Manufacturing engineering and technology in SI units

Serope Kalpakjian, Steven R. Schmid

Chapter 2 Mechanical Behavior, Testing, and Manufacturing Properties of Materials - all with Video Answers

Educators

Chapter Questions

00:40

Problem 1

What is tension? What is shear?

Eric Mockensturm

Numerade Educator

Problem 2

Distinguish between engineering stress and true stress.

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Problem 3

In a stress-strain curve, what is the proportional limit? Is it different than the yield point?

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01:05

Describe the events that occur when a specimen undergoes a tension test. Sketch a plausible stressstrain curve, and identify all significant regions and points between them. Assume that loading continues up to fracture.

Khoobchandra Agrawal

Numerade Educator

Problem 5

What is ductility, and how is it measured?

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03:42

Problem 6

In the equation $\sigma=K \epsilon^n$, which represents the stress-strain curve for a material, and what is the significance of the exponent $n$ ?

Ameer Said

Numerade Educator

Problem 7

What is strain-rate sensitivity, and how is it measured?

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02:10

Problem 8

What test can measure the properties of a material undergoing shear strain?

Hubert Agamasu

Numerade Educator

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Problem 9

What kind of loading is applied by scissors while cutting paper?

Rashmi Sinha

Numerade Educator

Problem 10

What testing procedures can be used to measure the properties of brittle materials, such as ceramics and carbides?

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Problem 11

Describe the differences between brittle and ductile fracture.

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00:50

Problem 12

What is hardness? Is it different from hardness number? Explain.

Hunza Gilgit

Numerade Educator

Problem 13

Describe the features of a Rockwell hardness test.

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Problem 14

What is a Leeb test? How is it different from a Rockwell A test?

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01:57

Problem 15

Differentiate between stress relaxation and creep.

Ameer Said

Numerade Educator

Problem 16

Describe the difference between elastic and plastic behavior.

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Problem 17

Explain what uniform elongation means in tension testing.

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Problem 18

Describe the difference between deformation rate and strain rate. What unit does each one have?

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Problem 19

Describe the difficulties involved in conducting a compression test.

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01:26

Problem 20

What is Hooke's law, Young's modulus, and Poisson's ratio?

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 21

Describe the difference between transgranular and intergranular fracture.

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Problem 22

What is the reason that yield strength is generally defined as a $0.2 \%$ offset strength?

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Problem 23

Why does the fatigue strength of a specimen or part depend on its surface finish?

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Problem 24

Explain how you would determine whether or not a material has an endurance limit.

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Problem 25

If striations are observed under microscopic examination of a fracture surface, what do they suggest regarding the mode of fracture?

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Problem 26

What is an Izod test? Why are Izod tests useful?

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02:01

Problem 27

Why does temperature increase during deformation?

Prabhu Ramji

Numerade Educator

Problem 28

What is a residual stress? How can residual stresses be removed?

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Problem 29

On the same scale for stress, the tensile true stress-true strain curve is higher than the engineering stress-engineering strain curve. Explain whether this condition also holds for a compression test.

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00:54

Problem 30

Explain why it is difficult to break a sheet of paper in tension, but easy to cut it with scissors.

Abhishek Jana

Numerade Educator

01:06

Problem 31

What are the similarities and differences between deformation and strain?

Surjit Tewari

Numerade Educator

01:13

Problem 32

Can a material have a negative Poisson's ratio? Give a rationale for your answer.

Surjit Tewari

Numerade Educator

Problem 33

Referring to Table 2.2, explain why there can be so much variation in the strength and elongation in a class of metal alloys.

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Problem 34

Referring to Table 2.2, explain why the stiffness of diamond has so much variation.

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Problem 35

It has been stated that the higher the value of $m$, the more diffuse the neck is, and likewise, the lower the value of $m$, the more localized the neck is. Explain the reason for this behavior.

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Problem 36

Explain why materials with high $m$ values, such as hot glass and taffy, when stretched slowly, undergo large elongations before failure. Consider events taking place in the necked region of the specimen.

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04:26

Problem 37

Explain if it is possible for stress-strain curves in tension tests to reach $0 \%$ elongation as the gage length is increased further.

Narayan Hari

Numerade Educator

Problem 38

With a simple sketch, explain whether it is necessary to use the offset method to determine the yield stress, $S_y$, of a material that has been highly cold worked.

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Problem 39

Explain why the difference between engineering strain and true strain becomes larger as strain increases. Does this difference occur for both tensile and compressive strains? Explain.

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01:04

Problem 40

Consider an elastomer, such as a rubber band. This material can undergo a large elastic deformation before failure, but after fracture it recovers completely to its original shape. Is this material brittle or ductile? Explain.

Narayan Hari

Numerade Educator

Problem 41

If a material (such as aluminum) does not have an endurance limit, how then would you estimate its fatigue life?

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Problem 42

What role, if any, does friction play in a hardness test? Explain.

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Problem 43

Which hardness tests and scales would you use for very thin strips of metal, such as aluminum foil? Explain.

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Problem 44

Consider the circumstance where a Vickers hardness test is conducted on a material. Sketch the resulting indentation shape if there is a residual stress on the surface.

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Problem 45

Which of the two tests, tension or compression, would require a higher capacity of testing machine, and why?

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Problem 46

In a Brinell hardness test, the resulting impression is found to be an ellipse. Give possible explanations for this result.

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Problem 47

List and explain briefly the conditions that induce brittle fracture in an otherwise ductile metal.

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Problem 48

List the factors that you would consider in selecting a hardness test. Explain why.

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Problem 49

List two situations where a material's toughness is important from a design standpoint.

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05:00

Problem 50

On the basis of Fig. 2.5, if a metal tension-test specimen is pulled and broken rapidly, where would the temperature be highest, and why?

Vinnu M

Numerade Educator

03:38

Problem 51

Comment on the temperature distribution if the specimen in Question 2.50 is pulled very slowly.

Ajay Singhal

Numerade Educator

Problem 52

Comment on your observations regarding the contents of Table 2.2.

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Problem 53

Is the disk test applicable to a ductile material? Why or why not?

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Problem 54

Refer to Table 2.4, and note the true strain encountered by a material in different manufacturing processes. Explain why some typical strains are large and others are small.

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Problem 55

Refer to Table 2.4, and sketch the original and deformed shape of a 25 mm specimen subjected to the largest typical strain for each process. What are your observations regarding strains that can be achieved?

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Problem 56

If a tension test on carbon steel is conducted at room temperature, and then with a bath of boiling water, would you expect the strength to be different? Explain.

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Problem 57

What hardness test is suitable for determining the hardness of a thin ceramic coating on a piece of metal?

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Problem 58

Wire rope consists of many wires that bend and unbend as the rope is run over a sheave. A wire-rope failure is investigated, and it is found that some of the wires, when examined under a scanning electron microscope, display cup-and-cone failure surfaces, while others display transgranular fracture surfaces. Explain these observations.

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03:01

Problem 59

A statistical sampling of Rockwell $C$ hardness tests are conducted on a material, and it is determined that the material is defective because of insufficient hardness. The supplier claims that the tests are flawed because the diamond-cone indenter was probably dull. Is this a valid claim? Explain.

Aimal Hassan

Numerade Educator

Problem 60

In a Brinell hardness test, the resulting impression is found to be elliptical. Give possible explanations for this result.

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Problem 61

In the machining of an extruded aluminum block to produce a smart phone case, it is seen that there is significant warpage after machining. Explain why. What would you do to reduce this warpage?

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Problem 62

Some coatings are extremely thin-some as thin as a few nanometers. Explain why even the Knoop test is not able to obtain reliable results for such coatings. Recent investigations have attempted to use highly polished diamonds (with a tip radius around 5 nm ) to indent such coatings in atomic force microscopes. What concerns would you have regarding the appropriateness of the results?

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02:55

Problem 63

Select an appropriate hardness test for each of the following materials, and justify your answer:
1. Cubic boron nitride
2. Lead
3. Cold-drawn $0.5 \% C$ steel
4. Diamond
5. Caramel candy
6. Granite.

Bhumika Jayee

Numerade Educator

Problem 64

Referring to Fig. 2.13, the material for testers is either steel, tungsten carbide, or diamond. Why isn't diamond used for all of the tests?

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Problem 65

A paper clip is made of wire 1 mm in diameter. If the original material from which the wire is made is a rod 50 mm in diameter, calculate the longitudinal engineering and true strains that the wire has undergone during processing.

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01:33

Problem 66

A $150-\mathrm{mm}$-long strip of metal is stretched in two steps, first to 250 mm and then to 500 mm . Show that the total true strain is the sum of the true strains in each step; in other words, the true strains are additive. Show that, in the case of engineering strains, the strains cannot be added to obtain the total strain.

Narayan Hari

Numerade Educator

06:02

Problem 67

Identify the two materials in Fig. 2.5 that have the lowest and the highest uniform elongations. Calculate these quantities as percentages of the original gage lengths.

Ameer Said

Numerade Educator

Problem 68

Plot the ultimate strength versus stiffness for the materials listed in Table 2.2, and prepare a threedimensional plot for these materials where the third axis is their maximum elongation in 50 mm .

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Problem 69

If you remove the layer of material ad from the part shown in Fig. 2.30d-for instance, by machining or grinding-which way will the specimen curve? (Hint: Assume that the part shown in sketch $d$ in the figure is composed of four horizontal springs held at the ends. Thus, from the top down, you have compression, tension, compression, and tension springs.)

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01:23

Problem 70

Prove that the true strain at necking equals the strain hardening exponent.

Narayan Hari

Numerade Educator

04:26

Problem 71

Percent elongation is always defined in terms of the original gage length, such as 50 mm . Explain how percent elongation would vary as the gage length of the tensile-test specimen increases. (Hint: Recall that necking is a local phenomenon.)

Narayan Hari

Numerade Educator

01:08

Problem 72

Make a sketch showing the nature and distribution of residual stresses in Fig. 2.31a and b, prior to the materials being cut. (Hint: Assume that the split parts are free from any stresses; then force these parts back to the shape they originally had.)

Chai Santi

Numerade Educator

Problem 73

You are given the $K$ and $n$ values of two different metals. Is this information sufficient to determine which metal is tougher? If not, what additional information do you need?

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05:16

Problem 74

A cable is made of two strands of different materials, $A$ and $B$, and cross sections as follows:

For material $A, K=500 \mathrm{MPa}, n=0.6, A_o=0.00060 \mathrm{~m}^2$.
For material $B, K=300 \mathrm{MPa}, n=0.6, A_o=0.00030 \mathrm{~m}^2$.
Calculate the maximum tensile force that this cable can withstand prior to necking.

Chai Santi

Numerade Educator

01:16

Problem 75

On the basis of the information given in Fig. 2.5, calculate the ultimate tensile strength (engineering) of 304 stainless steel.

Manik Pulyani

Numerade Educator

02:16

Problem 76

In a disk test performed on a specimen 30 mm in diameter and 8 mm thick, the specimen fractures at a stress of 180 MPa . What was the load on at fracture?

Ben Nicholson

Numerade Educator

01:31

Problem 77

A piece of steel has a hardness of 275 HB . Calculate its tensile strength, in MPa.

Anand Jangid

Numerade Educator

01:01

Problem 78

A metal has the following properties: $S_{\mathrm{ut}}=500 \mathrm{MPa}$ and $n=0.25$. Calculate its strength coefficient, $K$.

Narayan Hari

Numerade Educator

01:30

Problem 79

Using only Fig. 2.5, calculate the maximum load in tension testing of an annealed copper specimen with an original diameter of 10 mm .

Narayan Hari

Numerade Educator

Problem 80

Estimate the modulus of resilience for a highly cold worked piece of steel having a hardness of 300 HB; for a piece of highly cold worked copper with a hardness of 100 HRB .

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01:01

Problem 81

A metal has a strength coefficient $K=600 \mathrm{MPa}$ and $n=0.25$. Assuming that a tensile-test specimen made from this metal begins to neck at a true strain of 0.25 , show that the ultimate tensile strength is 362 MPa .

Narayan Hari

Numerade Educator

01:06

Problem 82

Plot the true stress-true strain curves for the materials listed in Table 2.3.

Ameer Said

Numerade Educator

04:44

Problem 83

The design specification for a metal requires a minimum hardness of 80 HRA. If a Rockwell test is performed and the depth of penetration is $80 \mu \mathrm{~m}$, is the material acceptable?

Jacquelinne S. Mejia Sandoval

Numerade Educator

02:05

Problem 84

Calculate the major and minor pyramid angles for a Knoop indenter, and compare your results with those obtained from Vickers and Rockwell A indenters.

Ajay Singhal

Numerade Educator

01:14

Problem 85

If a material has a target hardness of 300 HB , what is the expected indentation diameter?

Narayan Hari

Numerade Educator

Problem 86

A Rockwell A test was conducted on a material and a penetration depth of 0.15 mm was recorded. What is the hardness of the material? What material would typically have such a hardness value? If a Brinell hardness test were to be conducted on this material, give an estimate of the indentation diameter if the load used was 1500 kg .

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Problem 87

For a cold-drawn $0.5 \%$ carbon steel, will a Rockwell C test or a Brinell test at 500 kg result in a deeper penetration?

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01:16

Problem 88

A material is tested in tension. Over a $25-\mathrm{mm}$ gage length, the engineering strain measurements are $0.01,0.02,0.03,0.04,0.05,0.1,0.15,0.2,0.5$, and 1.0 . Plot the true strain versus engineering strain for these readings.

Manik Pulyani

Numerade Educator

01:54

Problem 89

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 $50 \%$ for the following materials: (a) $1100-\mathrm{O}$ aluminum; (b) annealed copper; (c) annealed 304 stainless steel; and (d) annealed 70-30 brass.

Narayan Hari

Numerade Educator

03:37

Problem 90

A bar 2 m long is bent and then stress relieved. The radius of curvature to the neutral axis is 1 m . The bar is 30 mm thick and is made of an elastic, perfectly plastic material with $S_y=500 \mathrm{MPa}$ and $E=207 \mathrm{GPa}$. Calculate the length to which this bar should be stretched so that, after unloading, it will become and remain straight.

James Kiss

Numerade Educator

Problem 91

Take a cubic piece of metal with a side length $l_o$ and deform it plastically to the shape of a rectangular parallelepiped of dimensions $l_1, l_2$, and $l_3$. Assuming that the material is rigid and perfectly plastic, show that volume constancy requires that the following expression be satisfied: $\epsilon_1+\epsilon_2+\epsilon_3=0$.

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Problem 92

List and explain the desirable mechanical properties of (a) an automobile body panel, (b) a paper clip, (c) a leaf spring for a truck, (d) a bracket for a bookshelf, (e) a backpack shoulder strap, (f) a wire coat hanger, (g) the clip for a pen, and (h) a lens for an optical microscope.

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Problem 93

When making a hamburger, you may have observed the type of cracks shown in Fig. 2.20d. What would you do to avoid such cracks? [Note: Test hamburger patties by compressing them at different temperatures, and observe the crack path (i.e., the path through the fat particles, the meat particles, or their interface).]

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04:33

Problem 94

An inexpensive claylike material called Silly Putty ${ }^{\text {® }}$ is generally available in stores that sell toys and games. Obtain a sample and perform the following experiments: (a) Shape it into a ball, and drop it onto a flat surface. (b) Reround the ball and place a heavy book on it for one minute. (c) Shape the putty into a long rod, and pull on it-first slowly, then very quickly. Describe your observations, referring to the specific sections in this chapter where each particular observation is relevant.

Eric Mockensturm

Numerade Educator

Problem 95

Make individual sketches of the mechanisms of testing machines that, in your opinion, would be appropriate for tension, for torsion, and for compression testing of specimens at different rates of deformation. What modifications would you make on these machines to include the effects of temperature on material properties?

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Problem 96

In tension testing of specimens, mechanical and electronic instruments are typically used to measure elongation. Make sketches of instruments that would be suitable for this purpose, commenting on their accuracy. What modifications would you make to these instruments to include the use of specimens at elevated temperatures?

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01:39

Problem 97

Obtain small pieces of different metallic and nonmetallic materials, including stones. Rub them against each other, observe the scratches made, and order them in a manner similar to the Mohs hardness numbering system.

Kashif Qureshi

Numerade Educator

01:17

Problem 98

Demonstrate the stress-relaxation phenomenon by tightly stretching thin plastic strings between two nails placed at the ends of a long piece of wood. Pluck the strings frequently, to test the tension as a function of time. Repeat the test at a higher temperature by placing the fixture in an oven set on low.

Manik Pulyani

Numerade Educator

Problem 99

Demonstrate the impact toughness of a piece of round chalk by first using a triangular file to produce a V-notch on the cylindrical surface (as shown in Fig. 2.19a) and then bending the chalk to break it.

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03:51

Problem 100

Using a large rubber band and a set of weights, obtain the force-displacement curve for the rubber band. Is the result different from the stress-strain curves shown in Fig. 2.4? Explain.

Keshav Singh

Numerade Educator

Problem 101

Design a test protocol to obtain the work of plastic deformation by measuring the temperature rise in a workpiece, assuming that there is no heat loss and that the temperature distribution is uniform throughout. If the specific heat of the material decreases with increasing temperature, will the work of deformation calculated using the specific heat at room temperature be higher or lower than the actual work done? Explain.

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Problem 102

Find or prepare some solid circular pieces of brittle materials, such as chalk, ceramics, etc. and subject them to the type of test shown in Fig. 2.9 by using the jaws of a simple vise. Describe your observations as to how the materials fracture. Repeat the tests, using ductile materials, such as clay, soft metals, and describe your observations.

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00:25

Problem 103

Take several rubber bands and pull them at different temperatures, including from a frozen state. Comment on their behavior such as ductile or brittle.

Dading Chen

Numerade Educator

Problem 104

Devise a simple fixture for conducting the bend tests shown in Fig. 2.11. Test sticks of various brittle materials by loading them with dead weights until they break. Verify the statement in the text that the specimens on the right in the figure will fracture sooner than the ones on the left.

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Problem 105

By pushing a small ball bearing against the top surfaces of various materials, such as clay and dough, observe the shape of the indentation with a magnifier, referring to those shapes shown in Fig. 2.14a and b.

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Problem 106

Describe your observations regarding Fig. 2.14c.

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Problem 107

Embed a small steel ball in a soft block of material such as clay, and compress the clay as shown in Fig. 2.24a. Then cut the clay carefully along the center plane and observe the deformation of the material. Repeat the experiment by embedding a small round jelly bean in the clay and deforming the material. Comment on your observations.

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03:55

Problem 108

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 stress to which the soft metal is subjected? Explain.

Surjit Tewari

Numerade Educator

05:52

Problem 109

Devise a simple experiment, and perform tests on materials commonly found around the house by bending them at different temperatures for a qualitative assessment of their transition temperature, as shown in Fig. 2.25.

Keshav Singh

Numerade Educator

Problem 110

Obtain some solid and some tubular metal pieces, and slit them as shown in Fig. 2.31. Comment on whether there are any residual stresses in the parts prior to slitting them.

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Problem 111

Explain how you would obtain an estimate of the hardness for a carbon nanotube (see Section 8.6.2).

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01:13

Problem 112

Without using the words "stress" or "strain," define elastic modulus.

Kamlesh Goyal

Numerade Educator

05:48

Problem 113

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 or a round disk) can be subjected to hydrostatic tension, or one approaching this state of stress. (Note that a thin-walled, internally pressurized spherical shell is not a correct answer, because it is subjected only to a state of plane stress.)

Chai Santi

Numerade Educator

Problem 114

Assume that you are running four-point bending tests on a number of identical specimens of the same length and cross section, but with increasing distance between the upper points of loading. (See Fig. 2.19b.) What changes, if any, would you expect in the test results? Explain.

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Problem 115

Describe a test protocol, complete with forces and geometry, that you execute to determine the quality of food. Consider the crispness of an apple or snack chip, and then consider the softness of cake.

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