of the load applied. - Experimental data show that the pyramid hard- ness number is independent of the load if loads greater than 3 kg are applied. - How- ever, for loads less than 3 kg, the hardness is affected by the load, depending on the strain-hardening exponent of the material being tested.. - The Knoop hardness H K is the hardness number obtained by dividing the load applied to a special rhombic-based pyramid indenter by the projected area of the indentation.. - The specimen is then positioned under the indenter and the load is applied for 10 to 20 s.The specimen is then located under the microscope again and the length of the long diagonal is measured. - The Knoop hard- ness number is then determined by means of the equation. - As such, it is greatly influenced by the elastic modulus of the material being tested.. - rately registering the value of the load and the amount of deformation that occurs to the specimen. - The minimum length of the reduced sec- tion for a standard specimen is four times its diameter. - In addition to the tensile properties of strength, rigidity, and ductility, the tensile test also gives information regarding the stress-strain behavior of the material. - Strength is a property of a material—it is a measure of the ability of a material to withstand stress or it is the load-carrying capacity of a material. - (Residual stresses may be considered as being caused by unseen loads.) The numerical value of the stress is determined by dividing the actual load or force on the part by the actual cross section that is supporting the load. - sure of the strength of a material, it is more appropriate to call such data either strength-nominal strain or nominal stress-strain data. - The load-versus-gauge-length data, or an elastic stress-strain curve drawn by the machine, are needed to determine Young's modulus of elasticity of the material as well as the proportional limit. - 7.15 with an expanded strain axis, which is necessary for the determination of the yield strength. - FIGURE 7.15 The elastic-plastic portion of the engineering stress-strain curve for annealed A40 titanium.. - In this case it is necessary to record simultaneously the cross-sectional area of the specimen and the load on it. - The load-deformation data in the plastic region of the tensile test of an annealed titanium are listed in Table 7.4. - These data are a continuation of the tensile test in which the elastic data are given in Table 7.3.. - The load-diameter data in Table 7.4 are recorded during the test and the remain- der of the table is completed afterwards. - Quite frequently, in calculating the strength or the ductility of a cold-worked material, it is necessary to determine the value of the strain £ that is equivalent to the amount of the cold work. - The most significant difference between the shape of this stress-strain curve and that of the load-deformation curve in Fig. - The stress-strain data obtained from the tensile test of the annealed A40 titanium listed in Tables 7.3 and 7.4 are plotted on logarithmic coordinates in Fig. - The elastic portion of the stress-strain curve is also a straight line on logarithmic coordi- nates as it is on cartesian coordinates. - When plotted on cartesian coordinates, the slope of the elastic modulus is different for the different materials. - The slope of the stress-strain curve in logarithmic coordinates is called the strain-strengthening expo- nent because it indicates the increase in strength that results from plastic strain. - Some of the fully annealed aluminum alloys have this type of curve.. - All the tensile properties are defined in this section and are briefly dis- cussed on the basis of the tensile test described in the preceding section.. - It is the slope of the straight-line (elas- tic) portion of the stress-strain curve when drawn on cartesian coordinates. - The modulus of elasticity of the titanium alloy whose tensile data are reported in Table 7.3 is shown in Fig. - The elastic limit is the greatest stress which a material is capable of withstanding without any permanent deformation after removal of the load. - 7.15 to determine the yield strength of the A40 titanium. - The tensile strength is the value of nominal stress obtained when the maximum (or ultimate) load that the tensile specimen supports is divided by the original cross- sectional area of the specimen. - The percent reduction of area and the strain at ultimate load e M are the best measure of the ductility of a material.. - The fracture strain is the true strain at fracture of the tensile specimen. - Because of the ductility rela- tionship, we express it here as. - A true material property is not significantly affected by the size of the specimen. - This relation is derived on the basis of the load-deformation curve shown in Fig. - The load at any point along this curve is equal to the product of the true stress on the specimen and the corresponding area. - is also equal to the applied load L w divided by the actual cross- sectional area of the specimen A w. - Therefore, the yield strength of the previously cold-worked (stretched) specimen is approximately. - Thus it is apparent that the plastic portion of the a - e curve is approximately the locus of yield strengths for a material as a function of the amount of cold work. - However, on the basis of the concepts of the tensile test presented here, two relations are derived in Ref. - These relations are derived on the basis of the load-deformation characteristics of a material as represented in Fig. - where (S u ) 0 = tensile strength of the original non-cold-worked specimen and A 0 = its original area.. - The percent cold work associated with the deformation of the specimen from A 0. - As stated earlier, this fact led to the wide acceptance of the Brinell hardness scale. - The ratio of the tensile strength of a material to its Brinell hardness number is identified by the symbol K B , and it is a function of both the load used to determine the hardness and the strain-strengthening exponent of the material.. - From these curves it is apparent that K 8 varies directly with m and inversely with the load or diameter of the indentation d. - A test was conducted on a heat of alpha brass to see how accurately the tensile strength of a material could be predicted from a hardness test when the strain- strengthening exponent of the material is not known. - D = diameter of the ball, and d - diameter of the indentation. - The experimentally determined value of the tensile strength for this brass was 40 500 psi, which is just 2 percent lower than the predicted value.. - What is the tensile strength of a heat that has a Brinell hardness number of 28 when measured with a 500-kg load? The diameter of the indentation for this hardness number is 4.65. - They serve as a basis of comparison and specification of the toughness of a material.. - The area under the tensile stress-strain curve is also a mea- sure of the ability of a material to absorb energy (its toughness). - Figure 7.22b does the same for the Izod V-notch specimen, and the details of the notch are shown in Fig. - There are several mod- ifications of the standard V-notch specimen. - Both have a 1-mm radius at the bottom rather than the 0.25- mm radius of the V-notch. - (c) details of the notch.. - At the low testing temperature the fracture is of the cleavage type, which has a bright, faceted appearance. - At the higher temperatures the fractures are of the shear type, which has a fibrous appearance. - A part may fail with a load that induced stresses in it that lie between the yield strength and the tensile strength of the material even if the load is steady and con- stant rather than alternating and repeating as in a fatigue failure. - The creep rate is the slope of the strain-time creep curve in the steady-creep region, referred to as a stage 2 creep. - Thus the three variables that affect the creep rate of the specimen are (1) nominal stress, (2) tem- perature, and (3) time.. - The extension occurs at a decreasing rate in this portion of the creep curve.. - The temperature where these two portions of the grains are equal is called the equicohesive temperature. - The mechanical properties are simply listed as the experimentally obtained values for each of the many conditions of a given metal.. - Both the format of the data and the actual mechan- ical properties listed are different from the traditional handbook presentations.. - One of the main advantages is that it requires much less space. - Table 7.6 includes some of the properties of very-high-strength steels. - Also, the stresses are compressive on one side of the splines and tensile on the other. - The negative sign in front of the function is needed because Eq. - In some design situations, the actual value of the yield strength in a given part for a specific amount of cold work may be 50 percent less than the value that would be listed in the materials handbook. - 8 makes it possible for the design engineer to make a reasonable prediction of the mechani- cal properties of a fabricated part. - Y indicates the total percent of the alloys present.. - [7.2] for details of the unified numbering system (UNS).. - The third and fourth digits (ZZ in the code) have no numerical significance but simply relate to the chemical composition of the alloys.. - It is simply a means of defining the chemical compo- sition of the specific alloys. - The second part consists of two digits corresponding to rounded-off percentages of the two main alloying elements
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