Coupled, multiple cracking systems in multilayered composite materials

Multidirectional composite laminates have been increasingly used as primary load-bearing structures in many -applications such as aircraft frames, wings, and turbine or wind-mill blades, owing to their excellent weight-to-strength ratios, better environmental resistance, and much improved long-term durability. Such high--performance polymer matrix composites typically consist of dozens of unidirectional plies of ~0.1 mm thick and aligned in different directions. However, because of the highly heterogeneous nature of such materials, they exhibit very complex progressive damage processes which are dominated by the nucleation, propagation, merging, bifurcation of many different systems of small cracks (intraply cracks, delaminations, microbuckle induced kinking, etc) before they eventually grow to a sufficiently large damage zone of structural criticality. In the past, this complex problem has been addressed by various continuum damage mechanics models, which are of phenomenological nature and merely consider the load-bearing loss of the damaged materials, but with no explicit representation of these crack systems. More recently, the need to address such subcritical cracks has been increasingly appreciated because their evolution represents a significant portion of the structural life and they can facilitate many unexpected early structure failure upon changing of loading or environmental conditions. However, up to date there still lack effective analytical or numerical methods that can faithful predict the evolution of such cracking systems, let along to quantify their effects on structural criticality. The difficulties arise from multiple fronts: (i) a lack of adequate understanding of the damage process zones associated with different types of small cracks; (ii) the in situ critical stress or strain conditions responsible for crack nucleation and propagation; (iii) numerical or analytical platforms that can account for the arbitrary nucleation and propagation of multiple cracks in a way that is consistent to the material failure/damaging descriptions. In this presentation, I shall first review the much improved understandings of how such composite materials fail at subply (microscopic) level under in situ loading, which was enabled only recently by the microscopic computer tomography, X-ray technology. The improved understanding thus allows us to construct realistic material failure descriptions based on the in situ stresses–displacement relations (as appose to the classic global laminar stress–strain relations). I shall then introduce a newly developed numerical platform named augmented finite element method (A-FEM), which can explicitly embed microscopic material failure descriptions (as cohesive failure models) in any structural models. Thus, the formation and propagation of nonlinearly coupled multiple cracks can take place at any locations dictated by the in situ local stresses. We shall demonstrate with several complex laminate systems that the numerical performance of the A-FEM based platform is very effective in dealing with such problems with very high fidelity. More critically, the method can effectively link the evolution of the complex damage processes with structural performance, which represents a big step towards the quantification of subcritical crack growth to final structural criticality

Augmented finite element method for progressive damage in complex heterogeneous materials

High-fidelity simulations of damage evolution are approaching realization for a number of material systems, thanks to significant advances in modeling methods and experimental imaging. Nevertheless, significant challenges remain, many of which relate to the difficulty of developing practicable formulations for dealing with materials containing complex material heterogeneity and reinforcement architectures. Heterogeneity poses special problems with the accurate prediction of local stress and strain fields, which can vary strongly with local material features; and with predicting cracks and localized damage bands, which can appear during damage evolution not only on the material boundaries, but also on other surfaces that cannot be specified a priori . In this article, we present a new finite element method named augmented finite element method (A-FEM) that can explicitly account for the arbitrary cracking in either 2D or 3D heterogeneous solids. The A-FEM employs internal nodes to facilitate the subdomain stiffness integration and to describe the strong (or weak) discontinuity across the crack planes (or bonded interface) in a mathematically rigorous way. A local algorithm is used to record the evolving crack front based on local elemental stresses. The crack initiation and propagation is account for by nonlinear cohesive zone models. We shall demonstrate with several classic fracture problems that the numerical performance of our new A-FEM is orders of magnitude more efficient, accurate, and robust when compared with other parallel methods. Finally we shall show that when applied to the complex textile CMCs, the A-FEM can successfully predict the multiple, arbitrary crack development up to final catastrophic failure, and the predicted global stress–strain relations are very consistent with experimental results

Augmented finite element method for virtual testing of high temperature CMCs

Ceramic matrix composites (CMCs) have been increasingly used in high heat flux applications due to their ultra-high temperature resisting capabilities. However, CMCs are prone to processing-induced or in-serve cracking due to the large thermal stresses. Thermally-induced cracking are dangerous because they provide pathways for further damaging processes such as oxidation and vapor-assisted corrosion, which may lead to catastrophic failure [1]. High-fidelity thermal-mechanical analyses to CMCs with consideration of arbitrary cracking are very challenging because the heterogeneous nature makes it impossible to know the cracking locations a priori. Yet correct and efficient treatment of crack coalescence and bifurcation is critical for simulating the complex, multiple crack damage states in these materials. In the past years we have been developing a new simulation method named augmented finite element method (A-FEM) with temperature DoFs that can efficiently and faithfully account for the arbitrary cracking and the post-crack material damage accumulation in CMCs [2, 3]. The high accuracy and efficiency of the A-FEM is enabled by three key numerical capabilities developed in recent years: 1) a novel condensation method that enables mesh insensitive and accurate fracture predictions with mesh sizes 10~50 times larger, and computational times 100x~1000x times shorter, than other methods such as X-FEM, G-FEM, and PNM; 2) a unified cohesive zone model (CZM) that can predict static, fatigue, or dynamic crack initiation in general heterogeneous materials, followed by coupled crack propagation until final failure; and 3) a novel and very fast method to avoid numerical divergence due to unstable crack growth. The high-fidelity simulation capabilities pave the way for achieving virtual testing of complex CMCs at various scales from microscopic fiber/matrix interaction to structural integrity, all with explicit consideration of multiple cracking and crack interactions. In this study, the concept and procedure of a top-down virtual testing strategy will be first introduced, with emphases on the needs for novel experimental methods for basic property characterizing and results validation and advanced numerical methods for high-fidelity predictions at all important scales. The virtual testing scheme will then be demonstrated by a detailed review of a recent exercise on a high-temperature textile CMC, including the use of micro-computer-tomography (mCT) for material heterogeneity characterization, the generation of virtual test specimens with the statistic tow/matrix information from the mCT characterization, full 3D A-FEM modeling of the virtual specimen for material and structural performance evaluation, and validation of the A-FEM simulated results against independent experimental testing results. The presentation will conclude with key lessons learned from this exercise and important future needs to make the virtual testing for routine engineering design practice

A cohesive network approach for modelling fibre and matrix damage in composite laminates

In the current study a high fidelity analysis approach is used to predict the failure process of notched composite structures. Discrete cracking is explicitly modelled by incorporating cohesive interface elements along potential failure paths. These elements form an interconnected network to account for the interaction between interlaminar and intralaminar failure modes. Finite element models of these configurations were created in the commercial analysis software ABAQUS and a user defined material subroutine (UMAT) was used to describe the behaviour of the cohesive elements. The material subroutine ensured that the model remained stable despite significant damage, which is a significant challenge for implicit damage simulations. Two analysis approaches were adopted using either the as-measured or modified (in-situ) ply strengths. Both approaches were capable of closely predicting the mean ultimate strength for a range of hole diameters. However, using the measured ply properties resulted in extensive matrix cracking in the surface ply which caused a deviation from the experimentally measured surface strain. The results demonstrate that high fidelity physically based modelling approaches have the ability to complement or replace certain experimental programs focussed on the design and certification of composite structures

Micromechanical Analyses of Debonding and Matrix Cracking in Dual-Phase Materials

Failure in elastic dual-phase materials under transverse tension is studied numerically. Cohesive zones represent failure along the interface and the augmented finite element method (A-FEM) is used for matrix cracking. Matrix cracks are formed at an angle of 55 deg−60 deg relative to the loading direction, which is in good agreement with experiments. Matrix cracks initiate at the tip of the debond, and for equi-biaxial loading cracks are formed at both tips. For elliptical reinforcement the matrix cracks initiate at the narrow end of the ellipse. The load carrying capacity is highest for ligaments in the loading direction greater than that of the transverse direction.</jats:p

Modelling and quantifying Mode I interlaminar fracture in particle-toughened CFRPs

Four-dimensional time-resolved Synchrotron Radiation Computed Tomography (SRCT) has been used to capture Mode I delamination propagation in particle-toughened Carbon Fibre Reinforced Polymers (CFRPs). Digital Volume Correlation (DVC) was used in order to measure ply opening displacements at the crack tip, permitting the interlayer strain ahead of the crack tip to be quantified. Estimates at which toughening particles de-bonded and/or fractured were made, giving insight into the effects of particle type and particle size on the fracture mico-mechanisms. The experiments are complemented by a 2D plane-strain finite element (FE) model, which investigated the effects of particle strength and toughness on the ply opening displacement and crack path by modelling the particles as 1D cohesive segments. Previous work has shown that Mode I crack propagation in particle-toughened interlayers involves a process zone rather than a distinct crack tip. Therefore, Augmented Finite Element Method (A-FEM) elements were used in the simulation, since the elements can account for both bifurcating and merging cracks within a single element. The nodal displacements in the simulation were compared to the DVC results, illustrating a potential path through which more complex FE simulations may be validated against experimental results in the future

A novel evolutionary algorithm for dynamic constrained multiobjective optimization problems

The file attached to this record is the author's final peer reviewed version.To promote research on dynamic constrained multiobjective optimization, we first propose a group of generic test problems with challenging characteristics, including different modes of the true Pareto front (e.g., convexity–concavity and connectedness–disconnectedness) and the changing feasible region. Subsequently, motivated by the challenges presented by dynamism and constraints, we design a dynamic constrained multiobjective optimization algorithm with a nondominated solution selection operator, a mating selection strategy, a population selection operator, a change detection method, and a change response strategy. The designed nondominated solution selection operator can obtain a nondominated population with diversity when the environment changes. The mating selection strategy and population selection operator can adaptively handle infeasible solutions. If a change is detected, the proposed change response strategy reuses some portion of the old solutions in combination with randomly generated solutions to reinitialize the population, and a steady-state update method is designed to improve the retained previous solutions. Experimental results show that the proposed test problems can be used to clearly distinguish the performance of algorithms, and that the proposed algorithm is very competitive for solving dynamic constrained multiobjective optimization problems in comparison with state-of-the-art algorithms

Multi-population evolution based dynamic constrained multiobjective optimization under diverse changing environments

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic constrained multiobjective optimization involves irregular changes in the distribution of the true Pareto-optimal fronts, drastic changes in the feasible region caused by constraints, and the movement directions and magnitudes of the optimal distance variables due to diverse changing environments. To solve these problems, we propose a multi-population evolution based dynamic constrained multiobjective optimization algorithm. In this algorithm, we design a tribe classification operator to divide the population into different tribes according to a feasibility check and the objective values, which is beneficial for driving the population toward the feasible region and Pareto-optimal fronts. Meanwhile, a population selection strategy is proposed to identify promising solutions from tribes and exploit them to update the population. The optimal values of the distance variables vary differently with dynamic environments, thus, we design a dynamic response strategy for solutions in different tribes that estimates their distances to approach the Pareto-optimal fronts and regenerates a promising population when detecting environmental changes. In addition, a scalable generator is designed to simulate diverse movement directions and magnitudes of the optimal distance variables in real-world problems under dynamic environments, obtaining a set of improved test problems. Experimental results show the effectiveness of test problems, and the proposed algorithm is impressively competitive with several chosen state-of-the-art competitors

Fracture analyses of plastically -deforming adhesive joints.

A general modeling approach is developed for analyzing the fracture of plastically-deforming adhesive joints in this dissertation. This model involves using an embedded-process-zone (EPZ) model to represent the fracture of the adhesive and a nonlinear finite-element analysis (FEA) to calculate the elastic-plastic deformation of adherends. The EPZ model uses both the intrinsic joint toughness and the cohesive stresses to simulate the fracture process and allows the fracture of the adhesive to be coupled with the elastic-plastic deformation of the adherends. An important feature of the model is that the mode-mixedness is a natural outcome of the deformation history. As a result, the fracture of a plastically-deforming adhesive joint can be predicted without an a-priori knowledge of the mode-mixedness. A systematic procedure to determine the model parameters experimentally is demonstrated. It is found that the parameters required for a numerical simulation can be obtained by comparing numerical and experimental results of two simple fracture tests: the wedge induced fracture of double-cantilever beams and the three-point bending of adhesively-bonded end-notched-flexure (ENF) specimens. More importantly, it is demonstrated that once the parameters have been found, the model can be used without any modification to simulate the fracture of other adhesive joints with different dimensions or different joint geometries under general loading conditions. Based on this modeling approach, the fracture of a variety of plastically-deforming adhesive joints is simulated and the numerical predictions are compared with the associated experimental results. It is found that the numerical calculations are capable of providing quantitative predictions of adhesive joints under Mode-I (DCBs, symmetrical T-peel and 90&deg;-peel joints), mode-II (ENF specimens) and mixed-mode (single lap-shear and asymmetrical T-peel joints) loading conditions. In addition, many important features related to the coupling effects between the fracture process and macroscopic plasticity are revealed in this study. In summary, this study establishes an effective analytical tool that is able to provide quantitative predictions of the fracture of plastic ally-deforming adhesive joints under general load conditions, which are of great importance to many key industries.Ph.D.Applied SciencesMechanical engineeringMechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132498/2/9963921.pd