Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 6.13, Problem 97SEP
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A 3-mm-long gold alloy wire intended to electricallybond a computer chip to its package has an initial diameter of30 μm. During testing, it is pulled axially with a load of 15grams-force. If the wire diameter decreases uniformly to29 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.
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 172 GPa (25 × 106 psi), and that elastic deformation terminates at a strain
of 0.008. For plastic deformation, assume that the relationship between stress and strain is described by Equation 6.19, in which the
values for K and n are 6900 MPa (1 × 106 psi) and 0.25, respectively. Furthermore, plastic deformation occurs between strain values of
0.008 and 0.61, at which point fracture occurs.
J/m³
A load of 22 kips is gradually applied to a 2-in round rod, 10 ft long. The total elongation is observed to be 0.03 in. If the stretching is entirely elastic,
A. what is the modulus of elasticity, and
B. what material would you judge it to be, wrought iron or stainless steel?
C. how much energy is absorbed by the rod?
D. Suppose that the material is aluminum alloy 3003-H14 (Table AT 3, Faires); compute its elongation for the same load. Is this within elastic action?
Chapter 6 Solutions
Foundations of Materials Science and Engineering
Ch. 6.13 - (a) How are metal alloys made by the casting...Ch. 6.13 - Why are cast metal sheet ingots hot-rolled first...Ch. 6.13 - What type of heat treatment is given to the rolled...Ch. 6.13 - Describe and illustrate the following types of...Ch. 6.13 - Describe the forging process. What is the...Ch. 6.13 - What is the difference between open-die and...Ch. 6.13 - Describe the wire-drawing process. Why is it...Ch. 6.13 - Distinguish between elastic and plastic...Ch. 6.13 - Define (a) engineering stress and strain and (b)...Ch. 6.13 - Define (a) modulus of elasticity, (b) yield...
Ch. 6.13 - (a) Define the hardness of a metal. (b) How is the...Ch. 6.13 - What types of indenters are used in (a) the...Ch. 6.13 - What are slipbands and slip lines? What causes the...Ch. 6.13 - Describe the slip mechanism that enables a metal...Ch. 6.13 - (a) Why does slip in metals usually take place on...Ch. 6.13 - Prob. 16KCPCh. 6.13 - What other types of slip planes are important...Ch. 6.13 - Define the critical resolved shear stress for a...Ch. 6.13 - Describe the deformation twinning process that...Ch. 6.13 - What is the difference between the slip and...Ch. 6.13 - Prob. 21KCPCh. 6.13 - Prob. 22KCPCh. 6.13 - What experimental evidence shows that grain...Ch. 6.13 - (a) Describe the grain shape changes that occur...Ch. 6.13 - How is the ductility of a metal normally affected...Ch. 6.13 - (a) What is solid-solution strengthening? Describe...Ch. 6.13 - What are the three main metallurgical stages that...Ch. 6.13 - Describe the microstructure of a heavily...Ch. 6.13 - Describe what occurs microscopically when a...Ch. 6.13 - When a cold-worked metal is heated into the...Ch. 6.13 - Describe what occurs microscopically when a...Ch. 6.13 - When a cold-worked metal is heated into the...Ch. 6.13 - Prob. 33KCPCh. 6.13 - Prob. 34KCPCh. 6.13 - Prob. 35KCPCh. 6.13 - Prob. 36KCPCh. 6.13 - Prob. 37KCPCh. 6.13 - Why are nanocrystalline materials stronger? Answer...Ch. 6.13 - A 70% Cu30% Zn brass sheet is 0.0955 cm thick and...Ch. 6.13 - A sheet of aluminum alloy is cold-rolled 30% to a...Ch. 6.13 - Calculate the percent cold reduction when an...Ch. 6.13 - Prob. 42AAPCh. 6.13 - What is the relationship between engineering...Ch. 6.13 - A tensile specimen of cartridge brass sheet has a...Ch. 6.13 - A 0.505-in.-diameter rod of an aluminum alloy is...Ch. 6.13 - In Figure 6.23, estimate the toughness of SAE 1340...Ch. 6.13 - The following engineering stress-strain data were...Ch. 6.13 - Prob. 49AAPCh. 6.13 - A 0.505-in.-diameter aluminum alloy test bar is...Ch. 6.13 - A 20-cm-long rod with a diameter of 0.250 cm is...Ch. 6.13 - Prob. 52AAPCh. 6.13 - Prob. 53AAPCh. 6.13 - Prob. 54AAPCh. 6.13 - Prob. 55AAPCh. 6.13 - Prob. 56AAPCh. 6.13 - A specimen of commercially pure titanium has a...Ch. 6.13 - Prob. 58AAPCh. 6.13 - Prob. 59AAPCh. 6.13 - Prob. 60AAPCh. 6.13 - Prob. 61AAPCh. 6.13 - Prob. 62AAPCh. 6.13 - Prob. 63AAPCh. 6.13 - Prob. 64AAPCh. 6.13 - Prob. 65SEPCh. 6.13 - Prob. 66SEPCh. 6.13 - A 20-mm-diameter, 350-mm-long rod made of an...Ch. 6.13 - Prob. 68SEPCh. 6.13 - Prob. 69SEPCh. 6.13 - Consider casting a cube and a sphere on the same...Ch. 6.13 - When manufacturing complex shapes using cold...Ch. 6.13 - Prob. 74SEPCh. 6.13 - Draw a generic engineering stress-strain diagram...Ch. 6.13 - (a) Draw a generic engineering stress-strain...Ch. 6.13 - Prob. 77SEPCh. 6.13 - Prob. 78SEPCh. 6.13 - Prob. 79SEPCh. 6.13 - The material for a rod of cross-sectional area...Ch. 6.13 - What do E, G, v, Ur, and toughness tell you about...Ch. 6.13 - A cylindrical component is loaded in tension until...Ch. 6.13 - Referring to Figures 6.20 and 6.21 (read the...Ch. 6.13 - (a) Show, using the definition of the Poissons...Ch. 6.13 - A one-inch cube of tempered stainless steel (alloy...Ch. 6.13 - Prob. 87SEPCh. 6.13 - Prob. 88SEPCh. 6.13 - Prob. 89SEPCh. 6.13 - Prob. 90SEPCh. 6.13 - Prob. 91SEPCh. 6.13 - Prob. 92SEPCh. 6.13 - Prob. 93SEPCh. 6.13 - Prob. 94SEPCh. 6.13 - Starting with a 2-in.-diameter rod of brass, we...Ch. 6.13 - Prob. 96SEPCh. 6.13 - Prob. 97SEPCh. 6.13 - Prob. 98SEPCh. 6.13 - The cupro-nickel substitutional solid solution...Ch. 6.13 - Prob. 100SEP
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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
- 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_forwardA steel rod (initial diameter: 3.2 mm, initial length: 42 mm) is extended by auniaxial tensile load of 4800 N in 120 seconds. At this load, the length of therod is measured as 49,2 mm. Calculate the followings:(a) Stress and strain occurred on the rod at this load.(b) Initial strain rate.(c) Diameter of the rod at this load.(Yield strength : 380 MPa, Ultimate Tensile Strength: 670 MPa,Modulus of Elasticity: 210000 MPa were given for this material)arrow_forwardA gauge # 10 HSLA steel for an automotive application has a Young’s modulus of 200 GPa, a yield strength of 370 MPa and a ultimate tensile strength of 440 MPa. What is the punch force needed to punch a square hole with a side length of 20 mm on this HSLA steel? Show your work.arrow_forward
- The lower yield point for a certain plain carbon steelbar is found to be 135 MPa, while a second bar of the samecomposition yields at 260 MPa. Metallographic analysisshows that the average grain diameter is 50μm in the firstbar and 8μm in the second bar.a. Predict the grain diameter needed to cause a loweryield point of 205 MPa.b. If the steel could be fabricated to form a stablegrain structure of 500 nm grains, what strengthwould be predicted?c. Why might you expect the upper yield point to bemore alike in the first two bars than the lower yieldpoint?arrow_forwardcompute the tensile strength and ductility of a cylindrical copper rod if it is cold worked such that the diameter is reduced from 12 to 10 mmarrow_forwardb) A metal wire is cold drawn from a radius of 5.75 mm to a radius of 3.25 mm. Compute the percent of the cold reduction in this process. (Ans: 68.05% c) A certain metal has a modulus of elasticity of 115 GPa, and its plastic deformation begins at a stress of 275 MPa. Calculate the maximum elongation to which it can be stretched without plastic deformation, if the metal has a length of 120 mm.arrow_forward
- Using the tensile test simulation tool, a. generate the stress-strain curve for aluminum b. Indicate the following points in the stress-strain curve for aluminum and give the corresponding values: limit of proportionality elastic limit 0.2% offset yield stress (include the graph illustrating how this was determined) ultimate stress fracture stress c. Calculate modulus of elasticity. d. compare aluminum with nylon (include the related graph) and answer the following: Which has higher tensile strength? Provide the necessary values to support the answer. Which is stiffer? Support your answer with calculations.arrow_forward1. An aluminium rod of circular cross section is to withstand 250kN of tensile load for a structural application. The minimum length of the rod is 4.2m but must deform elastically to no more than 7mm when the tensile force is applied. Take that the engineering yield stress limit and the Young’s modulus of the material are 260 MPa and 70 GPa respectively.If a safety factor of 2 is adequate, design an appropriate rod and state why factor of safety is important in your analysis. 2. Explain the differences in the grain structure between a metal which has been cold worked and another same cold worked piece but has been fully re-crystallised. Why are small angle grain boundaries not as effective in interfering with the motion of dislocation as high angle grain boundaries?arrow_forwardAn ordinary mild steel bar has been prestressed to a working stress of 200 MPa. If the Young's modulus of steel is 200 GPa and permanent negative strain due to shrinkage and creep is 0.0008, what is the effective stress left in the steel?arrow_forward
- A non-cold-worked cylindrical rod with an initial length of 800 mm and diameter of 15 mm is to be deformed using a tensile load of 45 kN. Of the materials listed below, which are possible candidates if you assume that failure of the system occurs when the rod plastically deforms? Do the possible candidates change if you change your assumption to the system failing at the onset of necking in the rod? Justify your choice(s). Material Young’s Modulus (GPa) Yield Strength (MPa) 1040 Steel UTS (MPa) Elongation (%) 680 205 440 25 Brass 100 185 310 68 Сopper 125 160 220 44arrow_forwardA 30 cm long, 12 mm diameter carbon steel rod was subjected to 15.5 kN of tension. Calculate: (a) the stress and strain in the rod (b) the amount that it stretches, (c) its change in diameter and its stiffness (k= EA/L), (d) If the force was only 4.5 kN, by what amount would the rod have stretched?arrow_forwardwhy use yield strength not tensile strength? You are drawing wire which you want the wire to elongate pernamently, and not return back to original shape .arrow_forward
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