On the Theory of Elasticity of Microinhomogeneous Media with Account for Stochastic Changes in the Connectivity of Constituent Components

The paper proposes a mathematical model aimed at calculating the effective elastic moduli of a micro-inhomogeneous two-component isotropic composite material, which components are connected randomly depending on the level of their relative volumetric contents. A stochastic equation is formulated for the connectivity parameter of the constituent components, according to which, with an increase in the volumetric content of the filler, individual inclusions build the structures of the matrix mixture in the form of interpenetrating frameworks, and then turn into a new binding matrix with individual inclusions from the material of the rest of the old matrix. The algorithm for the numerical solution of this stochastic differential equation is constructed in accordance with the Euler-Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random connectivity function of the constituent components of the composite material. A variant of the method aimed at calculating the mathematical expectation of a random connectivity function of the constituent components has been developed and the corresponding differential equation has been obtained for it. It is shown that the numerical solution of this equation and the average value of the production factor function calculated for all realizations of stochastic trajectories give close numerical values. New macroscopic constitutive relations are found for microinhomogeneous materials with a variable microstructure and their effective elastic moduli are calculated. It is noted that the formulas for these effective elastic moduli generalize the known results for isotropic composite materials. The values of the effective elastic moduli, constructed according to the expressions obtained in the paper, lie within the Khashin-Shtrikman range for the lower and upper bounds of the effective elastic moduli of the composite materials. The numerical analysis of the developed models showed a good agreement with the known experimental data.

Evaluation of Stress Distribution of Isotropic, Composite, and FG Beams with Different Geometries in Nonlinear Regime via Carrera-Unified Formulation and Lagrange Polynomial Expansions

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research.

GLOBAL-LOCAL PROGRESSIVE DAMAGE ANALYSIS OF COMPOSITE LAMINATES USING LAYER-WISE HIGHER-ORDER STRUCTURAL MODELSv

The objective of the current work is to develop a global-local framework for the progressive damage analysis of composite laminated structures. The technique involves two sequential analyses—an initial low-fidelity 3D-FE based linear analysis of the global structure, followed by the local nonlinear analysis of critical regions where damage is likely to occur. The numerical models used for the local analysis are developed using higher-order layer-wise structural theories obtained via the Carrera Unified Formulation. Composite damage is modelled using the CODAM2 model based on continuum damage mechanics, and the nonlinear problem is solved using explicit time integration schemes. Preliminary assessments are carried out to validate the proposed global-local framework by considering open-hole tensile specimens of quasi-isotropic composite laminates. Both full-scale CUF models and the proposed global-local approach are used to predict the tensile strength of the specimen. It is shown that the obtained results are in good agreement with experiment data, thus validating the framework, and a multi-fold improvement in computational time is demonstrated.

3D Modelling of the Scattering of the Fundamental Anti-Symmetric Lamb Mode (A0) Propagating within a Point-Impacted Transverse-Isotropic Composite Plate

The present paper deals with an effort to model impact damage in 3D-FE simulation. In this work, we studied the scattering behavior of an incident A0 guided wave mode propagating towards an impacted damaged zone created within a quasi-isotropic composite plate. Besides, barely visible impact damage of the desired energy was created and imaged using ultrasonic bulk waves in order to measure the size of the damage. The 3D-FE frequency domain model is then used to simulate the scattering of an incident guided wave at a frequency below an A1 cut-off with a wavelength comparable to the size of the damaged zone. The damage inside the plate is modeled as a conical-shaped geometry with decayed elastic stiffness properties. The model was first validated by comparing the directivity of the scattered fields for the A0 Lamb mode predicted numerically with the experimental measurements. The modeling of the impact zone with conical-shape geometry showed that the scattering directivity of the displacement field depends significantly on the size (depth and width) of the conical damage created during the point-impact of the composite with potential applications allowing the determination of the geometric characteristics of the impacted areas.

Coda Waves for Health Monitoring of Composites Under Low-Velocity Impact

Coda waves have been shown to be sensitive to lab-controlled defects such as very small holes in fibrous composite material. In the real world, damages are subtler and more irregular. The main objective of this work is to investigate coda wave capability to detect low-velocity impact damages. The emphasis is to detect the presence of barely visible impact damages using ultrasonic waves. Detection of incipient damage state is important as it will grow over the life of the structure. Differential features, previously used in similar work, have been utilized to detect realistic impact damages on carbon fiber composites. Quasi-isotropic composite laminates were subjected to low-velocity impact energy ranging from 2J to 4.5J. Two differential features reported could be used detect the presence of damage. It is also observed that ply orientation can be a deterministic factor for indicating damages. The size and shape of the impact damage has been characterized using ultrasonic C-scans. Results indicate that coda waves can be used for the detection of damage due to low-velocity impact.

Modelling Anisotropy Influence on Guided Wave Scattering at Composite Delaminations

Carbon fibre reinforced composite laminates are widely used in aerospace structures but are prone to barely visible impact damage (BVID). Depending on impact severity, delaminations can form below the surface of the laminate, reducing the load bearing capacity. Efficient structural health monitoring (SHM) of composite panels can be achieved using guided waves propagating along the structure. Propagation and scattering of the A0 Lamb wave mode in a quasi-isotropic composite laminate was modelled using full three-dimensional (3D) Finite Element (FE) simulations. Individual ply layers were modelled using homogeneous unidirectional composite material properties to accurately capture the anisotropy effects. FE predictions for scattering and energy trapping at delaminations were compared to experimental measurements. Noncontact, full-wavefield guided wave measurements were obtained using a laser vibrometer. Good agreement was found between experiments and FE predictions. The effect of delamination shape and depth was investigated through a numerical parameter study. The angular dependency of the amplitude of the scattered wave was calculated. The influence of ply layer anisotropy on wave propagation in an undamaged laminate was investigated numerically. The sensitivity of guided waves for the detection of delaminations due to barely visible impact damage (BVID) in composite panels has been verified.

The Elastic Characterization of Composite Based on Ultrasonic Waves

Anisotropic composite materials have been extensively utilized in mechanical, automotive, aerospace and other engineering areas due to high strength-to-weight ratio, superb corrosion resistance, and exceptional thermal performance. As the use of composite materials increases, determination of material properties, mechanical analysis and failure of the structure become important for the design of composite structure. In particular, the fatigue failure is important to ensure that structures can survive in harsh environmental conditions. Despite technical advances, fatigue failure and the monitoring and prediction of component life remain major problems. In general, cyclic loadings cause the accumulation of micro-damage in the structure and material properties degrade as the number of loading cycles increases. Repeated subfailure loading cycles cause eventual fatigue failure as the material strength and stiffness fall below the applied stress level. Hence, the stiffness degradation measurement can be a good indication for damage evaluation. The elastic characterization of composite material using mechanical testing, however, is complex, destructive, and not all the elastic constants can be determined. In this work, an in-situ method to non-destructively determine the elastic constants will be studied based on the time of flight measurement of ultrasonic waves. This method will be validated on an isotropic metal sheet and a transversely isotropic composite plate.