scholarly journals Multiscale Evaluation of The Elastic Behavior for The Metal-Coated Lattice Structures

2020 ◽  
Author(s):  
Sina Soleimanian ◽  
Xiang Wang ◽  
Min Chen ◽  
Yanqing Yu ◽  
Ji Li ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Volume Fraction ◽  
Effective Properties ◽  
Unit Cell ◽  
Homogenization Theory ◽  
Elastic Behavior ◽  
Coating Film ◽  
Specific Modulus ◽  
The Impact

Abstract Well-developed Additive Manufacturing leads to a variety of material and structure design. With the combination of 3D printing and plating technique, metal-coated resin lattice is investigated to achieve a light weight design with minimal economic cost and admirable material properties. In this paper, numerical approaches integrated with classical homogenization theory is adopted to study the effective mechanical characterizations of the BCC (Body-Centered-Cubic) metal-coated lattices. The selection of RVE (Representative Volume Element) is discussed for obtaining objective effective properties. Moreover, the impact of unit cell rod diameter and coating film thickness are investigated. A sensitivity analysis of these two parameters is conducted based on the advanced hypercube sampling methods. The results reveal that multiple-unit-cells lead to more stable homogenized properties than single unit cell. The Increase of volume fraction may improve the elastic modulus and specific modulus remarkably. However, the increase of thickness of coating film only leads to monotonously increased elastic modulus. For this reason, there exists an optimal coating film thickness for the specific modulus of the lattice structure.

On the Effective Properties of 3D Metamaterials

2016 ◽  
Author(s):  
Mohamed Abdelhamid ◽  
Aleksander Czekanski
Keyword(s):  
Elastic Modulus ◽  
Effective Properties ◽  
Lattice Structure ◽  
Surface Elasticity ◽  
Geometric Parameters ◽  
Stiffness Tensor ◽  
Loading Direction ◽  
Octet Truss ◽  
The Impact ◽  
Effective Mechanical Properties

A continuum-based model is developed for the octet-truss unit cell in order to describe the effective mechanical properties (elastic modulus) of the lattice structure. This model is to include different geometric parameters that impact the structural effects; these parameters are: lattice angle, loading direction, thickness to diameter ratio, diameter to length ratio, and ellipticity. All these geometric parameters are included in the stiffness matrix, and the impact of each parameter on the stiffness tensor is investigated. Specifically, the effect of the lattice angle on the elastic moduli is discussed, and the loading direction of the highest elastic modulus is investigated for different lattice angles. Furthermore, the Gurtin-Murdoch model of surface elasticity is used to include the size effect in the stiffness tensor, as well as anisotropy of this model is investigated.

scholarly journals Second order homogenization of quasi-periodic structures

2018 ◽  
Vol 40 (4) ◽  
pp. 325-348
Author(s):  
Duc Trung Le ◽  
Jean-Jacques Marigo
Keyword(s):  
General Framework ◽  
Volume Fraction ◽  
Effective Properties ◽  
Periodic Structures ◽  
Expansion Method ◽  
Second Order ◽  
Unit Cell ◽  
One Dimensional ◽  
Minimization Problems ◽  
Asymptotic Expansion Method

The paper develops a general framework to derive the effective properties of quasi-periodic elastic medium. By using the asymptotic expansion method, the solution is expanded to the second order by solving a sequence of minimization problems. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by solving several families of microscopic problems posed on the unit cell and which bring into play only the microstructure. As an illustrative example, we consider an anti-plane elastic case of a heterogeneous cylinder made of a bi-layer laminate and submitted to the gravity. The unit cell being one-dimensional, all the associated elementary problems can be solved in a closed form and one shows that the effective energy of the medium expanded up to the second order depends not only on the strain gradient, but also on the gradient of the volume fraction \(\theta\) characterizing the repartition of the two materials in the laminate.

On Thermal Interface Materials With Polydisperse Fillers: Packing Algorithm and Effective Properties

2018 ◽  
Author(s):  
Piyas Chowdhury ◽  
Kamal Sikka ◽  
Anuja De Silva ◽  
Indira Seshadri
Keyword(s):  
Thermal Conductivity ◽  
Elastic Modulus ◽  
Volume Fraction ◽  
Effective Properties ◽  
Material Design ◽  
High Volume ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Packing Algorithm ◽  
Interface Materials

Thermal interface materials (TIMs), which transmit heat from semiconductor chips, are indispensable in today’s microelectronic devices. Designing superior TIMs for increasingly demanding integration requirements, especially for server-level hardware with high power density chips, remains a particularly coveted yet challenging objective. This is because achieving desired degrees of thermal-mechanical attributes (e.g. high thermal conductivity, low elastic modulus, low viscosity) poses contradictory challenges. For instance, embedding thermally conductive fillers (e.g. metallic particles) into a compliant yet considerably less conductive matrix (e.g. polymer) enhances heat transmission, however at the expense of overall compliance. This leads to extensive trial-and-error based empirical approaches for optimal material design. Specifically, high volume fraction filler loading, role of filler size distribution, mixing of various filler types are some outstanding issues that need further clarification. To that end, we first forward a generic packing algorithm with ability to simulate a variety of filler types and distributions. Secondly, by modeling the physics of heat/force flux, we predict effective thermal conductivity, elastic modulus and viscosity for various packing cases.

scholarly journals Aluminum Matrix Composites with Weak Particle Matrix Interfaces: Effective Elastic Properties Investigated Using Micromechanical Modeling

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6083
Author(s):  
Aharon Farkash ◽  
Brigit Mittelman ◽  
Shmuel Hayun ◽  
Elad Priel
Keyword(s):  
Elastic Properties ◽  
Effective Properties ◽  
Aluminum Matrix ◽  
Unit Cell ◽  
Micromechanical Modeling ◽  
Aluminum Matrix Composites ◽  
Matrix Composites ◽  
Element Analysis ◽  
Effective Elastic Properties ◽  
The Impact

The impact of weak particle-matrix interfaces in aluminum matrix composites (AMCs) on effective elastic properties was studied using micromechanical finite-element analysis. Both simplified unit cell representations (i.e., representative area or volume elements) and “real” microstructure-based unit cells were considered. It is demonstrated that a 2D unit cell representation provides accurate effective properties only for strong particle-matrix bond conditions, and underpredicts the effective properties (compared to 3D unit cell computations) for weak interfaces. The computations based on real microstructure of an Al–TiB2 composite fabricated using spark plasma sintering (SPS) show that, for weak interfaces, the effective elastic properties under tension are different from those obtained under compression. Computations show that differences are the result of the local stress and strain fields, and contact mechanics between particles and the matrix. Preliminary measurements of the effective elastic properties using the ultrasonic pulse-echo technique and compression experiments support the trends observed in computational analysis.

Effect of the Pre-Strain on the Elastic Behavior of a Dual-Phase Steel with Different Martensite Contents

2021 ◽  
Vol 1016 ◽  
pp. 1555-1560
Author(s):  
Matthias Wallner ◽  
Reinhold Schneider ◽  
Katharina Steineder ◽  
Daniel Krizan ◽  
Thomas Hebesberger ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Elastic Modulus ◽  
Modulus Of Elasticity ◽  
Volume Fraction ◽  
Hardness Test ◽  
Martensite Phase ◽  
Elastic Behavior ◽  
Present Contribution ◽  
Martensite Volume Fraction ◽  
Dislocation Movement

The modulus of elasticity is an important parameter for an accurate prediction of the springback in sheet metal forming processes. With increasing plastic deformation, this modulus behaves nonlinearly and declines, which leads to an unpredictable springback behavior. The most cited reason for this nonlinearity is the dislocation movement during plastic deformation that especially occurs with multiphase steels. The present contribution investigates the nonlinear unloading behavior and the resulting decrease of the elastic modulus from a differently heat treated DP980 steel. The heat treatments set five different microstructures with martensite volume fractions in the range of 42 to 95 %. By means of the tensile test, a decline of the elastic modulus according to pre-strain was examined by evaluating the chord-modulus during unloading at different strain levels. In addition, a nano-hardness test was performed. It turned out that in all heat treatment conditions, a pronounced decrease in the modulus of elasticity up to 25% from the initial value occurred. With decreasing annealing temperature and lower martensite volume fraction, respectively, the martensite hardness increased, leading to higher hardness differences between the ferrite and the martensite phase in the microstructure. This led to an increase of strain hardening, i.e. to an increased formation of fresh mobile dislocations in the vicinity of the harder martensite phase during plastic deformation. As a result, the modulus of elasticity decreased more sharply. Thus, in the present contribution, an interplay between the martensite volume fraction and its hardness on the decrease of elastic modulus could be clearly manifested.

A new micromechanics approach for predicting the elastic response of polymer nanocomposites reinforced with randomly oriented and distributed wavy carbon nanotubes

2017 ◽  
Vol 51 (20) ◽  
pp. 2899-2912 ◽  
Author(s):  
MK Hassanzadeh-Aghdam ◽  
R Ansari ◽  
A Darvizeh
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Polymer Nanocomposites ◽  
Random Distribution ◽  
Volume Fraction ◽  
Unit Cell ◽  
Elastic Behavior ◽  
Random Orientation ◽  
Reinforced Polymer ◽  
The Matrix

A comprehensive investigation is carried out into the elastic behavior of carbon nanotube-reinforced polymer nanocomposites using two combined analytical micromechanical methods. A unit cell-based micromechanical method is developed to model the random distribution of carbon nanotubes within the polymer matrix. Also, the Eshelby method is used for modeling the random orientation state of carbon nanotubes within the matrix. Two fundamental aspects affecting the mechanical behavior of carbon nanotube/polymer nanocomposites, including the carbon nanotube waviness and the interphase formed due to the non-boned interaction between the carbon nanotube and the surrounding polymer, are considered in the unit cell method. Comparisons between the results of present method and experimental data reveal that for more realistic predictions, five important factors including, random orientation and random distribution of carbon nanotubes, interphase, waviness and transversely isotropic behavior of carbon nanotube should be considered in the modeling of carbon nanotube-reinforced polymer nanocomposites. The effects of volume fraction, number of waves and waviness factor of carbon nanotube as well as the type of random distribution of CNTs within the matrix on the elastic modulus of the polymer nanocomposites are studied.

A New 3-D Unit Cell Model Used in Homogenization Estimation of Effective Properties of Particle-Filled Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1269-1273
Author(s):  
Yong Ouyang ◽  
Xiao Ling Hu ◽  
Xiu Liu ◽  
Wen Bo Luo
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Cell Model ◽  
Particle Volume Fraction ◽  
Calculated Data ◽  
Effective Elastic Modulus ◽  
Unit Cell ◽  
Unit Cell Model ◽  
Particle Volume ◽  
Periodic Microstructures

A new 3D unit cell model is developed for homogenization calculation of composites containing randomly dispersed ellipsoid inclusions. The new unit cell is constructed using the Ansys Parameter Design Language (APDL), taking the inclusion volume fraction, inclusion orientation and spatial dispersion as variables. A series of unit cells containing multiple ellipsoids, showing random distributions in particle size and position, were constructed and used for finite element calculation at microscale, the effective modulus of the composites with periodic microstructures, which modeled by the unite cells, were then estimated by homogenization. The influences of particle volume fraction and the particle stiffness on the effective elastic modulus of the composites were examined. The estimated results were compared with different particle volume fractions were calculated, and the calculated data was compared with other classic models.

scholarly journals A Multi-Scale Approach to Predict the Impact Resistance of Braided Composites using Progress Failure

2017 ◽  
Vol 26 (1) ◽  
pp. 096369351702600
Author(s):  
Xu Lei ◽  
Khazar Hayat ◽  
Sung Kyu Ha
Keyword(s):  
Effective Properties ◽  
Impact Resistance ◽  
Unit Cell ◽  
Braided Composites ◽  
Damage Models ◽  
Multi Scale ◽  
Constituent Material ◽  
Unit Cells ◽  
Plastic Resin ◽  
The Impact

A novel multi-scale approach based on micromechanics of failure together with the progressive damage models of the fibre and matrix constituents is presented to predict the impact resistance of braided composites. The meso- and micro-scale unit-cells of the braided composites with both thermosetting and thermos-plastic resin systems, were employed, and the effective properties of the braided tows, in the meso unit cell, were updated using the micro unit cell for which the degradation of constituent material properties were incorporated.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Low-carbon cast microalloyed steel intercritically heat-treated at different temperatures: microstructure and mechanical properties

2021 ◽  
Vol 21 (2) ◽  
Author(s):  
Hadi Torkamani ◽  
Shahram Raygan ◽  
Carlos Garcia Mateo ◽  
Yahya Palizdar ◽  
Jafar Rassizadehghani ◽  
...  
Keyword(s):  
Carbon Content ◽  
Volume Fraction ◽  
Block Size ◽  
Tensile Tests ◽  
Total Elongation ◽  
Martensite Phase ◽  
Low Carbon ◽  
Steel Increase ◽  
Different Temperatures ◽  
The Impact

AbstractIn this study, dual-phase (DP, ferrite + martensite) microstructures were obtained by performing intercritical heat treatments (IHT) at 750 and 800 °C followed by quenching. Decreasing the IHT temperature from 800 to 750 °C leads to: (i) a decrease in the volume fraction of austenite (martensite after quenching) from 0.68 to 0.36; (ii) ~ 100 °C decrease in martensite start temperature (Ms), mainly due to the higher carbon content of austenite and its smaller grains at 750 °C; (iii) a reduction in the block size of martensite from 1.9 to 1.2 μm as measured by EBSD. Having a higher carbon content and a finer block size, the localized microhardness of martensite islands increases from 380 HV (800 °C) to 504 HV (750 °C). Moreover, despite the different volume fractions of martensite obtained in DP microstructures, the hardness of the steels remained unchanged by changing the IHT temperature (~ 234 to 238 HV). Applying lower IHT temperature (lower fraction of martensite), the impact energy even decreased from 12 to 9 J due to the brittleness of the martensite phase. The results of the tensile tests indicate that by increasing the IHT temperature, the yield and ultimate tensile strengths of the DP steel increase from 493 to 770 MPa, and from 908 to 1080 MPa, respectively, while the total elongation decreases from 9.8 to 4.5%. In contrast to the normalized sample, formation of martensite in the DP steels could eliminate the yield point phenomenon in the tensile curves, as it generates free dislocations in adjacent ferrite.

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