Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 11.13, Problem 90AAP
A reaction-bonded silicon nitride ceramic has a strength of 250 MPa and a fracture toughness of 3.4. What is the largest-sized internal flaw that this material can support without fracturing? (Use Y = 1 in the fracture-toughness equation.)
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A ceramic with KIc = 4 MPa m1/2 contains pores with radius a = 5 µm due
to incomplete sintering. These pores lead to a decrease in the failure stress
of the material in both tension and compression. One in every ten grainboundary junctions contains a void; the grain size of the ceramic is 50 µm.
The ceramic fails in compression when the length ℓ of each crack generated
at the voids equals one-half of the spacing between the voids.
(a) Determine the compression strength of the ceramic, using the equation
from Sammis and Ashby.
(b) Determine the tensile strength of the ceramic, assuming flaws with
size a.
A ceramic component with Young’s modulus of 300 GPa and a KIc of 4 MPa.m1/2 is to survive a water quench from 500°C to room temperature of 25°C. If the largest flaw in that material is on the order of 2 μm, what is the maximum value of thermal expansion coefficient (α) for this ceramic required to survive the quench? Assume that there are 20 flaws of 2 μm size. Poisson ratio of the ceramic material is 0.25.
Computational analysis has determined that a particular design of glass ceramic component has a maximum allowable tensile stress
of 21 MPa
Your development team has suggested that a specific grade of Wollastonite with a Youngs Modulus of 99 GPa and a specific surface
energy of 0.059 J/m2 may be suitable.
What would be the maximum allowable size of any internal pores or defects in the glass ceramic component?
(This question has only one correct answer)
O a. 8.43 um
b. 8.86 mm
O c. 8.86 μm
O d. 17.72 μm
e. 16.86 mm
O f. 16.86 μm
g. 8.43 mm
Chapter 11 Solutions
Foundations of Materials Science and Engineering
Ch. 11.13 - Define a ceramic material.Ch. 11.13 - Prob. 2KCPCh. 11.13 - Prob. 3KCPCh. 11.13 - Prob. 4KCPCh. 11.13 - Prob. 5KCPCh. 11.13 - Prob. 6KCPCh. 11.13 - Prob. 7KCPCh. 11.13 - What fraction of the octahedral interstitial sites...Ch. 11.13 - Prob. 9KCPCh. 11.13 - Describe the perovskite structure. What fraction...
Ch. 11.13 - Prob. 11KCPCh. 11.13 - Prob. 12KCPCh. 11.13 - Prob. 13KCPCh. 11.13 - Prob. 14KCPCh. 11.13 - Describe the feldspar network structure.Ch. 11.13 - Prob. 16KCPCh. 11.13 - Prob. 17KCPCh. 11.13 - Describe two methods for preparing ceramic raw...Ch. 11.13 - Prob. 19KCPCh. 11.13 - Prob. 20KCPCh. 11.13 - Prob. 21KCPCh. 11.13 - Prob. 22KCPCh. 11.13 - Prob. 23KCPCh. 11.13 - Prob. 24KCPCh. 11.13 - Prob. 25KCPCh. 11.13 - Prob. 26KCPCh. 11.13 - What are the purposes of drying ceramic products...Ch. 11.13 - Prob. 28KCPCh. 11.13 - What is the vitrification process? In what type of...Ch. 11.13 - Prob. 30KCPCh. 11.13 - Prob. 31KCPCh. 11.13 - Prob. 32KCPCh. 11.13 - Prob. 33KCPCh. 11.13 - Prob. 34KCPCh. 11.13 - Prob. 35KCPCh. 11.13 - Prob. 36KCPCh. 11.13 - Prob. 37KCPCh. 11.13 - Prob. 38KCPCh. 11.13 - Why do most ceramic materials have low thermal...Ch. 11.13 - Prob. 40KCPCh. 11.13 - Prob. 41KCPCh. 11.13 - Prob. 42KCPCh. 11.13 - Prob. 43KCPCh. 11.13 - Prob. 44KCPCh. 11.13 - Prob. 45KCPCh. 11.13 - Prob. 46KCPCh. 11.13 - How is a glass distinguished from other ceramic...Ch. 11.13 - Prob. 48KCPCh. 11.13 - Prob. 49KCPCh. 11.13 - Prob. 50KCPCh. 11.13 - Prob. 51KCPCh. 11.13 - Prob. 52KCPCh. 11.13 - Prob. 53KCPCh. 11.13 - Prob. 54KCPCh. 11.13 - Prob. 55KCPCh. 11.13 - Prob. 56KCPCh. 11.13 - Prob. 57KCPCh. 11.13 - Prob. 58KCPCh. 11.13 - Prob. 59KCPCh. 11.13 - Prob. 60KCPCh. 11.13 - Prob. 61KCPCh. 11.13 - Prob. 62KCPCh. 11.13 - Prob. 63AAPCh. 11.13 - Prob. 64AAPCh. 11.13 - Prob. 65AAPCh. 11.13 - Prob. 66AAPCh. 11.13 - Prob. 67AAPCh. 11.13 - Prob. 70AAPCh. 11.13 - Calculate the ionic packing factor for (a) MnO and...Ch. 11.13 - Prob. 72AAPCh. 11.13 - Prob. 73AAPCh. 11.13 - Prob. 74AAPCh. 11.13 - Prob. 75AAPCh. 11.13 - Prob. 77AAPCh. 11.13 - Prob. 78AAPCh. 11.13 - Prob. 79AAPCh. 11.13 - Prob. 80AAPCh. 11.13 - Prob. 81AAPCh. 11.13 - Why are triaxial porcelains not satisfactory for...Ch. 11.13 - Prob. 83AAPCh. 11.13 - Prob. 84AAPCh. 11.13 - Prob. 85AAPCh. 11.13 - What causes the lack of plasticity in crystalline...Ch. 11.13 - Prob. 87AAPCh. 11.13 - Prob. 88AAPCh. 11.13 - Prob. 89AAPCh. 11.13 - A reaction-bonded silicon nitride ceramic has a...Ch. 11.13 - Prob. 91AAPCh. 11.13 - Prob. 92AAPCh. 11.13 - Prob. 93AAPCh. 11.13 - Prob. 94AAPCh. 11.13 - How does the silica network of a simple silica...Ch. 11.13 - Prob. 96AAPCh. 11.13 - Prob. 97AAPCh. 11.13 - Prob. 98AAPCh. 11.13 - Prob. 99AAPCh. 11.13 - Prob. 100AAPCh. 11.13 - Prob. 101AAPCh. 11.13 - Prob. 102AAPCh. 11.13 - Prob. 103AAPCh. 11.13 - Prob. 104AAPCh. 11.13 - Prob. 105AAPCh. 11.13 - Prob. 106AAPCh. 11.13 - Prob. 107AAPCh. 11.13 - Prob. 108SEPCh. 11.13 - Prob. 109SEPCh. 11.13 - Prob. 110SEPCh. 11.13 - Prob. 111SEPCh. 11.13 - Prob. 112SEPCh. 11.13 - Alumina (A12O3) and chromium oxide (Cr2O3) are...Ch. 11.13 - (a) How are the ceramic tiles used in the thermal...Ch. 11.13 - The nose cap and the wing leading edges of the...Ch. 11.13 - Prob. 116SEPCh. 11.13 - Prob. 117SEPCh. 11.13 - Prob. 118SEPCh. 11.13 - Prob. 119SEPCh. 11.13 - Prob. 120SEPCh. 11.13 - Prob. 121SEPCh. 11.13 - Prob. 122SEPCh. 11.13 - Prob. 123SEPCh. 11.13 - Prob. 124SEPCh. 11.13 - Prob. 125SEPCh. 11.13 - Prob. 126SEPCh. 11.13 - Prob. 127SEPCh. 11.13 - Prob. 128SEPCh. 11.13 - Prob. 129SEP
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- A sodium silicate glass has no surface defects as etching has removed them. Calculate the Fracture Toughness using Griffith formula for that glass. Having Young's modulus = 70 GNM¯ 2, surface energy Ys = 0.56 Jm² and Fracture Strength: 100 MNm².arrow_forward3. Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight of 95.94 g/mol. Compute its theoretical density.4. For a brass alloy, the stress at which plastic deformation begins is 345 MPa and the modulus of elasticity is 103 GPa.a. What is the maximum load that may be applied to a specimen with a cross-sectionalarea of 130 mm2 without plastic deformation?b. If the original specimen length is 76 mm, what is the maximum length to which itmay be stretched without causing plastic deformation?arrow_forwardA piece of BCC single-crystal metal is oriented such that tensile stress is applied along a [131] direction. If slip occurs on a (011) plane and in a [111] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 12 MPa.arrow_forward
- The maximum principal strain failure criterion is appropriate for ceramic materials". Is this true or false?arrow_forwardHelp me pleasearrow_forwardDetermine the critical resolved shear stress on a BCC single crystal if a normal stress of 10 MPa along [100] direction causes slip system on (110) plan along [1-11], one-bar one-one, direction.arrow_forward
- A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied parallel to the [100] direction. If the critical resolved shear stress for this material is 1.18 MPa, calculate the magnitude of applied stress necessary to cause slip to occur on the (111) plane in the [1-10] direction.arrow_forward1. Calculate the shear stress of aluminum material with shear modulus of 24 GPa, displace 0.2 cm along the x-direction. www The interatomic spacing between the atoms is 3.2 mm. (arrow_forwardThe mean fracture strength of a batch of alumina components is measured to be 400 MPa. What size of defects would you expect to find in the material? (Take the fracture toughness of alumina to be 4 MPam½ and Y to be 1.8).arrow_forward
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