Strength of a matrix with elliptic criterion reinforced by rigid inclusions with imperfect interfaces

Bignonnet, François; Dormieux, Luc; Lemarchand, Éric

doi:10.1016/j.euromechsol.2015.02.003

Cited by 9 publications

(14 citation statements)

References 17 publications

(26 reference statements)

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“…This result was shown for the effective yield stress by Suquet [44] and Idiart [16] for given particle volume fraction, whereby it is further shown here that this sharp transition is weakly sensitive to the particle volume fraction (at least for volume fractions up to 40%). This, in turn, may have significant implications in the strengthening of the composite and possible debonding/failure of the particle/matrix interface [4], since beyond that contrast ratio the particle stops deforming. This of course leads to stress and strain concentrations in the matrix/article interface.…”

Section: Discussionmentioning

confidence: 99%

“…Figure 5 shows the variation of the calculated effective flow stress from the unit cell finite element calculations with the contrast ratio r = σ ). 4 For that data shown in Fig. 5, the maximum difference between the predictions (39) and the results of the unit cell finite element calculations is 3% (note that the vertical axis in Fig.…”

Section: The Effective Yield Stressmentioning

confidence: 99%

“…4 Of all possible choices for µ 0 shown in Fig. 1, the Hashin-Shtrikman lower bound H-S − (µ 0 = µ (1) ) gives the best estimate by comparison to the predictions of the unit cell results.…”

Section: The Effective Yield Stressmentioning

confidence: 99%

“…The study of the effect of J 3 , in turn, allows for a complete analysis of general triaxial loading states. As a consequence of the applied periodic boundary conditions and the symmetry of the problem, the macroscopic (average) deformation of the unit cell is entirely described by the displacements of the "reference vertices" (2,4,5), as shown in Fig. 4, which can be written in the form…”

Section: The Strain Concentration Tensorsmentioning

confidence: 99%

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A methodology for the estimation of the effective yield function of isotropic composites

Papadioti

Danas

Aravas

2016

International Journal of Solids and Structures

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In this work we derive a general model for N −phase isotropic, incompressible, rateindependent elasto-plastic materials at finite strains. The model is based on the nonlinear homogenization variational (or modified secant) method which makes use of a linear comparison composite (LCC) material to estimate the effective flow stress of the nonlinear composite material. The homogenization approach leads to an optimization problem which needs to be solved numerically for the general case of a N −phase composite. In the special case of a two-phase composite an analytical result is obtained for the effective flow stress of the elasto-plastic composite material. Next, the model is validated by periodic three-dimensional unit cell calculations comprising a large number of spherical inclusions (of various sizes and of two different types) distributed randomly 1 in a matrix phase. We find that the use of the lower Hashin-Shtrikman bound for the LCC gives the best predictions by comparison with the unit cell calculations for both the macroscopic stress-strain response as well as for the average strains in each of the phases. The formulation is subsequently extended to include hardening of the different phases. Interestingly, the model is found to be in excellent agreement even in the case where each of the phases follows a rather different hardening response.Keywords: Homogenization; Elasto-plasticity; Composite materials; Finite strains * Corresponding author. Fax: +30 2421 074009. E-mail addresses: aravas@uth.gr (N. Aravas), kdanas@lms.polytechnique.fr (K. Danas). 1 IntroductionThe present work deals with the analytical and numerical estimation of the effective as well as the phase average response of N−phase incompressible isotropic elasto-plastic metallic composites. Special attention is given to particulate microstructures, i.e., composite materials which can be considered to comprise a distinct matrix phase and an isotropic distribution of spherical particles [46] (or in a more general setting an isotropic distribution of phases [45]). In the present study, the particles are considered to be stiffer than the matrix phase, which is the case in most metallic materials of interest, such as TRIP steels, dual phase steels, aluminum alloys and others. Such materials, usually contain second-phase particles (e.g., intermetallics, carbon particles) or just second and third phase variants (e.g., retained austenite, bainite, martensitic phases). In addition, these phases/particles tend to reinforce the yield strength of the composite while they usually have different strength and hardening behavior than the host matrix phase.In the literature of nonlinear homogenization there exists a large number of studies for twophase composite materials. The reader is referred to Ponte Castañeda and Suquet [33], Ponte Castañeda [32], Idiart et al. [15], and Idiart [16] for a review of the nonlinear homogenization schemes such as the ones used in the present work and relevant estimates. Nonetheless, very few studies exist in the conte...

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Section: Discussionmentioning

confidence: 99%

Section: The Effective Yield Stressmentioning

confidence: 99%

Section: The Effective Yield Stressmentioning

confidence: 99%

Section: The Strain Concentration Tensorsmentioning

confidence: 99%

See 2 more Smart Citations

A methodology for the estimation of the effective yield function of isotropic composites

Papadioti

Danas

Aravas

2016

International Journal of Solids and Structures

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“…Using the strength homogenization procedure presented in Bignonnet et al (2015), the macroscopic strength of the argillite could therefore be described by an elliptic criterion, even though its apparent macroscopic porosity is less than 1/3.…”

Section: Dry Casementioning

confidence: 99%

A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model

Bignonnet

Dormieux

Kondo

2016

International Journal of Plasticity

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International audienceA micro-mechanical constitutive model for the plastic behavior of cohesive granular materials with hardening due to porosity changes is proposed. The plasticity model is based on a re-interpretation of a micro-mechanical strength model for cohesive frictional granular media. The hardening law by porosity changes explicitly stems from the homogenization process. The micro-macro plasticity model, analytical and fully explicit, depends only on two constant material parameters with a clear physical signification at the microscopic scale: the friction angle and the tensile strength of the grain to grain interfaces. The seminal ideas of critical state soil mechanics are retrieved: critical state line, state boundary surface in the stress/porosity space, hardening or softening due to change in porosity and ability to describe both dilatancy and contrac-tancy. The established micro-mechanical model is very similar to the phenomenological modified Cam clay model, providing to the latter a microstructural based interpretation

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A micromechanical‐based elasto‐viscoplastic model for the Callovo‐Oxfordian argillite: Algorithms, validations, and applications

Zeng

Shao

Yao

2019

Num Anal Meth Geomechanics

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SummaryFor a potential geological barrier of high‐level radioactive waste repositories in France, the long‐term mechanical behavior of the Callovo‐Oxfordian (COx) argillite is the most concern for engineers. In this paper, a micromechanical‐based elasto‐viscoplastic model is proposed, and its numerical realization is our main object. The COx argillite is considered as a three‐phase composite consists of porous clay, quartz, and calcite. By assigning appropriate constitutive laws to those constituents, the macroscopic elasto‐viscoplastic behavior of the COx argillite is determined with an extended Hill's incremental approach. The numerical aspects includes (a) a new formulation is proposed for the plastic multiplier when adopting the overstress (Perzyna) model to define the viscoplastic strain. Meanwhile, a new formulation is also proposed to solve it within the framework of an implicit returning mapping scheme. (b) The corresponding consistent tangent moduli are strictly derived by extending the method proposed for solving plastic problems; (c) the efficiency of the proposed integration algorithms for the local constitutive equations and the homogenization procedure are validated, receptively, by a built‐in porous plasticity model of a commercial finite element (FE) program ABAQUS and by FE computations of a two‐phase unit cell; and (d) the proposed micromechanical model is finally applied to simulate experiment data in short‐term triaxial compression tests and long‐term triaxial creep tests. And the numerical results show that it is able to reflect the variation of the mechanical behavior with respect to the varied mineralogical compositions.

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Strength of a matrix with elliptic criterion reinforced by rigid inclusions with imperfect interfaces

Cited by 9 publications

References 17 publications

A methodology for the estimation of the effective yield function of isotropic composites

A methodology for the estimation of the effective yield function of isotropic composites

A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model

A micromechanical‐based elasto‐viscoplastic model for the Callovo‐Oxfordian argillite: Algorithms, validations, and applications

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