Effect of Precipitate Morphology on the Gradient-Dependent Behaviour of Two-Phase Single Crystals

1999 ◽  
Vol 578 ◽  
Author(s):  
E. P. Busso ◽  
F. T. Meissonnier ◽  
N. P. O'Dowd
Keyword(s):  
Volume Fraction ◽  
Large Strain ◽  
Deformation Gradient ◽  
Slip Rate ◽  
Strengthening Mechanism ◽  
Precipitate Size ◽  
Two Phase ◽  
Precipitate Morphology ◽  
Fully Implicit ◽  
Rate Dependent

AbstractIn this work a recently proposed gradient and rate-dependent crystallographic formulation is used to investigate the macroscopic behaviour of a precipitated single crystal. It relies on strain gradient concepts to account for the additional strengthening mechanism caused by presence of interfacial and geometrically necessary dislocations (GNDs). The total slip resistance is assumed to be due to a mixed population of mobile and sessile forest obstacles arising from both statistically stored dislocations (SSDs) and GNDs. The non-local crystallographic theory is implemented numerically into the finite element method. It requires the calculation of the slip rate gradients at the element level to determine the evolutionary behaviour of the GND densities, and a fully implicit numerical algorithm within a large strain kinematics framework and non-isothermal conditions. The effects of the relevant microstructural features (precipitate size, morphology and volume fraction) and deformation gradient-related length scales on the macroscopic behaviour is investigated and compared with experimental results.

A two-phase thermomechanical theory for granular suspensions

2016 ◽  
Vol 808 ◽  
pp. 410-440 ◽  
Author(s):  
D. Monsorno ◽  
C. Varsakelis ◽  
M. V. Papalexandris
Keyword(s):  
Volume Fraction ◽  
Constant Density ◽  
Two Phase ◽  
Important Special Case ◽  
Carrier Fluid ◽  
Thermomechanical Theory ◽  
Rate Dependent ◽  
Granular Suspensions ◽  
Developed Pressure ◽  
Viscous Stresses

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.

Fully Coupled Two-Phase Composite Model for Microstructure Evolution during Non-Proportional Severe Plastic Deformation

2018 ◽  
Vol 385 ◽  
pp. 234-240 ◽  
Author(s):  
Alexey Shutov
Keyword(s):  
Plastic Deformation ◽  
Severe Plastic Deformation ◽  
Large Strain ◽  
Deformation Gradient ◽  
Composite Model ◽  
Loading Path ◽  
Extended Model ◽  
Two Phase ◽  
Dislocation Cells ◽  
Fully Coupled

A fully coupled micro-macro interaction model is proposed for the grain refinement caused by severe plastic deformation of cell-forming metallic materials. The model is a generalization of a previously proposed two-phase composite model suggested for the evolution of dislocation populations corresponding to the interior of the dislocation cells and dislocation cell walls. Just as within the original framework, the evolution of the material microstructure depends on the applied hydrostatic pressure, strain rate, and the loading path. Backstresses are used to define a measure of the strain path change. Thereby, the model can describe the experimentally observed dissolution of dislocation cells and the reduction of dislocation densities occurring shortly after load path changes. The large strain kinematics is accounted for in a geometrically exact manner using the nested split of the deformation gradient tensor, proposed by Lion. Within the extended model, the macroscopic strength of the material depends on the microstructural parameters. In that sense, the new model is fully coupled. It is thermodynamically consistent, objective, and w-invariant under isochoric changes of the reference configuration. A physical interpretation is provided for the nested multiplicative split in terms of the two-phase microstructure composite model.

Morphology, Distribution and Identification of Micro-Constituents Along Grain Boundaries in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 176-177
Author(s):  
D. E. Fornwalt ◽  
A. R. Geary ◽  
B. H. Kear
Keyword(s):  
Electron Microscope ◽  
Grain Boundaries ◽  
Volume Fraction ◽  
Rupture Life ◽  
Stress Rupture ◽  
High Volume ◽  
Precipitate Morphology ◽  
Stress Rupture Life ◽  
Nickel Base ◽  
Scanning Electron

A systematic study has been made of the effects of various heat treatments on the microstructures of several experimental high volume fraction γ’ precipitation hardened nickel-base alloys, after doping with ∼2 w/o Hf so as to improve the stress rupture life and ductility. The most significant microstructural chan§e brought about by prolonged aging at temperatures in the range 1600°-1900°F was the decoration of grain boundaries with precipitate particles.Precipitation along the grain boundaries was first detected by optical microscopy, but it was necessary to use the scanning electron microscope to reveal the details of the precipitate morphology. Figure 1(a) shows the grain boundary precipitates in relief, after partial dissolution of the surrounding γ + γ’ matrix.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

scholarly journals Fully Implicit Stress Update Algorithm for Distortion−Based Anisotropic Hardening with Cross−Loading Effect: Comparative Algorithmic Study and Application to Large−Size Forming Problem

2021 ◽  
Vol 11 (12) ◽  
pp. 5509
Author(s):  
Hongjin Choi ◽  
Seonghwan Choi ◽  
Soo-Chang Kang ◽  
Myoung-Gyu Lee
Keyword(s):  
Predictive Accuracy ◽  
Large Strain ◽  
Implicit Scheme ◽  
Loading Path ◽  
Plastic State ◽  
Loading Conditions ◽  
Integration Algorithm ◽  
Implicit Algorithm ◽  
Fully Implicit ◽  
Large Size

A fully implicit stress integration algorithm is developed for the distortional hardening model, namely the e−HAH model, capable of simulating cross−hardening/softening under orthogonal loading path changes. The implicit algorithm solves a complete set of residuals as nonlinear functions of stress, a microstructure deviator, and plastic state variables of the constitutive model, and provides a consistent tangent modulus. The number of residuals is set to be 20 or 14 for the continuum or shell elements, respectively. Comprehensive comparison programs are presented regarding the predictive accuracy and stability with different numerical algorithms, strain increments, material properties, and loading conditions. The flow stress and r−value evolutions under reverse/cross−loading conditions prove that the algorithm is robust and accurate, even with large strain increments. By contrast, the cutting−plane method and partially implicit Euler backward method, which are characterized by a reduced number of residuals, result in unstable responses under abrupt loading path changes. Finally, the algorithm is implemented into the finite element modeling of large−size, S−rail forming and the springback for two automotive steel sheets, which is often solved by a hybrid dynamic explicit–implicit scheme. The fully implicit algorithm performs well for the whole simulation with the solely static implicit scheme.

Strengthening mechanism in two-phase FeCoCrNiMnAl high entropy alloy coating

2020 ◽  
Vol 530 ◽  
pp. 147205 ◽  
Author(s):  
Yan Cui ◽  
Junqi Shen ◽  
Sunusi Marwana Manladan ◽  
Keping Geng ◽  
Shengsun Hu
Keyword(s):  
Alloy Coating ◽  
Strengthening Mechanism ◽  
High Entropy Alloy ◽  
Two Phase ◽  
High Entropy

scholarly journals Nonlinear multiscale simulation of instabilities due to growth of an elastic film on a microstructured substrate

2020 ◽  
Vol 90 (11) ◽  
pp. 2397-2412
Author(s):  
Iman Valizadeh ◽  
Oliver Weeger
Keyword(s):  
Deformation Gradient ◽  
Multiscale Simulation ◽  
Numerical Results ◽  
Unit Cell ◽  
Homogeneous Material ◽  
Two Phase ◽  
Biological Phenomena ◽  
Elastic Film ◽  
Living Tissues ◽  
Analytical Approaches

Abstract The objective of this contribution is the numerical investigation of growth-induced instabilities of an elastic film on a microstructured soft substrate. A nonlinear multiscale simulation framework is developed based on the FE2 method, and numerical results are compared against simplified analytical approaches, which are also derived. Living tissues like brain, skin, and airways are often bilayered structures, consisting of a growing film on a substrate. Their modeling is of particular interest in understanding biological phenomena such as brain development and dysfunction. While in similar studies the substrate is assumed as a homogeneous material, this contribution considers the heterogeneity of the substrate and studies the effect of microstructure on the instabilities of a growing film. The computational approach is based on the mechanical modeling of finite deformation growth using a multiplicative decomposition of the deformation gradient into elastic and growth parts. Within the nonlinear, concurrent multiscale finite element framework, on the macroscale a nonlinear eigenvalue analysis is utilized to capture the occurrence of instabilities and corresponding folding patterns. The microstructure of the substrate is considered within the large deformation regime, and various unit cell topologies and parameters are studied to investigate the influence of the microstructure of the substrate on the macroscopic instabilities. Furthermore, an analytical approach is developed based on Airy’s stress function and Hashin–Shtrikman bounds. The wavelengths and critical growth factors from the analytical solution are compared with numerical results. In addition, the folding patterns are examined for two-phase microstructures and the influence of the parameters of the unit cell on the folding pattern is studied.

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