Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Chapter 2, Problem 52QTP
A 250-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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A commercially-pure copper wire originally 10.00 m long is pulled until its final length is 10.10 m. It is annealed, then pulled again to a final length of 10.20 m. What is the engineering strain associated with each of the two steps in the process? What is the true strain for each step? What are the total engineering and true strains for the combined steps? Finally, what agreement (if any) is there between the total strains calculated as the sum of two steps of 0.10 m vs. a single step of 0.20 m?
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Chapter 2 Solutions
Manufacturing Engineering & Technology
Ch. 2 - Distinguish between engineering stress and true...Ch. 2 - In a stress-strain curve, what is the proportional...Ch. 2 - Describe the events that take place when a...Ch. 2 - What is ductility, and how is it measured?Ch. 2 - In the equation =Kn, which represents the true...Ch. 2 - What is strain-rate sensitivity, and how is it...Ch. 2 - What test can measure the properties of a material...Ch. 2 - What testing procedures can be used to measure the...Ch. 2 - Describe the differences between brittle and...Ch. 2 - What is hardness? Explain.
Ch. 2 - Describe the features of a Rockwell hardness test.Ch. 2 - What is a Leeb test? How is it different from a...Ch. 2 - Differentiate between stress relaxation and creep.Ch. 2 - Describe the difference between elastic and...Ch. 2 - Explain what uniform elongation means in tension...Ch. 2 - Describe the difference between deformation rate...Ch. 2 - Describe the difficulties involved in conducting a...Ch. 2 - What is Hookes law? Youngs modulus? Poissons...Ch. 2 - Describe the difference between transgranular and...Ch. 2 - What is the reason that yield strength is...Ch. 2 - Why does the fatigue strength of a specimen or...Ch. 2 - If striations are observed under microscopic...Ch. 2 - What is an Izod test? Why are Izod tests useful?Ch. 2 - Why does temperature increase during plastic...Ch. 2 - What is residual stress? How can residual stresses...Ch. 2 - On the same scale for stress, the tensile true...Ch. 2 - What are the similarities and differences between...Ch. 2 - Can a material have a negative Poissons ratio?...Ch. 2 - It has been stated that the higher the value of m,...Ch. 2 - Explain why materials with high m values, such as...Ch. 2 - With a simple sketch, explain whether it is...Ch. 2 - Explain why the difference between engineering...Ch. 2 - Consider an elastomer, such as a rubber band. This...Ch. 2 - If a material (such as aluminum) does not have an...Ch. 2 - What role, if any, does friction play in a...Ch. 2 - Which hardness tests and scales would you use for...Ch. 2 - Consider the circumstance where a Vickers hardness...Ch. 2 - Which of the two tests, tension or compression,...Ch. 2 - List and explain briefly the conditions that...Ch. 2 - List the factors that you would consider in...Ch. 2 - On the basis of Fig. 2.5, can you calculate the...Ch. 2 - If a metal tension-test specimen is rapidly pulled...Ch. 2 - Comment on your observations regarding the...Ch. 2 - Will the disk test be applicable to a ductile...Ch. 2 - What hardness test is suitable for determining the...Ch. 2 - Wire rope consists of many wires that bend and...Ch. 2 - A statistical sampling of Rockwell C hardness...Ch. 2 - In a Brinell hardness test, the resulting...Ch. 2 - Some coatings are extremely thinsome as thin as a...Ch. 2 - Select an appropriate hardness test for each of...Ch. 2 - A paper clip is made of wire 0.5 mm in diameter....Ch. 2 - A 250-mm-long strip of metal is stretched in two...Ch. 2 - Identify the two materials in Fig. 2.5 that have...Ch. 2 - Plot the ultimate strength vs. stiffness for the...Ch. 2 - If you remove the layer of material ad from the...Ch. 2 - Prove that the true strain at necking equals the...Ch. 2 - Percent elongation is always defined in terms of...Ch. 2 - You are given the K and n values of two different...Ch. 2 - A cable is made of two strands of different...Ch. 2 - On the basis of the information given in Fig. 2.5,...Ch. 2 - In a disk test performed on a specimen 1.00 in. in...Ch. 2 - A piece of steel has a hardness of 300 HB....Ch. 2 - A metal has the following properties: UTS = 70,000...Ch. 2 - Using only Fig. 2.5, calculate the maximum load in...Ch. 2 - Estimate the modulus of resilience for a highly...Ch. 2 - A metal has a strength coefficient K = 100,000 psi...Ch. 2 - Plot the true stresstrue strain curves for the...Ch. 2 - The design specification for a metal requires a...Ch. 2 - Calculate the major and minor pyramid angles for a...Ch. 2 - If a material has a target hardness of 300 HB,...Ch. 2 - A Rockwell A test was conducted on a material and...Ch. 2 - For a cold-drawn 0.5% carbon steel, will a...Ch. 2 - A material is tested in tension. Over a 1-in. gage...Ch. 2 - A horizontal rigid bar cc is subjecting specimen a...Ch. 2 - List and explain the desirable mechanical...Ch. 2 - When making a hamburger, you may have observed the...Ch. 2 - An inexpensive claylike material called Silly...Ch. 2 - In tension testing of specimens, mechanical and...Ch. 2 - Demonstrate the impact toughness of a piece of...Ch. 2 - Using a large rubber band and a set of weights,...Ch. 2 - Find or prepare some solid circular pieces of...Ch. 2 - Take several rubber bands and pull them at...Ch. 2 - Devise a simple fixture for conducting the bend...Ch. 2 - By pressing a small ball bearing against the top...Ch. 2 - Describe your observations regarding Fig. 2.14c.Ch. 2 - Embed a small steel ball in a soft block of...Ch. 2 - Devise a simple experiment, and perform tests on...Ch. 2 - Obtain some solid and some tubular metal pieces,...Ch. 2 - Explain how you would obtain an estimate of the...Ch. 2 - Without using the words stress or strain, define...Ch. 2 - We know that it is relatively easy to subject a...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 1. What are the elastic modulus (E) and the Poisson's ratio () used to indicate? 2. Illustrate the differences between actual stress and engineered stress with strain, and also describe their underlying physical concepts. 3. If the engineering strain is 2% for a specific state of uniaxial stress, what is the real strain? Please solve for all in full detail and step by steparrow_forwardA steel rod is subjected to a force of 5 kN. The initial length of the rod is 690 mm and after elongation its length is equal to 700 mm. Estimate engineering and true strain.arrow_forwardHow can the principal normal strains and maximum in-plane shear strain be determined?arrow_forward
- How can the engineers transform the strains in order to obtain their values inother directions?arrow_forwardA specimen of copper having a rectangular cross section 1.20 in. x 1.5 in.) is pulled in tension with 20,000lbf force, producing only elastic deformation. Calculate the resulting strain.arrow_forwardstress-strain behavior for the brass specimen shown in Figure 6.12, determine the following: (a) The modulus of elasticity (b) The yield strength at a strain offset of 0.002 (c) The maximum load that can be sustained by a cylindrical specimen hav- ing an original diameter of 12.8 mm (0.505 in.) (d) The change in length of a specimen originally 250 mm (10 in.) long that is subjected to a tensile stress of 345 MPa (50,000 psi)arrow_forward
- A 3-mm-long gold alloy wire intended to electrically bond a computer chip to its package has an initial diameter of 30 µm. During testing, it is pulled axially with a load of 15 grams-force. If the wire diameter decreases uniformly to 29 µm, compute the following: (a) The final length of the wire. (b) The true stress and true strain at this load. (c) The engineering stress and strain at this load.arrow_forwardHow can we determine the direction of the strains?arrow_forwardA material has a strength coefficient of 150,000 psi. At the onset of plastic deformation, the material had an 18 percent increase over its initial length, and at the beginning of non-uniform deformation, the material experienced an engineering strain of 0.58. Calculate the engineering and true strains at yield. Also, calculate the engineering and true strains at the point where a maximum engineering stress is experienced by the material. Determine the strain-hardening index. Calculate the ultimate tensile strength. Calculate the modulus of elasticity. Given: K = 150,000 psi 18% increase in length ey = 0.58 Want: ey =? eu =? n =? UTS =? E =? εy =? εu =?arrow_forward
- A specimen of some metal having a rectangular cross section 9.74 mm x 13.5 mm is pulled in tension with a force of 796 N, which produces only elastic deformation. Given that the elastic modulus of this metal is 79 GPa, calculate the resulting strain. iarrow_forwardA tensile specimen is elongated to twice its original length. Determine the engineering strain and true strain for this test? If the values are different explanations why they are different?arrow_forwardA 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 a force of 40, 000 N. If the deformation is totally elastic, what is the strain experienced by the specimen along the longitudinal direction?arrow_forward
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