### Abstract

A crystal-mechanics-based constitutive model for polycrystalline shape-memory materials has been developed. The model has been implemented in a finite-element program. In our finite-element model of a polycrystal, each element represents one crystal, and a set of crystal orientations which approximate the initial crystallographic texture of the shape-memory alloy are assigned to the elements. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate. Pseudoelasticity experiments in tension, compression, and shear have been performed on an initially textured polycrystalline Ti-Ni alloy. In order to determine the material parameters for Ti-Ni, the stress-strain results from a finite-element calculation of a polycrystalline aggregate subjected to simple tension have been fit to corresponding results obtained from the physical experiment. Using the material parameters so determined, the predicted pseudoelastic stress-strain curves for simple compression and thin-walled tubular torsion of the initially textured Ti-Ni are shown to be in good accord with the corresponding experiments. Our calculations also show that the crystallographic texture is the main cause for the observed tension-compression asymmetry in the pseudoelastic response of Ti-Ni. The predictive capability of the model for the variation of the pseudoelastic behavior with temperature is shown by comparing the calculated stress-strain response from the model against results from experiments of Shaw and Kyriakides (J. Mech. Phys. Solids 43 (1995) 1243) on Ti-Ni wires at a few different temperatures. By performing numerical experiments, we show that our model is able to qualitatively capture the shape-memory effect by transformation. We have also evaluated the applicability of a simple Taylor-type model for shape-memory materials. Our calculations show that the Taylor model predicts the macroscopic pseudoelastic stress-strain curves in simple tension, simple compression and tubular torsion fairly well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.

Original language | English |
---|---|

Pages (from-to) | 709-737 |

Number of pages | 29 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 49 |

Issue number | 4 |

Publication status | Published - Apr 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- A. Phase transformation
- B. Constitutive behavior
- B. Crystal plasticity
- C. Finite elements
- C. Mechanical testing

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of the Mechanics and Physics of Solids*,

*49*(4), 709-737.

**Polycrystalline shape-memory materials : Effect of crystallographic texture.** / G. Thamburaja, T Prakash; Anand, L.

Research output: Contribution to journal › Article

*Journal of the Mechanics and Physics of Solids*, vol. 49, no. 4, pp. 709-737.

}

TY - JOUR

T1 - Polycrystalline shape-memory materials

T2 - Effect of crystallographic texture

AU - G. Thamburaja, T Prakash

AU - Anand, L.

PY - 2001/4

Y1 - 2001/4

N2 - A crystal-mechanics-based constitutive model for polycrystalline shape-memory materials has been developed. The model has been implemented in a finite-element program. In our finite-element model of a polycrystal, each element represents one crystal, and a set of crystal orientations which approximate the initial crystallographic texture of the shape-memory alloy are assigned to the elements. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate. Pseudoelasticity experiments in tension, compression, and shear have been performed on an initially textured polycrystalline Ti-Ni alloy. In order to determine the material parameters for Ti-Ni, the stress-strain results from a finite-element calculation of a polycrystalline aggregate subjected to simple tension have been fit to corresponding results obtained from the physical experiment. Using the material parameters so determined, the predicted pseudoelastic stress-strain curves for simple compression and thin-walled tubular torsion of the initially textured Ti-Ni are shown to be in good accord with the corresponding experiments. Our calculations also show that the crystallographic texture is the main cause for the observed tension-compression asymmetry in the pseudoelastic response of Ti-Ni. The predictive capability of the model for the variation of the pseudoelastic behavior with temperature is shown by comparing the calculated stress-strain response from the model against results from experiments of Shaw and Kyriakides (J. Mech. Phys. Solids 43 (1995) 1243) on Ti-Ni wires at a few different temperatures. By performing numerical experiments, we show that our model is able to qualitatively capture the shape-memory effect by transformation. We have also evaluated the applicability of a simple Taylor-type model for shape-memory materials. Our calculations show that the Taylor model predicts the macroscopic pseudoelastic stress-strain curves in simple tension, simple compression and tubular torsion fairly well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.

AB - A crystal-mechanics-based constitutive model for polycrystalline shape-memory materials has been developed. The model has been implemented in a finite-element program. In our finite-element model of a polycrystal, each element represents one crystal, and a set of crystal orientations which approximate the initial crystallographic texture of the shape-memory alloy are assigned to the elements. The macroscopic stress-strain responses are calculated as volume averages over the entire aggregate. Pseudoelasticity experiments in tension, compression, and shear have been performed on an initially textured polycrystalline Ti-Ni alloy. In order to determine the material parameters for Ti-Ni, the stress-strain results from a finite-element calculation of a polycrystalline aggregate subjected to simple tension have been fit to corresponding results obtained from the physical experiment. Using the material parameters so determined, the predicted pseudoelastic stress-strain curves for simple compression and thin-walled tubular torsion of the initially textured Ti-Ni are shown to be in good accord with the corresponding experiments. Our calculations also show that the crystallographic texture is the main cause for the observed tension-compression asymmetry in the pseudoelastic response of Ti-Ni. The predictive capability of the model for the variation of the pseudoelastic behavior with temperature is shown by comparing the calculated stress-strain response from the model against results from experiments of Shaw and Kyriakides (J. Mech. Phys. Solids 43 (1995) 1243) on Ti-Ni wires at a few different temperatures. By performing numerical experiments, we show that our model is able to qualitatively capture the shape-memory effect by transformation. We have also evaluated the applicability of a simple Taylor-type model for shape-memory materials. Our calculations show that the Taylor model predicts the macroscopic pseudoelastic stress-strain curves in simple tension, simple compression and tubular torsion fairly well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.

KW - A. Phase transformation

KW - B. Constitutive behavior

KW - B. Crystal plasticity

KW - C. Finite elements

KW - C. Mechanical testing

UR - http://www.scopus.com/inward/record.url?scp=0000857947&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000857947&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000857947

VL - 49

SP - 709

EP - 737

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 4

ER -