Homogenization and localization of unidirectional fiber-reinforced composites with evolving damage by FVDAM and FEM approaches: A critical assessment

doi:10.1016/j.engfracmech.2020.107280

Engineering Fracture Mechanics

Volume 239, November 2020, 107280

https://doi.org/10.1016/j.engfracmech.2020.107280 Get rights and content

Highlights

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Evolving interfacial debonding in fibrous composites is simulated using the FVDAM and FEM computational approaches.
•
FVDAM with cohesive interface capabilities is fully and critically assessed against the FEM for the first time.
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Homogenized response and concomitant localized stresses are calculated with good agreement.
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Shortcomings of finite-element solution of unit cell interfacial debonding are highlighted.

Abstract

The recently-developed finite-volume direct averaging micromechanics (FVDAM) with progressive damage simulation capability modeled using the cohesive zone model is critically and fully assessed vis-à-vis Abaqus, a widely-adopted commercial finite-element code with cohesive element for the first time. The evolving debonding along the fiber/matrix interface of a unidirectional metal matrix composite is simulated using comparable bilinear traction-displacement separation laws in the two computational approaches. Differences between the two approaches are highlighted, including shortcomings of the Abaqus-based finite-element analysis of evolving damage. These shortcomings include the need of optimizing the compressive stiffness of the interface in order to: avoid material interpenetration; predict correct homogenized response; prevent numerical instabilities. These problems are not present in our version of the finite-volume homogenization approach since the traction-separation relations in the affected normal direction are directly eliminated when the interface is under compression. Nonetheless, comparison of the homogenized response and localized stress fields generated by the finite-element and finite-volume techniques demonstrates good agreement between the two approaches provided that a suitable compression factor is chosen in Abaqus.

Introduction

Fiber-reinforced composites continue to play a significant role in the emerging technologies, including aerospace, civil, marine, automotive and many other industries, due to their high performance. To make the best use of these materials, it is critically important to have a good understanding and predictive capability of their failure behavior. Nonetheless, simulation of damage evolution in fiber-reinforced materials remains a challenging problem due to the myriad of failure mechanisms and modes, and their complex nature that may be activated at different scales [1], [2]. To naturally track the evolution of localized failure modes, Barenblatt [3], [4] proposed the cohesive zone model (CZM) for fracture of brittle materials. During the past 30 years, the model has been actively developed by numerous researchers and has proven to be an effective tool to simulate crack initiation and propagation [5], [6], [7], [8], [9], [10], [11].

The majority of CZM applications are based on variational techniques, especially the finite-element method. With the emergence of numerical approaches, the stress and displacement fields in the analysis domain involving complex geometries, material properties, boundary conditions can be accurately determined. The CZM has been extensively implemented into various commercial finite-element tools through cohesive or interface elements. In the commercial software Abaqus, for instance, the cohesive elements are inserted a priori between bulk elements along a predefined path, leading to the so-called intrinsic cohesive zone model [11]. However, care must be taken when the finite-element method is applied to track crack opening and propagation with CZM on account of large moduli mismatch induced stress gradients within the heterogeneous microstructures. Convergence of both interfacial tractions and displacements requires extensive mesh refinement in the cohesive zone to ensure self-equilibrated stress fields upon minimization of total potential energy. Thus far, there has been very little discussion of the numerical instabilities encountered in the finite-element calculation of stress–strain response, the detailed interfacial opening process in terms of interfacial discontinuity, and interfacial traction, as well as localized stress fields of heterogeneous materials in the presence of evolving damage.

It is only relatively recently that the cohesive zone model has been incorporated into finite-volume based techniques to simulate damage evolution, cf., Tu and Pindera [12], [13], and Tu and Chen [14]. A fundamental difference between the finite-volume and finite-element based solutions of the unit cell problem in heterogeneous materials is the manner of satisfying local, and thus global, equilibrium equations [15], [16]. While the minimization of total potential energy within the finite-element framework leads to ultimate satisfaction of the unit cell’s global equilibrium with sufficient mesh refinement, the finite-volume approach enforces equilibrium in the integral sense for every subvolume at each level of mesh refinement.

Hence in this contribution, CZM-FVDAM’s ability and accuracy in predicting interfacial debonding of fiber-reinforced metal matrix composite materials are critically and thoroughly assessed against the commercial finite-element code, Abaqus extensively used by the design and development and research communities. The chosen material system is SiC/Ti in which premature fiber/matrix interfacial debonding occurs at low transverse normal stresses due to fiber/matrix interface degradation produced by a fabrication-induced chemical reaction. We note that in the Abaqus simulations, large compressive stiffness is employed to avoid material penetration when the interface is under normal compressive stress. The choice of interfacial stiffness affects the correctness of simulation results because of the extent of fictitious material interpenetration that may occur if the stiffness is too low. Conversely, unnecessarily large interfacial stiffness may produce incorrect results. Hence, the effects of compressive stiffness on the numerical stability of the finite-element algorithm, the homogenized response, interfacial tractions, and displacement discontinuities of the unit cell are extensively investigated. The interfacial traction-separation relations implemented in FVDAM and Abaqus are illustrated in great detail by tracking the interfacial separation process, as well as local stress components within the composite microstructures to demonstrate stress transfer mechanisms due to the progressively interfacial debonding.

The new contributions of the present work include:

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for the first time that a thorough and comprehensive study of the comparison between finite-volume and finite-element based homogenization of unidirectional composites in the presence of evolving damage is presented.
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demonstration that optimized compressive stiffness of the interface needs to be identified for the finite-element cohesive element in order to: avoid material interpenetration; predict correct homogenized response; prevent numerical instabilities.
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demonstration that the numerical instabilities encountered in the finite-element homogenization technique are magnified with increasing fiber/matrix stiffness ratio, which is not the issue in the finite-volume scheme.

Section snippets

Cohesive zone models in FVDAM and ABAQUS

In this contribution, the repeating unit cell is subjected to plane strain constraint and hence 2D plane strain elements CPE4 available in Abaqus are used to discretize the analysis domain. Fig. 1 shows the representative unit cell used in FVDAM and Abaqus simulations of the unidirectional SiC/Ti composite in the cross-section normal to the fiber direction with the highlighted cohesive zone around the entire fiber. The elastic moduli and Poisson’s ratios of SiC fiber and titanium matrix are $E_{f} =$

Effect of interfacial stiffness under compressive normal stress

In the actual implementation of the cohesive zone model, one important question that needs to be addressed is how to treat the interfacial behavior when the interface is under normal compressive stress. The most common approach is to use large stiffness along normal direction to resist interpenetration, which is also used by the commercial finite element packages such as Abaqus and Ansys. In contrast, when the interface is under compressive normal stress, the corresponding auxiliary equation in

Summary and conclusion

In this contribution, we critically examine the predictive capability of finite-volume and finite-element homogenization techniques in the calculation of stress–strain response of metal matrix composites in the presence of evolving interfacial damage, under biaxial strain loading. Good agreements have been obtained between the predictions of both approaches for the homogenized responses, interfacial quantity distributions and stress field distributions provided that a suitable compression

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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The cohesive interface model originally proposed by Barenblatt (1959, 1962) and Dugdale (1960) is generally accepted, which has been further extended by Needleman and coworkers (Needleman, 1987; Xu and Needleman, 1994). The latter works have been extensively adopted in the literature to track interface separation in heterogeneous materials (Bormann et al., 2019; Elices et al., 2002; Tu and Chen, 2020a, b; Tu and Pindera, 2014; van den Bosch et al., 2007). The general interface model unifies all the aforementioned interface models, allowing for both traction and displacement discontinuities across the interface.
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Homogenization and localization of unidirectional fiber-reinforced composites with evolving damage by FVDAM and FEM approaches: A critical assessment

Highlights

Abstract

Introduction

Section snippets

Cohesive zone models in FVDAM and ABAQUS

Effect of interfacial stiffness under compressive normal stress

Summary and conclusion

Data availability

Declaration of Competing Interest

Compos B Engng

Mech Mater

J Appl Math Mech

J Mech Phys Solids

Int J Solids Struct

Engng Fract Mech

Mech Res Commun

Compos B Engng

Engng Fract Mech

Compos B Engng