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materials science engineering

Questions and Answers of Materials Science Engineering

Show that Equations 6.18a and 6.18b are valid when there is no volume change during deformation.
Demonstrate that Equation 6.16, the expression defining true strain, may also be represented by when specimen volume remains constant during deformation. Which of these two expressions is more
Using the data in Problem 6.28 and Equations 6.15, 6.16, and 6.18a, generate a true stress?true strain plot for aluminum. Equation 6.18a becomes invalid past the point at which necking begins;
A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.20 is produced when a true stress of 575MPa (83,500psi) is applied; for the same metal, the value of K
For some metal alloy, a true stress of 415MPa (60,175psi) produces a plastic true strain of 0.475. How much will a specimen of this material elongate when a true stress of 325MPa (46,125psi) is
The following true stresses produce the corresponding true plastic strains for a brass alloy: What true stress is necessary to produce a true plastic strain of 0.25?
For a brass alloy, the following engineering stresses produce the corresponding plastic engineering strains, prior to necking: On the basis of this information, compute the engineering stress
Find the toughness (or energy to cause fracture) for a metal that experiences both elastic and plastic deformation. Assume Equation 6.5 for elastic deformation, that the modulus of elasticity is
For a tensile test, it can be demonstrated that necking begins when Using Equation 6.19, determine the value of the true strain at this onset of necking.
Taking the logarithm of both sides of Equation 6.19 yieldsThus, a plot of log σT versus log ∈T in the plastic region to the point of necking should yield a straight line having a slope of n
A cylindrical specimen of a brass alloy 7.5 mm (0.30 in.) in diameter and 90.0 mm (3.54 in.) long is pulled in tension with a force of 6000 N (1350lbf); the force is subsequently released. (a)
A steel alloy specimen having a rectangular cross section of dimensions 12.7 mm ? 6.4 mm (0.5 in. ? 0.25 in.) has the stress?strain behavior shown in figure. If this specimen is subjected to a
(a) A 10-mm-diameter Brinell hardness indenter produced an indentation 1.62 mm in diameter in a steel alloy when a load of 500 kg was used. Compute the HB of this material.(b) What will be the
Estimate the Brinell and Rockwell hardnesses for the following: (a) The naval brass for which the stress?strain behavior is shown in Figure 6.12. (b) The steel alloy for which the stress?strain
Using the data represented in figure, specify equations relating tensile strength and Brinell hardness for brass and nodular cast iron, similar to Equations 6.20a and 6.20b for steels.
Cite five factors that lead to scatter in measured material properties.
Below are tabulated a number of Rockwell B hardness values that were measured on a single steel specimen. Compute average and standard deviation hardness values
Upon what three criteria are factors of safety based?
Determine working stresses for the two alloys that have the stress?strain behaviors shown in Figures 6.12 and 6.21.
A large tower is to be supported by a series of steel wires. It is estimated that the load on each wire will be 11,100 N (2500lbf). Determine the minimum required wire diameter assuming a factor of
(a)?Gaseous hydrogen at a constant pressure of 1.013MPa (10atm) is to flow within the inside of a thin-walled cylindrical tube of nickel that has a radius of 0.1 m. The temperature of the tube is to
Consider the steady-state diffusion of hydrogen through the walls of a cylindrical nickel tube as described in Problem 6.D2. One design calls for a diffusion flux of 5 × 10-8 mol/m2-s, a tube radius
To provide some perspective on the dimensions of atomic defects, consider a metal specimen that has a dislocation density of 104 mm-2. Suppose that all the dislocations in 1000 mm3 (1 cm3) were
Consider two edge dislocations of opposite sign and having slip planes that are separated by several atomic distances as indicated in the diagram. Briefly describe the defect that results when these
Is it possible for two screw dislocations of opposite sign to annihilate each other? Explain your answer.
For each of edge, screw, and mixed dislocations, cite the relationship between the direction of the applied shear stress and the direction of dislocation line motion.
(a) Define a slip system.(b) Do all metals have the same slip system? Why or why not?
(a) Compare planar densities (Section 3.11 and Problem 3.54) for the (100), (110), and (111) planes for FCC.(b) Compare planar densities (Problem 3.55) for the (100), (110), and (111) planes for BCC.
One slip system for the BCC crystal structure is {110}. In a manner similar to Figure, sketch a {110}-type plane for the BCC structure, representing atom positions with circles. Now, using arrows,
One slip system for the HCP crystal structure is {0001}. In a manner similar to Figure, sketch a {0001}-type plane for the HCP structure and, using arrows, indicate three different slip directions
Equations 7.1a and 7.1b, expressions for Burgers vectors for FCC and BCC crystal structures, are of the form where a is the unit cell edge length. Also, since the magnitudes of these Burgers
(a) In the manner of Equations 7.1a, 7.1b, and 7.1c, specify the Burgers vector for the simple cubic crystal structure. Its unit cell is shown in Figure. Also, simple cubic is the crystal structure
Sometimes cos ( cos ( in Equation 7.2 is termed the Schmid factor. Determine the magnitude of the Schmid factor for an FCC single crystal oriented with its [100] direction parallel to the loading
Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 43.1° and 47.9°, respectively, with the tensile axis. If the critical
A single crystal of aluminum is oriented for a tensile test such that its slip plane normal makes an angle of 28.1° with the tensile axis. Three possible slip directions make angles of 62.4°,
Consider a single crystal of silver oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a [101] direction, and is initiated at an applied
A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [110] direction. If the critical resolved shear stress for this
(a) A single crystal of a metal that has the BCC crystal structure is oriented such that a tensile stress is applied in the [010] direction. If the magnitude of this stress is 2.75MPa, compute the
Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a [102] direction. If slip occurs on a (111) plane
The critical resolved shear stress for iron is 27MPa (4000psi). Determine the maximum possible yield strength for a single crystal of Fe pulled in tension.
List four major differences between deformation by twinning and deformation by slip relative to mechanism, conditions of occurrence, and final result.
Briefly explain why small-angle grain boundaries are not as effective in interfering with the slip process as are high-angle grain boundaries.
(a) From the plot of yield strength versus (grain diameter)?1/2 for a 70 Cu?30 Zn cartridge brass, Figure, determine values for the constants ?0 and ky in Equation 7.7. (b) Now predict the yield
The lower yield point for an iron that has an average grain diameter of 5 × 10-2 mm is 135MPa (19,500psi). At a grain diameter of 8 × 10-3 mm, the yield point increases to 260MPa (37,500psi). At
If it is assumed that the plot in figure is for noncold-worked brass, determine the grain size of the alloy in Figure 7.19; assume its composition is the same as the alloy in Figure 7.15.
In the manner of Figures 7.17b and 7.18b, indicate the location in the vicinity of an edge dislocation at which an interstitial impurity atom would be expected to be situated. Now briefly explain in
(a) Show, for a tensile test, that if there is no change in specimen volume during the deformation process (i.e., A0l0 = Adld). (b) Using the result of part (a), compute the percent cold work
Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the
Two previously undeformed specimens of the same metal are to be plastically deformed by reducing their cross-sectional areas. One has a circular cross section, and the other is rectangular; during
A cylindrical specimen of cold-worked copper has a ductility (%EL) of 25%. If its cold-worked radius is 10 mm (0.40 in.), what was its radius before deformation?
(a) What is the approximate ductility (%EL) of a brass that has a yield strength of 275MPa (40,000psi)?(b) What is the approximate Brinell hardness of a 1040 steel having a yield strength of 690MPa
Experimentally, it has been observed for single crystals of a number of metals that the critical resolved shear stress τcrss is a function of the dislocation density ρD aswhere τ0 and A are
Briefly cite the differences between recovery and recrystallization processes.
Estimate the fraction of recrystallization from the photomicrograph in Figure 7.21c.
Explain the differences in grain structure for a metal that has been cold worked and one that has been cold worked and then recrystallized.
(a) What is the driving force for recrystallization?(b) For grain growth?
(a) From Figure, compute the length of time required for the average grain diameter to increase from 0.01 to 0.1 mm at 500?C for this brass material. (b) Repeat the calculation at 600?C.
The average grain diameter for a brass material was measured as a function of time at 650?C, which is tabulated below at two different times: (a) What was the original grain diameter? (b) What grain
An undeformed specimen of some alloy has an average grain diameter of 0.040 mm. You are asked to reduce its average grain diameter to 0.010 mm. Is this possible? If so, explain the procedures you
Grain growth is strongly dependent on temperature (i.e., rate of grain growth increases with increasing temperature), yet temperature is not explicitly given as a part of Equation 7.9.(a) Into which
An uncold-worked brass specimen of average grain size 0.008 mm has a yield strength of 160MPa (23,500psi). Estimate the yield strength of this alloy after it has been heated to 600°C for 1000 s, if
Determine whether or not it is possible to cold work steel so as to give a minimum Brinell hardness of 225, and at the same time have a ductility of at least 12%EL. Justify your decision.
Determine whether or not it is possible to cold work brass so as to give a minimum Brinell hardness of 120 and at the same time have a ductility of at least 20%EL. Justify your decision.
A cylindrical specimen of cold-worked steel has a Brinell hardness of 250.(a) Estimate its ductility in percent elongation.(b) If the specimen remained cylindrical during deformation and its original
It is necessary to select a metal alloy for an application that requires a yield strength of at least 345MPa (50,000psi) while maintaining a minimum ductility (%EL) of 20%. If the metal may be cold
A cylindrical rod of 1040 steel originally 15.2 mm (0.60 in.) in diameter is to be cold worked by drawing; the circular cross section will be maintained during deformation. A cold-worked tensile
A cylindrical rod of copper originally 16.0 mm (0.625 in.) in diameter is to be cold worked by drawing; the circular cross section will be maintained during deformation. A cold-worked yield strength
A cylindrical 1040 steel rod having a minimum tensile strength of 865MPa (125,000psi), a ductility of at least 10%EL, and a final diameter of 6.0 mm (0.25 in.) is desired. Some 7.94 mm (0.313 in.)
What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of 2.5 × 10-4 mm (10-5 in.) and a crack length of 2.5 × 10-2 mm (10-3 in.) when
Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm (0.01 in.) and having
If the specific surface energy for soda-lime glass is 0.30 J/m2, using data contained in Table 12.5, compute the critical stress required for the propagation of a surface crack of length 0.05 mm.
A polystyrene component must not fail when a tensile stress of 1.25MPa (180psi) is applied. Determine the maximum allowable surface crack length if the surface energy of polystyrene is 0.50 J/m2
A specimen of a 4340 steel alloy having a plane strain fracture toughness of 45MPα√m (41ksi√in) is exposed to a stress of 1000MPa (145,000psi). Will this specimen experience fracture if it is
Some aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 35MPα√m (31.9 ksi√in). It has been determined that fracture results at a stress of
Suppose that a wing component on an aircraft is fabricated from an aluminum alloy that has a plane strain fracture toughness of 40MPα√m (36.4ksi√in). It has been determined that fracture results
A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55MPα√m (50ksi√in) If, during service use, the plate is exposed to a tensile stress of 200MPa
Calculate the maximum internal crack length allowable for a 7075-T651 aluminum alloy (Table 8.1) component that is loaded to a stress one half of its yield strength. Assume that the value of Y is
A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane strain fracture toughness of 77.0MPα√m (70.1ksi√in) and a yield strength of 1400MPa
Following is tabulated data that were gathered from a series of Charpy impact tests on a ductile cast iron. (a) Plot the data as impact energy versus temperature. (b) Determine a ductile-to-brittle
Following is tabulated data that were gathered from a series of Charpy impact tests on a tempered 4140 steel alloy. (a) Plot the data as impact energy versus temperature. (b) Determine a
A fatigue test was conducted in which the mean stress was 50MPa (7250psi) and the stress amplitude was 225MPa (32,625psi).(a) Compute the maximum and minimum stress levels.(b) Compute the stress
A cylindrical 1045 steel bar (Figure) is subjected to repeated compression-tension stress cycling along its axis.?If the load amplitude is 22,000 N (4950lbf), compute the minimum allowable bar
An 8.0 mm (0.31 in.) diameter cylindrical rod fabricated from a red brass alloy (Figure) is subjected to reversed tension-compression load cycling along its axis. If the maximum tensile and
A 12.5 mm (0.50 in.) diameter cylindrical rod fabricated from a 2014-T6 alloy (Figure) is subjected to a repeated tension-compression load cycling along its axis. Compute the maximum and minimum
The fatigue data for a brass alloy are given as follows: (a) Make an S?N plot (stress amplitude versus logarithm cycles to failure) using these data. (b) Determine the fatigue strength at 5 ? 105
Suppose that the fatigue data for the brass alloy in Problem 8.18 were taken from torsional tests, and that a shaft of this alloy is to be used for a coupling that is attached to an electric motor
The fatigue data for a ductile cast iron are given as follows: (a) Make an S?N plot (stress amplitude versus logarithm cycles to failure) using these data. (b) What is the fatigue limit for this
Suppose that the fatigue data for the cast iron in Problem 8.20 were taken for bending-rotating tests, and that a rod of this alloy is to be used for an automobile axle that rotates at an average
Three identical fatigue specimens (denoted A, B, and C) are fabricated from a nonferrous alloy. Each is subjected to one of the maximum-minimum stress cycles listed below; the frequency is the same
Cite five factors that may lead to scatter in fatigue life data.
Briefly explain the difference between fatigue striations and beachmarks both in terms of(a) Size and(b) Origin.
List four measures that may be taken to increase the resistance to fatigue of a metal alloy.
Give the approximate temperature at which creep deformation becomes an important consideration for each of the following metals: nickel, copper, iron, tungsten, lead, and aluminum.
The following creep data were taken on an aluminum alloy at 400?C (750?F) and a constant stress of 25MPa (3660psi). Plot the data as strain versus time, then determine the steady-state or minimum
A specimen 750 mm (30 in.) long of an S-590 alloy (Figure) is to be exposed to a tensile stress of 80MPa (11,600psi) at 815?C (1500?F). Determine its elongation after 5000 h. Assume that the total of
For a cylindrical S-590 alloy specimen (Figure) originally 10 mm (0.40 in.) in diameter and 500 mm (20 in.) long, what tensile load is necessary to produce a total elongation of 145 mm (5.7 in.)
If a component fabricated from an s-590 alloy (figure 8.30) is to be exposed to a tensile stress of 300mpa (43,500psi) at 650(c (1200(f), estimate its rupture lifetime.
A cylindrical component constructed from an S-590 alloy (Figure) has a diameter of 12 mm (0.50 in.). Determine the maximum load that may be applied for it to survive 500 h at 925(C(1700(F).
From Equation 8.19, if the logarithm of is plotted versus the logarithm of ?, then a straight line should result, the slope of which is the stress exponent n. Using Figure 8.31, determine the value
(a) Estimate the activation energy for creep (i.e., Qc in Equation 8.20) for the S-590 alloy having the steady-state creep behavior shown in figure. Use data taken at a stress level of 300MPa

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