Manufacturing Engineering and Technology

Serope Kalpakjian, Steven R. Schmid

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

Educators

Chapter Questions

Problem 1

Distinguish between engineering stress and true stress.

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Problem 2

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 take place when a specimen undergoes a tension test. Sketch a plausible stress-strain curve, and identify all significant regions and points between them. Assume that loading continues up to fracture.

Khoobchandra Agrawal

Numerade Educator

Problem 4

What is ductility, and how is it measured?

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03:42

Problem 5

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

Ameer Said

Numerade Educator

Problem 6

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

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02:10

Problem 7

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

Hubert Agamasu

Numerade Educator

Problem 8

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

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Problem 9

Describe the differences between brittle and ductile fracture.

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03:50

Problem 10

What is hardness? Explain.

Mohammad Mehran

Numerade Educator

Problem 11

Describe the features of a Rockwell hardness test.

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Problem 12

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

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01:57

Problem 13

Differentiate between stress relaxation and creep.

Ameer Said

Numerade Educator

Problem 14

Describe the difference between elastic and plastic behavior.

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Problem 15

Explain what uniform elongation means in tension testing.

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Problem 16

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

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Problem 17

Describe the difficulties involved in conducting a compression test.

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01:26

Problem 18

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

Sri Datta Vikas Buchemmavari

Numerade Educator

Problem 19

Describe the difference between transgranular and intergranular fracture.

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02:47

Problem 20

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

Khoobchandra Agrawal

Numerade Educator

Problem 21

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

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Problem 22

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 23

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

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Problem 24

Why does temperature increase during plastic deformation?

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Problem 25

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

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Problem 26

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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01:06

Problem 27

What are the similarities and differences between deformation and strain?

Surjit Tewari

Numerade Educator

01:13

Problem 28

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

Surjit Tewari

Numerade Educator

Problem 29

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 30

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

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Problem 31

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

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Problem 32

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 33

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 34

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 35

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

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Problem 36

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

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Problem 37

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 38

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

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Problem 39

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

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Problem 40

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

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04:26

Problem 41

On the basis of Fig. 2.5, can you calculate the percent elongation of the materials listed? Explain.

Narayan Hari

Numerade Educator

05:00

Problem 42

If a metal tension-test specimen is rapidly pulled and broken, where would the temperature be highest, and why?

Vinnu M

Numerade Educator

Problem 43

Comment on your observations regarding the contents of Table 2.2.

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02:09

Problem 44

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

Manik Pulyani

Numerade Educator

Problem 45

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

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Problem 46

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. Comment on these observations.

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03:01

Problem 47

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 diamondcone indenter was probably dull. Is this a valid claim? Explain.

Aimal Hassan

Numerade Educator

Problem 48

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

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Problem 49

Some coatings are extremely thin-some as thin as a few nanometers. Explain why even the Knoop test is not able to give 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 test results?

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02:18

Problem 50

Select an appropriate hardness test for each of the following materials, and justify your answer:
a. Cubic boron nitride
b. Lead
c. Cold-drawn $0.5 \% \mathrm{C}$ steel
d. Diamond
e. Caramel candy
f. Granite

Shazia Naz

Numerade Educator

03:00

Problem 51

A paper clip is made of wire 0.5 mm in diameter. If the original material from which the wire is made is a rod 25 mm in diameter, calculate the longitudinal engineering and true strains that the wire has undergone during processing.

Nicholas Mogoi

Numerade Educator

Problem 52

A $250-\mathrm{mm}$-long strip of metal is stretched in two steps, first to 300 mm and then to 400 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.

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Problem 53

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.

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Problem 54

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

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Problem 55

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 56

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

Narayan Hari

Numerade Educator

04:26

Problem 57

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 58

Make a sketch showing the nature and distribution of residual stresses in Fig. 2,31a and b, prior to the material's 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 59

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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03:36

Problem 60

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

For material $A, K=415 \mathrm{MPa}, n=0.5, A_o=380 \mathrm{~mm}^2$;
For material $B, K=210 \mathrm{MPa}, n=0.5, A_o=190 \mathrm{~mm}^2$.
Calculate the maximum tensile force that this cable can withstand prior to necking.

Prabhat Tyagi

Numerade Educator

01:16

Problem 61

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

Problem 62

In a disk test performed on a specimen 25 mm in diameter and 6 mm thick, the specimen fractures at a stress of 275 MPa . What was the load on it?

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Problem 63

A piece of steel has a hardness of 300 HB . Calculate its tensile strength, in MPa and in psi.

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01:01

Problem 64

A metal has the following properties: UTS $=480 \mathrm{MPa}$ and $n=0.20$. Calculate its strength coefficient, $K$.

Narayan Hari

Numerade Educator

01:30

Problem 65

Using only Fig. 2,5, calculate the maximum load in tension testing of an annealed copper specimen with an original diameter of 5 mm .

Narayan Hari

Numerade Educator

Problem 66

Estimate the modulus of resilience for a highly cold worked piece of steel having a hardness of 250 HB , and for a piece of highly cold-worked copper with a hardness of 100 HRB.

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01:01

Problem 67

A metal has a strength coefficient $K=690 \mathrm{MPa}$ 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 409 MPa .

Narayan Hari

Numerade Educator

01:06

Problem 68

Plot the true stress-true strain curves for the materials listed in Table 2.,3,

Ameer Said

Numerade Educator

04:44

Problem 69

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 $60 \mu \mathrm{~m}$, is the material acceptable?

Jacquelinne S. Mejia Sandoval

Numerade Educator

02:05

Problem 70

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 71

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

Narayan Hari

Numerade Educator

Problem 72

A Rockwell A rest 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 bardness 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 73

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 74

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

01:45

Problem 75

A horizontal rigid bar $c-c$ is subjecting specimen a to tension and specimen $b$ to frictionless compression such that the bar remains horizontal, (See Fig. P2.75.) The force F is located at a distance ratio of $2: 1$. Both specimens have an original cross-sectional area of $645 \mathrm{~mm}^2$ and the original lengths are $a=203 \mathrm{~mm}$, and $b=114 \mathrm{~mm}$. The material for specimen a has a true stress-true strain curve of $\sigma=100,000 \epsilon^{0.5}$. Plot the true stress-true strain curve that the material for specimen $b$ should have for the bar to remain horizontal.
Figure can't copy

Narayan Hari

Numerade Educator

03:17

Problem 76

List and explain the desirable mechanical properties of (a) an elevator cable, (b) a paper clip, (c) a leaf spring for a truck, (d) a bracket for a bookshelf, (e) piano wire, (f) a wire coat hanger, (g) the clip for a pen, and (h) a staple.

Ryan Hood

Numerade Educator

Problem 77

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 parties 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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Problem 78

An inexpensive claylike material called Silly Putty 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.

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Problem 79

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 80

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 81

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

Problem 82

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.

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Problem 83

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 84

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? Comment.

Keshav Singh

Numerade Educator

Problem 85

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 86

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, etc., and describe your observations.

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00:25

Problem 87

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 88

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 89

By pressing 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 90

Describe your observations regarding Fig. 2.14c.

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Problem 91

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 slice 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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05:52

Problem 92

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 93

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

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00:59

Problem 94

Explain how you would obtain an estimate of the hardness for a carbon nanotube. (See Section 8.6,2.)

Suman Saurav Thakur

Numerade Educator

01:13

Problem 95

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

Kamlesh Goyal

Numerade Educator

05:48

Problem 96

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