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engineering
the science and engineering of materials
The Science And Engineering Of Materials 7th Edition Donald R. Askeland, Wendelin J. Wright - Solutions
Assume that instead of a spherical nucleus, we have a nucleus in the form of a cube of length x. Calculate the critical dimension x* of the cube necessary for nucleation. Write an equation similar to Equation 9-1 for a cubical nucleus, and derive an expression for x* similar to Equation 9-2. Δ6
Explain the term inoculation.
Suppose that solid nickel was able to nucleate homogeneously with an undercooling of only 22°C. How many atoms would have to group together spontaneously for this occur? Assume that the lattice parameter of the solid FCC nickel is 0.356 nm.
Using Equation 9-2, demonstrate that interfacial energy (σsl) has units of J/m2 in SI. 20. Tm ΔΗ, ΔΤ (9-2)
Why is it that nuclei seen experimentally are often sphere-like but faceted? Why are they sphere-like and not like cubes or other shapes?
Derive the formula for the rate of change in total energy change (i.e., the derivative of DG with respect to r) as a function of the radius r of the solid nucleus. Begin with Equation 9-1. Numerically, how is the critical point at which solidification proceeds defined? ΔΟ = 4 mr16, + 4mros (9-1)
If the total change in free energy of a molten metal is 5.34 x 10-17 J upon formation of the first stable solid and the free energy per unit volume is 217.7 J/cm3, approximate the radius of the first stable spherical solid. The surface free energy of the solid-liquid interface is 100 x
Of the ferrous elements, which has the lowest undercooling required for homogeneous nucleation? Does this have any practical significance?
Calculate the total interfacial surface energy for 1016 spheres of copper, each with the critical radius r*.
Does ice melt at 0°C? Explain.
Does water freeze at 0°C and boil at 100°C? Explain.
From the thermodynamic point of view, what two things must occur for solidification from liquid to solid to proceed?
Define the following terms: nucleation, embryo, heterogeneous nucleation, and homogeneous nucleation.
Why are ceramic materials not prepared by melting and casting?
What do the terms “primary” and “secondary” processing mean?
Give examples of materials based on inorganic glasses that are made by solidification.
1. What is chilled white iron and what is it used for?2. What kinds of defects may exist in chilled white iron?
What are the differences between the stress intensity factor (KI) and the plane strain fracture toughness (KIc)? Explain.
A 120 in. annealed rod with a crosssectional area of 0.86 in.2 was extruded from a 5083-O aluminum alloy and axially loaded. Under load, the length of the rod increased to 120.15 in. No plastic deformation occurred.(a) Find the modulus of elasticity of the material and calculate its allowable
Explain the role of mechanical properties in load-bearing applications using realworld examples.
Explain the importance of mechanical properties in functional applications (e.g., optical, magnetic, electronic, etc.) using real-world examples.
Explain the importance of understanding mechanical properties in the processing of materials.
Define “engineering stress” and “engineering strain.”
Define “modulus of elasticity.”
Define “plastic deformation” and compare it to “elastic deformation.”
What is strain rate? How does it affect the mechanical behavior of polymeric and metallic materials?
Why does Silly Putty® break when you stretch it very quickly?
What is meant by the term “stress relaxation”?
Draw a schematic diagram showing the development of strain in an elastic and viscoelastic material. Assume that the load is applied at some time t = 0 and taken off at some time t.
Calculate the maximum force that a 0.2-in. diameter rod of Al2O3, having a yield strength of 35,000 psi, can withstand with no plastic deformation. Express your answer in both lbs and N.
Define “true stress” and “true strain.” Compare with engineering stress and engineering strain.
At what point does necking typically initiate during a tensile test?
Write down the formulas for calculating the stress and strain for a sample subjected to a tensile test. Assume the sample shows necking.
What is necking? How does it lead to reduction in engineering stress as true stress increases?
Two rods in the form of single crystals for pure tin show wildly different yield strengths at the 0.2% offset yield strength. What would be the cause of this phenomenon?
Develop an expression for the engineering strain along the loading axis of a bar subjected to tension prior to any necking that may occur. Your expression should be a function only of the bar’s initial and instantaneous diameters. Assume that the volume is constant.
The cable of a hoist has a cross-sectional area of 80 mm2. The hoist is used to lift a crate weighing 500 kg. The free length of the cable is 30 m. Assume all deformation is elastic.(a) What is the stress on the cable?(b) How much will the cable extend if it is made from steel (E = 200 GPa)?(c) How
A force of 4000 lbs is applied to a cylindrical metal bar that is 0.505 in. in diameter. This load produces a reduction in diameter of 0.0003 in. The deformation is purely elastic. What is the Poisson’s ratio of this material if the elastic modulus is 15 X 106 psi?
(a) A 0.4-in.-diameter, 12-in.-long titanium bar has a yield strength of 50,000 psi, a modulus of elasticity of 16 X 106 psi, and a Poisson’s ratio of 0.30. Determine the length and diameter of the bar when a 500-lb load is applied.(b) When a tensile load is applied to a 1.5-cm-diameter copper
A cylindrical bar of steel, 10 mm in diameter, is to be deformed elastically by application of a force along the bar axis (axial loading). Determine the force that will produce an elastic reduction of 0.003 mm in the diameter. The Poisson’s ratio is 0.30, and the modulus of elasticity is 207 GPa
A standard 0.505-in.-diameter tensile bar was machined to a 2.00-in.-gage length from a copper-nickel alloy and the following data were collected:After fracture, the gage length was 2.75 in. and the diameter was 0.365 in. Plot the engineering stress strain curve and calculate(a) The 0.2% offset
A specimen of an AISI-SAE type 416 stainless steel with a 0.505-in. diameter was machined to a 2.00-in.-gage length and the following data were collected:After fracture, the gage length was 2.20 in. and the diameter was 0.325 in. Plot the engineering stress strain curve and calculate(a) The 0.2%
Define the terms “flexural strength” and “flexural modulus.”
Why is it that we often conduct a bend test on brittle materials?
A square specimen of MgO is loaded using a three-point bend test. Compute the minimum possible thickness of the specimen without fracture, given that the applied load is 95 lbs, the flexural strength is 15 ksi, and the separation between load points is 2 in.
Ceramics are much stronger in compression than in tension. Explain why.
Dislocations have a major effect on the plastic deformation of metals, but do not play a major role in the mechanical behavior of ceramics. Why?
What controls the strength of ceramics and glasses?
What does the term “hardness of a material” mean?
What is the hardest material (natural or synthetic)? Is it diamond?
Explain the terms “macrohardness” and “microhardness.”
A Brinell hardness measurement, using a 10-mm-diameter indenter and a 500-kg load, produces an indentation of 2.5 mm on a steel plate.(a) Determine the Brinell hardness number (HB) of the steel plate; and(b) approximate the tensile strength of the steel.
A Brinell hardness measurement, using a 10-mm-diameter indenter and a 500 kg load, produces an indentation of 4.5 mm on an aluminum plate. Determine the Brinell hardness number (HB) of the metal.
When a 3000 kg load is applied to a 10-mm-diameter ball in a Brinell test of a steel, an indentation of 3.1 mm diameter is produced. Estimate the tensile strength of the steel.
Why is it necessary to perform calibrations on a standard prior to performing a nanoindentation experiment?
The elastic modulus and hardness of MgO are determined to be 306 GPa and 9.2 GPa, respectively, using nanoindentation testing with a diamond tip. The Poisson’s ratio of the MgO is 0.17. The maximum load is 150 mN at this particular indentation depth. Determine the contact stiffness S. Take β = 1.
Plot the Charpy V-notch data below for commercial steel. Label the upper and lower energy shelves on your plot. Would you recommend this steel for service conditions below 10°C ? Explain. Temperature (°C) Impact Energy (J) 50 75 40 75 30 70 20 58 10 37 24 15 10 4 0 -10 -20 -30 -40
What is meant by the term “notch sensitivity?”
What is the difference between a tensile test and an impact test? Explain why the toughness values measured using impact tests may not always correlate with tensile toughness measured using tensile tests.
What is the ductile to brittle transition temperature (DBTT)?
How is tensile toughness defined in relation to the true stress strain diagram?How is tensile toughness related to impact toughness?
Name a specific application for which understanding size-dependent mechanical behavior may be important to the design process.
What factors contributed to NASA’s Columbia 2003 accident?
Define the terms “viscosity,” “apparent viscosity,” and “kinematic viscosity.”
What caused NASA’s Challenger 1986 accident?
What two equations are used to describe Bingham plastic-like behavior?
What is a Newtonian material? Give an example.
What is meant by the terms “shear thinning” and “shear thickening” materials?
Many paints and other dispersions are not only shear thinning, but also thixotropic. What does the term “thixotropy” mean?
A hollow shaft made from AISI 4340 steel has an outer diameter Do of 4 in. and an inner diameter Di of 2.5 in. The shaft rotates at 46 rpm for one hour during each day. It is supported by two bearings and loaded in the middle with a load W of 5500 lbf. The distance between the bearings L is 78 in.
Alumina (Al2O3) is a brittle ceramic with low toughness. Suppose that fibers of silicon carbide SiC, another brittle ceramic with low toughness, could be embedded within the alumina. Would doing this affect the toughness of the ceramic matrix composite? Explain.
A wing component on an aircraft is fabricated from an aluminum alloy that has a plane strain fracture toughness of 26 MPa√m. It has been determined that fracture results at a stress of 112 MPa when the maximum internal crack length is 8.6 mm. For this same component and alloy, compute the stress
Calculate the maximum internal crack length allowable for a titanium alloy component that is loaded to a stress that is half of its yield strength. Assume that the geometry factor is 1.5. The yield strength of this alloy is 132 ksi, and the fracture toughness is 50 ksi √in.
A steel alloy with a plane strain fracture toughness of 55 MPaÏm is exposed to a stress of 1020 MPa. Will this component fracture if it is known that the largest surface crack is 0.5 mm long? Assume the geometry factor to be 1.0.
A polymer that contains internal flaws 1 mm in length fails at a stress of 25 MPa. Determine the plane strain fracture toughness of the polymer. Assume that f = 1.
A manufacturing process that unintentionally introduces cracks to the surface of a part was used to produce load-bearing components. The design requires that the component be able to withstand a stress of 450 MPa. The component failed catastrophically in service. You are a failure analysis engineer
Explain how the fracture toughness of ceramics can be obtained using hardness testing. Explain why such a method provides qualitative measurements.
Explain the terms intergranular and transgranular fractures. Use a schematic to show grains, grain boundaries, and a crack path that is typical of intergranular and transgranular fracture in materials.
What are the characteristic microstructural features associated with ductile fracture?
Turbochargers Are Us, a new start-up company, hires you to design their new turbocharger. They explain that they want to replace their metallic superalloy turbocharger with a high-tech ceramic that is much lighter for the same configuration.Silicon nitride may be a good choice, and you ask Ceramic
What are the characteristic microstructural features associated with a brittle fracture in a metallic material?
What materials typically show a conchoidal fracture?
Briefly describe how fiber-reinforced composite materials can fail.
Concrete has exceptional strength in compression, but it fails rather easily in tension. Explain why.
What controls the strength of glasses? What can be done to enhance the strength of silicate glasses?
Sketch a schematic of the strength of ceramics and that of metals and alloys as a function of probability of failure. Explain the differences you anticipate.
Why does the strength of ceramics vary considerably with the size of ceramic components?
The high-strength steel in Figure 7-20, which has a critical fracture toughness of 80 MPa√m, is subjected to an alternating stress varying from 2900 MPa Crack growth rate (m/cycle) 10-10 10-11 10-12 10-13 10-14 10-15 I Power law behavior =C(AK)" dN No crack growth Rapid unstable- crack
What parameter tells us about the variability of the strength of ceramics and glasses?
The acrylic polymer from which Figure 7-30 was obtained has a critical fracture toughness of 2 MPa√m. It is subjected to a stress alternating between -10 and +10 MPa. Calculate the growth rate of a surface crack when it reaches a length of 5 x 10-6 m if f = 1.0. Crack growth rate
A 2-cm-diameter, 20-cm-long bar of an acetal polymer (Figure 7-28) is loaded on one end and is expected to survive one million cycles of loading, with equal maximum tensile and compressive stresses, during its lifetime. What is the maximum permissible load that can be applied? Stress amplitude
Why do glass fibers of different lengths have different strengths?
A nickel-based alloy (INCONEL® alloy 801) beam (Figure 7-29) is annealed and subjected to a cyclical load of 100 N with equal maximum and minimum stresses. The beam diameter is 5 mm, and the beam length is 50 mm. What is the expected lifetime of the beam in number of cycles to failure? If the
Explain the significance of the Weibull distribution.
The high-strength steel in Figure 7-20 is subjected to a stress alternating at 200 revolutions per minute between 600 MPa and 200 MPa (both tension). Calculate the growth rate of a surface crack when it reaches a length of 0.2 mm in both m/ cycle and m/s. Assume that f = 1.0. Crack growth rate
Your boss asks you to calculate the design stress for a brittle nickel-aluminide rod she wants to use in a high-temperature design where the cylindrical component is stressed in tension. You decide to test rods of the same diameter and length as her design in tension to avoid the correction for the
Research the Aloha Airlines Flight 243 accident in 1988 using online resources and explain the factors that led to the breach and rupture of the main fuselage.
A fatigue test was performed in which the mean stress was 70 MPa and the stress amplitude was 210 MPa. Compute the maximum and minimum stress.
Calculate the constants C and n in Equation 7-18 for the crack growth rate of an acrylic polymer. da dN = C(AK)" (7-18)
The acrylic polymer from which Figure 7-30 was obtained is subjected to an alternating stress between 15 MPa and 0 MPa. The largest surface cracks initially detected by nondestructive testing are 0.001 mm in length. If the critical fracture toughness of the polymer is 2 MPaÏm, calculate the number
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