Three-Phase Cylinder Model of One-Dimensional Hexagonal Piezoelectric Quasi-Crystal Composites

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Junhong Guo ◽  
Ernian Pan
Keyword(s):  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Interphase Layer ◽  
Effective Moduli ◽  
Fiber Volume ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Three Phase ◽  
Cylinder Model

A three-phase cylinder model (inclusion/matrix/composite) is proposed and analyzed for one-dimensional (1D) piezoelectric quasi-crystal composites. The exact closed-form solutions of the stresses of the phonon and phason fields and the electric field are derived under far-field antiplane mechanical and in-plane electric loadings via the Laurent expansion technique. Numerical results show that the thickness and material properties of the interphase layer can significantly affect the induced fields in the inclusion and interphase layer. Furthermore, the generalized self-consistent method is applied to predict analytically the effective moduli of the piezoelectric quasi-crystal composites. It is observed from the numerical examples that the effective moduli of piezoelectric quasi-crystal composites are very sensitive to the fiber volume fraction as well as to the individual material properties of the fiber and matrix. By comparing QC/PE with QC1/QC2, PE/QC, and PZT-7/epoxy, we found that using QC as fiber could, in general, enhance the effective properties, a conclusion which is in agreement with the recent experimental results.

scholarly journals Comparison of Different Parameters to Evaluate Delamination in Edge Trimming of Basalt Fiber Reinforced Plastics (BFRP)

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5326
Author(s):  
María Dolores Navarro-Mas ◽  
María Desamparados Meseguer ◽  
Joaquín Lluch-Cerezo ◽  
Juan Antonio García-Manrique
Keyword(s):  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Basalt Fiber ◽  
Cutting Speed ◽  
Depth Of Cut ◽  
Fiber Reinforced ◽  
Fiber Volume ◽  
One Dimensional ◽  
Dimensional Parameters ◽  
Edge Trimming

Delamination is one of the main problems that occur when machining fiber-reinforced composite materials. In this work, Types I and II of delamination are studied separately in edge trimming of basalt fiber reinforced plastic (BFRP). For this purpose, one-dimensional and area delamination parameters are defined. One-dimensional parameters (Wa and Wb) allow to know average fibers length while the analysis of area delamination parameters (Sd) allow to evaluate delamination density. To study delamination, different tests are carried out modifying cutting parameters (cutting speed, feed per tooth and depth of cut) and material characteristics (fiber volume fraction and fiber orientation). Laminates with a lower fiber volume fraction do not present delamination. Attending to one-dimensional parameters it can be concluded that Type II delamination is more important than Type I and that a high depth of cut generates higher values of delamination parameters. An analysis of variance (ANOVA) is performed to study area parameters. Although delamination has a random nature, for each depth of cut, more influence variables in area delamination are firstly, feed per tooth and secondly, cutting speed.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

The Effects of Layer-by-Layer Thickness and Fiber Volume Fraction Variation on the Mechanical Performance of a Pressure Vessel

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Emre Özaslan ◽  
Ali Yetgin ◽  
Bülent Acar ◽  
Volkan Coşkun ◽  
Tarık Olğar
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Material Properties ◽  
Fiber Volume Fraction ◽  
Mechanical Performance ◽  
Volume Fraction ◽  
Element Model ◽  
Layer By Layer ◽  
Fiber Volume ◽  
Filament Wound

Abstract Due to high stiffness/weight ratio, composite materials are widely used in aerospace applications such as motor case of rockets which can be regarded as a pressure vessel. The most commonly used method to manufacture pressure vessels is the wet filament winding. However, the mechanical performance of a filament wound pressure vessel directly depends on the manufacturing process, manufacturing site environmental condition, and material properties of matrix and fiber. The designed pressure vessel may not be manufactured because of the mentioned issues. Therefore, manufacturing of filament wound composite structures are based on manufacturing experience and experiment. In this study, effects of layer-by-layer thickness and fiber volume fraction variation due to manufacturing process on the mechanical performance were investigated for filament wound pressure vessel with unequal dome openings. First, the finite element model was created for designed thickness dimensions and constant material properties for all layers. Then, the model was updated. The updated finite element model considered the thickness of each layer separately and variation of fiber volume fraction between the layers. Effects of the thickness and fiber volume fraction on the stress distribution along the motor axial direction were shown. Also hydrostatic pressurization tests were performed to verify finite element analysis in terms of fiber direction strain through the motor case outer surface. Important aspects of analyzing a filament wound pressure vessel were addressed for designers.

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.

scholarly journals An Energy-Based Model of Longitudinal Splitting in Unidirectional Fiber-Reinforced Composites

1999 ◽  
Vol 67 (3) ◽  
pp. 437-443 ◽  
Author(s):  
K. Oguni ◽  
G. Ravichandran
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Confining Pressure ◽  
Fiber Reinforced Composites ◽  
Fiber Direction ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Fiber Volume ◽  
Unidirectional Fiber ◽  
Longitudinal Splitting

Unidirectional fiber-reinforced composites are often observed to fail in a longitudinal splitting mode in the fiber direction under far-field compressive loading with weak lateral confinement. An energy-based model is developed based on the principle of minimum potential energy and the evaluation of effective properties to obtain an analytical approximation to the critical stress for longitudinal splitting. The analytic estimate for the compressive strength is used to illustrate its dependence on material properties, surface energy, fiber volume fraction, fiber diameter, and lateral confining pressure. The predictions of the model show good agreement with available experimental data. [S0021-8936(00)02003-1]

Effect of Microvoids on Anomalous Moisture Absorption of Quartz/BMI Composite Laminates

2014 ◽  
Author(s):  
Keith R. Hurdelbrink ◽  
Gorkem E. Guloglu ◽  
Jacob P. Anderson ◽  
Landon R. Grace ◽  
Zahed Siddique ◽  
...  
Keyword(s):  
Fiber Volume Fraction ◽  
Moisture Absorption ◽  
Volume Fraction ◽  
Model Parameters ◽  
Absorption Model ◽  
Matrix Interface ◽  
Fiber Volume ◽  
One Dimensional ◽  
Fiber Matrix Interface ◽  
Fiber Matrix

The focus of this paper was to investigate the effects of microvoid content in quartz/BMI laminates on both short and long-term moisture absorption dynamics. The moisture absorption characteristics for the laminates were experimentally obtained by water immersion tests at 25°C of three-ply quartz/BMI samples that contain voids, ranging from 8.6% to 13.7% by volume. The void levels were obtained by conditioning the prepreg at different moisture levels for 48 hours in an environmental chamber before curing in a hot press. The curing process was carried out at 69 kPa, which leads to a more uniform fiber volume fraction for the laminates. Having a constant fiber volume fraction ensures the same amount of fiber-matrix interface present in all the test samples, therefore eliminating the effect of fiber-matrix interface as an experimental variable. It is shown that the presence of microvoids leads to an increased non-Fickian absorption behavior. Hence, the anomalous, non-Fickian absorption parameters are obtained by using a one-dimensional absorption model that accounts for both bound and unbound free water within the laminate. It is shown that the microvoids act as storage sites for moisture which can be described by the one-dimensional, non-Fickian absorption model. Finally, possible relationships between the four absorption model parameters and the process-induced microvoid content are discussed.

scholarly journals Effective properties of particulate nano-composites including Steigmann–Ogden model of material surface

2021 ◽  
Author(s):  
Lidiia Nazarenko ◽  
Henryk Stolarski ◽  
Holm Altenbach
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Surface Effects ◽  
Particulate Composites ◽  
Material Surface ◽  
Effective Moduli ◽  
Nano Particle ◽  
Shear Moduli ◽  
Conditional Moments ◽  
Theoretical Predictions

AbstractThe objective of this work is inclusion of the Steigmann-Ogden interface in the Method of Conditional Moments to investigate the influence of surface effects on the effective properties of random particulate composites. The particular focus is centered on accounting for the surface bending stiffness. To this end, the notion of the energy-equivalent inhomogeneity developed for Gurtin–Murdoch interface is generalized to include the surface bending contribution. The crucial aspect of that generalization is identification of the formula defining energy associated with the surface bending. With the help of that formula, the real nano-particle and its surface are replaced by equivalent inhomogeneity with properties incorporating the surface effects. Closed-form expressions for the effective moduli of a composite with a matrix and randomly distributed spherical inhomogeneities are derived. The normalized shear moduli of nanoporous material as a function of void volume fraction is analyzed and evaluated in the context of other theoretical predictions.

Micromechanical Analysis of Heterogeneous Composites using Hybrid Trefftz FEM and Hybrid Fundamental Solution Based FEM

2013 ◽  
Vol 29 (4) ◽  
pp. 661-674 ◽  
Author(s):  
C. Y. Cao ◽  
Q.-H. Qin ◽  
A. B. Yu
Keyword(s):  
Fundamental Solution ◽  
Volume Fraction ◽  
Effective Properties ◽  
Multiscale Simulation ◽  
Homogenization Method ◽  
Micromechanical Modeling ◽  
Future Application ◽  
Fiber Volume ◽  
Mesh Density ◽  
Properties Of Composites

ABSTRACTIn this paper, a new algorithm is developed based on the homogenization method integrating with the newly developed Hybrid Treffe FEM (HT-FEM) and Hybrid Fundamental Solution based FEM (HFS-FEM). The algorithm can be used to evaluate effective elastic properties of heterogeneous composites. The representative volume element (RVE) of fiber reinforced composites with periodic boundary conditions is introduced and used in our numerical analysis. The proposed algorithm is assessed through two numerical examples with different mesh density and element geometry and used to investigate the effect of fiber volume fraction, fiber shape and configuration on the effective properties of composites. It is found that the proposed algorithm is insensitive to element geometry and mesh density compared with the traditional FEM (e.g. ABAQUS). The numerical results indicate that the HT-FEM and HFS-FEM are promising in micromechanical modeling of heterogeneous materials containing inclusions of various shapes and distributions. They are potential to be used for future application in multiscale simulation.

Tensile Properties of Random Distribution Short SMA Fiber Reinforced Composites

2011 ◽  
Vol 488-489 ◽  
pp. 686-689
Author(s):  
Hong Shuai Lei ◽  
Bo Zhou ◽  
Zhen Qing Wang ◽  
Xiao Qiang Wang
Keyword(s):  
Random Distribution ◽  
Volume Fraction ◽  
Effective Elastic Modulus ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Fiber Volume ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Three Phase

Shape memory alloy (SMA) reinforced composites have been widely used in aerospace engineering fields. In this paper, four basic assumptions were presented to simply the research model based on the Eshelby’s equivalent inclusion method and Mori-Tanaka scheme. Based on the three-phase equivalent system and two-step equivalent process, the effective elastic modulus and thermal expansion coefficient of unidirectional random distribution short SMA fiber reinforced composites were derived. The tensile mechanical properties of composites with fiber volume fraction (15%), size (L=3, D=1; L=5, D=1), and number (N= 30, 50), were simulated using software ANSYS12.0, and discussed the failure mode of the composites.

ELASTIC-PLASTIC FRACTURE BEHAVIOR ANALYSIS ON A GRIFFITH CRACK IN THE CYLINDRICAL THREE-PHASE COMPOSITES WITH GENERALIZED IRWIN MODEL

2014 ◽  
Vol 06 (04) ◽  
pp. 1450045 ◽  
Author(s):  
M. FAN ◽  
D. K. YI ◽  
Z. M. XIAO
Keyword(s):  
Shear Modulus ◽  
Plastic Zone ◽  
Fracture Behavior ◽  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Orientation Angle ◽  
Modulus Ratio ◽  
Crack Orientation ◽  
Fiber Volume ◽  
Three Phase

Elastic-plastic stress analysis on a matrix crack interacting with near-by circular inclusions (the fibers) in fiber-reinforced composites has been carried out. The crack is initiated near one of the inclusions, while the effect of other inclusions in the composite is considered through simulating the composite material by the cylindrical three-phase model. To more accurately study the fracture behavior of the crack, plastic zone correction is introduced first time for such a crack-inclusion interaction problem. To determine the plastic zone sizes (PZSs) at the crack tips, a generalized Irwin model is proposed for the current mixed-mode problem where the von Mises stress yielding criterion is employed. With the aid of distributed dislocation method, the physical problem is formulated into a set of singular integral equations and solved through a numerical schism. The effective stress intensity factor (SIF), the PZS, crack tip opening displacement (CTOD) are evaluated accordingly. In the numerical examples, the influence of the crack orientation angle, the fiber/matrix shear modulus ratio, and fiber volume fraction on the fracture behavior of the crack is discussed in detail. It is found that the crack orientation angle has great effect on the normalized values of PZS, CTOD, and effective SIF, while the effects of shear modulus ratio and fiber volume fraction depend highly on the conditions of the inclusion (the fiber) and matrix.

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