Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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41<br />
Objective<br />
Linear<br />
Ferromagnets<br />
Non-linear<br />
properties<br />
Electric.<br />
Conduct.<br />
Tensors<br />
Elasticity<br />
Symmetry<br />
Transformations of Stress & Strain Vectors<br />
!<br />
• It is useful to be able to transform the axes<br />
of stress tensors when written in vector<br />
form (equation on the left). The table<br />
(right) is taken from Newnham’s book. In<br />
vector-matrix form, the transformations<br />
are:<br />
$ # 1"<br />
' +<br />
& ) -<br />
&<br />
# " 2)<br />
-<br />
& # " ) - 3<br />
& ) = -<br />
&<br />
# " 4)<br />
-<br />
& # " 5)<br />
-<br />
& )<br />
% # "<br />
-<br />
6(<br />
,<br />
* 11 * 12 * 13 * 14 * 15 * 16<br />
* 21 * 22 * 23 * 24 * 25 * 26<br />
* 31 * 32 * 33 * 34 * 35 * 36<br />
* 41 * 42 * 43 * 44 * 45 * 46<br />
* 51 * 52 * 53 * 54 * 55 * 56<br />
* 61 * 62 * 63 * 64 * 65 * 66<br />
. $ # ' 1<br />
0 & )<br />
0 &<br />
# 2)<br />
0 & # ) 3<br />
0 & )<br />
0 &<br />
# 4)<br />
0 & # 5)<br />
0 & )<br />
/ % # 6(<br />
!<br />
"<br />
# i = $ ij# j<br />
%1<br />
# i = $ ij<br />
# " j<br />
%1T<br />
& " i = $ ij & j<br />
T<br />
&i = $ ij&<br />
" j
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