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Unformatted text preview: one 55% Materials Science and Engineering 564 mixmam Mechanical behavior and micrmimcmrc
Winter 2007 Midterm Exam February 16, 2007 Instructions:
Enter your 4 digit course code here: KE Y You have approximately 50 minutes to complete this exam. Answer all 8 questions. Write your answers in the spaces provided. Always provide complete answers, including
units where applicable. Work you show may count for partial credit. You may use your onesided sheet of personal notes and a calculator.
The point values for each question are given below. Good luck! TOTAL: /100 1/9 MSE 564 Midterm Feb. 16, 2007 Engineering versus True Strain (12 points) Company A takes a bar of length L; and imposes a strain of—O. 15, thereby changing the length to L2. The bar of length L2 is then shipped to Company B where a strain of 0.15 is imposed, changing the length to L3 = 1 m. a. Calculate the initial length L1 to 4 signiﬁcant ﬁgures, assuming engineering
strains were imposed. X/ﬂ ’
G : g5 €4.52: LZ*L\ : Li A FONS L\ L'l
+3 ‘
12> ‘1}: 0‘85 (c)
Lt
624’3 :1 u : 0J5, ‘13 : {.15 (7—) ‘l (‘C Lemma it 3:3, 323;. ~tt—sztsm15ia CW5“ (‘5 Md (2') l ‘
M$‘E§», % _~. (mt; miss)
Lt ' l m "r" ’ r '7‘: 1116 2.3:”
L‘ {we me. an m
b. Calculate the initial length L; to 4 signiﬁcant ﬁgures, assuming true str . were *Q'ls’l’ Ovlg: Q SL3 :lm h! v? commaﬂ? $563. ﬁgwes l owlif; misgik page 2 / 9pages total MSE 564 Midterm Feb. 16, 2007 2. Computing strain (12 points)
A cube of material with 1 cm edge length is deformed. The table below lists the
coordinates (in cm) of points A, B, and C and 0 before and after deformation. A/ 2 Point before def after def 0 0,0,0 0,0,0 A 1,0,0 1.003,0.005,0.001 B 0,1,0 0.003,0.995,0.002 C 0,0,1 0.002,0.001,1.001 a. Calculate ayy. H page 3 / 9pages total b3 MSE 564 Midterm Feb. 16, 2007 Computing stress along an offaxis (10 points)
A cubic crystal is stressed to the state 20 o o
hm)= o o 0 MPa
0 0 10 where the 1, 2, and 3 directions are aligned to the cube directions of the crystal as
shown below. Compute the stress 01'1', where the 1' direction is indicated in the ﬁgure. 1’=[1101 Co; gm : Q12]_[to<131 :9 Co; rat/,5 : [no] [Gollﬂfgw
a c +2 V2, 7“ ﬁx“ +"2
6:1" ‘3 1. 7. (CD/WP; "t 42%“ Ab Quilts page 4 / 9pages total 4. MSE 564 Midterm Feb. 16, 2007 Crystal elasticity (10 points)
An aluminum single crystal is loaded with the stress state 20 o o
(oij)= o o 0 MPa
0 0 10 where the 1, 2, and 3 directions are aligned to the cube directions of the crystal. It
deforms elastically. Determine the resulting strain 522. Note the properties for Al
below. ' _
1.57  1011Pal 0.57. 1011%1 3.5110'11Pa'1 (as Q; =2 3130] J?— ' 4 0 +2;
62 = 3M 5" a Szzﬁ/+ 3;; cs;
0 O O
+ 324%? Sag/é"? 321.;(4
' $2" 'Q" 913 L Q2 ': Sta :Q 0 sq \(SH T75“) (3m toQ’P )
::  {.71 ‘ \o'L+ ”( thu; Stain wiS§thi “‘ ﬁnaﬁwuvij" wronj page 5 / 9pages total 5. MSE 564 Midterm Feb. 16, 2007 Correlation between wavy slip and stacking fault energy (10 points) Discuss why wavy slip is associated with a large stacking fault energy, as shown in
the table below. Stacking fault Strainhardening Slip energ mJ/m2 exonent 11 character
Stainless Steel < 10 ~0.45 Planar
Cu ~90 ~O.3 Planar/wavy
Al ~25 0 ~0. 1 5 Wa page 6 / 9pages total 6. MSE 564 Midterm Feb. 16, 2007 Stages of Defamation (12 points) a. Sketch the shape of a tensile stresstensile strain curve for a single crystal
showing (and labeling) stage 1, stage II, and stage III portions of deformation. 0 b. Describe the transition from stage I to stage II in terms of the transition that occurs in crystal slip. page 7 / 9pages total MSE 564 Midterm Feb. 16, 2007 Holoman Relation (10 points) A bar of copper is pulled in tension with the result that the cross sectional area
reduces from an initial value of 0.31 in2 to a ﬁnal value of 0.22 in2. Estimate the
yield strength of the deformed piece, using a Holoman relation with a work
hardening exponent of 0.3, initial yield strength of 60 MPa, and initial yield strain
of 0.002. 0.3 5.9;. 3 “3.9
£20 A
+3 QT: JM in 3 “gm 4&3“. “QM .3 ﬁpégf"
\\ Mm a £0 N WWW WWMZe
c5“  5" 931+ ~ 2%0 “Pa
{4‘3 CLBOZ. i page 8 / 9pages total MSE 564 Midterm Feb. 16, 2007 Miscellaneous questions about structure and properties (24 points) Circle "True" or "False" for each of the statements below. (a) A steel is loaded in tension and exhibits an upper yield point followed by
homogeneous ﬂow. If the steel had been strained at twice the rate, an upper
yield point would not be present: "True" (b) Durin agig of aluminum alloys, solid solution strengthening decreases: "False" (c) Work hardening that doubl islocation density generally will generally double
yield strength: "True" 6 (d) Potent solution strengthenin . mes from solute atoms positioned at
nonsymmetric lattice sites: & "False" (e) Single crystal metal samles generally do not show an easy glide regime
(regime I): "True"
(f) Strengtheii'lj due to so ute additions scales as (solute concentration)'1/2: "True"
(g) For a materl such as steel, increasing strain rate and decreasing temperature .0 I increase the stress necessary to plastically deform the material:
"False" (h) ceamic sample loaded in tension will generally sustain a .. : tress than the
modulus of rupture from a 4point bend test of that sample: "False" END OF EXAM page 9 / 9pages total ...
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 Winter '08
 Anderson
 Deformation, Midterm Feb.

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