• Coupled systems mechanics
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• v.5 no.4
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• pp.329-340
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• 2016

The trigonal shape memory alloys (SMAs) have a great potential to be utilized as the applications with special purposes, such as actuators with high operation frequency. Most studies on the trigonal microstructures typically focus on the well-known classic herringbone pattern, but many other patterns are also possible, such as non-classic herringbone, toothbrush and checkerboard patterns. In the current work, a systematic procedure is developed to find all possible laminate twin microstructures by using geometrically linear compatibility theory. The procedure is verified by SEM images with the information of crystallographic axes of unitcells obtained by EBSD, showing good agreement. Many interesting trigonal R-phase patterns are found in the specimen. Then, their incompatibility are analyzed with nonlinear compatibility theory. The relationship between such incompatibility and the likelihood of occurrence of the microstructures is revealed. The current procedure is rapid, computationally efficient and sufficiently general to allow further extension to other crystal systems and materials.