scholarly journals Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys

2020 ◽  
Vol 26 ◽  
pp. 115
Author(s):  
Sergio Conti ◽  
Johannes Diermeier ◽  
David Melching ◽  
Barbara Zwicknagl
Keyword(s):  
Linear Elasticity ◽  
Elastic Moduli ◽  
Scaling Laws ◽  
Volume Fraction ◽  
Upper And Lower Bounds ◽  
Minimal Energy ◽  
Logarithmic Corrections ◽  
Energy Scaling ◽  
Two Phases ◽  
Martensitic Variants

We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms of the problem parameters, which represent the shape of the nucleus, the quotient of the elastic moduli of the two phases, the surface energy constant, and the volume fraction of the two martensitic variants. We identify several different scaling regimes, which are distinguished either by the exponents in the parameters, or by logarithmic corrections, for which we have matching upper and lower bounds.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

Direct imaging of order-disorder and antiphase domain structures in Ti3Al intermetallic compound

1990 ◽  
Vol 48 (4) ◽  
pp. 480-481
Author(s):  
H. Q. Ye ◽  
T.S. Xie ◽  
D. Li
Keyword(s):  
Intermetallic Compound ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Antiphase Domain ◽  
Atomic Scale ◽  
Orientation Relationships ◽  
Domain Structures ◽  
Α Phase ◽  
Diffraction Patterns ◽  
Two Phases

The Ti3Al intermetallic compound has long been recognized as potentially useful structural materials. It offers attractive strength to weight and elastic modulus to weight ratios. Recent work has established that the addition of Nb to Ti3Al ductilized this compound. In this work the fundamental problem of this alloy, i.e. order-disorder and antiphase domain structures was investigated at the atomic scale.The Ti3Al+10at%Nb alloys used in this study were treated at 1060°C and then aged at 700°C for 2 hours. The specimens suitable for TEM were prepared by standard jet electrolytic-polishing technique. A JEM-200CX electron microscope with an interpretable resolution of about 0.25 nm was used for HREM.The [100] and [001] projections of the α2 phase were shown in Fig.l.The alloy obtained consist of at least two phases-α2(Ti3Al) and β0 structures. Moreover, a disorder α phase with small volume fraction was also observed. Fig.2 gives [100] and [001] diffraction patterns of the α2 phase. Since lattice parameters of the ordered α2 (a=0.579, c=0.466 nm) and disorder α phase (a0=0.294≈a/2, c0=0.468 nm) are almost the same, their diffraction patterns are difficult to be distinguished when they are overlapped with epitaxial orientation relationships.

Finite Element Model to Predict the Bioconversion Rate of Glucose to Fructose using Escherichia coli K12 for Sugar Production from Date

2015 ◽  
Vol 11 (1) ◽  
pp. 105-113 ◽  
Author(s):  
Maher Trigui ◽  
Karim Gabsi ◽  
Walid Zneti ◽  
Suzelle Barrington ◽  
Ahmed Noureddine Helal
Keyword(s):  
Escherichia Coli ◽  
Induction Time ◽  
Volume Fraction ◽  
Element Model ◽  
Initial Concentration ◽  
Computational Fluids Dynamics ◽  
Date Syrup ◽  
Computational Fluids ◽  
Two Phases ◽  
Inoculum Volume

Abstract In this study, Bioconversion process of glucose to fructose from date syrup using Escherichia coli K12 is modeled using a commercial computational fluids dynamics (CFD) code fluent FLUENT 6.3.23 [8] which we implemented a user-defined functions (UDF) to simulate the interrelationships at play between various phases. A two phases CFD model was developed using an Eulerian – Eulerian approach to calculate the fructose volume fraction produced during time. The bioconversion process was studied as function of three initial concentration of glucose (0.14, 0.242 and 0.463gL–1), three induction time (60, 120 and 180 mn) and three inoculum volume (100, 120 and 150mL). The numerical results are compared with experimental data for bioconversion rate and show good agreement (R2= 0.894). The optimal condition of diffusion was obtained by applying an initial concentration of glucose less than 0.2gL–1 and induction time great than 100 minutes.

Effect of Ferrite Volume Fraction on Mechanical Properties of X80 Pipeline Steel

2014 ◽  
Vol 989-994 ◽  
pp. 212-215
Author(s):  
J. Liu ◽  
G. Zhu ◽  
W. Mao
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Work Hardening ◽  
Single Phase ◽  
Volume Fraction ◽  
Pipeline Steel ◽  
X80 Pipeline Steel ◽  
Hardening Behavior ◽  
Two Phases ◽  
Better Than

The effect of volume fraction of ferrite on the mechanical properties including strength, plasticity and wok hardening was systematically investigated in X80 pipeline steel in order to improve the plasticity. The microstructures with different volume fraction of ferrite and bainite were obtained by heat-treatment processing and the mechanical properties were tested. The work hardening behavior was analyzed by C-J method. The results show that the small amount of ferrite could effectively improve the plasticity. The work hardening ability and the ratio of yield/tensile strength with two phases of ferrite/bainite would be obviously better than that with single phase of bainite. The improvement of plasticity could be attributed to the ferrite in which more plastic deformation was afforded.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

Transformation Textures in Unstable Austenitic Steel

2002 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
R. Kubler ◽  
M. Berveiller ◽  
M. Cherkaoui ◽  
K. Inal
Keyword(s):  
Martensitic Transformation ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Slip Rate ◽  
Transformation Strain ◽  
Dislocation Motion ◽  
Lattice Spin ◽  
Two Phases ◽  
The One ◽  
Elastic Plastic Materials

During the martensitic transformation in elastic-plastic materials, the local transformation strain as well as the plastic flow inside austenite are strongly related with the crystallographic orientation of the austenitic lattice. Two mechanisms involved in these materials, i.e., plasticity by dislocation motion and martensitic phase formation are coupled through kinematical constraints so that the lattice spin of the austenitic grains is different from the one due to classical slip. In this work, the lattice spin ω˙eA of the austenitic grains is related with the slip rate on the slip systems of the two phases, γ˙A and γ˙M, the evolution of the martensite volume fraction f˙ and the overall rotation rate Ω˙ of the grains. This new relation is integrated in a micromechanical model developed for unstable austenite in order to predict the evolution of the austenite texture during TRansformation Induced Plasticity (TRIP). Results for the evolution of the lattice orientation during martensitic transformation are compared with experimental data obtained by X-ray diffraction on a 304 AISI steel.

Scaling laws for delay-sensitive traffic in Rayleigh fading networks

2008 ◽  
Vol 464 (2096) ◽  
pp. 2187-2205 ◽  
Author(s):  
Nikhil Karamchandani ◽  
Massimo Franceschetti
Keyword(s):  
Rayleigh Fading ◽  
Scaling Laws ◽  
Scaling Limit ◽  
Network Size ◽  
Upper And Lower Bounds ◽  
Destination Node ◽  
Delay Constraint ◽  
Delay Sensitive ◽  
Remote Surveillance ◽  
Emergency Scenarios

The throughput of delay-sensitive traffic in a Rayleigh fading network is studied by adopting a scaling limit approach. The case of the study is that of a pair of nodes establishing a data stream that has routing priority over all the remaining traffic in the network. For every delay constraint, upper and lower bounds on the achievable information rate between the two endpoints of the stream are obtained as the network size grows. The analysis concerns decentralized schemes , in the sense that all nodes make next-hop decisions based only on local information, namely their channel strength to other nodes in the network and the position of the destination node. This is particularly important in a fading scenario, where the channel strength varies with time and hence pre-computing routes can be of little help. Natural applications are remote surveillance using sensor networks and communication in emergency scenarios.

scholarly journals Dimension reduction for thin films prestrained by shallow curvature

2021 ◽  
Vol 477 (2247) ◽  
Author(s):  
Silvia Jiménez Bolaños ◽  
Marta Lewicka
Keyword(s):  
Dimension Reduction ◽  
Scaling Laws ◽  
Three Dimensional ◽  
Riemannian Metrics ◽  
Regular Solutions ◽  
Shell Models ◽  
Energy Scaling ◽  
New Energy ◽  
Monge Ampere ◽  
Equivalent Conditions

We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the Föppl–von Kármán equations, we find the Γ -limits of the rescaled energies, identify the optimal energy scaling laws, and display the equivalent conditions for optimality in terms of both the prestrain components and the curvatures of the related Riemannian metrics. When the stretching-inducing prestrain carries no in-plane modes, we discover similarities with the previously described shallow shell models. In higher prestrain regimes, we prove new energy upper bounds by constructing deformations as the Kirchhoff–Love extensions of the highly perturbative, Hölder-regular solutions to the Monge–Ampere equation obtained by means of convex integration.

Interphase influences on the mechanical behavior of carbon nanotube–shape memory polymer nanocomposites: A micromechanical approach

2018 ◽  
Vol 30 (3) ◽  
pp. 463-478 ◽  
Author(s):  
MK Hassanzadeh-Aghdam ◽  
MJ Mahmoodi ◽  
R Ansari ◽  
A Darvizeh
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Shape Memory ◽  
Polymer Nanocomposites ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Shape Memory Polymer ◽  
Micromechanical Model ◽  
Elastic Behavior ◽  
Interphase Region

The effects of interphase characteristics on the elastic behavior of randomly dispersed carbon nanotube–reinforced shape memory polymer nanocomposites are investigated using a three-dimensional unit cell–based micromechanical method. The interphase region is formed due to non-bonded van der Waals interaction between a carbon nanotube and a shape memory polymer. The influences of temperature, diameter, volume fraction, and arrangement type of carbon nanotubes within the matrix as well as two interphase factors, including adhesion exponent and thickness on the carbon nanotube/shape memory polymer nanocomposite’s longitudinal and transverse elastic moduli, are explored extensively. Moreover, the results are presented for the shape memory polymer nanocomposites containing randomly oriented carbon nanotubes. The obtained results clearly demonstrate that the interphase region plays a crucial role in the modeling of the carbon nanotube/shape memory polymer nanocomposite’s elastic moduli. It is observed that the nanocomposite’s elastic moduli remarkably increase with increasing interphase thickness or decreasing adhesion exponent. It is found that when the interphase is considered in the micromechanical simulation, the shape memory polymer nanocomposite’s elastic moduli non-linearly increase as the carbon nanotube diameter decreases. The predictions of the present micromechanical model are compared with those of other analytical methods and available experiments.

On a Spring-Network Model and Effective Elastic Moduli of Granular Materials

1999 ◽  
Vol 66 (1) ◽  
pp. 172-180 ◽  
Author(s):  
K. Alzebdeh ◽  
M. Ostoja-Starzewaski
Keyword(s):  
Granular Materials ◽  
Disordered Systems ◽  
Granular Media ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Medium ◽  
Solid State Physics ◽  
Two Phase ◽  
Effective Medium Theories ◽  
The Individual

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

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