D. Leguillon

Sorbonne University | UPMC · Institut Jean Le Rond d'Alembert (IJLRA) - UMR 7190

Defining the tensile strength of a brittle material like glass is not easy and the presence of residual stresses further complicates the problem. Indeed, measuring the tensile strength by a standard bending test in glass specimens is more a measurement of the presence of surface defects than the determination of a material parameter. This explains...

We study the problem of crack front segmentation into facets under mixed mode I+III loading. Discrete facet network nucleation is determined based on the match asymptotic expansion approach of the coupled criterion considering both the influence of T-stress (parallel to the initial crack front) and mode-dependent fracture properties. We show that c...

The fracture toughness of glass is increased by the introduction of reinforced platelets made of a second constituent with high modulus, strength and/or ductility. In such composites different toughening mechanisms appear. In particular, the borosilicate glass/Al2O3 platelet composite introduced in 1996 is a very attractive solution for industrial...

Unlike isotropic homogenous materials, 3D printing polymers are anisotropic in terms of their strength and fracture toughness properties, according to previous research. Therefore, the lowest strength must be accurately measured before the extensive application of any 3D printing materials. Certain 3D printing materials have been increasingly emplo...

The relevance of the phase-field approach to simulate the fracture in porous ceramics has been investigated. For this purpose, the conditions for the crack initiation using the phase-field model have been compared to the theoretical predictions of the coupled criterion considering a pure V-notch singularity and a crack blunted by a cavity. For two...

An extension of the coupled criterion (CC) of finite fracture mechanics is established in order to assess dynamic crack initiation. The main change compared to the classical quasi-static approach consists in considering the crack velocity profile during initiation instead of assuming an instantaneous crack initiation. The proposed approach enables...

In the Phase Field methodology there is a length parameter related to the size of the damage region, which is proportional to the Irwin length. In this work, we apply the Phase Field methodology to the analysis of fracture at the micro-scale in brittle materials, studying the role of this length parameter when the size of the specimen is of the ord...

The matched asymptotic (MA) approach of the coupled criterion (CC) enables studying crack initiation at a pore located near a free edge, which leads to a competition between three possible crack initiation mechanisms, namely crack initiation in the ligament, at the pore side opposite to the free edge or simultaneously at both pore sides. The mechan...

In the framework of Finite Fracture Mechanics theory, the Coupled Criterion predicts crack onset based, totally or partially according to the situation, on an energy condition. Due to the smallness of the specimens at the micro-scale, this condition may become difficult to be satisfied given the very small volume of the structures, leading to an ap...

The intrinsic performance of epoxy adhesives seems to designate them as the ideal solution for assembling certain materials. Pore can have an influence on the load at which the first crack is initiated and on the final strength. In the context of damage tolerance, this work aims to explore the effect of small voids that cannot be detected by conven...

Solid Oxide Cell (SOC) is a high-temperature electrochemical device that can be operated in both fuel and electrolysis modes. It is constituted of a dense electrolyte in Yttria Stabilized Zirconia (YSZ) sandwiched between two porous electrodes. The hydrogen electrode is classically made of a cermet composed of Nickel and YSZ (Ni-YSZ). Because of sy...

A model based on the Phase Field approach has been developed to simulate the local fracture in porous electrode microstructures. The model capacity to predict the crack nucleation and propagation has been studied with theoretical considerations. For the model validation, micro-compression tests have been performed on porous YSZ micro-pillars. As ex...

The tensile load at debonding onset between stiff particles and a soft matrix is predicted with the coupled criterion which combines a stress and an energy conditions. A finite element model of a representative volume element is implemented in order to consider the influence of the size of the particles, the particle volume fraction, mixed mode con...

Piezoelectric thin films are vulnerable to fracture, which results in degradation of the structural integrity and device performance in piezoelectric microelectromechanical systems (PiezoMEMS). This work explains the fracture process as a combination of a crack initiation event in the piezoelectric film followed by crack propagation through the rem...

Unidirectional tensile tests of PMMA square hole specimens result in mixed mode crack initiation at the square hole corners, highlighted by inclined cracks with respect to the V-notch bisector. Generalized stress intensity factors (GSIF) of the opening and shear modes at a V-notch are derived experimentally in a direct manner from digital image cor...

Prediction of surface cracking in ceramics due to quenching is performed numerically using either the coupled criterion or a cohesive zone model. Under such a thermal shock, a network of short cracks with minimal spacing between them initiate and propagate until some of them stop while the others continue propagating. The numerical implementation c...

The 2D stress intensity factor at the tip of a crack plays an essential role in the models of brittle fracture to predict the growth of a pre-existing crack. The coupled criterion, based on a twofold condition in energy and stress, extends the results to the initiation of a new crack at any 2D singular points. The generalized stress intensity facto...

An implementation of the coupled criterion (CC) for crack initiation simulation in the commercial finite element (FE) code Abaqus/Standard is proposed. This finite fracture mechanics approach allows crack initiation to be modeled by fulfilling simultaneously a stress and an energy conditions, which results in the determination of the loading level...

Based on the unique additive manufacturing process, a dual-notch void model is proposed to explain three tensile strengths of a 3D printed polymer along three major directions. This model incorporates the strength/notch angle relation and provides a relative magnitude of three tensile strengths, i.e., Sx (axial strength) > Sy (transverse strength)...

Predicting the maximum load that a (quasi-)brittle specimen can sustain is an important scientific and practical issue. A natural approach is to search for a criterion. Strength and toughness criteria are well suited for simple specimen having either no defect or an existing crack. When defects (notches, or cavities, …) are present, the criterion i...

Failure of bi-material joints is affected significantly by the elastic material properties of both adherends as well as by geometrical parameters such as material interface orientation. Addressing these effects, scarf joint specimens made of a polymer foam and either PMMA or aluminum are examined employing a four-point bending test setup with varyi...

In this work, we present a numerical model to deal with the fracture of damaged materials within the framework of the finite fracture mechanics (FFM). Continuum damage mechanics combined with the regularization techniques is first applied to determine the damage field. The transition from continuous damage field to discontinuous crack occurs when t...

L'amorçage de fissures dans des éprouvettes trouées en PMMA sous sollicitation de compression est caractérisé expérimentalement et modélisé avec le critère couplé et des modèles de zones cohésives. La nucléation abrupte/spontanée d'une fissure d'une longueur finie est prédite par les deux approches. Ce caractère abrupt de l'amorçage est également m...

Under compression, mode I cracking in the loading direction is observed in PMMA rhombus hole specimens. Except for specimens containing flaws, spontaneous initiation is observed experimentally with the abrupt nucleation of a crack at the rhombus V-notch tip. With increasing hole angle and size, the force for crack initiation decreases whereas the c...

Numerical predictions of initiation loading and crack length in a rhombus hole specimen made of a brittle material under quasi-static compression using either cohesive zone model or coupled criterion based on finite fracture mechanics are compared. Both methods lead to the conclusion that crack initiation results in a crack jump over a finite lengt...

A numerical study of crack front segmentation under mode I + III loading is proposed. Facets initiation ahead of a parent crack is predicted through a tridimensional application of the coupled criterion. Crack initiation shape, orientation and spacing are determined for any mode mixity ratio by coupling a stress and an energy criterion using matche...

Criteria for predicting initiation of cracks in brittle materials like ceramics are based on two parameters: the material fracture toughness and the tensile strength. Standardized experiments exist to estimate the former. However, the tensile strength is often taken from experiments (mainly uniaxial bending) on specimens with various geometries and...

The effect of small critical flaws on the strength of polycrystalline ceramic materials is analyzed with the help of an initiation criterion combining both a stress and an energy conditions. If the size of the defect is smaller than the characteristic material length, numerical predictions reveal that the defect (either sharp or blunt) has no effec...

The failure of quasi-brittle specimen weakened by sharp or blunted notches and cavities is analyzed under quasi-static loading. The load at failure is obtained with the Thick Level Set (TLS) damage modeling. In this model, the damage gradient is bounded implying that the minimal distance between a point where damage 0 (sound material) to 1 (fully d...

Crack initiation of scarf adhesive joints with similar adherends is predicted through 2D and 3D applications of the coupled criterion. The joint adhesive crack initiation topology and loading are determined as a function of the joint angle and of the specimen width, using both an energy and a stress criterion consisting of the maximum interface nor...

Until now, the coupled stress and energy criterion has mainly been used in 2D applications, but it is possible to extend it to a 3D case. Herein the crack initiation in epoxy/aluminum bimaterial specimens under four point bending is predicted through a 3D numerical application of the coupled criterion. The stress and the energy conditions are compu...

Sub-micron films deposited on a flexible substrate are now commonly used in electronic industry. The main damaging mode of these systems is a multi-cracking of the film under the action of thermal and mechanical stresses. This multi-cracking phenomenon is described using the coupled criterion based on the simultaneous fulfilment of an energy and a...

A finite fracture approach based on the Coupled Criterion is used to analyze multi-cracking in a woven ceramic matrix composite. In-situ micrographic observations obtained during tensile and bending tests performed on chemical vapor infiltrated SiC/SiC samples are utilized to identify cracking mechanisms. A two dimensional finite element model is g...

The coupled criterion is a finite fracture mechanics approach which couples an energy condition and a stress condition to predict crack initiation at stress concentration points. It is here used to study various cracking mechanisms in composite materials at different scales. The paper focuses on edge delamination at the mesoscale and also considers...

The proposed numerical model for simulating two-dimensional cracking process in brittle materials is based on the coupled criterion (CC) which enters in the general framework of Finite Fracture Mechanics. It states that both the energy and stress conditions should be fulfilled to predict the crack creation in brittle solids. Special numerical appro...

Multi-cracking of brittle thin layers and coating is a phenomenon difficult to model especially because of the large number of cracks that may occur. It is overcome herein by conducting calculations, not on the whole structure, but only on a simplified cell that is representative of the structure by periodic duplication. The coupled criterion is ap...

At V-notched tips in specimens made of quasi-brittle materials a small damaged or plastic zone is evident that cannot not be neglected in terms of dissipated energy and stress state, although it is small. Herein, to predict the failure initiation at the notch tip, we extend the finite fracture mechanics (FFM) coupled criterion, which requires a sim...

Different criteria are available in the literature to assess the fracture behaviour of sharp V-notches. A typical and well-known criterion is based on the application of the notch stress intensity factors (NSIFs), which are able to quantify the intensity of the stress fields ahead of the notch tip.

This contribution gives an overview of different fracture-mechanics issues occurring in layered ceramics designed with internal compressive residual stresses (such as the edge cracking, crack arrest by the compressive layer or crack deflection/bifurcation) and proposes an effective approach to describe the initiation and/or propagation of cracks in...

Cohesive zone models and criteria based on finite fracture mechanics are two alternatives to analyze edge debonding. A comparison between the two approaches is presented in this paper. The coupled criterion which combines a stress and an energy conditions to estimate crack initiation is used and compared with a bilinear cohesive law. Predictions of...

The high compressive stresses in ceramic laminates utilized to enhance their fracture resistance may lead to the formation of edge cracks at the surface of the compressive layers. In this work, a 2D parametric numerical model is developed to assess the effect of residual stress and thickness of the compressive layers on the edge crack formation, by...

The objective of the paper is to analyze four point bending tests performed on samples of an epoxy-type thermoset polymer oxidized under several conditions, and to predict the failure mechanisms. Different responses are observed depending on the oxidation time: for small durations there is a linear elastic phase followed by an abrupt failure of the...

Different criteria are available in the literature to assess the fracture behaviour of sharp V-notches. A typical and well-known criterion is based on the application of the Notch Stress Intensity Factors (NSIFs), which are able quantify the intensity of the stress field ahead of the notch vertex. This work considers two recent energy-based criteri...

Crack initiation in brittle materials is not covered by classical fracture mechanics that deals only with the growth of pre-existing cracks. In order to overcome this deficiency, the Finite Fracture Mechanics concept assumes the instantaneous formation of cracks of finite size at initiation. Within this framework, a coupled criterion was proposed a...

The strength of an open-holed composite plate subjected to tensile loading is analysed with the help of a coupled strength-and-energy criterion. Analytical and numerical models are used to determine the stress distribution from and energy released by crack nucleation in the vicinity of the hole. It is shown that the hole size effect can be describe...

Layered ceramic materials (also referred to as “ceramic laminates”) are becoming one of the most promising areas of materials technology aiming to improve the brittle behavior of bulk ceramics. The utilization of tailored compressive residual stresses acting as physical barriers to crack propagation has already succeeded in many ceramic systems. Re...

Material or geometrical discontinuities within a structure induce a localized stress concentration which may initiate a crack leading to catastrophic failure in brittle materials. To assess crack initiation in the vicinity of a V-notch, a criterion based on the strain energy density (SED) averaged over a volume surrounding the notch tip is an attra...

In the literature, the problem of crack nucleation from the V-notch tip is generally treated with stress or energy approaches. Considering pure Mode 2 loading conditions, the expression of the critical Mode 2 NSIF at failure as derived according to the averaged strain energy density (SED) criterion is compared with those given by two different vers...

During the operating life of an Advanced Gas-cooled Reactor, the core, made of thousands of graphite bricks, is subjected to internal stresses arising because of dimensional changes due to irradiation. It may lead to crack initiation and propagation especially in notched areas (called keyway corners). Understanding this phenomenon for the coming ye...

In this paper, accurate numerical analyses of the stress distributions within the adhesive in scarf joints under elastic assumption using 3D models are developed. An elastic limit model that takes into account the hydrostatic stress and von Mises equivalent stress, permit to define the more stressed parts of the adhesive with respect to the scarf a...

One novel approach to improve the apparent toughness of ceramics is to design a multilayer architecture with embedded layers having compressive residual stresses. Surface cracks propagating during mechanical loading can be deflected within the compressive layers, in order to delay the final fracture of the whole structure. The design of high toughn...

Geomaterials such as rocks and concrete are brittle or quasi-brittle materials. Tensile tests carried out to observe the initial phases of crack nucleation are difficult to achieve because of the unstable nature of the tests. Instead, compression tests on drilled specimens offer a greater stability. When subjected to a compressive loading, two oppo...

This article is aimed at comparing two models based on the same assumptions to analyze the failure of adhesively bonded joints. These models combine the use of two criteria: a stress criterion for the initiation of micro-cracks and an energy criterion for the propagation of these micro-cracks to create a macro-crack. The first model only requires e...

The tests leading to the determination of the strength of brittle materials show a very wide scattering and a noticeable difference between flexural and tensile strengths. The corresponding statistics are usually described by the Weibull law, which only partly explained the observed difference. From a theoretical point of view, the coupled criterio...

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection...

This article is aimed at comparing two models based on the same assumptions to analyze the failure of adhesively bonded joints. These models combine the use of two criteria: a stress criterion for the initiation of micro-cracks and an energy criterion for the propagation of these micro-cracks to create a macro-crack. The first model only requires e...

The failure initiation of a brazed sample made of silicon carbide substrates and submitted to bending is analyzed with the help of a criterion which combines a maximum incremental energy release rate and a maximum tensile stress conditions. Two different modes of cracking are considered to develop in the vicinity of the free edge between the brazed...

Functionalized thin films of ceramic material are used in catalytic converters as a catalyst support. A degradation of the catalytic performances can be caused by thermal and chemical effects leading to the formation of cracks and the detachment of fragments. Understanding the formation of the lattice of cracks and the spalling is challenging in fr...

The onset of an edge crack in compressive layers of a ceramic laminate undergoing residual stresses is predicted using the stress–energy coupled criterion based on the data of the tensile strength and the toughness of the material under consideration. The proposed criterion does not contain any adjustable parameter, which is its indisputable advant...

The onset of edge debonding within a bonded specimen submitted to bending is modeled with two numerical approaches: the coupled criterion and the cohesive zone model. The comparison of the results obtained with the both approaches evidences that (i) the prediction of edge debonding strongly depends on the shape of the cohesive law and (ii) the trap...

Microstructure of a cermet Ni–YSZ bi-layer is analysed on the basis of three dimensional reconstructions obtained on both functional layer and cell support. Microstructural parameters of gas, ionic and electronic phases are determined in terms of phase connectivity, mean particles diameter, particles size distribution, specific surface area, tortuo...

The extension of the 2D coupled criterion is based on the joint used of the 3D singularity theory and matched asymptotic expansions. Formally, the formulation of the 3D criterion is similar to that of the 2D case, although some differences appear to establish it. Moreover an additional hypothesis on the geometry of the crack extensions is needed, o...

Microstructure of a cermet Ni-YSZ bi-layer is analysed on the basis of three dimensional reconstructions obtained on both functional layer and cell support. Microstructural parameters of gas, ionic and electronic phases are determined in terms of phase connectivity, mean particles diameter, particles size distribution, specific surface area, tortuo...

The scarf joint is a usual experimental assembly employed to analyze the mechanical behavior of an adhesive. In fact, using a unique type of bonded assembly with a classic tensile testing machine, various tensile-shear loadings of the adhesive can be applied by changing the value of the scarf angle. In this paper, accurate numerical analyses of the...

The stricter environmental regulations impose a drastic reduction of vehicles emissions and a longer durability of the automotive catalyst. The studies of the catalyst evolution in real conditions are very expensive. It is interesting to elaborate an ageing process to well simulate the real conditions of the automotive catalyst ageing at the labora...

The role of the adhesive thickness in the failure of bonded joints is a controversial issue. On the one hand, analytical and numerical models show that the bonding strength is improved as the adhesive thickness increases, on the other hand experimental observations lead to the opposite conclusion. Taking advantage of the thinness of the adhesive la...

The prediction of the failure load of bonded joints is a major issue in order to increase the confidence in the design of such assemblies. The aim of this paper is to present a method to predict the strength of adhesive joints. The failure could be initiated if two criteria are fulfilled: (i) an energy criterion and (ii) a stress criterion. The com...

CO $_{2}$ storage at depth is a promising way to reduce the spread of greenhouse gases in the atmosphere. Obviously the sedimentary cover should ensure the sealing of reservoirs. The latter are periodically fractured to allow injection and we propose a model to predict the maximum bearable gas pressure before reinitiating these fractures in the ca...

The adhesive thickness has a strong influence on the crack initiation in a bonded assembly. Indeed, the thiner the adhesive thickness, the higher the strength. In order to describe this influence, several cohesive zone models (bilinear, tri-linear and trapezoidal) are used, using a linear elastic stiffness defined as the ratio between the Young's m...

Different mechanisms (cooling, drying, and ageing) lead to the formation of crack patterns on the surface of some materials that are very difficult to describe in detail. We propose a model based on the coupled criterion using two necessary conditions for the nucleation of cracks: an energy condition and a stress condition. This model is applied to...

Introduction Singularities Modal mixity Brittle fracture mechanics Nucleation of cracks Deflection of a crack at an interface Conclusion Bibliography

The strength of an open holed composite plate subjected to tensile loading is analysed with the help of a coupled strength and energy criterion. Analytical and numerical models are used to determine the stress distribution and the energy released by crack nucleation in the vicinity of the hole. It is shown that the hole size effect can be described...

A methodology is proposed to assess the contribution of residual stresses to the debonding risk in multilayers used as cells for energy conversion at elevated temperature. The conditions of an interface crack extension, given by the Energy Release Rate (ERR) and mode-mixity, are fully investigated for thermal and mechanical loadings. Mode-mixity is...

The failure criterion for v-notched specimens developed for mixed-mode loadings by Yosibash et al. [Yosibash, Z., Priel, E., Leguillon, D., 2006. A failure criterion for brittle elastic materials under mixed mode loading. Int. J. Fract. 141(1), 289–310.] is generalised in order to consider the influence of the shear stresses and the mode-dependence...

The failure initiation of a brazed structure made of Silicon Carbide components is analysed by means of a two-scale analysis and a twofold failure criterion using both a maximum released energy and a maximum tensile stress conditions. In a first step, two asymptotic expansions are settled to describe the perturbation caused by the emergence of the...

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip ma...