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Creep and Fracture Analysis Homework

This document contains a homework assignment with 3 problems related to materials issues in mechanical design. Problem 1 involves analyzing creep rate data for a polycrystalline oxide at different temperatures and stresses. Problem 2 examines creep mechanisms in aluminum, including calculating dominant mechanisms and estimating stress requirements. Problem 3 analyzes fracture strength data for alumina plates to estimate surface energy using Griffith fracture theory.

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136 views2 pages

Creep and Fracture Analysis Homework

This document contains a homework assignment with 3 problems related to materials issues in mechanical design. Problem 1 involves analyzing creep rate data for a polycrystalline oxide at different temperatures and stresses. Problem 2 examines creep mechanisms in aluminum, including calculating dominant mechanisms and estimating stress requirements. Problem 3 analyzes fracture strength data for alumina plates to estimate surface energy using Griffith fracture theory.

Uploaded by

winter_snow714
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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MECH 532:

Materials Issues in Mechanical Design Homework #6 Fall 2018

Homework # 6
Problem 1: The following data were obtained for creep of a polycrystalline oxide having a grain
diameter of 10µm.

Stress Strain Rate


(MPa) at T= 1700 K at T = 1810 K at T = 1940 K
10 2.0 × 10−8 7.0 × 10−8 4.2 × 10−7
20 4.0 × 10−8 1.4 × 10−7 8.4 × 10−7
30 6.0 × 10−8 2.1 × 10−7 1.3 × 10−6
40 8.0 × 10−8 2.8 × 10−7 1.7 × 10−6
50 2.3 × 10−7 8.0 × 10−7 4.8 × 10−6
60 5.0 × 10−7 1.8 × 10−6 1.1 × 10−5
70 9.9 × 10−7 3.5 × 10−6 2.1 × 10−5
80 1.8 × 10−6 6.3 × 10−6 3.8 × 10−5
90 3.1 × 10−6 1.1 × 10−5 6.5 × 10−5
100 4.9 × 10−6 1.7 × 10−5 1.0 × 10−4

(a) Plot (logarithmic coordinates) creep rate vs. stress for three temperatures. Identify on your
plot the stress regimes that correspond to diffusional creep and those that correspond to
power-law creep.

(b) Does the difusional creep region correspond to Nabarro-Herring creep or to Coble creep?

(c) On the graph you developed for part (a), plot creep rate vs. stress at 1700 K for this material
if the grain size were increased to 20µm.

Problem 2: The following data is useful in determining the strain rate of aluminum for Nabarro-
Herring Creep, Coble Creep and power-law creep.

Parameter Value
Atomic Volume (Ω) 1.2 × 10−29 m3 /atom
Lattice Diffusion Coefficient, D0L 3.5 × 10−6 m2 /s
QL 2.0 × 10−19 J/atom
Grain Size (d) 1.0 × 10−5 m
Coble Creep Diffusion Coefficient, D0C 1.0 × 10−5 m2 /s
QC 1.2 × 10−19 J/atom
A for power law creep 2.5 × 109
Stress exponent for power law creep 4.8
Shear Modulus 25 GPa
Burgers Vector 0.286 nm

MECH 532 Page 1 of 2


MECH 532:
Materials Issues in Mechanical Design Homework #6 Fall 2018

(a) Determine the dominant creep mechanism for each stress and temperature combination given
below (use a computer program for this problem)
T(K) = 600, 700, 800, 900, 1000
σ (MPa) = 1, 3, 10, 30, 100

(b) You are asked to consider development of an aluminum-based material for service at 475◦ C.
The requirements are that the material should creep only 1% in 1000 hours at this temper-
ature. Estimate the stress required to cause pure aluminum of 10-µm grain size to creep at
this rate. What is the dominant creep mechanism?

(c) Briefly describe an approach you would use for designing an aluminum alloy to meet the
requirements stipulated in part (b).

Problem 3: A set of thin plates of Al2 O3 that have various length cracks cut through the plate
are tested in tension to failure. These plates have the same cracked geometry as that discussed
in derivation of Griffith fracture. The crack lengths and failure stresses are recorded in the table
below. Assuming alumina has a Young’s modulus of E=380 GPa, estimate the surface energy
under the assumptions of classical Griffith fracture.

Crack Length Fracture Strength


µm MPa
101 57.3
305 33.5
697 21.5
912 17.8
1220 16.7
1390 15.6

MECH 532 Page 2 of 2

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