Modelling 3D-woven composites on the macroscale: Predicting damage initiation and inelastic phenomena

Composites with 3D-woven reinforcement have been slowly making their way into different industries. The interlacement of yarns, not only in-plane but also through-thickness, means that in many applications 3D-woven composites can outperform their laminated counterparts. In particular, this includes increased out-of-plane stiffness and strength, damage tolerance and specific energy absorption capabilities. The widespread adoption of 3D-woven composites in industry however, requires the development of efficient computational models that can capture the material behaviour. The current work takes a few steps towards the long term goal of developing a phenomenologically based macroscale model to predict how 3D-woven composites deform and eventually fail under mechanical loading. Following a brief introduction to the research field, the feasibility of extending stress-based failure initiation criteria for unidirectional laminated composites, to 3D-woven composites is explored. In particular it is shown that the extension of the LaRC05 criteria presents a number of challenges and leads to inaccurate predictions. Instead strain-based failure criteria inspired by LaRC05 are proposed. They produce results that are qualitatively more reasonable when evaluated numerically for tensile, compressive and shear tests. As a next step, a thermodynamically consistent framework for modelling the mechanical response of 3D-woven composites on the macroscale is presented. The proposed framework decomposes the stress and strain tensors into two main parts motivated by the material architecture. This allows for the convenient separation of the modelling of the shear behaviour from the modelling of the behaviour along the reinforcement directions. In particular, this division allows for the straightforward addition and modification of various inelastic phenomena observed in 3D-woven composites.The framework is then used to simulate experimental results of a 3D glass fibre reinforced epoxy composite. A viscoelastic model is incorporated into the framework to capture non-linear behaviour associated with tensile loading along the horizontal weft reinforcement as well as non-linear shear behaviour. In detail, to capture the shear behaviour, a crystal plasticity inspired approach is considered. As such, it is assumed that inelastic strain strictly develops on localised slip planes oriented by the reinforcement architecture. The viscous parameters are calibrated against experimental results, and a preliminary validation of the model is performed for an off-axis tension test

Macroscale Modelling of 3D-Woven Composites: Inelasticity, Progressive Damage and Final Failure

Composites with 3D-woven reinforcement have been slowly making their way into different industrial applications. The interlacement of yarns, not only in-plane but also through-thickness, means that in many applications 3D-woven composites can outperform their laminated counterparts. In particular, this includes increased out-of-plane stiffness and strength, damage tolerance and specific energy absorption properties. The widespread adoption of 3D-woven composites in industry however, requires the development of accurate and efficient computational models that can capture the material behaviour. In terms of computational efficiency, the most promising choice is to treat the material as a homogeneous and anisotropic solid. This is referred to as a macroscale model. Developing a macroscale model, which can predict how 3D-woven composites deform and eventually fail, is the main focus of this work. Particular attention is given to predicting the relevant non-linear behaviours that lead to energy absorption. A framework for modelling the mechanical response of 3D-woven composites on the macroscale is presented. The proposed framework decomposes the stress and strain tensors into two main parts motivated by the material architecture. This allows for a convenient separation of the modelling of the shear behaviour from the modelling of the behaviour along each of the reinforcement directions. In particular, this division allows for a straightforward addition and modification of various non-linear phenomena observed in 3D-woven composites. As a next step, material modelling approaches are considered and added to the framework in order to capture these non-linear phenomena. This includes the use of a viscoelastic model as well as a combined elasto-plastic and continuum damage model to capture the development of permanent deformations and stiffness reduction mechanisms. Finally, an anisotropic phase-field model extension is developed in order to induce local softening and failure in a way which does not induce spurious mesh-dependencies in finite element analyses. The model predictions are compared to experimental tests and show good agreement. The aim has been to develop a model that allows the constitutive relations to be identified directly from uniaxial cyclic stress-strain tests without the need for complex calibration schemes. However, characterising the out-of-plane behaviour is not trivial. Therefore, the current work also explores the use of high-fidelity mesoscale models as an additional source of data for model calibration and validation

Macroscale modelling of 3D-woven composites: Elasto-plasticity and progressive damage

There is a growing need across multiple industries for lightweight materials with improved material performance and reduced manufacturing costs. Composites with 3D-woven reinforcement could help fill this need. Their use however, requires the development of computationally efficient and industrially applicable material models to predict their non-linear behaviour. This work proposes a macroscale elasto-plasticity and damage model to capture the experimentally observed inelastic strains and stiffness reductions. The model is general, thermodynamically consistent and allows for various non-linear phenomena to be added and calibrated in a modular fashion depending on loading direction. Further it allows for a simplified parameter identification routine in which the damage and hardening laws are identified directly from experimental curves without the need for complex calibration routines. In order to demonstrate the applicability of the proposed macroscale model, focus is given to predicting the material response of a 3D glass fibre reinforced epoxy material system. The damage and hardening parameters are identified based on uniaxial tensile and in-plane shear experimental curves with unloading cycles. The model performance is validated against an off-axis tensile test with unloading cycles and shows good agreement to the experimental result

A framework for macroscale modelling of inelastic deformations in 3D-woven composites

The use of 3D-woven composite materials has shown promising results. Along with weight-efficient stiffness and strength, they have demonstrated encouraging out of plane properties, damage tolerance and energy absorption capabilities. The widespread adoption of 3D-woven composites in industry however, requires the development of efficient computational models that can capture the material behaviour. The following work proposes a framework for modelling the mechanical response of 3D-woven composites on the macroscale. This flexible and thermodynamically consistent framework, decomposes the stress and strain tensors into two main parts motivated by the material architecture. The first is governed by the material behaviour along the reinforcement directions while the second is driven by shear behaviours. This division allows for the straightforward addition and modification of various inelastic phenomena observed in 3D-woven composites. In order to demonstrate the applicability of the framework, focus is given to predicting the material response of a 3D glass fibre reinforced epoxy composite. Prominent non-linearities are noted under shear loading and loading along the horizontal weft yarns. The behaviour under tensile loading along the weft yarns is captured using a Norton style viscoelasticity model. The non-linear shear response is introduced using a crystal plasticity inspired approach. Specifically, viscoelasticity is driven on localised slip planes defined by the material architecture. The viscous parameters are calibrated against experimental results and off axis tensile tests are used to validate the model

The Gibbs Phenomenon and its Resolution

It is well known that given an arbitrary continuous and periodic function f(x), it is possible to represent it as a Fourier series. However, attempting to approximate a discontinuous or non periodic function, using a Fourier series, yields very poor results. Large oscillations and overshoots appear around the points of discontinuity. Regardless of the number of terms that are included in the series, these overshoots do not disappear, they simply move closer to the point of discontinuity. This is known as the Gibbs phenomenon. In the 1990's David Gottlieb and Chi-Wang Shu introduced a new method, entitled the Gegenbauer procedure, which completely removes the Gibbs phenomenon. We will review their method, as well as present a number of examples to illustrate its effect. Going one step further we will discover that not all orthogonal polynomials may be treated equal in terms of this Gegenbauer procedure. When replacing Gegenbauer polynomials with Chebyshev or Legendre polynomials, it appears as though the inability to vary ultimately makes them ineffective.

PREDICTING NON-LINEAR SHEAR DEFORMATION AND FAILURE IN 3D FIBRE-REINFORCED COMPOSITES

A class of composite materials with fully 3D fibre-reinforcements have shown weight efficient strength and stiffness characteristics, as well as promising energy absorption capabilities. In fact, Khokar et al. \cite{khokar} have demonstrated that, in bending, such a 3D-CFRP I-beam has two to three times the specific energy absorption capability of a steel I-beam with equivalent geometry. Note, the considered woven reinforcement has both horizontal and vertical weft yarns interlacing warp yarns in a grid-like set. This fibre network suppresses delamination and allows for stable and progressive damage growth in a quasi-ductile manner. While the considered 3D fibre-reinforced composite shows promise, developing a computationally efficient material model is crucial to supporting the material\u27s widespread adoption across multiple industries. With the ultimate goal of developing a macroscale homogenised model to predict how the material deforms and eventually fails under loading, this work proposes a candidate for a phenomenologically based orthotropic viscoelastic damage model.Previous experimental results indicate that this class of 3D fibre-reinforced composites exhibits linear material behaviour when loaded along one of the three nominal fibre directions. Shear loading however, produces a prominent non-linear response. This is likely due to the viscoelastic behaviour and damage of the polymer. In order to capture both the aforementioned linear and non-linear behaviours, a model inspired by crystal plasticity with viscoelastic slip planes is proposed. Specifically, a Norton type viscoelasticity model driven by shear tractions in preferred material planes is adopted. These planes are determined by the three reinforcement directions. As such, viscoelastic strain strictly develops when there is pronounced shear loading in these planes.To enable the model to account for material degradation and failure, the components of the stiffness tensor\ua0 are assumed to degrade in accordance with pertinent damage modes. For this purpose models for unidirectional laminated composites such as Maimi et al. (extended to 3 reinforcement directions,) as well as those for 3D fibre-reinforced composites Marcin et al. explored. The applicability of the proposed model is assessed against results from mechanical experiments carried out under tensile, compressive and shear loading

Predicting non-linear shear deformation in 3D-fibre reinforced composites

The strategic use of 3D-fibre reinforced composite materials has shown promising results. Along with weight efficient stiffness and strength, they have shown encouraging energy absorption capabilities. The following work proposes a general framework for modelling the mechanical response of 3D fibre-reinforced composites. The framework decomposes the stress and strain tensors into two main parts; one driven by the behaviour of the fibre reinforcement, the other driven by the non-linear matrix response under off-axis loading. The non-linear response specifically is introduced into the model using viscoelastic slip planes, in an analogous way to that of a crystal plasticity model. A prototype model is analysed in order to illustrate the capabilities of the proposed framework

Evaluation of damage initiation models for 3D-woven fibre composites

Three dimensional (3D) fibre-reinforced composites have shown weight efficient strength and stiffness characteristics as well as promising energy absorption capabilities. In the considered class of 3D-reinforcement, vertical and horizontal weft yarns interlace warp yarns. The through-thickness reinforcements suppress delamination and allow for stable and progressive damage growth in a quasi-ductile manner. With the ultimate goal of developing a homogenised computational model to predict how the material will deform and eventually fail under loading, this work proposes candidates for failure initiation criteria. The criteria are evaluated numerically for tensile, compressive and shear tests. The extension of the LaRC05 stress based failure criteria to this class of 3D-woven composites is one possibility. This however, presents a number of challenges which are discussed. These challenges are related to the relative high stiffness in all directions, which produce excessively high shear components when projected onto potential off-axis failure planes. To circumvent these challenges, strain based criteria inspired by LaRC05 are formulated. Results show that strain based failure predictions for the simulated load cases are qualitatively more reasonable

On Variationally Consistent Homogenisation for Composite Structural Elements

In the current contribution, a new method for computational multiscale, or so-called FE2, modellingof composite structures is proposed. This method allows the inclusion of detailed microormesoscale composite features e.g. manufacturing defects, reinforcement architectures, matrixcracks etc. and their impact on the mechanical response. However it does not requirethat these features be fully resolved in the macro-scale analysis. In FE2, at least two geometricalscales, the macro scale and the subscale(s), are linked in a nested FE procedure: on themacroscale, the homogenised material response (normally the stress) is given by a volume averagedlower scale quantity (the locally varying stress) obtained from a coupled subscale FEanalysis driven by imposed macroscopic strains or tractions. Of special concern here is to devisea computationally efficient procedure in which the macroscopic problem can be modelledby structural finite elements (beams, plates and shells) while the nested subscale problem ismodelled with continuum elements.Several authors have indeed previously contributed to this field, cf. e.g. Refs [1], [2], [3].Therein, a mixture of in-plane displacement (periodic or Dirichlet) and out-of-plane traction(free) boundary conditions (BCs) have been proposed for the subscale problem. Commonly,they are all based on predefined assumptions on the kinematics of the macroscale problemas well as the assumption that the macroscale in-plane bending response is well represented.However, sufficient consideration has not yet been given to the appropriate handling of the outof-plane shear response. In fact, we have previously shown that using a mixture of displacementand traction based BCs for the subscale problem is not appropriate to capture a consistent outof-plane shear response with increasing geometrical size of the subscale problem [4].Alternatively, we propose herein a new approach based on Variationally Consistent Homogenisation(VCH) [5]. The advantage of this approach is that the macroscopic problem,i.e. the complete shell theory, does not have to be specified beforehand. Instead, the appropriateproblems on the macroscale and the subscale are derived from the fully resolved problem.We will in the current contribution present the modelling framework and discuss the resultsof using alternative prolongation (macro-to-subscale) and homogenisation (sub-to-macroscale)strategies and how these influence the accuracy in predictions of e.g. the transverse shear responseof a thin-walled composite with various subscale features