By Edwin P. Alexander
Американские локомотивы 1900-1950
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The model uses the multilinear kinematic hardening model of ANSYS ®. It is composed of 3 adjoining lines starting in the origin. Steady state creep was modeled by equation 1, which must be implemented to ANSYS ® by little modifications in source code. E. = C 1 . [sinh(C3 · 0')] c 2 C4 ) . C4 correspond with A, 11m, ~/s, QIk. The parameter ho must be set to zero in order to skip all evolution equations, because SnPb37 Solder does not undergo cyclic hardening. The use of viscoplastic elements considers only elasticity and steady state creep, which leads to increasing errors, when deformations are little or strain rates are high.
2: Step relaxation response These strain increments will result into stress increments, with initial values LiS; , which subsequently relax with time (1-;1). (Note that ;0 and ;1 will be the same for an infinitesimal time increment). (M'j -~) (2) Here Cij represent so-called relaxation moduli functions. It should be noted that we could straightforwardly establish these functions by an experiment, only in case that the strains and initial strains are not continuously changing. :: ..................................
G ,....... ;,.... ;,... ,,) a'; ] ] , . , ~I ] ] , . -1 ] ] , . •.. *_................. -......... ---.. _-.. _- --... _-------------- ~::::~~:~~:~~ :~ ::::::::::::::: ------- ------- ........ .... •........ -. i[[(i(~,a(~,(t-~] for polymers being used in electronic packages is still a challenging task. 4. the stress level dependency is assumed to be less important, resulting into the relations for "linear state dependent viscoelasticity". 3 INCREMENTAL RELATIONSIDP If we want to implement the general constitutive relation (5) into a finite element program, we actually need an incremental stress-strain relation.