On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

“…Analytical models and their applications presented in [20][21][22][23] describes the disturbance of an existing applied-stress field to be uniform in the infinity in contrast to the Mizutani's and Ceniga's analytical cell models [17,37]. The cell models resulting from a differential approach describe a thermal-stress field not to exist in the absence of the inclusion.…”

Section: Introductionmentioning

confidence: 97%

“…Analytical models of elastic stresses, including the thermal stresses, in an inclusion (=precipitate)-matrix system are usually determined using Eshelby's and Mori-Tanaka concepts [20][21][22][23]. The concepts result from mathematical techniques belonging more or less to Theoretical Physics represented by an integration approach to use the Green's functions, ordinary Newtonian potential and biharmonic potential [20].…”

Section: Introductionmentioning

confidence: 99%

Analytical Models of Thermal-Stress Induced Phenomena in Isotropic Multi-Particle-Matrix System

Ceniga

2008

Journal of Thermal Stresses

View full text Add to dashboard Cite

The paper presents four topics dealing with phenomena induced by elastic thermal stresses acting in an isotropic multi-particle-matrix system to represent a model system applicable to real multi-phase materials of a precipitation-matrix type. The isotropic multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix to be imaginarily divided into cubic cells containing a central spherical particle. Formulae for the thermal stresses to be investigated within the cubic cell represents functions of the particle volume fraction v and the particle radius R. The thermal stresses originate during a cooling process as a consequence of the difference m − p in the thermal expansion coefficients m and p of the matrix and the particle, respectively. Additionally, such temperature range is considered within which the multi-particle-matrix system exhibits elastic deformations regarding the yield stress and the particle-matrix boundary adhesion strength. Analytical fracture mechanics to represent the first topic of this paper results from the determination of a curve integral of the thermal-stress induced elastic energy density. The curve elastic energy density results in the determination of the critical particle radii R pc and R mc as reasons of the crack initiation in the spherical particle and the matrix for m − p < 0 and m − p > 0, respectively. Consequently, the crack propagation to follow the crack initiation is a consequence of the particle radius R > R qc (q = p m). Finally, a shape of the crack in a plane perpendicular to the direction of the crack propagation in the particle (q = p) and the matrix (q = p) is described by the function f q related to the ideal-brittle components. With regard to the crack initiation, the analytical determination of the radius R qc is considered for any multi-phase materials of a precipitation-matrix type. With regard to the crack propagation, the analytical determination of the function f q along with an analysis concerning the crack dimension and directions of the crack propagation is considered for ceramic multi-phase materials which are generally assumed to be idealbrittle. The thermal stresses induce resistance against compressive or tensile mechanical 862 ANALYTICAL MODELS OF THERMAL-STRESS INDUCED PHENOMENA 863 loading for m − p > 0 or m − p < 0, respectively. The analytical determination of the resistance results from the elastic energy gradient to represent the second topic of this paper. Derived by two equivalent mathematical techniques, the gradient within the cubic cell is defined as a surface integral of the thermal-stress induced elastic energy density. Consequently the 'surface' elastic energy density results in the analytical determination of the system strengthening to represent the third topic of this paper. Representing the fourth topic of this paper, an analytical model of stresses originating in isotropic crystalline lattices are derived. The stresses in the lattices are a consequence of the presence of a central substit...

show abstract

“…Three main approaches to model transformation toughening have been used. One is an Eshelby-type approach (e. g. McMeeking and Evans, 1982;Yang and Zhu, 1998;Yi and Gao, 2000;Yi et al, 2001;Li and Yang, 2002;Fischer and Boehm, 2005). Another is the finite element method (FEM), (e.g., Zeng et al, 1999Zeng et al, , 2004Vena et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Fundamental formulation for transformation toughening

2010

International Journal of Solids and Structures

View full text Add to dashboard Cite

a b s t r a c tIn this paper, the transformation toughening problem is addressed in the framework of plane strain. The fundamental solution for a transformed strain nucleus located in an infinite plane is derived first. With this solution, the transformed inclusion problems are formulated by a Green's function method, and the interaction of a crack tip with a single transformation source is found. On the basis of this solution, the fundamental formulations for toughening arising from martensitic and ferroelastic transformation are formulated also using the Green's function method. Finally, some examples are provided to demonstrate the validity and relevance of the fundamental formulations proposed in the paper.

show abstract

On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

Cited by 22 publications

References 19 publications

Size effects on the martensitic phase transformation of NiTi nanograins

Size effects on the martensitic phase transformation of NiTi nanograins

Analytical Models of Thermal-Stress Induced Phenomena in Isotropic Multi-Particle-Matrix System

Fundamental formulation for transformation toughening

Contact Info

Product

Resources

About