Effects of structural and material length scales on stress-induced martensite macro-domain patterns in tube configurations. (English) Zbl 1167.74526
Summary: This paper studies the effects of structural and material length scales on the equilibrium domain patterns in thin-walled long tube configurations during stress-induced elastic phase transition under displacement-controlled quasi-static isothermal stretching. A nonconvex and nonlocal continuum model is developed and implemented into a finite element code to simulate the domain formation and evolution during the phase transition. The morphology and evolution of the macro-domains in different tube geometries are investigated by both analytical (energy analysis) and numerical (nonlocal finite element) methods. Energy minimization is used as the principle to explain the experimentally observed macroscopic domain patterns in a NiTi polycrystal tube. It is found that the domain pattern, as the minimizer of the system energy, is governed by the relative values of the material length scale \(g\), tube-wall thickness \(h\) and tube radius \(R\) through two nondimensional factors: \(h/R\) and \(g/R\). Physically, \(h/R\) and \(g/R\) serve as the weighting factors of bending energy and domain-wall energy over the membrane energy in the minimization of the total energy of the tube system. Theoretical predictions of the effects of these length scales on the domain pattern are quantified and confirmed by the computational parametric study. They all agree qualitatively well with the available experimental observations.
MSC:
| 74N05 | Crystals in solids |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74G65 | Energy minimization in equilibrium problems in solid mechanics |
Keywords:
macroscopic deformation patterns; thin-walled tube configuration; structural and material length scales; domain-wall energy; membrane energy and bending energy; nonconvex and nonlocal elasticityReferences:
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