Samit Roy

Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM)

A new multiscale simulation approach is introduced that couples atomistic-scale simulations using molecular dynamics (MD) with continuum-scale simulations using the recently developed material point method (MPM). In MPM, material continuum is represented by a finite collection of material points carrying all relevant physical characteristics, such as mass, acceleration, velocity, strain and stress. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A silicon single crystal under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. The coupled MD/MPM simulations show that silicon under nanometric tension experiences, with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress–strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in the rest of the material.

Two-Dimensional Mixed Mode Crack Simulation Using the Material Point Method

The material point method (MPM) has demonstrated its capabilities in the simulation of impact/contact/penetration and interfacial crack growth problems. Because of the use of material points in the description of a continuum, consistent with the particle description (atoms) using molecular dynamics (MD), it is natural to couple MPM with MD for simulation from atomistic to continuum levels. However, in addressing plane stress/plane strain problems, the MPM algorithm and simulation examples available in literature use a regular grid mesh with uniform square cells and enforce velocity and displacement continuities through its background grid, resulting in limitations in dealing with stress concentration, inclined dislocations and inclined crack, etc. In this article, an irregular mesh is implemented in MPM to eliminate the limitations resulting from the use of a regular mesh. The ray-crossing algorithm is employed to determine which cell a material point belongs to after deformation for interpolation and extrapolation of variables between material points and grid nodes. As an example to demonstrate the capability of the MPM using irregular mesh, the stress field in a continuum with an inclined crack is determined using arbitrary quadrilateral cells in the background grid mesh. The use of irregular mesh in MPM was validated by comparing MPM results with ABAQUS/Explicit simulation. The proposed method of using irregular mesh will be an essential element in using MPM to couple with atomistic scale simulation so that MPM can address inclined dislocations and cracks emanating from the atomistic simulation.

Stress intensity factor for an elliptic inclusion in orthotropic laminates subjected to freeze-thaw: Model verification

Verifications and applications of an analytical model developed previously for the calculation of mode-I stress intensity factor of a pre-existing crack in an orthotropic composite structure due to the phase transition of trapped moisture are presented in this paper. The verifications are based on comparisons of the stresses in an elliptic elastic inclusion and the stress intensity factor with a special case of isotropy (for which there exists an analytical solution) and with finite element analysis for the case of orthotropy. The results indicate that the stress state in a slender elliptic elastic inclusion can be used to approximate the stress field at the crack face, which could subsequently be adopted to determine the stress intensity factor. Analyses of the delamination and fatigue life prediction for freeze-thaw cycling are provided as specific applications of the model.

A Coupled Hygrothermal Cohesive-Layer Constitutive Model for Simulating Debond Growth

The objective of this paper is to model the synergistic bond degradation mechanisms that may occur at the interface between a Fiber Reinforced Polymer (FRP) and concrete. For this purpose, a two-dimensional cohesive layer constitutive model with a prescribed traction-separation law is constructed from basic principles of continuum mechanics and thermodynamics, taking into account non-Fickian hygrothermal effects that are likely to occur within the cohesive layer. The model is implemented in a test-bed finite element code (NOVA-3D). Benchmark comparisons of finite element predictions with analytical results for a double cantilever beam specimen for model verification are performed. Results from demonstration cases involving bond degradation are also presented.

Matrix Cracking and Delaminations in Orthotropic Laminates Subjected to Freeze-Thaw: Model Development

With the increasing use of fibre composites in applications such as cryogenic liquid hydrogen tanks and repair/retrofitting of bridges, the diffusion and freezing of moisture to form ice is an issue of growing importance. The volumetric expansion of water when it freezes to form ice results in stress concentrations at the inclusion tip that may synergistically interact with the residual tensile stresses in a laminate at low temperatures to initiate a crack. In addition, understanding the long-term effect of daily and/or seasonal freeze-thaw cycling on crack growth in a laminate is of vital importance for structural durability. The objective of this paper is to establish a theoretical framework for the calculation of the stress intensity factor (KI) of a pre-existing crack in a composite structure due to the phase transition of trapped moisture. The constrained volume expansion of trapped moisture due to freezing is postulated to be the crack driving force. The principle of minimum strain energy is employed to calculate the elastic field within an orthotropic laminate containing an idealized elliptical elastic inclusion in the form of ice. It is postulated that a slender elliptical elastic inclusion can be used to approximate the stress field at the crack face, which can subsequently be used to calculate the stress intensity factor, KI, for the crack. The verification of the analytical model predictions and some potential applications will be published in a separate paper.

Characterization and modeling of strength enhancement mechanisms in a polymer/clay nanocomposite

The compressive failure of continuous fiber reinforced composites has received considerable attention in the recent years because it typically occurs at a stress level that is 40-50 % below the tensile strength of the composite. This paper is primarily focused on enhancing the compressive strength of polymer matrix composites (PMC) through a series of modifications in material composition and thermoplastic pultrusion manufacturing process variables. Low-cost commodity resins such as polypropylene (PP), suffer primarily due to low compressive strength. Enhancement of the compressive strength of pultruded thermoplastic composites is achieved by improving the yield strength of the surrounding matrix in shear and reducing fiber misalignment in the composite through optimization of manufacturing process variables. The dispersed platelets are typically one micron in length but only a nanometer in thickness. A single-screw extruder was used to facilitate nanoclay dispersion in PP. This new family of materials exhibits enhanced stiffness and strength of the matrix material, through the inclusion of exfoliated nano-scale montmorillonite particles in the fabrication of resin pre-impregnated (prepreg) glass fiber filaments. After the prepreg was pultruded to form a composite laminate, uniaxial compression tests were performed to determine compression strength of the laminate. Scanning Electron Micrographs (SEM) were taken to examine the failure surfaces. Transmission Electron Microscopy (TEM), were also employed to reveal all nano-scale platelet morphologies, namely exfoliated, intercalated and stacked structures within the samples. Dramatic improvement in compressive strength and compressive modulus were observed with relatively low nanoclay loadings. Compressive strength tests were also performed on aged pultruded PP composite with 0% and 1 % nanoclay loadings, and the data were compared with compressive strength data for unaged specimens. A significant increase (12-20%) in compressive strength was observed after the specimens have been aged for 15 months under ambient conditions. However, a 30% decrease in compressive modulus due to aging was recorded for specimens with 1% clay loading. Multi-scale simulations of nanoclay/polymer interface behavior are currently in progress in order to understand the strength enhancement mechanism.

MODELING OF CRACK OPENING DISPLACEMENT DUE TO DELAMINATION USING FIRST-ORDER SHEAR LAMINATE THEORY

In the present paper the crack opening displacement associated with delaminations that initiate from a matrix crack in a graphite-epoxy laminate (IM6/3501-6) subjected to mechanical and/or thermal loading is calculated using the sublaminate-wise first-order shear laminate theory and verified using a two-dimensional finite element analysis. The delamination induced crack opening displacement (DOD) for known delamination length and crack density is predicted for [0/902]S laminate system with a matrix crack in the 90o plies and delaminations growing uniformly from the matrix crack tip in the 0/90 interfaces. The effect of immediate neighboring ply orientation on DOD is studied by predicting DOD for the [θ/902]S (θ =0o to 90o) laminate system. In order to study the effect of stacking sequence on DOD, two laminate stacking sequences, [0/θ/902]S and [θ/0/902]S (θ =0o to 90o) are examined. It is seen for the examined laminates that the lay-up orientation of the ply adjacent to the 90oplies affects the DOD, whereas the stacking sequence of the neighboring ply groups do not influence the DOD significantly.

Non-Linear Viscoelastic and Physical Ageing Characterisation of Thermoset PR-500 Epoxy Resin

It is now well known that because of their polymeric matrices (and sometimes their use of viscoelastic fibres) structural polymer composites can exhibit creep or stress relaxation behaviour, leading to delayed failure long after the initial design and fabrication process. In addition, these time-dependent viscoelastic properties are significantly influenced by the sub-T physical ageing of these materials. Therefore any durability study of polymer composites for elevated use-temperature applications should address both the nonlinear viscoelastic response and the physical ageing effect of the constituents. The material nonlinearity in the resin has a ‘softening’ effect whereas physical ageing causes polymers to become stiffer and more brittle with age, increasing the likelihood of the more rapid progression of various damage states. Therefore, coupled material nonlinear and physical ageing conditions should be analysed to predict which effect would dominate under the applied loads and duration of loading. The primary objective of this paper is to present an experimental investigation of the nonlinear viscoelastic response of the PR500 resin at various stress levels. Also, the physical ageing characterisation results for a set of temperature and stress conditions are summarised. The properties summarised were successfully used in a multi-scale micro-mechanical methodology1, to study the AS4/PR500 five-harness satin woven-fibre composite laminate. PR500 is the polymer matrix that was modelled using the data presented here.

Simulation and Mechanical Characterization of Crosslinked Nanostructured Silica Aerogels

Crosslinked silica aerogel (x-aerogel) is low density nanostructured porous material with good mechanical properties. The mechanical characterization tests of x-aerogel were performed to establish the feasibility of using this material in different engineering applications as a multi-functional material. Mechanical response of x-aerogel was studied under compression, three-point bending, tension and DMA (dynamic mechanical analysis) tests. A primary glass transition temperature of 130 °C was identified for xaerogel material through DMA. Under uniaxial compression, x-aerogel was found linearly elastic under small strains (<4%), then exhibited yield behavior (until 40% strain), followed by densification and inelastic hardening. At room temperature, the compressive Young’s modulus and Poisson’s ratio were determined to be 129±8 MPa and 0.18, respectively, while the average specific compressive strength was 3.89×10 Nm/kg, which is higher than other conventional materials. Flexural response of x-aerogel material was also studied at room and cryogenic temperature. The specific flexural strength at room temperature was found to be 2.16×10 Nm/kg. The average CTE of x-aerogel was found to be 4.8×10/ C. Numerical simulations were performed to develop a better understanding of structure-property response of highly porous x-aerogel material. The numerical models have attempted to incorporate micro-scale effects, such as particle stiffness, bond strength, particles frictional coefficient, and initial cluster porosity, into macro-scale structure-property relationship for the prediction of Young’s modulus and strength. Compression, tension and bending simulations were performed, and compared with corresponding experiments. Modeling methodology will provide insights for both stiffening and strengthening mechanisms and how these mechanisms can be optimized with minimum weight penalty. Therefore, it is envisioned that numerical modeling will greatly reduce the number of “trial-and-error” experiments necessary to further enhance the properties of this novel material.

Compressive strength enhancement of pultruded thermoplastic composites using nanoclay reinforcement

The compressive failure of continuous fiber reinforced composites has received considerable attention in the recent years because it typically occurs at a stress level that is 40-50 % below the tensile strength of the composite. This paper is primarily focused on enhancing the compressive strength of polymer matrix composites (PMC) through a series of modifications in material composition and thermoplastic pultrusion manufacturing process variables. Low-cost commodity resins such as polypropylene (PP), suffer primarily due to low compressive strength. Enhancement of the compressive strength of pultruded thermoplastic composites is achieved by improving the yield strength of the surrounding matrix in shear and reducing fiber misalignment in the composite through optimization of manufacturing process variables. The dispersed platelets are typically one micron in length but only a nanometer in thickness. A single-screw extruder was used to facilitate nanoclay dispersion in PP. This new family of materials exhibits enhanced stiffness and strength of the matrix material, through the inclusion of exfoliated nano-scale montmorillonite particles in the fabrication of resin pre-impregnated (prepreg) glass fiber filaments. After the prepreg was pultruded to form a composite laminate, uniaxial compression tests were performed to determine compression strength of the laminate. Scanning Electron Micrographs (SEM) were taken to examine the failure surfaces. Transmission Electron Microscopy (TEM), were also employed to reveal all nano-scale platelet morphologies, namely exfoliated, intercalated and stacked structures within the samples. Dramatic improvement in compressive strength and compressive modulus were observed with relatively low nanoclay loadings. Analytical models were developed within the framework of continuum mechanics to predict changes in deformation within the kink band with increased nanoclay loading.