Microstructure-Properties - Materials Science and Engineering

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40 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry The “RVE” • In order to describe the properties of a material, it is useful to define a representative volume element (RVE) that is large enough to be statistically representative of that region (but small enough that one can subdivide a body). • For example, consider a polycrystal: how many grains must be included in order for the element to be representative of that point in the material?
41 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Transformations of Stress & Strain Vectors ! • It is useful to be able to transform the axes of stress tensors when written in vector form (equation on the left). The table (right) is taken from Newnham’s book. In vector-matrix form, the transformations are: $ # 1" ' + & ) - & # " 2) - & # " ) - 3 & ) = - & # " 4) - & # " 5) - & ) % # " - 6( , * 11 * 12 * 13 * 14 * 15 * 16 * 21 * 22 * 23 * 24 * 25 * 26 * 31 * 32 * 33 * 34 * 35 * 36 * 41 * 42 * 43 * 44 * 45 * 46 * 51 * 52 * 53 * 54 * 55 * 56 * 61 * 62 * 63 * 64 * 65 * 66 . $ # ' 1 0 & ) 0 & # 2) 0 & # ) 3 0 & ) 0 & # 4) 0 & # 5) 0 & ) / % # 6( ! " # i = $ ij# j %1 # i = $ ij # " j %1T & " i = $ ij & j T &i = $ ij& " j
Page 1 and 2: 1 Objective Linear Ferromagnets Non
Page 11 and 12: 11 Objective Linear Ferromagnets No
Page 17 and 18: 17 Effect of symmetry on stiffness
Page 39: 39 Objective Linear Ferromagnets No

Microstructure-Properties - Materials Science and Engineering

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