Multiscale approaches for the failure analysis of fiber-reinforced composite structures using the 1D CUF

Composites provide significant advantages in performance, efficiency and costs; thanks to these features, their application is increasing in many engineering fields, such as aerospace, naval and mechanical engineering. Although the adoption of composites is rising, there are still open issues to be investigated, in particular, understanding their failure mechanism has a prominent role in enhancing component designs. Numerous methodologies are available to compute accurate stress/strain fields for laminated structures, multi-scale approaches are required when micro- and macro-scales are accounted for. Despite the increasing development in computer hardware, the computational effort of these methods is still prohibitive for extensive applications, especially when a high number of layers is considered. Then, the reduction of the computational time and cost required to perform failure analysis is still a challenging task. This work proposes two multiscale approaches for the failure analysis of fiber-reinforced composites. A concurrent multiscale approach ("Component-Wise") and a hierarchical method are developed based on the 1D Carrera Unified Formulation (CUF). 1D higher order elements are very powerful tools for multiscale analysis since they provide accurate stress and strain fields with very low computational costs

Evaluation of energy and failure parameters in composite structures via a Component-Wise approach

This paper deals with the static analysis of fiber reinforced composites via the Component-Wise approach (CW). The main aim of this work is the investigation of the CW capabilities for the evaluation of integral quantities such as the strain energy, or integral failure indexes. Such quantities are evaluated in the global structures and local volumes. The integral failure indexes, in particular, are proposed as alternatives to point-wise failure indexes. The CW approach has been recently developed as an extension of the 1D Carrera Unified Formulation (CUF). The CUF provides hierarchical higher-order structural models with arbitrary expansion orders. In this work, Lagrange-type polynomials are used to interpolate the displacement field over the element cross-sections. The CW makes use of the 1D CUF finite elements to model simultaneously different scale components (fiber, matrix, laminae and laminates) with a reduced computational cost. CW models do not require the homogenization of the material characteristics nor the definition of mathematical lines or surfaces. In other words, the material characteristics of each component, e.g. fibers and matrix, are employed, and the problem unknowns are placed above the physical surface of the body. In the perspective of failure analyses, the integral evaluation of failure parameters is introduced to determine critical portions of the structure where failure could take place. Integral quantities are evaluated using 3D integration sub-domains that may cover macro- and micro-volumes of the structure. The integral quantities can be evaluated directly on fiber and matrix portions. Numerical results are provided for different configurations and compared with solid finite element models. The results prove the accuracy of the CW approach and its computational efficiency. In particular, 3D local effects can be detected. The use of the integral failure index provides qualitatively reliable results; however, experimental campaigns should be carried out to relate such indexes to the failure occurrence

Fast two-scale computational model for progressive damage analysis of fiber reinforced composites

A fast two-scale finite element framework based on refined finite beam models for progressive damage analysis (PDA) of fiber reinforced composite is presented. The framework consists of a macroscale model to define the structural-level components, interfaced with a second sub-scale model at the fiber-matrix level. Refined finite beam elements are based on Carrera Unified Formulation (CUF), a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. The representative volume element (RVE) at the subscale is modeled with real material, e.g., fiber and matrix with details about packing and heterogeneity. Component-Wise approach (CW), an extension of refined beam kinematics based on Lagrange-type polynomials is used to model the constituents in the subscale. Each constituent in the subscale is modeled by the same finite element in the framework of the CW. The energy based crack band theory (CBT) is implemented within the subscale constitutive laws to predict the damage propagation in individual constituents. The communication between the two scales is achieved through the exchange of strain, stress and stiffness tensor at every integration point in the macroscale model. The efficiency of the framework is derived from the ability of CUF models to provide accurate three-dimensional displacement and stress fields at a reduced computational cost (approximately one order of magnitude of degrees of freedom less as compared to standard 3D brick elements). Numerical predictions are validated against the experimental results

Accurate predictions of thermoset resin glass transition temperatures from all-atom molecular dynamics simulation

To enable the design and development of the next generation of high-performance composite materials, there is a need to establish improved computational simulation protocols for accurate and efficient prediction of physical, mechanical, and thermal properties of thermoset resins. This is especially true for the prediction of glass transition temperature (Tg), as there are many discrepancies in the literature regarding simulation protocols and the use of cooling rate correction factors for predicting values using molecular dynamics (MD) simulation. The objectives of this study are to demonstrate accurate prediction the Tg with MD without the use of cooling rate correction factors and to establish the influence of simulated conformational state and heating/cooling cycles on physical, mechanical, and thermal properties predicted with MD. The experimentally-validated MD results indicate that accurate predictions of Tg, elastic modulus, strength, and coefficient of thermal expansion are highly reliant upon establishing MD models with mass densities that match experiment within 2%. The results also indicate the cooling rate correction factors, model building within different conformational states, and the choice of heating/cooling simulation runs do not provide statistically significant differences in the accurate prediction of Tg values, given the typical scatter observed in MD predictions of amorphous polymer properties

Curing-Induced Residual Stress and Strain in Thermoset Composites

Uncontrolled curing-induced residual stress and strain are significant limitations to the efficient design of thermoset composites that compromise their structural durability and geometrical tolerance. Experimentally validated process modeling for the evaluation of processing parameter contributions to the residual stress build-up is crucial to identify residual stress mitigation strategies and enhance structural performance. This work presents an experimentally validated novel numerical approach based on higher-order finite elements for the process modeling of fiber-reinforced thermoset polymers across two composite characteristic length scales, the micro and macro-scale levels. The cure kinetics is described using an auto-catalytic phenomenological model. An instantaneous linear-elastic constitutive law, informed by time-dependent material characterization, is used to evaluate the stress state evolution as a function of the degree of cure and time. Micromechanical modeling is based on Representative Volume Elements (RVEs) that account for random fiber distribution verified against traditional 3D FE analysis. 0/90 laminate testing at the macroscale validates the proposed approach with an accuracy of 9%

Thermoset Polymers Characterization as a Function of Cure State Using Off-stoichiometry Proxies

Rapid reaction kinetics often produce drastic changes in the thermo-chemo-mechanical characteristics of thermoset polymers over short time periods. Thus, it is a major challenge to quantify material properties over the entire spectrum of cure states at relevant temperatures with both efficiency and accuracy. This work presents a novel characterization technique as a function of the cure state of a difunctional epoxy with amine curing agent through off-stoichiometry mixing formulations that serve as proxies for the intermediately crosslinked polymer. Mass density, cure kinetics, and elastic and strength properties are characterized across four mixing ratios, and relative cure/crosslinked states of off-stoichiometry cases are quantified. Essential to this unique approach is the capability to eliminate time dependence resulting from reaction kinetics on characterizing intermediate crosslinking states. The procedure reported herein facilitates efficient and accurate measurement of properties of curing epoxies for building and validating computational process modeling frameworks developed for optimizing material performance

Chemical Shrinkage Characterization during Curing through Three-Dimensional Digital Image Correlation

Chemical shrinkage in thermosetting polymers drives residual stress development and induces residual deformation in composite materials. Accurate characterization of chemical shrinkage during curing is therefore vital to minimize residual stresses through process modeling and optimize composite performance. This work introduces a novel methodology to measure the pre- and post-gelation chemical shrinkage of an epoxy resin using three-dimensional digital image correlation (3D-DIC). Differential scanning calorimetry (DSC) is employed to calculate reaction kinetics and correlate chemical shrinkage with the degree of cure. Rheology experiments are conducted to quantify gelation and validate post-gelation. 3D-DIC post-gelation results show excellent agreement with rheology. Pre-gelation results show the effect of the in-situ curing in the proximity of constraints on the global strain behavior. This work introduced an innovative approach to characterize the chemical shrinkage of thermosets during curing, which will enable accurate residual stress prediction for enhancing thermoset composite performance and provide insight into the in-situ polymer behavior during processing

A novel approach to characterization of composite polymer matrix materials for integrated computational materials engineering approaches

This work presents a novel methodology for polymer matrix material characterization as a function of the degree of cure by performing mechanical testing of stoichiometric and off-stoichiometric formulations of the Hexion EPON 862/EPIKURE W (DGEBF/DETDA) system, a thermosetting epoxy resin with applications in the aerospace industry. Computational process models rely upon thorough material characterization in order to accurately predict the accumulation of mechanical performance-affecting residual stresses within composite materials. During the manufacturing of polymer matrix composites, the constituent matrix material transitions in phase from liquid to solid via chemical crosslinking of monomers known as the curing process. This phenomenon is an autocatalytic chemical reaction, presenting a challenge in the traditional characterization procedure, where mechanical properties are continuously evolving as a function of the degree of cure that is overcome in this work. Cure kinetics are characterized for each formulation through the Differential Scanning Calorimetry technique. Resin strength is determined for the stoichiometric cases through uniaxial, quasi-static tension testing. The resulting mechanical properties for the EPON 862/EPIKURE W system are discussed as a function of the degree of cure to serve as inputs for high-fidelity computational process models within the Integrated Computational Materials Engineering framework

Modeling cure induced damage in Fiber Reinforced Composites

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140491/1/6.2015-0967.pd