Identification of damaged zone in composite materials using displacement field measurements

This work presents an identification strategy of local elastic properties of orthotropic carbon-epoxy laminates for aviation industry. Based on global and local stages of study, this methodology uses the Finite Element Model Updating (FEMU) method as identification technique with simulated kinematic fields corresponding to tensile test response. The aim of this paper is to predict the spatial variation of elastic plane properties and to deduce the localization of damaged zones

Micromechanical modeling of brittle damage in composite materials: primary anisotropy, induced anisotropy and opening-closure effects

Inelastic deformation of various brittle materials such as concrete, rocks or composites has been widely explained by the existence, nucleation and growth of microcracks. The oriented nature of these microdefects, coupled with the unilateral contact of their lips (i.e. microcracks can be either open or closed depending on loading), leads to a complex anisotropic behaviour notably characterized by a recovery of some effective properties at the closure of microcracks. For composite materials, the interaction of these both features with their primary (structural) anisotropy makes things even more complex. Experimental investigations through ultrasonic measures on ceramic matrix composites confirm the stiffness modifications due to degradation process, both on the amplitude (when loading axes correspond to initial material axes) and on the type of resulting material symmetry, especially in the case of off-axis loadings [3]. Concerning the unilateral effect, some authors have put in evidence the partial recovery of elastic properties at the closure of microcracks but these studies are often restricted to axial properties or to defects configurations coinciding with to the structural anisotropy of the material [1,8]. In terms of representation, the simultaneous description of the damage induced anisotropy and of the activation-deactivation process (the so-called unilateral effect) within a consistent modeling still remains a difficult and open research field, even in the context of initially isotropic materials. Indeed, mathematical or thermodynamical inconsistencies have been pointed out in existing formulations, such as discontinuities of the stress-strain response or non-uniqueness of the thermodynamic potential [4-5]. Concerning anisotropic microcracked materials, the analysis of their overall elastic properties is limited to configurations of open defects [6,7,9]. This paper aims to introduce a novel and original modeling approach for this problem within the framework of Continuum Damage Mechanics. In view of the lack of exhaustive experimental data on such aspects, we propose a micromechanics-based formulation of the resulting -generally fully- anisotropic multilinear response of orthotropic materials containing microcracks. On the basis of works by [2] for isotropic media, a strain-based homogenization approach is developed. This leads to a closed-form expression of the macroscopic free energy corresponding to 2D initially orthotropic materials weakened by arbitrarily oriented microcrack systems with account of closure effects. The consideration of such unilateral behavior constitutes one of the main contribution of the study. The explicit expressions obtained provide then a complete quantification of interaction effects both between primary and microcracks-induced anisotropies and between opening/closure states of cracks on the materials elastic properties. The thermodynamics framework finally gives a standard procedure for the formulation of the damage evolution law that ensures in all cases the verification of the thermodynamics second principle. Moreover, the association of the overall free energy expression derived with the standard evolution law introduces both oriented and closure effects due to microcracks in the material response and damage evolution. The model has been implemented within the finite-element code ABAQUS and various numerical simulations illustrate the representation capacities. Indeed, the formulation can account for the main features of brittle cracking kinetics, especially the load-induced anisotropy and the dissymmetry between initial damage thresholds in tension and compression

Effects of the Unified Viscoplastic Formulation and Temperature Terms on the Thermomechanical Behavior of Soldering Materials

Solder materials are critical packaging compounds and due to usually weakest melting temperature among packaging constitutive materials, thus, they are frequently subjected to a multitude of physical phenomena: creep, fatigue and combined hardening effects. The complexity and interaction of such factors must be considered in suitable way in the mechanical behavior modeling using the appropriate material behavior laws. The choice of the mechanical model depends on several factors such as the complexity of constitutive equations to be integrated, the availability and suitability of implementation in the FE codes, the number of parameters to be identified, the capability of the model to represent the most common physical features of the material… Following these observations and in order to deal with these critical remarks, comparisons between the most common unified viscoplastic models should be done in the local and finite element levels for the decision upon the most efficient model. That is the aim of this paper with application to a tin based solder token as the test material

Experimental and mechanical characterizations of a lead free solder alloy for electronic devices

Electronic power modules devices are paramount components in the aeronautical,automotive and military applications. The solder layers are the most critical parts of the module and are usually subjected in their whole life to complex loading conditions. To improve the design task, realistic thermoelastoviscoplastic and lifetime prediction models which can describe efficiently the deformation-damage of the electrical device must be chosen carefully. Some of the most common behavior models are based on the separation between creep and plasticity deformations such as power law, Garofalo, Darveaux… So, to take into account the creep-plasticity interaction, the thermal cycling as well as the hardening-softening effects, unified viscoplastic models are increasingly being used to describe more efficiently the physical state of the material. We propose in this framework a survey of some unified viscoplastic models used in the electronic applications for the viscoplastic modeling of the solder as well as creep-fatigue life prediction rules. The models are used for the characterization of a SnAgCu solder and are briefly compared within tensile, creep data and stabilized responses

Caractérisation expérimentale du comportement mécanique d’assemblage haute température pour l’électronique de puissance

Ce papier a pour objectif l’étude expérimentale du comportement mécanique de deux types de connexions haute température mises en œuvre pour l’assemblage de composants d’électronique de puissance : une jonction réalisée par brasage en phase liquide transitoire (TLPB) d’Ag-In et une autre par brasage d’un eutectique Au88Ge12. Les connexions réalisées à partir d’inserts de cuivre sont caractérisées mécaniquement au moyen d’essais de cisaillement. Une analyse de la microstructure des jonctions en coupe et des faciès de rupture des deux connexions a également été menée. L’ensemble des essais et des analyses permettent de comparer le comportement mécanique et la faisabilité des deux connectiques d’électronique de puissance

Study of image characteristics on digital image correlation error assessment

In this paper, errors related to digital image correlation (DIC) technique applied to measurements of displacements are estimated. This work is based on the generation of synthetic images representative of real speckle patterns. With these images, various parameters are treated in order to determine their impact on the measurement error. These parameters are related to the type of deformation imposed on the speckle, the speckle itself (encoding of the image, image saturation) or the software (subset size)

Viscoplastic behavior of diamond die attach subjected to high temperature conditions

In power electronic applications, diamond based semi-conductors appears to be a new way to widely increase the capabilities of power electronic converters. The main prospective expected is an increasing in system integration and power capabilities. The Diamonix project concerns the elaboration of a single-crystal diamond substrate with electronic quality and its associated packaging. The designed structure has to resist to temperatures varying between -50°C and +300°C. This paper deals with an experimental and numerical study of the diamond die attach solution. The development of a packaging for diamond component relies in particular on a specific choice of solder’s alloys for the junction die/substrate. To carry out this junction, AuGe and AlSi eutectic alloys were chosen and characterized; the choice of these two kinds of solders i.e. AuGe and AlSi is motivated by the practical elaboration process and the restrictions of hazardous substances (RoHS). The first solder has a melting temperature of 356°C; the second has a higher melting point of 577°C. In this paper, we present some numerical results obtained from FE simulations of two 2D configurations of simplified electronic packaging. The power electronic packaging is composed of a diamond die and a copper metallized Si3N4 ceramic substrate which are brazed together with either AuGe or AlSi solder alloy. To predict the thermomechanical behavior of the solders, a particular constitutive behavior law was implemented as a User MATerial subroutine which is based on a viscoplastic unified McDowell formulation, coupled with porous damage equations. The mechanical law can describe precisely the viscoplastic damage phenomenon of solder subjected to high thermal cycling and to optimize the thermo-mechanical modeling for advanced package developmen

Vie tribologique à chaud et température interfaciale dans des contacts céramiques

Le frottement et l'usure de différents couples de céramiques oxydes (alumines) et non-oxyde (carbure de tungstène à liant cobalt) ont été étudiés à température ambiante et à haute température en s'attachant à mettre en relief l'incidence des phénomènes thermiques sur le comportement tribologique de ces matériaux. Un montage expérimental a tout d'abord été conçu et réalisé spécialement pour cette étude. Il permet la conduite d'essais de frottement en configuration pion-disque de l'ambiante à 900°C dans un large domaine de charges. Un modèle thermique a été élaboré afin d'évaluer les températures moyennes et éclairs dans un contact frottant en prenant en compte les conditions aux limites imposées par le montage expérimental. Les résultats sont exploités sous forme de cartes de températures spécifiques à un couple de matériaux et à un coefficient de frottement donné. L'étude tribologique met tout d'abord en évidence puis caractérise les discontinuités de comportement en frottement et usure à 20 et 800°C de deux alumines α à 99,7% et 94% de pureté. L'analyse en continue de l'usure associée aux observations microscopiques permettent de reconstituer la vie du contact en mettant en relief l'influence de la température d'essai et de la température générée par le frottement. Le frottement d'un cermet carbure de tungstène à 6% de cobalt a ensuite été étudié en frottement face à lui-même et face à des disques d'alumine

Identification of materials properties using displacement field measurement

The aim of this work is to identify parameters driving constitutive equations of materials with displacement field measurements carried out by image stereo-correlation during an unidirectional tensile test. We evaluate two identification techniques. The first one is the virtual fields method which consists in writing the principle of virtual work with particular virtual fields. It is generally used in the case of linear elasticity and it requires a perfect knowledge of the model in terms of boundary condition since the virtual fields used must be kinematically admissible. This method allows to determine parameters by a direct and fast calculation, without iterations. The second method is the finite element model updating method. It consists in finding constitutive parameters that achieve the best match between finite element analysis quantities and their experimental counterparts. This method is more adaptable than the virtual field method but it needs to spend more calculation time

Contribution à la modélisation non linéaire des matériaux et des structures

Le document présenté synthétise des activités de recherche liées à la mécanique non linéaire des matériaux et à la modélisation thermomécanique des structures. L’ensemble des développements associe des études expérimentales et numériques portant sur la modélisation du comportement élasto-viscoplastique d’alliages de brasure et au comportement viscoélastique non linéaire de films polymères. Cette activité se prolonge par plusieurs développements engagés autour de l’identification paramétrique des modèles de comportement. Ces axes de recherche ont contribué à l’enrichissement de modèles numériques de comportements de structures ou de procédés dont ils permettent une meilleure étude et compréhension. Les domaines applicatifs sont variés : aéronautique, astronautique, électronique de puissance et génie-chimique. Plusieurs applications originales de modélisations thermomécaniques sont exposées