Microplane modeling of martensite reorientation in shape memory alloys (1393/3/12) |
Two main parts of the inelastic strain in deformations of shape memory alloys are transformation- and reorientation- induced strains. In some constitutive models, a distinct term is assigned for reorientation of the product p hase according to variations of loading di-rection. In this work, a model is proposed in which there is not any separate expression for modeling the reorientation part. This model is based on Microplane theory and is inherently able to account for reorientation strains in multiaxial loadings. Stress-strain diagrams for uniaxial tension at different temperatures are simulated in order to compare the present ap-proach and another one in which the reorientation strain is separately stated. A very good agreement is seen indicating the capability of Microplane theory to predict the main charac-teristics of the behaviors of shape memory alloys. |
hape Memory Effect Behavior of NiTi Torque Tubes in Torsion (1393/3/12) |
n order to simulate the torsional behavior of NiTi torque tubes, two different 3D thermo-mechanical constitutive models are utilized. Firstly, an available incremental constitutive model is used in which a return mapping algorithm is implemented to numerically calculate the strains for any applied stresses. Secondly, Microplane theory is employed based on which 1D constitutive laws are considered for associated stress and strain components on any arbitrary plane passing through a material point followed by a homogenization process to generalize the 1D equations to a 3D macroscopic model. Both of the constitutive models are implemented in ABAQUS by developing UMAT. |
Microplane modeling of shape memory alloys in an alternative formulation (1393/3/12) |
In this work, a volumetric-deviatoric split in microplane formulation is considered for modeling of shape memory alloys. In the microplane theory, macroscopic stress tensor is projected into the microplane stresses that are decomposed to either Volumetric-Deviatoric-Tangential (V-D-T) split or Volumetric-Deviatoric (V-D) split. Then 1D constitutive laws are defined between associated microplane stress and microplane strain on any plane. The homogenization process is used according to which macroscopic strain tensor is obtained by integration strains on all orientations at a point. The constitutive formulation based on V-D-T split uses the principle of complementary virtual work (PCVW) to derive macroscopic strain tensor. It is shown that in the microplane models based on V-D-T split- which are derived from the PCVW |
Modify the Phase-Diagram to enter Effects of Loading History on Transformation Surface in Shape Memory Alloys (1393/3/12) |
In most of the existing SMA constitutive models, it is assumed that transformation starts when a thermodynamic driving force reaches a specified amount regardless of loading history. In this work, a phenomenological approach is used to develop an enhanced one-dimensional constitutive model in which loading history is directly considered as one of the main parameters affecting the transformation start conditions. To generalize the model to three-dimensional cases, a microplane formulation based on volumetric-deviatoric is employed. A free energy potential is defined at the microplane level, integratied over all orientations at a material point to provide the macroscopic free energy. |