Computing Thermoelastic Stress

Setting parameters and starting the computation of stress

Once temperature has been computed, CrysMAS can compute the von Mises stress and other stress coefficients. Prerequisite is that stress constants have been specified for the material of the sample.

The following tutorial task exemplifies the procedure:

The stress-strain relationship for a Thermoelastic anisotropic solid body in cylindrical coordinates and for the axisymmetrical case is defined as follows:

Stress-strain relationship 

Figure 69. Stress-strain relationship

  1. α = Thermal expansion coefficient

  2. T ref = Reference temperature for the relaxed body

  3. ε rr, ε φ φ , ε zz, ε rz = Strain components

  4. ¯C ij = Elastic material constants in the Voigt notation. Their dependence on the crystallographic orientation with respect to the cylindrical axis, i.e. the growth direction <111> or <100> and how to respect anisotropic effects is described in more details in the paper of J. C. Lambropoulos, see Bibliography .

To take into account the anisotropy of the material the elastic constants ¯Cij will be calculated as given by Lambropoulos.

Definition of the elastic constants for anisotropic materials given by Lambropoulos 

Figure 70. Definition of the elastic constants for anisotropic materials given by Lambropoulos

An important scalar for the discussion of stress in solid bodies, especially for crystal growth, is the von Mises Stress σ Mises, which is computed from the distinct stress components. In cylindrical coordinates it is defined as:

Definition of the von Mises stress 

Figure 71. Definition of the von Mises stress

Further details can be found in M. Kurz, Development of CrysMAS, 1998, see Bibliography .