The bain strain, lattice correspondences, and deformations related to martensitic transformations

Bowles, J.S; Wayman, C.M.

doi:10.1007/bf02642442

Cited by 69 publications

(29 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The change in crystal structure is achieved by a homogeneous deformation known as the Bain strain B, which although proposed in 1924 [11], has stood the test of time as the pure deformation which achieves the desired change with the smallest strains [12]. The diagonal terms of B are given by a α ′ /a γ , √ 2a α ′ /a γ and √ 2a α ′ /a γ , whereas the remaining terms are zero when B is defined relative to the principal axes.…”

Section: Crystallographic Theory: Orientation Relationshipsmentioning

confidence: 99%

Calculation of crystallographic texture due to displacive transformations

Bhadeshia

Abreu

Kundu

2008

International Journal of Materials Research

View full text Add to dashboard Cite

Displacive transformations involve the disciplined motion of atoms. As a result, there are clearly defined relationships between all aspects of the parent and product lattices. The theory for this is well established but has not been exploited in the calculation of transformation textures. This paper is a critical assessment of the methods for the estimation of crystallographic textures during the displacive transformation of austenite into martensite, bainite or Widmanstätten ferrite in steels. The discussion is limited to the case where austenite is not in a plastically deformed state prior to its transformation.

show abstract

Section: Crystallographic Theory: Orientation Relationshipsmentioning

confidence: 99%

Calculation of crystallographic texture due to displacive transformations

Bhadeshia

Abreu

Kundu

2008

International Journal of Materials Research

View full text Add to dashboard Cite

show abstract

“…Inside a single grain, the martensitic transformation is mainly based on the following assumptions: The lattice vectors of austenite and martensite possess mutual orientation relationships that depend on the crystallographic nature of the alloy [45]. Martensitic transformation produces predominantly a shear strain along well-defined planes, which is crystallographically reversible [46].…”

Section: Numerical Simulations Based On the Micromechanical Model Brimentioning

confidence: 99%

Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Chatziathanasiou

Chemisky

Meraghni

et al. 2015

Shap. Mem. Superelasticity

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract In the present study, a new transformation criterion that includes the effect of tension-compression asymmetry and texture-induced anisotropy is proposed and combined with a thermodynamical model to describe the thermomechanical behavior of polycrystalline shape memory alloys. An altered Prager criterion has been developed, introducing a general transformation of the axes in the stress space. A convexity analysis of such criterion is included along with an identification strategy aimed at extracting the model parameters related to tension-compression asymmetry and anisotropy. These are identified from a numerical simulation of an SMA polycrystal, using a self-consistent micromechanical model previously developed by Patoor et al. (J Phys IV 6(C1):277-292, 1996) for several loading cases on isotropic, rolled, and drawn textures. Transformation surfaces in the stress and transformation strain spaces are obtained and compared with those predicted by the micromechanical model. The good agreement obtained between the macroscopic and the microscopic polycrystalline simulations states that the proposed criterion and transformation strain evolution equation can capture phenomenologically the effects of texture on anisotropy and asymmetry in SMAs.

show abstract

“…The change in crystal structure is achieved by a homogeneous deformation known as the Bain strain B, which although proposed in 1924 [5] has stood the test of time as the pure deformation which achieves the desired change with the smallest strains [6]. The diagonal terms of the 3×3 matrix B are given by a α' /a γ , √2a α' /a γ and √2a α' /a γ , whereas the remaining terms are zero when B is defined relative to the principal axes.…”

Section: The Bain Strainmentioning

confidence: 99%

Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Bhadeshia

Kundu

Abreu

2009

Microstructure and Texture in Steels

View full text Add to dashboard Cite

This paper is an introduction to the mathematical estimation of the crystallographic texture and microstructure resulting from the displacive transformation of austenite in steels, under the influence of an externally applied system of stresses. It begins with an introduction to the problem, a description of the phenomenological theory of martensite crystallography, and the application of this theory along with a variant selection criterion to determine the texture due to solid-state, displacive transformation. It is demonstrated that there remain difficulties which make a complete closure between theory and experiment unlikely. Progress is needed in relating the chemical and mechanical driving forces for phase transformation to the evolution of overall volume fractions of different crystallographic variants.

show abstract

The bain strain, lattice correspondences, and deformations related to martensitic transformations

Cited by 69 publications

References 18 publications

Calculation of crystallographic texture due to displacive transformations

Calculation of crystallographic texture due to displacive transformations

Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

Mathematics of Crystallographic Texture in Martensitic and Related Transformations

Contact Info

Product

Resources

About