Computational modeling of the probabilistic impact response of flexible fabrics

The impact response of flexible woven fabrics is probabilistic in nature and described through a probabilistic velocity response curve or V₀–V₁₀₀ curve. Computational impact analyses based on deterministic methods are incapable of predicting the experimentally observed probabilistic fabric impact response. To overcome this limitation we have developed a probabilistic computational framework within a finite element analysis to predict the V₀–V₁₀₀ response. The finite element model is a yarn-based representation of the fabric architecture, with a principal stress based failure criterion implemented uniformly within each yarn, but varying for each yarn within the fabric. For each impact simulation, individual yarn strengths are mapped from experimentally obtained yarn strength distributions, resulting in fabric models with spatially non-uniform failure conditions. Impact simulations are run for the case of a spherical projectile of diameter 5.556 mm impacting a single layer of 50.8 × 50.8 mm, edge-clamped, unbacked, aramid fabric. Three different yarn strength models are implemented, representing spool yarns, and yarns extracted from greige and scoured woven fabrics. Decreases in yarn strength are found to correlate to decreases in the V₁, V₅₀, and V₉₉ velocities predicted by the simulations. The relationships between yarn strength distribution and probabilistic fabric impact response are discussed.     

Ballistic impact modeling of woven fabrics considering yarn strength,friction, projectile impact location,and fabric boundary condition effects

The combined effects of yarn tensile strength, inter-yarn friction, projectile impact location, and fabric clamping conditions on the probabilistic impact response of flexible woven Kevlar KM2 fabrics are studied using a 0.22 caliber spherical projectile. The statistical nature of yarn tensile strength is accounted for by mapping Weibull strength distributions onto the individual yarns of the fabric model. Variability in projectile impact location relative to the yarns at the impact site is accounted for by randomly selecting one of 25 predetermined impact locations around a warp-fill yarn cross-over location at the center of the fabric. Five different inter-yarn friction levels are deterministically implemented, ranging from 0.0 to 0.4. Two boundary conditions are considered, 4-sided clamped and 2-sided clamped. Forty impact simulations are used to generate a probabilistic impact response (PVR) curve for each test case, describing the probability of fabric penetration as a function of projectile impact velocity. The fabric V₅₀ velocity and impact performance variability were observed to decrease with increasing inter-yarn friction levels for the 4-sided clamped cases, while they increased for the 2-sided clamped cases.     

Finite element modeling of ballistic impact on multi-layer Kevlar 49 fabrics

This paper presents a material model suitable for simulating the behavior of dry fabrics subjected to ballistic impact. The developed material model is implemented in a commercial explicit finite element (FE) software LS-DYNA through a user defined material subroutine (UMAT). The constitutive model is developed using data from uniaxial quasi-static and high strain rate tension tests, picture frame tests and friction tests. Different finite element modeling schemes using shell finite elements are used to study efficiency and accuracy issues. First, single FE layer (SL) and multiple FE layers (ML) were used to simulate the ballistic tests conducted at NASA Glenn Research Center (NASA-GRC). Second, in the multiple layer configuration, a new modeling approach called Spiral Modeling Scheme (SMS) was tried and compared to the existing Concentric Modeling Scheme (CMS). Regression analyses were used to fill missing experimental data – the shear properties of the fabric, damping coefficient and the parameters used in Cowper-Symonds (CS) model which account for strain rate effect on material properties, in order to achieve close match between FE simulations and experimental data. The difference in absorbed energy by the fabric after impact, displacement of fabric near point of impact, and extent of damage were used as metrics for evaluating the material model. In addition, the ballistic limits of the multi-layer fabrics for various configurations were also determined.     

Finite element analysis of projectile size and shape effects on the probabilistic penetration response of high strength fabrics

The effects of projectile characteristics on the probabilistic impact response of single-layer fully-clamped flexible woven fabrics is numerically studied using a yarn-level fabric model with a statistical implementation of yarn strengths. Six small and large sized spherical, cylindrical, and conical projectiles of the same mass are considered. Probabilistic velocity response curves which describe the probability of fabric penetration as a function of projectile impact velocity are generated for each projectile type through a series of forty impact simulations at varying impact velocities. The probabilistic fabric impact response is observed to be strongly dependent on the shape of the projectile’s impact face and the manner of projectile–yarn interactions at the impact site.     

Numerical homogenization of textile composites based on shell element discretization

The paper presents a shell element based unit cell approach for numerical homogenization of fiber reinforced textile composites. The modeling strategy is set up within the framework of the Finite Element Method with special emphasis on numerical efficiency, which becomes particularly important in the perspective of non-linear implicit simulations. A single layer of fabric is considered and the tows as well as the unreinforced matrix pockets are discretized by shell elements which are coupled appropriately allowing for delamination between the constituents. The approach is discussed, and the linear as well as the geometrical non-linear mechanical response of an example fabric is compared to a continuum based discretization of the same fabric. Additionally, simulations including delaminations are conducted. The substantially improved numerical efficiency of the shell based approach is shown.     

Finite element analysis of textile composite preform stamping

The forming or draping of a textile composite preform may result in large changes in the fibrous microstructure of the preform. This change in the local fiber orientation leads to significant changes in the fabric permeability as well as the mechanical properties of the ensuing composite structure. Therefore, this change in orientation of the tows of the preform needs to be known accurately to calculate the various effective properties of the composite. A new finite element approach for stamping analysis of a plain-weave textile composite preform has been developed. This model is simple, efficient and can be used in the existing finite element codes. The model represents the preform as a mesh of 3-D truss elements and 3-D shell elements. The truss elements model the tows, which are allowed to both scissor and slide relative to one another. The shell elements represent a fictitious material that accounts for inter-tow friction and fiber angle jamming. The model takes into account large strains and large deformations. In-plane uniaxial tension tests have been performed on plain-weave specimens for determining the constitutive law of the transforming medium and to show the inter-tow sliding. Application of the model is demonstrated by simulating the stamping of a preform by a spherical punch. The results from the simulation show good correlation with results from the experiments.     

Anisotropic creep modeling of coated textile membrane using finite element analysis

Coated textile membranes (CTMs) form a class of flexible textile composites undergoing viscoelastic deformation because they consist of a polymeric reinforcement and matrix and are tensioned in service. In most CTMs, woven fabrics are frequently used as a reinforcement structure, causing anisotropic mechanical behavior including time dependent viscoelastic deformation. To describe such anisotropic and nonlinear time dependent deformation, the creep potential with three orthotropic parameters was introduced and incorporated into finite element software through a user material subroutine. The three parameters included in the creep potential were determined by carrying out off-axis coupon creep tests and using various mathematical formulae for the effective creep compliance. To validate the current creep modeling and its implementation in finite element software, off-axis coupon creep tests were re-simulated and compared with the experiments, showing that the present modeling can describe the anisotropic and nonlinear creep deformation of CTM with acceptable accuracy.     

Three-dimensional computational micro-mechanical model for woven fabric composites

This work presents a computational material model for plain-woven fabric composite for use in finite element analysis. The material model utilizes the micro-mechanical approach and the homogenization technique. The micro-mechanical model consists of four sub-cells, however, because of the existing anti-symmetry only two sub-cells have to be homogenized for prediction of the elastic material properties. This makes the model computationally very efficient and suitable for large-scale finite element analysis. The model allows the warp and fill yarns not to be orthogonal in the plane of the composite ply. This gives the opportunity to model complex-shaped composite structures with different braid angles. General homogenization procedure is employed with two levels of property homogenization. The model is programmed in MATLAB software and the predicted material properties of different composite materials are compared and presented. The material model shows good capability to predict elastic material properties of composites and very good computational efficiency.     

Adaptive multi-scale modeling of high velocity impact on composite panels

A computationally efficient adaptive multi-scale methodology for modeling composites under high rates of loading is proposed. The physically based model relies on micromechanical properties of the constituents only. The adaptive algorithm switches between two different constitutive laws. Initially, the material response is calculated based on effective linear-elastic, orthotropic material properties at the ply scale which are calculated using the rule of mixtures. A modified Hashin–Rotem criterion is then used to identify the switch to a more accurate micromechanical analysis based on the generalized method of cells (GMC). The methodology is verified by simulating tensile tests on laminates with different stacking sequences. Finally the model validated against experimental data for high-velocity impact on quasi-isotropic composite targets taken from the literature in order to illustrate the efficiency and accuracy of the proposed methodology.     

Finite element modeling of lamb wave propagation in anisotropic hybrid materials

A finite element approach for modeling of acoustic emission sources and signal propagation in hybrid multi-layered plates is presented. Modeling results are validated by Laser vibrometer measurements and comparison to calculated dispersion curves. We investigate hybrid plates as typically found in composite pressure vessels, composed of fiber reinforced polymers with arbitrary stacking sequences and attached metal or polymer materials. Hybrid plate thickness, the ratio between anisotropic and isotropic materials and material properties are varied. Lamb-wave propagation in a geometry representative of a pressure vessel is modeled. It is demonstrated, that acoustic emission sources in multi-layered structures can cause Lamb-waves superimposed by guided waves within the individual layers.     

Effect of statistical yarn tensile strength on the probabilistic impact response of woven fabrics

The probabilistic impact response of flexible woven fabrics can be described through the V₀–V₁₀₀ or probabilistic velocity response (PVR) curve which describes the probability of fabric penetration as a function of projectile impact velocity. One source of variability that affects the probabilistic nature of fabric impact performance is the statistical distribution of yarn tensile strengths. In this paper the effects of the statistical yarn strength distribution characteristics on the probabilistic fabric impact response are computationally studied using five different strength distributions with differing mean strengths and distribution widths. Corresponding fabric PVR curves are generated for each strength distribution using a probabilistic computational framework that involves randomly mapping yarn strengths onto the individual woven yarns of a fabric finite element model and then running a series of impact simulations for the case of a four-sided clamped fabric impacted at the center by a spherical projectile.     

FEM modeling of multilayered textile composites based on shell elements

The paper presents a shell element based unit cell approach for numerical homogenization of fiber reinforced textile laminates. The modeling strategy is set up within the framework of the Finite Element Method. Multilayer laminates comprising equal weaves are considered and the constituents, i.e. the tows as well as the unreinforced matrix pockets are discretized by shell elements only which are coupled appropriately. A study on the effective extensional laminate-shell stiffnesses is presented, the results are discussed, and are compared to approaches found in the literature. Additionally, geometrically nonlinear simulations are conducted and the results are compared with experimental tests from literature.     

A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite

Textile composites are well known for their excellent through thickness properties and impact resistance. In this study, a representative unit cell model of a triaxial braided composite is developed based on the composite fiber volume ratio, specimen thickness and microscopic image analysis. A meso-scale finite element (FE) mesh is generated based on the detailed unit cell dimensions and fiber bundle geometry parameters. The fiber bundles are modeled as unidirectional fiber reinforced composites. A micromechanical finite element model was developed to predict the elastic and strength material properties of each unidirectional composite by imposing correct boundary conditions that can simulate the actual deformation within the braided composite. These details are then applied in the meso-mechanical finite element model for a 0°/+60°/−60° triaxially braided T700s/E862 carbon/epoxy composite. Model correlations are conducted by comparing numerical predicted and experimental measured axial tension and transverse tension response of a straight-sided, single-layer (one ply thick) coupon. By applying a periodic boundary condition in the loading direction, the meso model captures the local damage initiation and global failure behavior, as well as the periodic free-edge warping effect. The failure mechanisms are studied using the field damage initiation contours and local stress history. The influence of free-edge effect on the failure behaviors is investigated. The numerical study results reveal that this meso model is capable of predicting free-edge effect and allows identification of its impact on the composite response.     

Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.     

A unit cell approach of finite element calculation of ballistic impact damage of 3-D orthogonal woven composite

This paper presents ballistic impact damages of 3-D orthogonal woven composite in finite element analysis (FEA) and experimental. A unit-cell model of the 3-D woven composite was developed to define the material behavior and failure evolution. A user-defined subroutine VUAMT was compiled and connected with commercial available FEA code ABAQUS/Explicit to calculate the ballistic penetration. Ballistic impact tests were conducted to investigate impact damage of 3-D kevlar/glass hybrid woven composite. Residual velocities of conically-cylindrical steel projectiles (Type 56 in China Military Standard) and impact damage of the composite targets after ballistic perforation were compared both in theoretical and experimental. The reasonable agreements between FEA results and experimental results prove the validity of the unit-cell model in ballistic limit prediction of the 3-D woven composite. We believe such an effort could be extended to bulletproof armor design with the 3-D woven composite.     

Finite element analyses on transverse impact behaviors of 3-D circular braided composite tubes with different braiding angles

This paper presents finite element analyses (FEA) on the transverse impact responses of 3-D circular braided composite tubes with the braiding angles of 15°, 30° and 45°. A finite element model of the braided composite tube was established at microstructure level to analyze the transverse impact behaviors. From the FEA results, the impact damage, deformation and stress distribution were obtained to analyze the damage mechanism. Stress propagation in lower braiding angle tubes was faster than that of the higher braiding angle. The impact responses of the braided composite tubes were also tested to obtain load–displacement curves and energy absorption for the comparisons with the FEA results. The impact damage and fracture morphology obtained from the FEA were in good agreement with the experimental results, which demonstrated the feasibility of the FEA model for the design of the braided tube.     

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.     

Micromechanics modeling of fatigue failure mechanisms in a hybrid polymer matrix composite

Initiation of fatigue damage for a hybrid polymer matrix composite material was studied via 3-Dimensional viscoelastic representative volume element modeling in order to gain further understanding. It was found that carbon fiber reinforced composites perform better in fatigue loading, in comparison to glass fiber reinforced composites, due to the fact that the state of stress within the matrix material was considerably lower for carbon fiber reinforced composites eliminating (or at least prolonging) fatigue damage initiation. The effect of polymer aging was also evaluated through thermal aging of neat resin specimens. Short-term viscoelastic material properties of unaged and aged neat resin specimens were measured using Dynamic Mechanical Analysis. With increasing aging time a corresponding increase in storage modulus was found. Increases in the storage modulus of the epoxy matrix subsequently resulted in a higher state of predicted stress within the matrix material from representative volume element analyses. Various parameters common to unidirectional composites were numerically investigated and found to have varying levels of impact on the prediction of the initiation of fatigue damage.     

The effect of hybridization on the ballistic impact behavior of hybrid composite armors

In the present study, effect of hybridization on the hybrid composite armors under ballistic impact is investigated using hydrocode simulations. The hybrid composite armor is constructed using various combinations and stacking sequences of fiber reinforced composites having woven form of fibers specifically high specific-modulus/high specific-strength Kevlar fiber (KF), tough, high strain-to-failure fiber Glass fiber (GF) and high strength/high stiffness Carbon fiber (CF). Different combinations of composite armors studied are KF layer in GF laminate, GF layer in KF laminate, KF layer in CF laminate and CF layer in KF laminate at various positions of hybridized layers for a fixed thickness of the target. In this article the results obtained from the finite element model are validated for the case of KF layer in a GF laminate with experimental predictions reported in the literature in terms of energy absorption and residual velocity and good agreement is observed. Further, the effect of stacking sequence, projectile geometry and target thickness on the ballistic limit velocity, energy absorbed by the target and the residual velocity are presented for different combinations of hybrid composite armors. The simulations show that, at a fixed thickness of the hybrid composite armor, stacking sequence of hybridized layer shows significant effect on the ballistic performance. The results also indicate energy absorption and ballistic limit velocity are sensitive to projectile geometry. Specifically, it is found that arranging the KF layer at the rear side, GF layer in the exterior and CF layer on the front side offers good ballistic impact resistance. The hybrid composite armor consisting of a CF layer in KF laminate acquires maximum impact resistance and is the best choice for the design compared to that of other combinations studied.     

Mechanics of textile composites: Micro-geometry

Textile fabric geometry determines textile composite properties. Textile process mechanics determines fabric geometry. In previous papers, the authors proposed a digital element model to generate textile composite geometry by simulating the textile process. The greatest difficulty encountered with its employment in engineering practice is efficiency. A full scale fiber-based digital element analysis would consume huge computational resources. Two advances are developed in this paper to overcome the problem of efficiency. An improved contact-element formulation is developed first. The new formulation improves accuracy. As such, it permits a coarse digital element mesh. Then, a static relaxation algorithm to determine fabric micro-geometry is established to replace step-by-step textile process simulation. Employing the modified contact element formulation in the static relaxation approach, the required computer resource is only 1–2% of the resource required by the original process. Two critical issues with regards to the digital element mesh are also examined: yarn discretization and initial yarn cross-section shape. Fabric geometries derived from digital element analysis are compared to experimental results.