Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
7
4
2009
SPECIAL ISSUE Computational Methods in Composite Materials and Structures
vii
Marcin
Kaminski
Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Lodz, Poland
Anastasia
Muliana
Modeling of Structure Evolution of Filled Elastomers under Uniaxial Elongation
251-261
Bernd
Lauke
Leibniz-Institut für Polymerforschung Dresden e.V., 01069 Dresden, Germany
I. A.
Morozov
Institute of Continuous Media Mechanics, Ural Branch of the Russian Academy of Sciences, 1 Acad. Korolev Str, Perm, 614013, Russia and Perm State National Research University, 15 Bukerev Str., Perm, 614990, Russia
The evolution of filler network structure in elastomers during elongation is investigated on the basis of computer modeling. The filler network is represented by spherical particles of different sizes, which are randomly filling a prismatic volume. No physical interaction forces between the particles on the molecular level are considered. The modeling is based on geometrical obstructions of particle ensembles. Interpenetrations of rigid particles during modeling of filling and subsequent stretching are forbidden, and only a minimal finite distance between the particles is allowed. The material is assumed to be incompressible. It was found that the number of nearest neighbors (coordination number) in a loosely filled material increases during stretching; however, in a densely filled material, this value decreases. The analysis of the size of unfilled spaces in the matrix has shown the occurrence of essential structural heterogeneities in the filler network. Stretching of a densely filled material results in appreciable mixing of particles whereby changes of the distances between originally neighboring particles exceed the macroscopic elongation of the material by several times. An analytical relation between the elongation of the composite and polymer chains via transmission ratio is proposed.
Fast Calculation of Elastic Fields in a Homogeneous Medium with Isolated Heterogeneous Inclusions
263-276
Sergey
Kanaun
Mechanical Engineering Department, Technological Institute of Monterrey, Mexico
This work is devoted to the calculation of static elastic fields in a homogeneous medium with a finite number of isolated heterogeneous inclusions. First, the problem is reduced to the solution of integral equations for strain fields inside the inclusions. Then, Gaussian approximating functions are used for discretization of these equations. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. The method is mesh-free, and the coordinates of the approximating nodes is the only geometrical information required in the method. If such nodes compose a regular lattice, the matrix of the discretized problem will have Toeplitz structure. By the calculation of matrix-vector products with such matrices, the fast Fourier transform technique may be used. The latter essentially accelerates the process of the iterative solution of the disretized problem. The results of calculations of elastic fields in a 2-D medium with an isolated heterogeneous inclusion and with several inclusions are presented.
Atomistic Simulations - Based Understanding of the Mechanism behind the Role of Second-Phase SiC Particles in Fracture Resistance of SiC-Si3N4 Nanocomposites
277-294
Vikas
Tomar
University of Notre Dame
Vikas
Samvedi
School of Aeronautics and Astronautics, Purdue University, West Lafayette-IN
One of the primary factors affecting the failure in high strength Silicon Carbide (SiC)-Silicon Nitride (Si3N4) nanocomposites is the placement of spherical nano-sized SiC particles in micro-sized Si3N4 grains. It has been found that as a result of a significant number of nanosized SiC particles being present in micro-sized Si3N4 grains, the SiC particles invariantly fall in wake regions of microcracks leading to significant structural strength. In this research, this mechanism is examined using 3-D molecular dynamics (MD) simulations of crack propagation in SiC-Si3N4 nanocomposites with cylindrical SiC inclusions. Analyses reveal that the second phase particles act as significant stress raisers bringing down the internal strength of the single crystal and bi-crystalline Si3N4 blocks by a factor of almost 2 times. With smaller SiC particle, the interfacial boundary in the bi-crystalline Si3N4 block acts as a stress reliever. However, with increase in the size of SiC particle and with decrease in the spacing between adjacent SiC particles the interfacial boundary's presence results in significant internal stress rise. The results point out that the placement of SiC particles along the interfacial boundaries will not always lead to strengthening of the nanocomposite. Overall, MD analyses confirm the earlier continuum simulation and experimental results concerning the effect of second phase SiC particles on the SiC-Si3N4 nanocomposite strength. In addition, MD analyses also point out that the strengthening of the nanocomposite by placing second phase particles along grain boundaries is only possible for a selective few second phase particle sizes.
Modeling of Viscoelastic Behavior of Ballistic Fabrics at Low and High Strain Rates
295-308
N. V.
David
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
Xin-Lin
Gao
Texas A&M University
J. Q.
Zheng
Program Executive Office-Soldier, U.S. Army, Haymarket, VA 20169, USA
Ballistic fabrics are made from high-performance polymeric fibers such as Kevlar®, Twaron®, and Spectra® fibers. These fibers often behave viscoelastically. The Kelvin-Voigt and Maxwell rheological (viscoelasticity) models have been used to characterize stress-strain relations of such fabrics at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this article, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model, which are both three-parameter viscoelasticity models, are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s-1 and 495 s-1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.
Crack-Centered Enrichment for Debonding in Two-Phase Composite Applied to Textile Reinforced Concrete
309-328
Rostislav
Chudoba
RWTH Aachen University
Jakub
Jerabek
Structural Statics and Dynamics, RWTH Aachen, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
Frank
Peiffer
Structural Statics and Dynamics, RWTH Aachen, Mies-van-der-Rohe-Str. 1, 52074 Aachen, Germany
This article introduces an enriched finite element representation of crack bridges suitable for simulating the complex damage processes in textile-reinforced concrete. The heterogeneity of both the matrix and the reinforcement occurs at similar length scales of the material structure. Consequently, an improved accuracy of approximation at the hot spots of damage is required to capture the relevant damage mechanisms. This is done by combining the extended finite element method with the variational multiscale approach. While the former is used to define the crack in the matrix, the latter serves for local resolution of the displacement fields in the vicinity of the crack. The approach is exemplified on a 1D example of a tension bar with interacting cracks and on the detailed analysis of debonding in a shear zone of a bending specimen
Modeling the Particle Size and Interfacial Hardening Effects in Metal Matrix Composites with Dispersed Particles at Decreasing Microstructural Length Scales
329-350
Rashid K. Abu
Al-Rub
Department of Civil Engineering, Catholic University of America, Washington, DC 20064, USA
The focus of this paper is on incorporating the particle size effect and the effect of particlematrix interfacial properties on the average onset of plasticity and strain hardening rates of metal matrix composites reinforced with hard, stiff, or soft particles. In order to achieve this objective, a higher-order gradient plasticity theory that explicitly includes the effect of interfacial energy at particle-matrix interfaces is formulated within the frameworks of virtual power and thermodynamic laws. The derived higher-order gradient plasticity theory also takes into account large variations in plastic strain tensor and effective plastic strain; namely, the gradient of plastic strain, the gradient of the effective plastic strain, and the accumulation of plastic strain gradients. Moreover, unlike the majority of the existing gradient plasticity theories in the literature, it is shown that the matrix nonlocal yield condition as well as a yield-like condition for the particle-matrix interface can be directly derived from the principle of virtual power without any further constitutive assumptions. Also, in this work the interfaces dissipate energy similar to the bulk material during plastic deformation. The interfacial yield condition takes into consideration the particle type (soft, stiff, hard) through the incorporation of the particle-matrix interfacial yield strength and interfacial hardening in case of dislocation transmission across the interface (i.e. shearing of particles). The proposed higher-order gradient plasticity theory is shown to be qualitatively successful in predicting the increase in the average yield strength, strain hardening rates, and flow stress as the particle size decreases and the particle interfacial strength increases.
A Multiscale Framework for Analyzing Thermo-Viscoelastic Behavior of Fiber Metal Laminates
351-370
Sourabh
Sawant
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA
Anastasia
Muliana
Fiber metal laminate (FML) is a multilayered composite system that consists of alternate layers of metal and fiber-reinforced polymers. These composite systems can exhibit timedependent behavior due to the time-dependent responses in one or more of their constituents. The time-dependent behavior is further intensified under the influence of high temperatures and stress levels, resulting in a nonlinear stress- and temperature-dependent viscoelastic response. A multiscale framework is formulated to predict the overall nonlinear time-dependent response of the FML by integrating different constitutive material models of the constituents. The multiscale framework includes a micromechanical model for ply level homogenization. The upper (structural) level uses a layered composite finite element (FE) with multiple integration points through the thickness. The micromodel is implemented at these integration points. It is also possible to develop a sublaminate model for a laminate-level homogenization and integrate it into continuum 3D or shell elements within the FE code. Thermoviscoelastic constitutive models of homogenous orthotropic materials are used at the lowest constituent level, that is, fiber, matrix, and metal. The nonlinear and time-dependent response of the constituents requires the use of suitable correction algorithms (iterations) at various levels of the framework.
The Stochastic Interface Defects in Composite Materials Subjected to Aging Processes
371-380
Marcin
Kaminski
Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Lodz, Poland
The main objective of this work is to propose a brand-new stochastic model of the interface defects appearing frequently between composite components. This model is based on the semicircular idealization of those defects and stochastic approximation of materialsâ€™ aging processes. Then, the stochastic interface defects so defined are located within the artificial interphase inserted between the existing constituents, the material properties (their probabilistic moments) of which are determined from the stochastic averaging rule. This interphase with the stochastic geometry and the stochastic material properties enables for further numerical homogenization of this composite in the microscale, if only a distribution of the assumed defects has the same probabilistic properties in each representative volume element.