Reza Vaziri

Composite forming is an intricate multi-physics process involving ply slippage, shearing, bending, and compaction within a viscous matrix. Existing simulation technologies primarily adopt shell-based modelling, often sidelining thickness effects and limiting the accuracy of ply-level defect predictions. In response to this limitation, this work integrates the Cosserat continuum (micropolar) theory, offering a mechanism-based approach to capturing the unique layered kinematics of composite layups.A Cosserat continuum extends the traditional continuum models by introducing an additional rotational degree of freedom, providing a framework for accommodating asymmetric shear behaviour and intrinsic bending observed experimentally during the forming process.This theory has been integrated into a custom-built 2D explicit finite element model in MATLAB. The model leverages high-order elements and a co-rotational edge tracking method to define material orientation. To capture the soft and highly deformable behaviours of the uncured composite materials during forming and consolidation, the model incorporates various constitutive responses such as nonlinear fibre-bed compaction, viscoelasticity, and inter-layer plastic slip.The accuracy of the model is demonstrated through extensive verification against analytical solutions and Abaqus models, affirming its robustness under large-strain and large-rotation conditions. The Cosserat-based model efficiently simulates layered structures with fewer nodes and by bypassing the need for contact algorithms, provided the macroscopic behaviour remains continuous. The model is further shown to provide its practical relevance in composite manufacturing by offering valuable insights into wrinkle formation during the consolidation of a C-Channel spar.This research represents a proof of concept, highlighting the potential of the explicit/Cosserat approach in accurately modelling the deformational response of composites during processing. Future enhancements could focus on increasing the speed of the explicit solver, or porting the methodology to a commercial platform as a user element subroutine.

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This work extends the Integrated Flow-Stress (IFS) model framework to new frontiers, including capturing the complex two-way interactions between the deformation of solid fiber-bed and the flow of fluid resin, as well as predicting the effect of an additional compressible phase (gas or porosity) on resin distribution and deformation of the part. The first generation of IFS models presented a sequential coupling between the flow model, based on Darcy’s law, and the stress model, based on Terzaghi’s principle, to find the distortion of composite part and its fiber volume fraction during prepreg processing. As the sequential coupling failed to account for the effect of solid deformation on resin flow, the 2nd generation 3-Phase IFS (3PIFS) model introduced a state variable called the solidification factor, which implicitly accounts for pressure sharing between the fluid and solid phases and controls the effective shear and bulk moduli of the composite system.The current Multiscale Viscoelastic 3PIFS model benefits from newly developed computational modules and material characterization procedures. Firstly, the set of governing equations in the original 3PIFS are reformulated in mixed form involving displacements and pressure as elemental degrees of freedom in order to facilitate their implementation in commercial finite-element codes. Secondly, this work uses a differential form viscoelastic material model as the constitutive equation of the resin to account for resin hardening and stress relaxation in complex multi hold cure cycles.Moreover, to find permissible values of the solidification factor during consolidation, the effect of this parameter on solid-fluid pressure-sharing is studied. This parameter is also characterized as a function of both the temperature and degree of cure. Finally, a multiscale porosity model is developed to capture the effects of gas entrapment and capillary pressure on the porosity distribution at micro- and macroscale in the prepreg. This model is verified and validated by comparing the predicted transverse strain, pressure, and porosity distribution to the results of several numerical and experimental tests in the literature involving prepreg’s cure and consolidation under one- and two-hold cure cycles.

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An accurate and efficient predictive tool for process modelling of fibre-reinforced polymeric composite materials is highly desirable because of high production cost and substantial risk involved in their manufacturing. Process modelling of composite materials is complex due to multitude of physical and chemical processes such as flow of resin and gaseous volatiles through the fibre-bed, thermochemical changes, and stress development. These phenomena are usually simulated sequentially in a so-called “integrated sub-model” framework.In the sequential method, (i) mapping of the results from one state to another is performed in a tedious and inefficient process, (ii) the concurrent occurrence of resin flow and stress development is ignored, (iii) the history of pressure during the flow regime of processing is relinquished, and (iv) the local spatial and temporal variations in resin gelation is not captured. Incorporating the main steps of process modeling into a unified module that captures the various phenomena in a continuous manner would help overcome the foregoing drawbacks of the sequential approach.In this thesis, a new methodology is presented to integrate the simulation of resin and gas flow and stress development into a unified computational modelling framework. The governing equations are developed for the general case of a composite system that initially is regarded as a three-phase liquid-gas-solid system and, as a consequence of curing, the resin undergoes a transition from a fluid-like state into an elastic solid forming a solid cured composite material. The employed constitutive equations provide a continuous representation of the evolving material behaviour while maintaining consistency with the formulations that are typically used to represent the material at each of the two processing extremes. The model is implemented in a 2D plane strain displacement-velocity-pressure (u-v-P) finite element code developed in MATLAB. Various numerical examples are presented to demonstrate the capability of the Integrated Flow-Stress (IFS) model to predict the flow-compaction and stress development throughout the curing process of thermoset composite materials. The interactive effects of resin flow, gas flow, and stress development are investigated and comparisons are made with the predicted results obtained from the application of the stress model alone.

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The progression of damage in composite laminates is influenced by the interactions of several failure/damage mechanisms including matrix cracking, fibre breakage, splitting and delamination. In capturing detailed prediction of various damage modes, it is important to maintain the efficiency of the computational models so that they can be readily used by engineers for damage tolerant design of composite components. Continuum damage models are commonly employed to simulate the smeared response of certain failure modes such as matrix cracking and fibre failure due to their higher numerical efficiency in comparison with discrete damage models. However, application of continuum damage based models for accurate prediction of the onset and propagation of macro-discrete damage modes (i.e. splitting and delamination) and their interactions with other failure modes is limited. This work presents an efficient methodology to capture the interacting effect of discrete and smeared cracks based on a combination of the continuum and discrete approaches. Here, delamination is the only damage mode captured by a discrete approach (cohesive zone interface), while all intra-laminar forms of damage including splitting are modelled using the non-local composite damage model (CODAM2) in a mesoscopic context. Through placement of discrete delamination interfaces and synchronizing the onsets of delamination and matrix cracks, the computational effort is markedly reduced. The effect of ply thickness and constraints imposed by neighbouring plies on initiation of intra-laminar matrix damage modes is also considered. A novel methodology involving a combination of physical and virtual tests on notched laminates is proposed to calibrate the in-situ fracture energies of intra-laminar damage modes.The numerical simulations are conducted using an enhanced version of CODAM2, implemented in the explicit finite element software, LS-DYNA, as a user-defined model (UMAT), together with a built-in tie-break cohesive interface in LS-DYNA to model delamination. The proposed approach is validated using various layups and notched specimen geometries under tensile loading. The reasonable agreement of the predictions with experiments in terms of global behaviour and detailed damage patterns proves the efficiency and applicability of the presented methodology for damage tolerant assessment of composite laminates. 

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Process models of composite materials are useful tools for understanding the effect of process parameters and variables and reducing manufacturing risks and costs. The sub-model approach for process modelling has been applied to thermoset composites since the early 1980s. In this approach, analysis is performed with different sub-models such as thermochemical, flow, void and stress, and the analysis results are sequentially transferred from one sub-model to the next, until the analysis is complete. In recent years there has been growing use of high performance thermoplastics such as PEEK and PEKK in aircraft structures, and hence process models for thermoplastics are increasingly of interest.During processing of thermoplastic materials, the material undergoes both melting and crystallization. Therefore a major component of the thermochemical/thermophysical sub-model for process modelling of thermoplastics is the crystallization/melt kinetics model. Most of the crystallization kinetics models in the literature are only valid for either constant temperatures or cooling at constant cooling rates. Furthermore, the number of melt kinetics models is very limited and their application restricted to small heating rates. As a material point in the part may undergo complex temperature cycles, a rate-type crystallization/melt kinetics model which is independent of the temperature cycle is desired.Another problem in processing is development of residual stresses and distortions, which are analyzed in the stress sub-model using mechanical response constitutive models such as thermo-elastic, CHILE and viscoelastic. Most thermoplastic materials such as PEEK are indeed viscoelastic, however their unrelaxed values of moduli are temperature dependent, ie their behaviour is ‘thermo-rheologically complex’.In this thesis the crystallization and melt behaviour of PEEK carbon fibre composites is investigated using DSC experiments. A rate type crystallization kinetics model is developed for prediction of degree of crystallinity during crystallization process. A concept of ‘master melt curve’ is introduced and is used along with the crystallization kinetics model for prediction of crystallinity change during an arbitrary process. Thermo-viscoelastic behaviour of the material is studied using DMA experiments. A thermo-viscoelastic (TVE) constitutive model is developed and is generalized to three dimensional cases. Some case studies are analyzed and validity of models are investigated.

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Composite materials are increasingly being used in advanced structural ap- plications. Debonding of adjacent laminate layers, also known as delamination, is considered to be one of the most dominant damage mechanisms affecting the behavior of composite laminates. Various numerical methods for simulating delamination in composite materials do exist, but they are generally limited to small-scale structures due to their complexity and high numerical cost. In this thesis, a novel technique aimed to allow efficient simulation of delamination in large-scale laminated composite structures is presented. During the transient analysis, continuum elements within regions where delamination has the potential to initiate are adaptively split through their thickness into two shell elements sandwiching a cohesive element. By elimi- nating the a priori requirement to implant cohesive elements at all possible spatial locations, the computational efforts are reduced, thus lending the method suitable for treatment of practical size structures. The methodol- ogy, called the local cohesive zone method (LCZ), is verified here through its application to Mode-I, Mode-II and Mixed-Mode loading conditions, and is validated using a dynamic tube-crushing loading case and plate impact events. Good agreement between the numerical results and the available experimental data is obtained. The results obtained using the LCZ method are compared favourably with the numerical results obtained using the con- ventional cohesive zone method (CZM). The numerical performance of the method and its efficiency is investi- gated. The efficiency of the method was found to be superior compared to that of the conventional CZM, and was found to increase with increasing model size. The LCZ method is shown to have a lower effect on reducing the structural stiffness of the structure, compared to the conventional CZM. The results obtained from the application of the LCZ method to the various cases tested are encouraging, and prove that the local and adaptive insertion of cohesive zones into a finite element mesh can effectively capture the delamination crack propagation in laminated composite structures. It is expected that further improvements in speed and accuracy will be attained once the algorithm is embedded within commercial finite element solvers as a built-in feature.

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Modern composites such as advanced fibre-reinforced and strand-based wood composites are increasingly being used in the new generation of aerospace and civil engineering structures. The structural analysis of such composites often requires knowledge of their effective (homogenized) properties. Several micromechanical models have been developed and are available in the literature for predicting the effective elastic properties of fibre-reinforced solid composites. However, the underlying assumptions in these models somewhat limit their application in solving some practical problems related to the viscoelastic behaviour of composite materials. Two seemingly different classes of composites, i.e. thermoset fibre-reinforced composites and strand-based wood composites with distinct viscoelastic properties are considered in this work due to their wide application in aerospace and construction industry. For viscoelastic analysis of such materials, aspects which require further investigations at the micro-scale are identified first. Specifically, available analytical micromechanics models are extended to predict the shear properties of thermoset fibre-reinforced composites during cure where the resin evolves from a viscous fluid to a viscoelastic solid. For strand-based composites consisting of high volume fraction of orthotropic wood strands, analytical micromechanics models are developed. These models are employed for predicting the effective elastic and viscoelastic properties of strand-based composites. The validity ranges of these models are then examined using experimental data or numerical reference solutions that employ the computational homogenization technique.To enable viscoelastic analysis of large scale composite structures with generally orthotropic properties, an efficient and easy-to-implement approach in the context of 3-D multi-scale modelling, is presented. A multi-scale modelling framework involving analyses at different scales for composites with two difference microstructures is developed and implemented in a general purpose finite element code, ABAQUS®. The accuracy of the developed multi-scale approach is demonstrated for some practical applications involving MOE (apparent modulus of elasticity in bending) prediction of strand-based wood composites. Using this approach, the effect of microstructural parameters (e.g. fibre geometry, orientation, waviness, volume fraction, etc.) on the time-dependent macroscopic response of orthotropic composite structures can be investigated, quantitatively.

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The usual approach to the process modeling of thermoset matrix composites is to divide the analysis into two distinct and sequential steps, first of flow-deformation behaviour and then of stress-deformation. In the current processing models, each of these two aspects is dealt with in a separate sub-model, typically called the flow module and stress module respectively. The flow module is relevant to the pre-gelation behaviour of resin, while the stress module is valid for the post-gelation composite material. In this thesis, the framework to integrate the flow and the stress modules into a unified module in finite element processing models is presented. The work is based on a two-phase model for analysis of resin flow and its resulting deformations in the composite material. Special measures are introduced to provide for additional capability of this model to account for the development of stresses in the curing composite material. These modifications are needed to ensure the accuracy of the model in both of resin flow and stress development regimes, and include the introduction of consistent compressibility in the mass conservation equation of the two-phase system, and a special decomposition of stresses of the system.The formulation is implemented for a pseudo-viscoelastic stress model in a 2D plane strain FE code in MATLAB. The approach may readily be extended to fully viscoelastic models. Various examples from single-element problems dealing with the development of residual stresses throughout a single-hold cure cycle to more geometrically complex composite laminates undergoing standard cure cycles are modeled by the integrated model and comparisons are made in one extreme to the flow-compaction behaviour by the standard flow models, and in the other extreme to the results obtained by the pseudo-viscoelastic approach.The model developed here is a promising tool for simulating processing of large-scale composite structures continuously from the very early stages of the process when the resin behaves in a fluid-like manner all the way to the final stage when it behaves as a 3D solid.

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Fibre reinforced polymers (FRP) are one of the fastest growing materials in advanced structural applications. Due to the complexity and existence of multiple and interactive modes of failure, there is a lack of comprehensive theory that describes the damage behaviour of these materials. The UBC Composite Damage Model (CODAM) is a sub-laminate based model that is designed to simulate the behaviour of laminated composites at the macro (structural) scale. Physical basis and numerical robustness are the main objectives of CODAM development. The original formulation of CODAM that was developed in the mid 1990’s suffers from material objectivity problem that results in spurious dependency of numerical predictions on the choice of the coordinate system. In this thesis, the objectivity issue of the original CODAM is identified and addressed through a new formulation called CODAM2. The new formulation is capable of predicting damage in various laminate lay-ups from quasi-isotropic to unidirectional. It is also capable of simulating the damage-induced orthotropy in the laminate. An orthotropic non-local averaging scheme is developed for CODAM2 to address the localization issue. Compared to isotropic averaging, the orthotropic scheme significantly improves the predicted crack direction and damage pattern in composite laminates. Unlike the conventional isotropic non-local averaging that performs the averaging over a circular (spherical in 3D) zone, in the orthotropic scheme the averaging is performed over an elliptical zone which requires the introduction of two length scales. The performance of CODAM2 equipped with orthotropic averaging is demonstrated through numerical examples. It is shown that the developed model is capable of accurately predicting the damage behaviour in various specimen geometries from sharp-notched to blunt-notched and open-hole specimens. The predictions of the model in terms of load-displacement, crack-tip position, damage height and crack directions agree well with experimental observations and measurements. CODAM2 provides a promising numerical tool to simulate the effect of damage on the behaviour of structures made of laminated composites. This model is computationally efficient and yet relatively simple to understand, calibrate and use in practical applications.

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British Columbia (BC) is in the midst of the largest outbreak of the Mountain Pine Beetle (MPB) ever recorded in western Canada. Technologies capable of converting stained lumber into market acceptable products are urgently required to reduce the impact of the growing volume of MPB killed lumber on the profitability of forestry in BC.New, thick MPB strand-based structural composite products can be produced and help absorb a large volume of MPB wood. With appropriate mechanical properties, such products can be used as beams, headers, and columns in the low-rise commercial, multi-family residential and single family residential markets.This work was focused on the duration-load and creep behaviour of thick MPB strand-based wood composite. The beam specimens were made in the Timber Engineering and Applied Mechanics Laboratory at UBC. A series of tests were conducted on the matched groups to investigate the creep-rupture behaviour. These investigations comprised of ramp load tests at three loading rates, long-term constant load tests at two stress levels and cyclic bending tests at six stress levels. A damage accumulation model was developed to study the creep-rupture behaviour. This model stipulates that the rate of damage growth is given in terms of the current strain rate and the previously accumulated damage, and a 5-parameter rheological model is applied to describe the viscoelastic constitutive relationship to represent the time-dependent strain, while the damage accumulation law acts as the failure criterion. The results of the long-term constant load tests were then interpreted by means of the creep-rupture model which had been shown to be able to represent the time-dependent deflection and time-to-failure data for different stress levels. The predictions of the model were verified using results from ramp load tests at different loading rates and results from cyclic loading tests at different stress levels. The creep-rupture model incorporates the short term strength of the material, the load history and predicts the deflection history as well as the time-to-failure. As it is a probabilistic model, it allows its incorporation into a time-reliability study of wood composites’ applications.

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From both numerical and experimental standpoints, it is very desirable to develop a general methodology that can be used to determine the strain-softening response and characteristic damage properties (e.g. fracture energy, damage height) of quasi-brittle materials. In the absence of a direct methodology, one has to conduct multiple experiments combined with trial-and-error procedures and/or simplifying assumptions regarding the damaging behaviour of the material in order to construct a strain-softening curve.In this study, a new methodology is developed that directly identifies the damaging constitutive response of composite materials using full-field measurements of kinematic variables. Using this methodology, the damage related properties can be extracted and the strain-softening response of composite materials under mode I loading can be obtained directly. Compared to other available indirect approaches, this method invokes fewer assumptions about the behaviour of the material and does not require any prior assumption regarding the shape of the constitutive response, as is required in other approaches.A series of compact compression and over-height compact tension tests are conducted on IM7/8552 quasi-isotropic laminates. Using the digital image correlation technique, full-field displacement vectors of the specimen surface are measured in each test. Based on the acquired data and using the basic principles of mechanics (equilibrium and compatibility), a family of approximate stress-strain curves are obtained. These approximate curves are then used in an iterative process to determine the optimized strain-softening response of the laminate. To validate the capability of the method to capture the local damaging behaviour of the composite laminate, a series of destructive tests such as deplying and sectioning are performed on the damaged specimens. The tested laminates are also simulated using finite element analyses of the specimens that employ the extracted strain-softening curve as input to a damage mechanics based material model. The proposed methodology provides insight into the details of damage propagation in composite materials and is a promising tool for characterizing the strain-softening behaviour of composite laminates in a relatively easy and direct manner.

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This thesis presents the development, implementation, and application of response sensitivities in numerical simulation of composite manufacturing. The sensitivity results include both first- and second-order derivatives. Such results are useful in many applications. In this thesis, they are applied in reliability analysis, optimization analysis, model validation, model calibration, as well as stand-alone measures of parameter importance to gain physical insight into the curing and stress development process. In addition to novel derivations and implementations, this thesis is intended to facilitate and foster increased use of response sensitivities in engineering analysis. The work presented in this thesis constitutes an extension of the direct differentiation method (DDM). This is a method that produces response sensitivities in an efficient and accurate manner, at the one-time cost of deriving and implementing sensitivity equations alongside the ordinary response algorithm. In this thesis, novel extensions of the methodology are presented for the composite manufacturing problem. The derivations include all material, geometry, and processing parameters in both the thermochemical and the stress development algorithms. A state-of-the-art simulation software is developed to perform first-order sensitivity analysis for composite manufacturing problems using the DDM. In this software, several novel techniques are employed to minimize the computational cost associated with the response sensitivity computations. This sensitivity-enabled software is also used in reliability, optimization, and model calibration applications. All these applications are facilitated by the availability of efficient and accurate response sensitivities.The derivation and implementation of second-order sensitivity equations is a particular novelty in this thesis. It is demonstrated that it is computationally feasible to obtain second-order sensitivities (the “Hessian matrix”) by the DDM for inelastic finite element problems. It is demonstrated that the direct differentiation approach to the computation of first- and second-order response sensitivities becomes increasingly efficient as the problem size increases, compared with the less accurate and less efficient finite different approach.

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