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engineering
mechanical engineering
Questions and Answers of
Mechanical Engineering
In a Brinell hardness test, the resulting impression is found to be an ellipse. Give possible explanations for this phenomenon.
What effect, if any, does friction have in a hardness test? Explain.
Describe the difference between creep and stress-relaxation phenomena, giving two examples for each as they relate to engineering applications.
Referring to the two impact tests shown in Fig. 2.31, explain how different the results would be if the specimens were impacted from the opposite directions.
If you remove layer ad from the part shown in Fig. 2.30d, such as by machining or grinding, which way will the specimen curve?
Is it possible to completely remove residual stresses in a piece of material by the technique described in Fig. 2.32 if the material is elastic, linearly strain hardening? Explain.
Referring to Fig. 2.32, would it be possible to eliminate residual stresses by compression instead of tension? Assume that the piece of material will not buckle under the uniaxial compressive force.
List and explain the desirable mechanical properties for the following: (a) Elevator cable, (b) Bandage, (c) Shoe sole, (d) Fish hook, (e) Automotive piston, (f) Boat propeller, (g) Gas-turbine
Make a sketch showing the nature and distribution of the residual stresses in Figs. 2.31a and b before the parts were split (cut). Assume that the split parts are free from any stresses.
Explain why the difference between engineering strain and true strain becomes larger as strain increases. Is this phenomenon true for both tensile and compressive strains? Explain.
It is possible to calculate the work of plastic de-formation by measuring the temperature rise in a work piece, assuming that there is no heat loss and that the temperature distribution is uniform
Explain whether or not the volume of a metal specimen changes when the specimen is subjected to a state of (a) Uniaxial compressive stress and (b) Uniaxial tensile stress, all in the elastic range.
We know that it is relatively easy to subject a specimen to hydrostatic compression, such as by using a chamber filled with a liquid. Devise a means whereby the specimen (say, in the shape of a cube
Referring to Fig. 2.19, make sketches of the state of stress for an element in the reduced section of the tube when it is subjected to(a) Torsion only,(b) Torsion while the tube is internally
A penny-shaped piece of soft metal is brazed to the ends of two flat, round steel rods of the same diameter as the piece. The assembly is then subjected to uniaxial tension. What is the state of
A circular disk of soft metal is being compressed between two flat, hardened circular steel punches having the same diameter as the disk. Assume that the disk material is perfectly plastic and that
A perfectly plastic metal is yielding under the stress state σ1, σ2, σ3, where σ1 > σ2 > σ3. Explain what happens if σ1 is increased.
What is the dilatation of a material with a Poisson's ratio of 0.5? Is it possible for a material to have a Poisson's ratio of 0.7? Give a rationale for your answer
As clearly as possible, define plane stress and plane strain.
Using the same scale for stress, we note that the tensile true stress-true strain curve is higher than the engineering stress-strain curve. Explain whether this condition also holds for a compression
What test would you use to evaluate the hardness of a coating on a metal surface? Would it matter if the coating was harder or softer than the substrate? Explain.
List the advantages and limitations of the stress-strain relationships given in Fig. 2.7.
Plot the data in Table 2.1 on a bar chart, showing the range of values, and comment on the results.
A hardness test is conducted on as-received metal as a quality check. The results indicate that the hardness is too high; thus the material may not have sufficient ductility for the intended
Explain why a 0.2% offset is used to determine the yield strength in a tension test.
Referring to Question 2.44, would the offset method be necessary for a highly strained-hardened material? Explain.
A strip of metal is originally 1.5 m long. It is stretched in three steps: first to a length of 1.75 m, then to 2.0 m, and finally to 3.0 m. Show that the total true strain is the sum of the true
A paper clip is made of wire 1.20 mm in diameter. If the original material from which the wire is made from a rod 15 mm in diameter, calculate the longitudinal and diametrical engineering and true
A material has the following properties: UTS = 50,000 psi and n = 0.25. Calculate its strength coefficient K.
Based on the information given in Fig. 2.6, calculate the ultimate tensile strength of annealed 70-30 brass.
Which of the two tests, tension or compression, requires a higher-capacity testing machine than the other? Explain.
Calculate the ultimate tensile strength (engineering) of a material whose strength coefficient is 400 MPa and of a tensile-test specimen that necks at a true strain of 0.20.
A cable is made of four parallel strands of different materials, all behaving according to the equation σ = Ke", where n = 0.3. The materials, strength coefficients and cross sections are as
Using only Fig. 2.6, calculate the maximum load in tension testing of a 304 stainless-steel round specimen with an original diameter of 0.5 in.
Using the data given in Table 2.1, calculate the values of the shear modulus G for the metals listed in the table.
Derive an expression for the toughness of a material represented by the equation a = K(e + 0.2)" and whose fracture strain is denoted as €f.
A cylindrical specimen made of a brittle material 1 in. high and with a diameter of 1 in. is subjected to a compressive force along its axis. It is found that fracture takes place at an angle of 45°
What is the modulus of resilience of a highly cold-worked piece of steel with a hardness of 300 HB? of a piece of highly cold-worked copper with a hardness of 150 HB?
Calculate the work done in frictionless compression of a solid cylinder 40 mm high and 15 mm in diameter to a reduction in height of 75% for the following materials: (1) 1100-O aluminum, (2) annealed
A material has a strength coefficient K = 100,000 psi Assuming that a tensile-test specimen made from this material begins to neck at a true strain of 0.17, show that the ultimate tensile strength of
A tensile-test specimen is made of a material rep-resented by the equation a = K(e + n)".(a) Determine the true strain at which necking will begin,(b) Show that it is possible for an engineering
Explain how the modulus of resilience of a material changes, if at all, as it is strained: (a) For an elastic, perfectly plastic material, and (b) For an elastic, linearly strain-hardening material.
Take two solid cylindrical specimens of equal diameter but different heights. Assume that both specimens are compressed (frictionless) by the same percent reduction, say 50%. Prove that the final
A horizontal rigid bar c-c is subjecting specimen a to tension and specimen b to frictionless compression such that the bar remains horizontal. The force F is located at a distance ratio of 2:1. Both
Inspect the curve that you obtained in Problem 2.61. Does a typical strain-hardening material behave in that manner? Explain.In problem 2.61A horizontal rigid bar c-c is subjecting specimen a to
In a disk test performed on a specimen 40 mm in diameter and 5 m thick, the specimen fractures at a stress of 500 MPa. What was the load on the disk at fracture?
In Fig. 2.32a, let the tensile and compressive residual stresses both be 10,000 psi and the modulus of elasticity of the material be 30 × 106 psi, with a modulus of resilience of 30 in.-lb/in.3. If
Show that you can take a bent bar made of an elastic, perfectly plastic material and straighten it by stretching it into the plastic range.
A bar 1 m long is bent and then stress relieved. The radius of curvature to the neutral axis is 0.50 m. The bar is 30 mm thick and is made of an elastic, perfectly plastic material with Y = 600 MPa
Assume that a material with a uniaxial yield stress Y yields under a stress state of principal stresses σ1, σ2, σ3, where σ1 > σ2 > σ3, Show that the superposition of a hydrostatic stress, p,
Give two different and specific examples in which the maximum-shear-stress and the distortion-energy criteria give the same answer.
A thin-walled spherical shell with a yield stress Y is subjected to an internal pressure p. With appropriate equations, show whether or not the pressure required to yield this shell depends on the
If you pull and break a tension-test specimen rapidly, where would the temperature be the highest? Explain why.
Show that, according to the distortion-energy criterion, the yield stress in plane strain is 1.15Y, where Y is the uniaxial yield stress of the material.
What would be the answer to Problem 2.70 if the maximum-shear-stress criterion were used? In problem 2.70 Show that, according to the distortion-energy criterion, the yield stress in plane strain is
A closed-end, thin-walled cylinder of original length I, thickness t, and internal radius r is subjected to an internal pressure (. Using the generalized Hooke's law equations, show the change, if
A round, thin-walled tube is subjected to tension in the elastic range. Show that both the thickness and the diameter of the tube decrease as tension increases.
Take a long cylindrical balloon and, with a thin felt-tip pen, mark a small square on it. What will be the shape of this square after you blow up the balloon: (1) A larger square, (2) A rectangle,
Take a cubic piece of metal with a side length I0 and deform it plastically to the shape of a rectangular parallelepiped of dimensions I1, I2, and I3, Assuming that the material is rigid and
What is the diameter of an originally 30-mm-diameter solid steel ball when it is subjected to a hydrostatic pressure of 5 GPa?
Determine the effective stress and effective strain in plane-strain compression according to the distortion-energy criterion.
(a) Calculate the work done in expanding a 2-mm-thick spherical shell from a diameter of 100 mm to 140 mm, where the shell is made of a material for which σ = 200 + 50e0.5 MPa. (b) Does your answer
A cylindrical slug that has a diameter of 1 in. and is 1 in. high is placed at the center of a 2-in.-diameter cavity in a rigid die. The slug is surrounded by a compressible matrix, the pressure of
Comment on the temperature distribution if the specimen in Question 2.7 is pulled very slowly.
A specimen in the shape of a cube 20 mm on each side is being compressed without friction in a die cavity, as shown in Fig. 2.35d, where the width of the groove is 15 mm. Assume that the linearly
Obtain expressions for the specific energy for a material for each of the stress-strain curves shown in Fig. 2.7, similar to those shown in Section 2.12.
A material with a yield stress of 70 MPa is subjected to principal (normal) stresses of σ1, σ2 = 0, and σ3 = -σ1/2. What is the value of σ1 when the metal yields according to the von Mises
A steel plate has the dimensions 100 mm × 100 mm × 5 mm thick. It is subjected to biaxial tension of σ1 = σ2 with the stress in the thickness direction of σ3 = 0. What is the largest possible
A 50-mm-wide, 1-mm-thick strip is rolled to a final thickness of 0.5 mm. It is noted that the strip has increased in width to 52 mm. What is the strain in the rolling direction?
An aluminum alloy yields at a stress of 50 MPa in uniaxial tension. If this material is subjected to the stresses σ1, = 25 MPa, σ2 = 15 MPa, and σ3 = -26 MPa, will it yield? Explain.
A cylindrical specimen 1 in. in diameter and 1-in. high is being compressed by dropping a weight of 200 lb on it from a certain height. After deformation, it is found that the temperature rise in the
A solid cylindrical specimen 100 mm high is compressed to a final height of 40 mm in two steps between frictionless platens; after the first step the cylinder is 70 mm high. Calculate the engineering
Assume that the specimen in Problem 2.87 has an initial diameter of 80 mm and is made of 1100-O aluminum. Determine the load required for each step.
Determine the specific energy and actual energy expended for the entire process described in the previous two problems.
In a tension test, the area under the true stress-true strain curve is the work done per unit volume (the specific work). We also know that the area under the load- elongation curve represents the
A metal has a strain-hardening exponent of 0.22. At a true strain of 0.2, the true stress is 20,000 psi.(a) Determine the stress-strain relationship for this material,(b) Determine the ultimate
The area of each face of a metal cube is 400 m2, and the metal has a shear yield stress, k, of 140 MPa. Compressive loads of kN and 80 kN are applied at different faces (say in the x- and
A tensile force of 9 kN is applied to the ends of a solid bar of 6.35 mm diameter. Under load, the diameter reduces to 5.00 mm. Assuming uniform deformation and volume constancy,(a) Determine the
Two identical specimens 10 mm in diameter and with test sections 25 mm long are made of 1112 steel. One is in the as-received condition and the other is annealed. What will be the true strain when
During the production of a part, a metal with a yield strength of 110 MPa is subjected to a stress state σ1, σ2 = σ1/3, σ3 = 0. Sketch the Mohr's circle diagram for this stress state. Determine
Estimate the depth of penetration in a Brinell hardness test using 500-kg load, when the sample is a cold-worked aluminum with a yield stress of 200 MPa.
A metal is yielding plastically under the stress state shown in the accompanying figure.(a) Label the principal axes according to their proper numerical convention (1, 2, 3). (b) What is the yield
What is the difference between a unit cell and a single crystal?
Explain the difference between preferred orientation and mechanical fibering.
Give some analogies to mechanical fibering (such as layers of thin dough sprinkled with flour).
A cold-worked piece of metal has been recrystallized. When tested, it is found to be anisotropic. Explain the probable reason for this behavior.
Does recrystallization completely eliminate mechanical fibering in a workpiece? Explain.
Explain why we may have to be concerned with the orange-peel effect on metal surfaces.
How can you tell the difference between two parts made of the same metal, one shaped by cold working and the other by hot working? Explain the differences you might observe.
Explain why the strength of a polycrystalline metal at room temperature decreases as its grain size increases.
What is the significance of some metals, such as lead and tin, having recrystallization temperatures at about room temperature?
You are given a deck of playing cards held together with a rubber band. Which of the material-behavior phenomena described in this chapter could you demonstrate with this setup? What would be the
Explain why we should study the crystal structure of metals.
What effects does recrystallization have on the properties of metals?
What is the significance of a slip system?
Explain what is meant by structure-sensitive and structure-insensitive properties of metals.
What is the relationship between nucleation rate and the number of grains per unit volume of a metal?
Explain the difference between recovery and recrystallization.
(a) Is it possible for two pieces of the same metal to have different recrystallization temperatures? Explain, (b) Is it possible for recrystallization to take place in some regions of a workpiece
Describe why different crystal structures exhibit different strengths and ductilities.
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