Scientific blog
January 
Saturday, 2 February, 2013, 10:10
Posted by Piotr Drzymala
We considered possible slip and twinning systems for any desired orientation of the crystal. Depending on the adopted strain tensor, which can describe simple compression or rolling, different values are obtained for the selected orientation of the stresses described by Euler angles. Through the rotation of vectors of the unit cell is an altered relationship between the angular direction on the stress and possible slip systems. In the first step a rate of deformation (macroscopic) is assumed, an equivalent strain tensoris calculated using the approach full constrains (FC) initial deformation for each orientation, represented as a cube with a side equal to 10 °. Five elements considered combinations of 7-elements selected collections slip, the choice was made by taking into account the largest shear stress for slip data in relation to the adopted apriori critical shear stress. Then solved (nk) = (7 5) = 21 systems of linear equations and five function minimized the sum of the products of the critical shear stress and deformation modules for data of slip systems. With so selected strains five nonlinear equations were solved amount of an unknown scalar product of the stress tensor and tensor Schmidt (hence the notation Lequeu), raised to the power of n <= 20 By minimizing the corresponding function is possible to approximate the solution of these equations and calculating the stress tensor and the setting of Secant visco-plastic modules susceptibility grains. The problem arose when calculating the inverse matrix of these modules due to the generally poor conditioning of the matrix, so their inverse matrices can contain large numerical errors.
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