On understanding the applicability of Mohr-Coulomb failure hypothesis for composite materials using UnitCells©

The applicability of Mohr-Coulomb (M-C) failure hypothesis for anisotropic composite materials is re-examined in this paper. Mohr-Coulomb failure theory has been widely referred to in the literature to study the failure of unidirectional (UD) fibre reinforced composites under transverse loading including the renowned Puck’s criteria. This has been partially validated based on the experimental correlations with the predictions made by the M-C criterion for a few set of test cases, which remains a debatable way of formulating composites failure criterion. It is brought to attention that Mohr utilised the concept of principal stresses in constructing principal circles and assumed that the outermost circle represents the critical state of failure. This hypothesis and its derivative “failure is dictated by the stresses acting on the fracture surface” have thus been used for formulating the criterion for isotropic materials that exhibit brittle fracture characteristics. However, the concept of principal stresses is not employable in the analysis of composites. Hence, the same hypothesis may not be applicable in studying composite materials. Also, the micromechanical aspects that lead to failure have not been taken into consideration in this hypothesis which can lead to incorrect predictions in the case of composite materials. The capability of an appropriately representative unit cell model in better understanding the micromechanical aspects and the implications of the hypothesis is studied by attempting micromechanical analysis of UD composites through UnitCells© tool. It is utilised to locate stress concentrations within the unit cell from which the likely angle of the fracture surface can be identified. It has also been shown that the stress concentrations could help locate the fracture angle for UD composite materials as a sufficient but not a necessary requirement due to the presence of non-linear behaviour before fracture. If one wishes to employ M-C failure hypothesis to formulate a failure criterion, the assumption that the failure is determined by the stresses exposed on fracture surface has to be made with caution

Development of Novel Tools for Stochastic Multiscale Finite Element Analysis of Composite Structures

A modular and generally applicable stochastic multi-scale finite element analysis (FEA) framework for investigating the structural performance of unidirectional and multi-directional textile fibre reinforced polymer (FRP) composites is presented. The framework enables studying global (stiffness) and local responses (strength) under the influence of geometric and material uncertainties across length scales. As heterogeneous and hierarchically built-up materials, predicting the behaviour of advanced laminated composite structures reliably is challenging, limiting their full exploitation. Following decades of macro-mechanical approaches, the past decade has seen increased adoption of multi-scale methods thanks to the ability to carefully consider the uncertainties related to microstructural features and constituent thermo-mechanical properties. Yet, the optimised representation of uncertainties and the means to mitigate the computational intractability of such approaches are not fully addressed. For this purpose, the requirements of properly modelling the microstructural features of FRP composites using representative volume elements (RVE) were investigated. The lack of reliable data quantifying the variability of meso-scale geometric features in textile composites was mitigated by performing segmentation and statistical analysis of X-ray CT images. The sensitivity of the global stiffness and localised damage initiation due to the uncertainties were studied using Monte Carlo simulations to reduce the uncertainties. A surrogate modelling implementation via user subroutines was developed to accelerate the multi-scale analysis of composite structures. Full-field strain measurement, acoustic emission and X-ray CT imaging of rectangular and open hole tension test coupons were used to validate the developed multiscale modelling framework. The novel contributions of this thesis include extensions to a modular multi-scale modelling technique incorporating uncertainties at two different length scales and the use of state-of-the-art machine learning models for composite microstructure characterisation and surrogate modelling. A software tool was also developed augmenting an existing FEA software to reduce multi-scale modelling workloads. These contributions pave the way for investigating the static and dynamic performance of composite structures, considering multi-scale uncertainties in a computationally efficient manner, to confidently exploit their many advantages

Onset Theory: Pushing the Design Envelope for Textile Composite Structures

Reliably predicting the failure behaviour of fibre reinforced polymer composite materials is a challenging endeavour. Despite decades of work, there is still significant lack of confidence in composite design practices owing to the limitations in generalisable failure prediction frameworks. This has a huge impact on the aerospace industry, where inflated structural weight from enforced design conservatism is felt acutely on the bottom lines of both aircraft manufacturers and aircraft operators. In the aerospace industry, where both structural efficiency and damage tolerance are critical, textile fabrics and unidirectional (UD) laminates are the widely used forms of composite materials. Although they are not as structurally efficient as unidirectional fibre composites (unitape), textile composites have many other inherent advantages, including: handlability, drapability, repairability, bondability and damage tolerance, which make them attractive structural materials. They are also often used in conjunction to create hybrid laminates which are both structurally efficient and damage tolerant. Boeing makes extensive use of both textile fabric and hybrid laminates, for which there is currently no accepted physics-based predictive failure theory. This report discusses the research findings made on the Project ID (LP150100653) in the field of understanding failure in textile fabric laminates using Onset Theory, a multi-scale damage modelling framework proposed by the researchers at The Boeing Company. Novel experimental methodologies and numerical modelling procedures were developed in the due course to explore the meso-mechanical level in the hierarchical framework. Non-destructive material characterisation techniques such as micro X-ray Computed Tomography (microCT) and Neutron Tomography (NT) are utilised in understanding the microstructure, fibre distribution and damage evolution in complex textile and hybrid composites. New material reconstruction algorithms are developed to generate geometric models of the textile architecture. A multi-scale finite element modelling procedure is developed for evaluating the stiffness and strength of textile composites by extending the framework of Strain Invariant Failure Theory (Onset Theory). The improved understanding of composites failure phenomenon thus achieved will help design optimal structures confidently with reduced design safety factors and also develop novel material architectures to suit different applications

On understanding the applicability of Mohr-Coulomb failure hypothesis for composite materials using UnitCells©

The applicability of Mohr-Coulomb (M-C) failure hypothesis for anisotropic composite materials is re-examined in this paper. Mohr-Coulomb failure theory has been widely referred to in the literature to study the failure of unidirectional (UD) fibre reinforced composites under transverse loading including the renowned Puck’s criteria. This has been partially validated based on the experimental correlations with the predictions made by the M-C criterion for a few set of test cases, which remains a debatable way of formulating composites failure criterion. It is brought to attention that Mohr utilised the concept of principal stresses in constructing principal circles and assumed that the outermost circle represents the critical state of failure. This hypothesis and its derivative “failure is dictated by the stresses acting on the fracture surface” have thus been used for formulating the criterion for isotropic materials that exhibit brittle fracture characteristics. However, the concept of principal stresses is not employable in the analysis of composites. Hence, the same hypothesis may not be applicable in studying composite materials. Also, the micromechanical aspects that lead to failure have not been taken into consideration in this hypothesis which can lead to incorrect predictions in the case of composite materials. The capability of an appropriately representative unit cell model in better understanding the micromechanical aspects and the implications of the hypothesis is studied by attempting micromechanical analysis of UD composites through UnitCells© tool. It is utilised to locate stress concentrations within the unit cell from which the likely angle of the fracture surface can be identified. It has also been shown that the stress concentrations could help locate the fracture angle for UD composite materials as a sufficient but not a necessary requirement due to the presence of non-linear behaviour before fracture. If one wishes to employ M-C failure hypothesis to formulate a failure criterion, the assumption that the failure is determined by the stresses exposed on fracture surface has to be made with caution