Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys

Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model

The fracture of bulk metallic glasses

It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

Advances in strength theories for materials under complex stress state in the 20th Century

http://parallel.bas.bg/~ppopov/publications/journal/popov.MECMAT.2006.pdf

Shape memory alloys, Part II: Modeling of polycrystals

Combined tension and torsion experiments with thin wall specimens of Cu-Al-Zn-Mn polycrystalline shape memory alloy (SMA) were performed at temperatureT =A
 f
 + 25 K. The general stress-strain behaviors due to the thermoelastic martensitic transformation, induced by a combination of external forces of axial load and torque, were studied. It is shown that the progress of martensitic transformation (MT) at general stress conditions can be well considered as triggered and controlled by the supplied mechanical work (a kind of equivalent stress) in the first approximation. Pseudoelastic strains in proportional as well as nonproportional combined tension-torsion loadings were found fully reversible, provided that uniaxial strains were reversible. The axial strain can be controlled by the change of torque andvice versa due to the coupling among tension and torsion under stress, not only in forward transformation, but also in reverse transformation on unloading. The pseudoelastic strains of SMA polycrystal are path dependent but well reproducible along the same stress path. The evolution of macroscopic strain response of SMA polycrystal, subjected to the nonproportional pseudoelastic loading cycles with imposed stress path, was systematically investigated. The results bring qualitatively new information about the progress of the MT in SMA polycrystal, subjected to the general variations of external stress.

Experimental Study on the Thermoelastic Martensitic Transformation in Shape Memory Alloy Polycrystal Induced by Combined External Forces

Elastic-plastic finite element polycrystal model

Thermomechanical behavior of shape memory alloy under complex loading conditions

Elastic–viscoplastic behavior of plain-woven GFRP laminates: Homogenization using a reduced domain of analysis

This paper introduces a phenomenological algorithm for simulation of rate independent hysteretic responses of shape memory alloys (SMAs) in cyclic uniaxial thermomechanical loads. The algorithm is proposed in a compact differential form that uses only seven well-defined material parameters and is adjustable to a particular alloy by fitting a single experimental pseudoelastic loop. It has been developed as a tool for predictions of history dependent uniaxial σ-e-T responses of SMA elements to be embedded into the smart structures and composites. Simulated model responses to a variety of thermomechanical loading paths, including partial internal loop behaviours, are demonstrated. The computer program with a numerically implemented algorithm is available on the Internet.

Masataka Tokuda

Papers

Experimental Study on the Thermoelastic Martensitic Transformation in Shape Memory Alloy Polycrystal Induced by Combined External Forces

Elastic-plastic finite element polycrystal model

Thermomechanical behavior of shape memory alloy under complex loading conditions

Elastic–viscoplastic behavior of plain-woven GFRP laminates: Homogenization using a reduced domain of analysis

An algorithm for prediction of the hysteretic responses of shape memory alloys