Computational Methods for Debonding in Composites

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Chapter 10 Elastoplastic Modeling of Multi-phase Metal Matrix Composite with Void Growth Using the Transformation Field Analysis and Governing Parameter Method Ernest T.Y. Ng and Afzal Suleman Abstract In this paper, we employ the combined Transformation Field Analysis (TFA) method and the Governing Parameter Method (GPM) to predict the overall elastoplastic behavior of multi-phase fibrous composite materials using Gurson- Tvergaard yield criterion in order to account for the effect of void growth in the matrix phase. For the homogenization scheme, we employ the TFA method with concentration factors determined by the Eshelby-Mori-Tanaka (EMT) theory. Regarding to the stress integration of the governing TFA equations, we employ an implicit integration scheme, namely the GPM. Furthermore, a necessary condition for the possible ranges of the governing parameters based on the GPM integration scheme is derived in a more general setting by including the rate of nucleation and coalescence within the context of writing the expression of the rate of change of porosity. To validate our proposed approach, we compare our results to both numerical and experimental results provided in the existing literature. 10.1 Introduction A metal matrix fiber-reinforced composite has many advantages over conventional engineering materials because of its light-weight and good formability under fabrication. However, the intrinsic inhomogeneities of fibrous composite materials has made the prediction of the mechanical behavior of such a material a great challenge over the past three decades. As described in the preceding paper by Ng and Suleman [19], the combined TFA-GPM provided a good approximation of determining the Ernest T.Y. Ng Department of Mechanical Engineering, University of Victoria, British Columbia, Canada, e-mail: eng@me.uvic.ca A. Suleman Instituto de Engenharia Mecánica, Instituto Superior Técnico (IDMEC-IST), Instituto Superior Técnico, Lisbon, Portugal, e-mail: suleman@ist.utl.pt 197
198 Ernest T.Y. Ng and A. Suleman overall elastoplastic behavior of multi-phase fiber-reinforced composite materials based on the von-Mises yield criterion. In this paper, we will employ the combined TFA-GPM approach but with Gurson-Tvergaard yield criterion instead of von-Mises yield criterion to predict the overall elastoplastic behavior of n-phase fiber-reinforced composites with isotropic strain hardening. Elastoplastic modelling of n-phase fiber-reinforced composites (advanced hybrid composites) has been proposed by many researchers. One elegant method, namely, the Transformation Field Analysis (TFA) [7] proposed by Dvorak has shown to have many advantages over the other models within the context of computational micromechanics. For instance, the algorithm can take account of the microgeometry of the fiber phase and is suitable for modelling multi-phase fibrous composites; it can accommodate with any inelastic constitutive relation, micromechanical model and uniform overall loading path. More importantly, it is also suitable for 3D modelling of multi-phase fiber-reinforced composite structures within the finite element method framework. To determine the concentration factors needed by the governing TFA equations, we invoke the Eshelby-Mori-Tanaka (EMT) theory [3, 8, 17]. However, the integration scheme employed in the original paper written by Wafa et al. is explicit [1]. Over the past years, implicit integration has shown to have more advantages over explicit integration in integrating the constitutive equation within the context of finite element analysis. Moreover, explicit integration even has complicated the numerical procedures for analyzing multi-phase fibrous composite material as discussed in the preceding paper. In this paper, the TFA method is used to predict the overall elastoplastic behavior of n-phase fiber-reinforced composites using Gurson-Tvergaard yield criterion. In order to integrate the overall TFA governing equations, an implicit stress integration scheme called the Governing Parameter Method (GPM) [15, 16] is used to replace the explicit integration scheme employed in the original paper by Wafa et al. In short, this paper has the following contributions: 1. Extend the widely used von-Mises yield criterion to a more general Gurson- Tvergaard yield criterion in order to account for the effects of void growth in the matrix phase; 2. Perform the mathematical analysis to obtain the necessary conditions for the ranges of the change of the mean plastic strain ∆eP m and the change of the effective plastic strain ∆ēP of the matrix phase within the context of the iterative algorithm based on the GPM and the Gurson-Tvergaard model; 3. Use the proposed approach to simulate a 4-phase fibrous composite material. The layout of the paper is as follow: Sect. 10.2 presents the micromechanics of elastoplastic analysis of multi-phase fiber-reinforced composite materials, this includes the governing TFA equations and the EMT equations; Sect. 10.3 outlines the stress integration scheme, this includes a general description to the GPM algorithm, the procedure to apply the GPM to solving the governing TFA equations; Sect. 10.4 includes the formulation of Gurson-Tvergaard plasticity within the context of GPM. More importantly, a necessary condition for the ranges of the change of the mean plastic strain ∆eP m and the change of the effective plastic strain ∆ēP
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Mechanical Response of Composites
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Pedro P. Camanho • C.G. Dávila S
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Preface The methodology for designi
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Acknowledgements The Editors of thi
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x Contents 3 Practical Challenges i
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xii Contents 8.2.4 Modelling Effect
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xiv Contents 13.1.2 EffectiveProper
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xvi List of Contributors Clara Schu
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Chapter 1 Computational Methods for
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1 Computational Methods for Debondi
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28 R. Rolfes et al. functions by me
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30 R. Rolfes et al. Microscale fibe
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32 R. Rolfes et al. symmetric, whic
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34 R. Rolfes et al. Fig. 2.5 Discre
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36 R. Rolfes et al. Unit cell (a) S
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38 R. Rolfes et al. stress state. T
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40 R. Rolfes et al. biaxial compres
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42 R. Rolfes et al. Damage Evolutio
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44 R. Rolfes et al. Fig. 2.14 Radia
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46 R. Rolfes et al. Table 2.2 Elast
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48 R. Rolfes et al. A dev is the de
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50 R. Rolfes et al. uniaxial compre
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52 R. Rolfes et al. Stress in MPa -
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54 R. Rolfes et al. 2.4.2 Results o
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56 R. Rolfes et al. 12. Hughes TJR
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58 B.N. Cox et al. inform models; a
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60 B.N. Cox et al. 3.2 The Structur
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62 B.N. Cox et al. be successfully
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64 B.N. Cox et al. high fluxes of c
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66 B.N. Cox et al. provides poor in
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68 B.N. Cox et al. For example, a c
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70 B.N. Cox et al. failures in comp
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72 B.N. Cox et al. mixed-mode crack
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Chapter 4 Analytical and Numerical
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4 Analytical and Numerical Investig
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Chapter 6 Study of Delamination in
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6 Study of Delamination with in Com
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Chapter 7 Interaction Between Intra
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14 Development of DST for the Model
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