The effect of oxidation on the crack growth resistance of titanium alloys is inves-tigated in thi... more The effect of oxidation on the crack growth resistance of titanium alloys is inves-tigated in this work. The oxidation process is modeled by modifying the Fickian diffusion problem in order to account for the chemical reaction (phase change) in the material. Two different variants of a fixed grid finite element method for nu-merical simulation of oxidation are used. The first approach taken is to locate the oxidation front and split the domain into metal and oxide subdomains. The second approach is based on reformulating the diffusion equations in both the oxide and metal, resulting in a single non-linear equation for the whole domain. After the oxidation process is modeled, the mechanical analysis is performed. In the finite element formulation of the mechanical problem, the influence of oxidation is intro-duced by the change of the elastic constants and the oxidation-induced eigenstrain. The applicability of both the oxidation and mechanical models is tested by simu-lating oxidati...
A model for the macroscopic mechanical behavior of porous shape memory alloys (SMAs) is presented... more A model for the macroscopic mechanical behavior of porous shape memory alloys (SMAs) is presented in this work. The derivation of the model is presented for the general case of a composite with phases undergoing rate-independent inelastic de-formations. Micromechanical averaging techniques are used to establish the effective elastic and inelastic behavior based on information about the mechanical response of the individual phases and shape and volume fraction of the inhomogeneities. An explicit expression for the effective tangent stiffness and an evolution equation for the effective inelastic strain are derived. The results for porous SMAs are obtained using a constitutive model with internal variables for dense SMAs and assuming zero stiffness for the inhomogeneities. A detailed study on the choice of the pore shape is also performed for a random distribution of pores. Finally, the numerical results are compared with experimental data for porous NiTi SMA processed from elemental p...
ABSTRACT This work focuses on establishing the properties -both static and dynamic - of porous SM... more ABSTRACT This work focuses on establishing the properties -both static and dynamic - of porous SMA materials, and their energy absorption capabilities. To accomplish this, micromechanics-based analysis of the overall behavior of SMAs is carried out in the present work. The porous SMA is modeled as a composite with a solid SMA matrix, which is in turn described by a constitutive model available in the literature, and elastic inclusions, which in the limit represent the voids in the porous material. The static macroscopic constitutive behavior of the material is established using both the Mori-Tanaka averaging method and the unit cell finite element method. The dynamic macroscopic constitutive behavior is described using the results obtained by the Mori-Tanaka averaging method.
This two-part paper reviews the latest developments in the modeling of shape memory alloys (SMAs)... more This two-part paper reviews the latest developments in the modeling of shape memory alloys (SMAs) constitutive behavior. The basic properties of SMAs are presented in Part I, including the shape memory effect, pseudoelasticity, as well as other properties such as the acquired and two-way shape memory effect, damping capacity and fatigue life. Part I focuses on the modeling at the single crystal level, dealing with the kinematics of the phase transformation and addressing different approaches for the development of the free energy and dissipation in order to derive constitutive equations. Some of the commonly used SMAs are reviewed by chemical composition and thermomechanical properties. The effects that different processing techniques have on their properties are also discussed. The kinematics associated with the martensitic phase transformation in a single crystal is described for a cubic to tetragonal and cubic to monoclinic transformation, and the lattice invariant strain by plastic slip is discussed. The transformation strain in a representative volume element (RVE) and its evolution are then defined. The free energy and dissipative potentials are derived together with the interaction energy for single variant and multivariant formulations in single crystals. A discussion on scale transitions to polycrystalline SMAs is finally presented. Part II deals with the polycrystalline modeling, considering both micromechanical approaches and phenomenological ones. It also includes considerations about the numerical implementation of SMA constitutive models and their integration into finite element codes.
The effect of oxidation on the crack growth resistance of titanium alloys is inves-tigated in thi... more The effect of oxidation on the crack growth resistance of titanium alloys is inves-tigated in this work. The oxidation process is modeled by modifying the Fickian diffusion problem in order to account for the chemical reaction (phase change) in the material. Two different variants of a fixed grid finite element method for nu-merical simulation of oxidation are used. The first approach taken is to locate the oxidation front and split the domain into metal and oxide subdomains. The second approach is based on reformulating the diffusion equations in both the oxide and metal, resulting in a single non-linear equation for the whole domain. After the oxidation process is modeled, the mechanical analysis is performed. In the finite element formulation of the mechanical problem, the influence of oxidation is intro-duced by the change of the elastic constants and the oxidation-induced eigenstrain. The applicability of both the oxidation and mechanical models is tested by simu-lating oxidati...
A model for the macroscopic mechanical behavior of porous shape memory alloys (SMAs) is presented... more A model for the macroscopic mechanical behavior of porous shape memory alloys (SMAs) is presented in this work. The derivation of the model is presented for the general case of a composite with phases undergoing rate-independent inelastic de-formations. Micromechanical averaging techniques are used to establish the effective elastic and inelastic behavior based on information about the mechanical response of the individual phases and shape and volume fraction of the inhomogeneities. An explicit expression for the effective tangent stiffness and an evolution equation for the effective inelastic strain are derived. The results for porous SMAs are obtained using a constitutive model with internal variables for dense SMAs and assuming zero stiffness for the inhomogeneities. A detailed study on the choice of the pore shape is also performed for a random distribution of pores. Finally, the numerical results are compared with experimental data for porous NiTi SMA processed from elemental p...
ABSTRACT This work focuses on establishing the properties -both static and dynamic - of porous SM... more ABSTRACT This work focuses on establishing the properties -both static and dynamic - of porous SMA materials, and their energy absorption capabilities. To accomplish this, micromechanics-based analysis of the overall behavior of SMAs is carried out in the present work. The porous SMA is modeled as a composite with a solid SMA matrix, which is in turn described by a constitutive model available in the literature, and elastic inclusions, which in the limit represent the voids in the porous material. The static macroscopic constitutive behavior of the material is established using both the Mori-Tanaka averaging method and the unit cell finite element method. The dynamic macroscopic constitutive behavior is described using the results obtained by the Mori-Tanaka averaging method.
This two-part paper reviews the latest developments in the modeling of shape memory alloys (SMAs)... more This two-part paper reviews the latest developments in the modeling of shape memory alloys (SMAs) constitutive behavior. The basic properties of SMAs are presented in Part I, including the shape memory effect, pseudoelasticity, as well as other properties such as the acquired and two-way shape memory effect, damping capacity and fatigue life. Part I focuses on the modeling at the single crystal level, dealing with the kinematics of the phase transformation and addressing different approaches for the development of the free energy and dissipation in order to derive constitutive equations. Some of the commonly used SMAs are reviewed by chemical composition and thermomechanical properties. The effects that different processing techniques have on their properties are also discussed. The kinematics associated with the martensitic phase transformation in a single crystal is described for a cubic to tetragonal and cubic to monoclinic transformation, and the lattice invariant strain by plastic slip is discussed. The transformation strain in a representative volume element (RVE) and its evolution are then defined. The free energy and dissipative potentials are derived together with the interaction energy for single variant and multivariant formulations in single crystals. A discussion on scale transitions to polycrystalline SMAs is finally presented. Part II deals with the polycrystalline modeling, considering both micromechanical approaches and phenomenological ones. It also includes considerations about the numerical implementation of SMA constitutive models and their integration into finite element codes.
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