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physics
modern physics

Questions and Answers of Modern Physics

Indium atoms are to be diffused into a silicon wafer using both pre-deposition and drive-in heat treatments; the background concentration of In in this silicon material is known to be 2 ( 1020
Carbon diffuses in iron via an interstitial mechanism-for BCC iron from one tetrahedral site to an adjacent one. In Section 4.3 (Figure 4.3b) we note that a general set of point coordinates for this
A sheet of steel 2.5-mm thick has nitrogen atmospheres on both sides at 900°C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this
It is desired to enrich the partial pressure of hydrogen in a hydrogen-nitrogen gas mixture for which the partial pressures of both gases are 0.1013 MPa (1 atm). It has been proposed to accomplish
A gas mixture is found to contain two diatomic A and B species (A2 and B2), the partial pressures of both of which are 0.1013 MPa (1 atm). This mixture is to be enriched in the partial pressure of
The wear resistance of a steel shaft is to be improved by hardening its surface by increasing the nitrogen content within an outer surface layer as a result of nitrogen diffusion into the steel; the
The wear resistance of a steel gear is to be improved by hardening its surface, as described in Design Example 5.1. However, in this case the initial carbon content of the steel is 0.15 wt%, and a
One integrated circuit design calls for the diffusion of aluminum into silicon wafers; the background concentration of Al in Si is 1.75 ( 1019 atoms/m3. The pre-deposition heat treatment is to be
Atoms of which of the following elements will diffuse most rapidly in iron? (A) Mo (B) C (D) W (C) Cr
Calculate the diffusion coefficient for copper in aluminum at 600(C. Pre-exponential and activation energy values for this system are 6.5 ( 10-5 m2/s and 136,000 J/mol, respectively.(A) 5.7 ( 10(2
Consider a cylindrical specimen of a steel alloy (Figure 6.22) 8.5 mm (0.33 in.) in diameter and 80 mm (3.15 in.) long that is pulled in tension. Determine its elongation when a load of 65,250 N
Figure 6.23 shows the tensile engineering stress-strain curve in the elastic region for a gray cast iron. Determine(a) The tangent modulus at 25 MPa (3625 psi) and(b) The secant modulus taken to 35
Using the solution to Problem 6.13, rank the magnitudes of the moduli of elasticity for the following hypothetical X, Y, and Z materials from the greatest to the least. The appropriate A, B, and n
A cylindrical specimen of steel having a diameter of 15.2 mm (0.60 in.) and length of 250 mm (10.0 in.) is deformed elastically in tension with a force of 48,900 N (11,000 lbf). Using the data
A cylindrical bar of aluminum 19 mm (0.75 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Using the data in Table 6.1, determine the force that produces
A cylindrical specimen of a metal alloy 10 mm (0.4 in.) in diameter is stressed elastically in tension. A force of 15,000 N (3,370 lbf) produces a reduction in specimen diameter of 7 × 10-3 mm (2.8
A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 30.00 and 30.04 mm, respectively, and its final length is 105.20 mm, compute
Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 10.0 mm (0.39 in.). A tensile force of 1500 N (340 lbf) produces an elastic reduction in diameter of 6.7 ×
A brass alloy is known to have a yield strength of 240 MPa (35,000 psi), a tensile strength of 310 MPa (45,000 psi), and an elastic modulus of 110 GPa (16.0 × 106 psi). A cylindrical specimen of
A cylindrical metal specimen 15.0 mm (0.59 in.) in diameter and 150 mm (5.9 in.) long is to be subjected to a tensile stress of 50 MPa (7250 psi); at this stress level, the resulting deformation will
A cylindrical metal specimen 10.7000 mm in diameter and 95.000 mm long is to be subjected to a tensile force of 6300 N; at this force level, the resulting deformation will be totally elastic.(a) If
Consider the brass alloy for which the stress-strain behavior is shown in Figure 6.12. A cylindrical specimen of this material 10.0 mm (0.39 in.) in diameter and 101.6 mm (4.0 in.) long is pulled in
A cylindrical rod 120 mm long and having a diameter of 15.0 mm is to be deformed using a tensile load of 35,000 N. It must not experience either plastic deformation or a diameter reduction of more
A cylindrical rod 500 mm (20.0 in.) long and having a diameter of 12.7 mm (0.50 in.) is to be subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of
A cylindrical specimen of a brass alloy having a length of 100 mm (4 in.) must elongate only 5 mm (0.2 in.) when a tensile load of 100,000 N (22,500 lbf) is applied. Under these circumstances, what
A load of 140,000 N (31,500 lbf) is applied to a cylindrical specimen of a steel alloy (displaying the stress-strain behavior shown in Figure 6.22) that has a cross-sectional diameter of 10 mm (0.40
A bar of a steel alloy that exhibits the stress-strain behavior shown in Figure 6.22 is subjected to a tensile load; the specimen is 375 mm (14.8 in.) long and has a square cross section 5.5 mm (0.22
A specimen of copper having a rectangular cross section 15.2 mm × 19.1 mm (0.60 in. × 0.75 in.) is pulled in tension with 44,500 N (10,000 lbf) force, producing only elastic deformation. Calculate
A cylindrical specimen of stainless steel having a diameter of 12.8 mm (0.505 in.) and a gauge length of 50.800 mm (2.000 in.) is pulled in tension. Use the load-elongation characteristics shown in
(a) Plot the data as engineering stress versus engineering strain.(b) Compute the modulus of elasticity.(c) Determine the yield strength at a strain offset of 0.002.(d) Determine the tensile strength
A cylindrical metal specimen 15.00 mm in diameter and 120 mm long is to be subjected to a tensile force of 15,000 N.(a) If this metal must not experience any plastic deformation, which of aluminum,
A cylindrical metal specimen having an original diameter of 12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.) is pulled in tension until fracture occurs. The diameter at the point of
Determine the modulus of resilience for each of the following alloys:Use the modulus of elasticity values in Table 6.1?
A cylindrical specimen of a nickel alloy having an elastic modulus of 207 GPa (30 × 106 psi) and an original diameter of 10.2 mm (0.40 in.) experiences only elastic deformation when a tensile load
A steel alloy to be used for a spring application must have a modulus of resilience of at least 2.07 MPa (300 psi). What must be its minimum yield strength?
Using data found in Appendix B, estimate the modulus of resilience (in MPa) of cold-rolled 17-7PH stainless steel?
Using the data in Problem 6.30 and Equations 6.15, 6.16, and 6.18a, generate a true stress-true strain plot for stainless steel. 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 0.16 is produced when a true stress of 500 MPa (72,500 psi) is applied; for the same metal, the value of
For some metal alloy, a true stress of 345 MPa (50,000 psi) produces a plastic true strain of 0.02. How much does a specimen of this material elongate when a true stress of 415 MPa (60,000 psi) is
The following true stresses produce the corresponding true plastic strains for a brass alloy:True Stress (psi) _______ True Strain60,000 ............................ 0.1570,000
For a brass alloy, the following engineering stresses produce the corresponding plastic engineering strains prior to necking:Engineering Stress (MPa) _______________ Engineering Strain315
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 103
An aluminum bar 125 mm (5.0 in.) long and having a square cross section 16.5 mm (0.65 in.) on an edge is pulled in tension with a load of 66,700 N (15,000 lbf) and experiences an elongation of 0.43
A cylindrical specimen of a brass alloy 10.0 mm (0.39 in.) in diameter and 120.0 mm (4.72 in.) long is pulled in tension with a force of 11,750 N (2640 lbf); the force is subsequently released.(a)
(a) Determine the elastic and plastic strain values.(b) If its original length is 610 mm (24.0 in.), what will be its final length after the load in part (a) is applied and then released?
(a) A 10-mm-diameter Brinell hardness indenter produced an indentation 2.50 mm in diameter in a steel alloy when a load of 1000 kg was used. Compute the HB of this material.(b) What will be the
(a) Calculate the Knoop hardness when a 500-g load yields an indentation diagonal length of 100 m.(b) The measured HK of some material is 200. Compute the applied load if the indentation diagonal
(a) What is the indentation diagonal length when a load of 0.60 kg produces a Vickers HV of 400?(b) Calculate the Vickers hardness when a 700-g load yields an indentation diagonal length of 0.050 mm?
Consider a cylindrical nickel wire 2.0 mm (0.08 in.) in diameter and 3 × 104 mm (1200 in.) long. Calculate its elongation when a load of 300 N (67 lbf) is applied. Assume that the deformation is
The following table gives a number of Rockwell G hardness values that were measured on a single steel specimen. Compute average and standard deviation hardness values.
The following table gives a number of yield strength values (in MPa) that were measured on the same aluminum alloy. Compute average and standard deviation yield strength values? 274.3
For a brass alloy, the stress at which plastic deformation begins is 345 MPa (50,000 psi), and the modulus of elasticity is 103 GPa (15.0 × 106 psi).(a) What is the maximum load that can be applied
A cylindrical rod of steel (E =207 GPa, 30 × 106 psi) having a yield strength of 310 MPa (45,000 psi) is to be subjected to a load of 11,100 N (2500 lbf). If the length of the rod is 500 mm (20.0
A large tower is to be supported by a series of steel wires; it is estimated that the load on each wire will be 13,300 N (3000 lbf). Determine the minimum required wire diameter, assuming a factor of
(a) Consider a thin-walled cylindrical tube having a radius of 65 mm is to be used to transport pressurized gas. If inside and outside tube pressures are 100 and 2.0 atm (10.13 and 0.2026MPa),
(a) Gaseous hydrogen at a constant pressure of 0.658 MPa (5 atm) is to flow within the inside of a thin-walled cylindrical tube of nickel that has a radius of 0.125 m. The temperature of the tube is
Consider the steady-state diffusion of hydrogen through the walls of a cylindrical nickel tube as described in Problem 6.D3. One design calls for a diffusion flux of 2.5 × 10-8mol/m2.s, a tube
A steel rod is pulled in tension with a stress that is less than the yield strength. The modulus of elasticity may be calculated as (A) Axial stress divided by axial strain (B) Axial stress divided
A cylindrical specimen of brass that has a diameter of 20 mm, a tensile modulus of 110 GPa, and a Poisson's ratio of 0.35 is pulled in tension with force of 40,000 N. If the deformation is totally
The following figure shows the tensile stress-strain curve for a plain-carbon steel.(1) What is this alloy's tensile strength?(A) 650 MPa(B) 300 MPa(C) 570 MPa(D) 3,000 MPa(2) What is its modulus of
A specimen of steel has a rectangular cross section 20 mm wide and 40 mm thick, an elastic modulus of 207 GPa, and a Poisson's ratio of 0.30. If this specimen is pulled in tension with a force of
A cylindrical specimen of under formed brass that has a radius of 300 mm is elastically deformed to a tensile strain of 0.001. If Poisson's ratio for this brass is 0.35, what is the change in
Consider a metal single crystal oriented such that the normal to the slip plane and the slip direction are at angles of 60° and 35°, respectively, with the tensile axis. If the critical resolved
A single crystal of zinc is oriented for a tensile test such that its slip plane normal makes an angle of 65° with the tensile axis. Three possible slip directions make angles of 30°, 48°, and
Consider a single crystal of nickel 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 [100] 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 [100] direction. If the magnitude of this stress is 4.0 MPa, compute the
Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [121] direction. If slip occurs on a (101) plane
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 [112] direction. If slip occurs on a (111) plane
The critical resolved shear stress for copper (Cu) is 0.48 MPa (70 psi). Determine the maximum possible yield strength for a single crystal of Cu pulled in tension?
Briefly explain why HCP metals are typically more brittle than FCC and BCC metals?
Describe in your own words the three strengthening mechanisms discussed in this chapter (i.e., grain size reduction, solid-solution strengthening, and strain hardening). Explain how dislocations are
(a) From the plot of yield strength versus (grain diameter)-1/2 for a 70 Cu-30 Zn cartridge brass in Figure 7.15, determine values for the constants σ0 and ky in Equation 7.7.(b) Now predict the
The lower yield point for an iron that has an average grain diameter of 1 × 10-2 mm is 230 MPa (33,000 psi). At a grain diameter of 6 × 10-3 mm, the yield point increases to 275 MPa (40,000 psi).
(a) Show, for a tensile test, thatIf 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 under formed 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 15%. If its cold-worked radius is 6.4 mm (0.25 in.), what was its radius before deformation?
(a) What is the approximate ductility (%EL) of a brass that has a yield strength of 345 MPa (50,000 psi)? (b) What is the approximate Brinell hardness of a 1040 steel having a yield strength of 620
(a) From Figure 7.25, compute the length of time required for the average grain diameter to increase from 0.03 to 0.3 mm at 600°C for this brass material. (b) Repeat the calculation, this time using
Consider a hypothetical material that has a grain diameter of 2.1 ( 10-2 mm. After a heat treatment at 600(C for 3 h, the grain diameter has increased to 7.2 ( 10-2 mm. Compute the grain diameter
A hypothetical metal alloy has a grain diameter of 1.7 ( 10-2 mm. After a heat treatment at 450(C for 250 min the grain diameter has increased to 4.5 ( 10-2 mm. Compute the time required for a
The average grain diameter for a brass material was measured as a function of time at 650°C, which is shown in the following table at two different times:Time (min)______________ Grain Diameter
An undeformed specimen of some alloy has an average grain diameter of 0.050 mm. You are asked to reduce its average grain diameter to 0.020 mm. Is this possible? If so, explain the procedures you
A non-cold-worked brass specimen of average grain size 0.01 mm has a yield strength of 150 MPa (21,750 psi). Estimate the yield strength of this alloy after it has been heated to 500°C for 1000 s,
The following yield strength, grain diameter, and heat treatment time (for grain growth) data were gathered for an iron specimen that was heat treated at 800(C. Using these data compute the yield
Determine whether it is possible to cold work steel so as to give a minimum Brinell hardness of 240 and at the same time have a ductility of at least 15%EL. Justify your answer.
Determine whether it is possible to cold work brass so as to give a minimum Brinell hardness of 150 and at the same time have a ductility of at least 20%EL? Justify your answer.
A cylindrical specimen of cold-worked steel has a Brinell hardness of 240. (a) Estimate its ductility in percent elongation. (b) If the specimen remained cylindrical during deformation and its
It is necessary to select a metal alloy for an application that requires a yield strength of at least 310 MPa (45,000 psi) while maintaining a minimum ductility (%EL) of 27%. If the metal may be cold
A cylindrical rod of 1040 steel originally 11.4 mm (0.45 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 brass originally 10.2 mm (0.40 in.) in diameter is to be cold worked by drawing; the circular cross section will be maintained during deformation. A cold-worked yield strength in
A cylindrical brass rod having a minimum tensile strength of 450 MPa (65,000 psi), a ductility of at least 13%EL, and a final diameter of 12.7 mm (0.50 in.) is desired. Some brass stock of diameter
Consider the brass alloy discussed in Problem 7.41. Given the following yield strengths for the two specimens, compute the heat treatment time required at 650oC to give a yield strength of 90 MPa.
Plastically deforming a metal specimen near room temperature generally leads to which of the following property changes? (A) An increased tensile strength and a decreased ductility (B) A decreased
A dislocation formed by adding an extra half-plane of atoms to a crystal is referred to as a (an) (A) Screw dislocation (B) Vacancy dislocation (C) Interstitial dislocation (D) Edge dislocation
The atoms surrounding a screw dislocation experience which kinds of strains? (A) Tensile strains (B) Shear strains (C) Compressive strains (D) Both B and C
What is the magnitude of the maximum stress that exists at the tip of an internal crack having a radius of curvature of 1.9 × 10-4 mm (7.5 × 10-6 in.) and a crack length of 3.8 × 10-2 mm (1.5 ×
Calculate the maximum internal crack length allowable for a Ti-6Al-4V titanium alloy (Table 8.1) component that is loaded to a stress one-half its yield strength. Assume that the value of Y is 1.50?
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 98.9 MPa(m (90 ksi(in) and a yield strength of 860 MPa (125,000
The following tabulated data were gathered from a series of Charpy impact tests on a tempered 4340 steel alloy.Temperature (°C) _______________ Impact Energy (J)0

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