Mechanics of Random Discontinuous Long-Fiber Thermoplastics—Part I: Generation and Characterization of Initial Geometry

Abstract

The deformation mechanics of dry networks of large-aspect-ratio fibers with random orientation controls the processing of long-fiber thermoplastics (LFTs) and greatly affects the mechanical properties of the final composites. Here, we generate initial geometries of fiber networks in a cubic unit cell with a fiber aspect ratio of lid =100 and fully periodic boundary conditions for later numerical simulation. The irreversible random sequential adsorption (RSA) process is first used to generate a quasi-random structure due to the excluded-volume requirements. In order to investigate the nonequilibrium character of the RSA, a second method, which is similar to the mechanical contraction method (MCM) (Williams and Philipse, 2003, "Random Packings of Spheres and Spherocylinders Simulated by Mechanical Contraction," Phys, Rev, E, 67, pp. 1-9) and based on a simplified Metropolis Monte Carlo (MC) simulation is then developed to produce quasiequilibrium fiber geometries. The RSA packing results (4>K4.423% when using a fiber aspect ratio of ¡00) are in good agreement with the maximum unforced random packing limits (Evans and Gibson, 1986, "Prediction of the Maximum Packing Eraction Achievable in Randomly Oriented " Compos. Sei. TechnoL, 25,. The fiber structures were characterized by several distribution functions, including pair-spatial and pair-orientation distributions, based on either the center-tocenter distance or the shortest distance between the particles. The results show that the structures generated by the RSA have an easily-detectable long-range spatial correlation but very little orientational correlation. In contrast, the quasi-equilibrium structures have reduced spatial correlation but increased short-range orientational correlation

Postbuckling behavior of functionally graded CNT-reinforced nanocomposite plate with interphase effect

“…2. The integer values of Euler angles θ ∈ (0, 2π) and ∅ ∈ ( −π 2 , π 2 ) are chosen in such a way that these values are randomly and uniformly distributed in the ranges specified, as per the procedure described by Abd El-Rahman and Tucker III [30]. To model the RVE, Boolean based RSA algorithm proposed by Liu et al [32], also shown in Fig.…”

“…Bailakanavar et al [29] proposed a hierarchical RSA algorithm to generate unit cells having randomly distributed fillers to achieve the fiber volume fraction up to 45% for the aspect ratios as high as 20. Abd El-Rahman and Tucker III [30] utilized the radial and shortest distance distribution functions to simulate the randomness of long fibers (i.e., l/d = 100). Recently, Song et al [31] developed RVE models containing a 3D network of reinforcements within the RVE and demonstrated that computationally homogenized models with material periodic conditions are independent of RVE size and proved that homogenized results are computationally efficient compared to the statistical models.…”

Mechanical characterization and postbuckling behavior of carbon nanotube–carbon fiber reinforced nanocomposite laminate

“…Therefore, FEM plays a crucial role in minimizing the computational cost of the simulation, and many researchers have utilized its capabilities to predict the mechanical properties of nanocomposite using the method of representative volume element (RVE). [8][9][10] An RVE of a nanocomposite material having a complex arrangement of randomly-oriented and -positioned CNTs reinforced in a matrix material can be realized through random sequential adsorption (RSA) 11 algorithm, that has been widely applied to model RVE [12][13][14][15][16] of conventional composites containing random fibers. Kari et al 12 established the fact that the effective material properties of the composite depends mainly on the volume fraction of reinforcement, regardless of its size and shape, and concluded that higher volume fractions can be achieved even by adding small size particles into the matrix material; similarly, Pan et al 13,14 utilized curved fibers to achieve higher volume fractions up to 35% using a computationally expensive optimization technique.…”

“…In 2012, Bailakanavar et al 15 proposed a more robust, efficient, and versatile parametric model to generate unit cells with randomly distributed inclusions to model a composite material having volume fraction up to 45% for the aspect ratios of fiber as high as 20. Rahman et al 16 used radial and shortest distance distribution function to simulate the randomness of relatively long fibers (l/d ¼ 100) and extended their work to study the mechanics of long-fiber thermoplastics 17 and achieved the volume fraction of 25%. The RSA algorithms used in the aforementioned studies involve tedious looping calculations to position and orient a new fiber in the existing fibers without any overlapping of fibers.…”

“…The studies demonstrating the extraordinary mechanical properties of CNTs [1][2][3] and the multiscale methods (i.e. method of RVE [8][9][10] and RSA technique [12][13][14][15][16] ) used to estimate these mechanical properties of nanocomposite at the macrolevel are very useful to explore the potential applications of CNTreinforced nanocomposite in the form of actual structures. 20,21 One of the most interesting characteristics of actual thin structures is to be able to withstand larger compression and shear loads after reaching bifurcation point, and evaluating the full loadcarrying capacity of these structures beyond the bifurcation point has been an area of intense study.…”