Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)
http://hdl.handle.net/10985/190
Fri, 08 Nov 2024 19:05:50 GMT2024-11-08T19:05:50ZLaboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)https://sam.ensam.eu:443/bitstream/id/4f20832b-25ad-47db-bde8-29565ee8975c/
http://hdl.handle.net/10985/190
Microstructure investigation of hydrothermal damage of aged SMC composites using Micro-computed tomography and scanning electron microscopy
http://hdl.handle.net/10985/19934
Microstructure investigation of hydrothermal damage of aged SMC composites using Micro-computed tomography and scanning electron microscopy
ABDESSALEM, Abir; TAMBOURA, Sahbi; DALY, Hachmi Ben; TCHARKHTCHI, Abbas; FITOUSSI, Joseph; MERAGHNI, Fodil
This paper presents an investigation on the effects of hydrothermal aging on Sheet Molding Compound (SMC) composite. Two different techniques were carried out to study the inner structure of aged SMC composite. Firstly, X-ray micro computed tomography (XµCT) was used to evaluate the changes using 3D images. The results showed cracks in all the composite structure with different shapes and volume in response to the hydrothermal conditions. The cracks results from the build up of an osmotic pressure in microcavities, which is proportional to water concentration. However, it was not possible to quantify separately the hydrothermal induced damage in the studied SMC composite material. Therefore, the XµCT analyzes were supplemented by a microscopic study. This step has been studied in terms of crack density evolution and crack propagation rate. The results obtained by XµCT technique and SEM observations show that the damage increases continuously with time and temperature during aging. The damage was found to be located in the voids contained in the matrix at early stage of aging. Then it is mostly developed into the fiber interface in the form of fiber/matrix interfacial debonding.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199342021-01-01T00:00:00ZABDESSALEM, AbirTAMBOURA, SahbiDALY, Hachmi BenTCHARKHTCHI, AbbasFITOUSSI, JosephMERAGHNI, FodilThis paper presents an investigation on the effects of hydrothermal aging on Sheet Molding Compound (SMC) composite. Two different techniques were carried out to study the inner structure of aged SMC composite. Firstly, X-ray micro computed tomography (XµCT) was used to evaluate the changes using 3D images. The results showed cracks in all the composite structure with different shapes and volume in response to the hydrothermal conditions. The cracks results from the build up of an osmotic pressure in microcavities, which is proportional to water concentration. However, it was not possible to quantify separately the hydrothermal induced damage in the studied SMC composite material. Therefore, the XµCT analyzes were supplemented by a microscopic study. This step has been studied in terms of crack density evolution and crack propagation rate. The results obtained by XµCT technique and SEM observations show that the damage increases continuously with time and temperature during aging. The damage was found to be located in the voids contained in the matrix at early stage of aging. Then it is mostly developed into the fiber interface in the form of fiber/matrix interfacial debonding.Microstructure investigation of hydrothermal damage of aged SMC composites using Micro-computed tomography and scanning electron microscopy
http://hdl.handle.net/10985/19755
Microstructure investigation of hydrothermal damage of aged SMC composites using Micro-computed tomography and scanning electron microscopy
ABDESSALEM, Abir; TAMBOURA, Sahbi; FITOUSSI, Joseph; DALY, Hachmi Ben; TCHARKHTCHI, Abbas; MERAGHNI, Fodil
This paper presents an investigation on the effects of hydrothermal aging on Sheet Molding Compound (SMC) composite. Two different techniques were carried out to study the inner structure of aged SMC composite. Firstly, X-ray micro computed tomography (XμCT) was used to evaluate the changes using 3D images. The results showed cracks in all the composite structure with different shapes and volume in response to the hydrothermal conditions. The cracks results from the build up of an osmotic pressure in microcavities, which is proportional to water concentration. However, it was not possible to quantify separately the hydrothermal induced damage in the studied SMC composite material. Therefore, the XμCT analyzes were supplemented by a microscopic study. This step has been studied in terms of crack density evolution and crack propagation rate. The results obtained by XμCT technique and SEM observations show that the damage increases continuously with time and temperature during aging. The damage was found to be located in the voids contained in the matrix at early stage of aging. Then it is mostly developed into the fiber interface in the form of fiber/matrix interfacial debonding.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/197552021-01-01T00:00:00ZABDESSALEM, AbirTAMBOURA, SahbiFITOUSSI, JosephDALY, Hachmi BenTCHARKHTCHI, AbbasMERAGHNI, FodilThis paper presents an investigation on the effects of hydrothermal aging on Sheet Molding Compound (SMC) composite. Two different techniques were carried out to study the inner structure of aged SMC composite. Firstly, X-ray micro computed tomography (XμCT) was used to evaluate the changes using 3D images. The results showed cracks in all the composite structure with different shapes and volume in response to the hydrothermal conditions. The cracks results from the build up of an osmotic pressure in microcavities, which is proportional to water concentration. However, it was not possible to quantify separately the hydrothermal induced damage in the studied SMC composite material. Therefore, the XμCT analyzes were supplemented by a microscopic study. This step has been studied in terms of crack density evolution and crack propagation rate. The results obtained by XμCT technique and SEM observations show that the damage increases continuously with time and temperature during aging. The damage was found to be located in the voids contained in the matrix at early stage of aging. Then it is mostly developed into the fiber interface in the form of fiber/matrix interfacial debonding.Numerical Investigation of the Limit Strains in Sheet Forming Involving Bending
http://hdl.handle.net/10985/10322
Numerical Investigation of the Limit Strains in Sheet Forming Involving Bending
ABED-MERAIM, Farid ; BALAN, Tudor
In this work, the finite element method is used to simulate a typical FLD test over tools of different radii. Parameters like the mesh density, element type, numerical determination of the onset of strain localization, limit strain definition etc. have been investigated. Finally, the limit strain for plane strain tension has been determined as a function of the thickness vs. tool radius (t/R) ratio. These simulations confirm that increasing the curvature of the tool increases the value of the limit strains. They also reveal that, as soon as bending becomes important, the practical relevance of the limit strains diminishes - At least with their current definition. The need for new strain localization models is emphasized, together with some of the associated challenges.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/103222008-01-01T00:00:00ZABED-MERAIM, Farid BALAN, TudorIn this work, the finite element method is used to simulate a typical FLD test over tools of different radii. Parameters like the mesh density, element type, numerical determination of the onset of strain localization, limit strain definition etc. have been investigated. Finally, the limit strain for plane strain tension has been determined as a function of the thickness vs. tool radius (t/R) ratio. These simulations confirm that increasing the curvature of the tool increases the value of the limit strains. They also reveal that, as soon as bending becomes important, the practical relevance of the limit strains diminishes - At least with their current definition. The need for new strain localization models is emphasized, together with some of the associated challenges.Prediction of material ductility and sheet metal formability in relation to plastic instabilities
http://hdl.handle.net/10985/20357
Prediction of material ductility and sheet metal formability in relation to plastic instabilities
ABED-MERAIM, Farid
In the literature dealing with plastic instabilities in general, many instability criteria have been developed, and some of them have been extensively applied to sheet metals to investigate their formability limits. Exhaustively reviewing these criteria is difficult, considering the multitude of variants deriving from some of these approaches. However, a review of the literature reveals that thecriteria can be classified into at least four distinct categories depending on their fundamental basis and theoretical or physical background. For stretched sheet metals, two forms of necking, namely diffuse and localized necking, may occur. It has been shown that diffuse necking occurs prior to localized necking, and it is now well recognized that the maximum allowable straining in sheet metal forming is determined by localized necking. For this reason, forming limit diagrams (FLDs) are commonly determined at localization in most of the current formability approaches. Early instability criteria were based on the maximum force principle (Considère, 1885), and its two-dimensional extension (Swift, 1952) for application to sheet metals. In their original form, these criteria were intended to allow for the prediction of diffuse necking. Later, these maximum-force-based criteria were extended to the prediction of localized necking, and some enhanced versions were developed to account for some key features (Hora, 1996; Mattiason, 2006). Note also that Hill’s zero-extension criterion (Hill, 1952), which predicts localized necking on the left-hand side of the FLD, was developed during the same time as Swift’s diffuse necking criterion. Another approach, which postulates a pre-existing defect in the material sheet, was proposed by Marciniak and Kuczynski (1967). This M–K model can be regarded as a complementary approach to Hill’s zero-extension criterion, which is only applicable to the left-hand side of the FLD, as no zero-extension direction exists for positive biaxial stretching. However, because localized necking in biaxial stretching is observed in practice, a pre-existing defect has to be introduced in the M–K model to capture this phenomenon, which may provide some justification for this imperfection theory. In addition to the aforementioned engineering approaches, another category of plastic instability criteria was developed based on a more fundamental background. Drucker and Hill’s theory (Drucker, 1956; Hill, 1958), also referred to as the general bifurcation criterion, represents another class of approaches for necking prediction. This condition of positiveness of the second-order work provides a lower bound for all of the bifurcation-based criteria in this category. In the same class of criteria, Valanis (1989) suggested using a limit-point bifurcation criterion, which is less conservative than the general bifurcation criterion but coincides with it within the framework of associative plasticity and small strains. With regard to localized modes of deformation, Stören and Rice (1975) proposed a bifurcation criterion characterized by the singularity of the acoustic tensor, also known as discontinuous bifurcation. It has been shown that this criterion corresponds to the loss of ellipticity of the partial differential equations governing the associated boundary value problem. In the same manner, some authors (e.g., Bigoni and Hueckel, 1991) have suggested the use of the more conservative condition of strong ellipticity, which has been shown to coincide with Rice’s criterion within the framework of associative plasticity and small strains. This condition of loss of strong ellipticity is also a special case of Drucker’s general bifurcation criterion, in which the bifurcation mode is restricted to localized (compatible) deformation modes. From this overview of the various approaches pertaining to strain localization criteria and indicators, an interesting observation can be made. While M–K analysis has been widely used in the literature, few applications of Rice’s ellipticity loss theory, mainly restricted to plane-stress assumptions, particular loading paths, and simple behavior models, have been attempted in sheet metal forming for quantifying metals in terms of their formability. In this presentation, various results relating to the prediction of plastic flow localization based on bifurcation theory will be shown for different constitutive modeling approaches. Also, comparisons will be conducted for the different approaches of plastic instability prediction. For some approaches, a classification of the criteria will be established, in terms of their conservative nature of prediction. Moreover, similarities or relationships between some approaches and associated criteria will be emphasized, whenever their underlying formulations make it possible.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/203572018-01-01T00:00:00ZABED-MERAIM, Farid In the literature dealing with plastic instabilities in general, many instability criteria have been developed, and some of them have been extensively applied to sheet metals to investigate their formability limits. Exhaustively reviewing these criteria is difficult, considering the multitude of variants deriving from some of these approaches. However, a review of the literature reveals that thecriteria can be classified into at least four distinct categories depending on their fundamental basis and theoretical or physical background. For stretched sheet metals, two forms of necking, namely diffuse and localized necking, may occur. It has been shown that diffuse necking occurs prior to localized necking, and it is now well recognized that the maximum allowable straining in sheet metal forming is determined by localized necking. For this reason, forming limit diagrams (FLDs) are commonly determined at localization in most of the current formability approaches. Early instability criteria were based on the maximum force principle (Considère, 1885), and its two-dimensional extension (Swift, 1952) for application to sheet metals. In their original form, these criteria were intended to allow for the prediction of diffuse necking. Later, these maximum-force-based criteria were extended to the prediction of localized necking, and some enhanced versions were developed to account for some key features (Hora, 1996; Mattiason, 2006). Note also that Hill’s zero-extension criterion (Hill, 1952), which predicts localized necking on the left-hand side of the FLD, was developed during the same time as Swift’s diffuse necking criterion. Another approach, which postulates a pre-existing defect in the material sheet, was proposed by Marciniak and Kuczynski (1967). This M–K model can be regarded as a complementary approach to Hill’s zero-extension criterion, which is only applicable to the left-hand side of the FLD, as no zero-extension direction exists for positive biaxial stretching. However, because localized necking in biaxial stretching is observed in practice, a pre-existing defect has to be introduced in the M–K model to capture this phenomenon, which may provide some justification for this imperfection theory. In addition to the aforementioned engineering approaches, another category of plastic instability criteria was developed based on a more fundamental background. Drucker and Hill’s theory (Drucker, 1956; Hill, 1958), also referred to as the general bifurcation criterion, represents another class of approaches for necking prediction. This condition of positiveness of the second-order work provides a lower bound for all of the bifurcation-based criteria in this category. In the same class of criteria, Valanis (1989) suggested using a limit-point bifurcation criterion, which is less conservative than the general bifurcation criterion but coincides with it within the framework of associative plasticity and small strains. With regard to localized modes of deformation, Stören and Rice (1975) proposed a bifurcation criterion characterized by the singularity of the acoustic tensor, also known as discontinuous bifurcation. It has been shown that this criterion corresponds to the loss of ellipticity of the partial differential equations governing the associated boundary value problem. In the same manner, some authors (e.g., Bigoni and Hueckel, 1991) have suggested the use of the more conservative condition of strong ellipticity, which has been shown to coincide with Rice’s criterion within the framework of associative plasticity and small strains. This condition of loss of strong ellipticity is also a special case of Drucker’s general bifurcation criterion, in which the bifurcation mode is restricted to localized (compatible) deformation modes. From this overview of the various approaches pertaining to strain localization criteria and indicators, an interesting observation can be made. While M–K analysis has been widely used in the literature, few applications of Rice’s ellipticity loss theory, mainly restricted to plane-stress assumptions, particular loading paths, and simple behavior models, have been attempted in sheet metal forming for quantifying metals in terms of their formability. In this presentation, various results relating to the prediction of plastic flow localization based on bifurcation theory will be shown for different constitutive modeling approaches. Also, comparisons will be conducted for the different approaches of plastic instability prediction. For some approaches, a classification of the criteria will be established, in terms of their conservative nature of prediction. Moreover, similarities or relationships between some approaches and associated criteria will be emphasized, whenever their underlying formulations make it possible.Modélisation multi-échelles en viscoplasticité endommageable de composites thermoplastiques renforcés par des fibres discontinues
http://hdl.handle.net/10985/11998
Modélisation multi-échelles en viscoplasticité endommageable de composites thermoplastiques renforcés par des fibres discontinues; Multiscale modeling in viscoplasticity coupled to damage of discontinuous fibers reinforced thermoplastic composites
ACHOUR, Nadia; CHATZIGEORGIOU, George; BONNAY, Kevin; MERAGHNI, Fodil
Un nouveau modèle multi-échelles en régime viscoplastique endommageable est développé pour un composite à matrice polypropylène renforcé par des fibres de verre courtes. Basé sur l’approche en champs moyens de Mori Tanaka, il intègre une matrice viscoplastique modélisée par un modèle phénoménologique nommé par ses auteurs DSGZ et des fibres de verres modélisées par un comportement élastique linéaire. Le modèle multi-échelles permet d’intégrer la microstructure du composite préalablement caractérisée par la microtomographie aux rayons X. L’introduction de la matrice viscoplastique dans le modèle de Mori Tanaka est rendu possible grâce à une implémentation par intégration implicite du modèle qui permet d’obtenir le module tangent nécessaire au mod èle d’homogénéisation. L’endommagement du matériau est intégré à travers du mécanisme de décohésion de l’interface fibre/ matrice. Ce mécanisme d’endommagement est modélisé par une loi cumulative de type Weibull. La dépendance à la vitesse de déformation du composite observée lors des essais dynamiques est intégrée au moyen de la prise en compte de la viscosité de la matrice. Les paramètres du modèle sont identifiés par une méthode inverse sur la base d’essais de traction à différentes vitesses et pour différentes orientations d’éprouvettes. Le modèle développé a été validé par comparaison avec des essais de traction.; A new multi-scale model accounting for viscoplasticity and damage is developed for a short-fiber reinforced polypropylene composite. In the proposed Mori Tanaka homogenization approach, the viscoplastic matrix is modeled through a phenomenological constitutive law named by its authors DSGZ and the glass fibers are considered as linear elastic. The multiscale model accounts for the composite’s microstructure, which is previously characterized by X-ray microtomography. The introduction of the viscoplastic matrix into the Mori Tanaka method is achieved thanks to an implicit integration scheme that enables the estimation of the necessary tangent modulus. The material damage mechanism is considered at the matrix/fiber interface and is modeled by a Weibull-type cumulative law. The rate dependence of the composite observed in the dynamic tests is integrated through the viscous behavior of the matrix. The model parameters are identified by an inverse method using tensile tests at different strain rates and for different orientations of samples. The model is subsequently validated by comparison with high speed tensile tests.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/119982017-01-01T00:00:00ZACHOUR, NadiaCHATZIGEORGIOU, GeorgeBONNAY, KevinMERAGHNI, FodilUn nouveau modèle multi-échelles en régime viscoplastique endommageable est développé pour un composite à matrice polypropylène renforcé par des fibres de verre courtes. Basé sur l’approche en champs moyens de Mori Tanaka, il intègre une matrice viscoplastique modélisée par un modèle phénoménologique nommé par ses auteurs DSGZ et des fibres de verres modélisées par un comportement élastique linéaire. Le modèle multi-échelles permet d’intégrer la microstructure du composite préalablement caractérisée par la microtomographie aux rayons X. L’introduction de la matrice viscoplastique dans le modèle de Mori Tanaka est rendu possible grâce à une implémentation par intégration implicite du modèle qui permet d’obtenir le module tangent nécessaire au mod èle d’homogénéisation. L’endommagement du matériau est intégré à travers du mécanisme de décohésion de l’interface fibre/ matrice. Ce mécanisme d’endommagement est modélisé par une loi cumulative de type Weibull. La dépendance à la vitesse de déformation du composite observée lors des essais dynamiques est intégrée au moyen de la prise en compte de la viscosité de la matrice. Les paramètres du modèle sont identifiés par une méthode inverse sur la base d’essais de traction à différentes vitesses et pour différentes orientations d’éprouvettes. Le modèle développé a été validé par comparaison avec des essais de traction.
A new multi-scale model accounting for viscoplasticity and damage is developed for a short-fiber reinforced polypropylene composite. In the proposed Mori Tanaka homogenization approach, the viscoplastic matrix is modeled through a phenomenological constitutive law named by its authors DSGZ and the glass fibers are considered as linear elastic. The multiscale model accounts for the composite’s microstructure, which is previously characterized by X-ray microtomography. The introduction of the viscoplastic matrix into the Mori Tanaka method is achieved thanks to an implicit integration scheme that enables the estimation of the necessary tangent modulus. The material damage mechanism is considered at the matrix/fiber interface and is modeled by a Weibull-type cumulative law. The rate dependence of the composite observed in the dynamic tests is integrated through the viscous behavior of the matrix. The model parameters are identified by an inverse method using tensile tests at different strain rates and for different orientations of samples. The model is subsequently validated by comparison with high speed tensile tests.Microstructural and experimental analysis of strain rate effect for short glass fiber reinforced polypropylene
http://hdl.handle.net/10985/10365
Microstructural and experimental analysis of strain rate effect for short glass fiber reinforced polypropylene
ACHOUR-RENAULT, Nadia; PELTIER, Laurent; FITOUSSI, Joseph; MERAGHNI, Fodil
The scope of this work is to provide a microstructural description and an experimental analysis of the strain rate effect on short glass fiber reinforced polypropylene.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103652015-01-01T00:00:00ZACHOUR-RENAULT, NadiaPELTIER, LaurentFITOUSSI, JosephMERAGHNI, FodilThe scope of this work is to provide a microstructural description and an experimental analysis of the strain rate effect on short glass fiber reinforced polypropylene.Implicit implementation and consistent tangent modulus of a viscoplastic model for polymers
http://hdl.handle.net/10985/10214
Implicit implementation and consistent tangent modulus of a viscoplastic model for polymers
ACHOUR-RENAULT, Nadia; CHATZIGEORGIOU, George; CHEMISKY, Yves; FITOUSSI, Joseph; MERAGHNI, Fodil
In this work, the phenomenological viscoplastic DSGZ model[Duan, Y., Saigal, A., Greif, R., Zimmerman, M. A., 2001. A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers. Polymer Engineering and Science 41 (8), 1322-1328], developed for glassy or semi-crystalline polymers, is numerically implemented in a three dimensional framework, following an implicit formulation. The computational methodology is based on the radial return mapping algorithm. This implicit formulation leads to the definition of the consistent tangent modulus which permits the implementation in incremental micromechanical scale transition analysis. The extended model is validated by simulating the polypropylene thermoplastic behavior at various strain rates (from 0:92s-1 to 258s-1) and temperatures (from 20°C to 60°C). The model parameters for the studied material are identified using a heuristic optimization strategy based on genetic algorithm. The capabilities of the new implementation framework are illustrated by performing finite element simulations for multiaxial loading.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102142015-01-01T00:00:00ZACHOUR-RENAULT, NadiaCHATZIGEORGIOU, GeorgeCHEMISKY, YvesFITOUSSI, JosephMERAGHNI, FodilIn this work, the phenomenological viscoplastic DSGZ model[Duan, Y., Saigal, A., Greif, R., Zimmerman, M. A., 2001. A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers. Polymer Engineering and Science 41 (8), 1322-1328], developed for glassy or semi-crystalline polymers, is numerically implemented in a three dimensional framework, following an implicit formulation. The computational methodology is based on the radial return mapping algorithm. This implicit formulation leads to the definition of the consistent tangent modulus which permits the implementation in incremental micromechanical scale transition analysis. The extended model is validated by simulating the polypropylene thermoplastic behavior at various strain rates (from 0:92s-1 to 258s-1) and temperatures (from 20°C to 60°C). The model parameters for the studied material are identified using a heuristic optimization strategy based on genetic algorithm. The capabilities of the new implementation framework are illustrated by performing finite element simulations for multiaxial loading.Simulation of ultra-thin sheet metal forming using phenomenological and crystal plasticity models
http://hdl.handle.net/10985/14056
Simulation of ultra-thin sheet metal forming using phenomenological and crystal plasticity models
ADZIMA, Francis; MANACH, Pierre-Yves; TABOUROT, Laurent; TOUTAIN, Sébastien; DIOT, Jean-Luc; BALAN, Tudor
Micro-forming of ultra-thin sheet metals raises numerous challenges. In this investigation, the predictions of state-of-the-art crystal plasticity (CP) and phenomenological models are compared in the framework of industrial bending-dominated forming processes. Sheet copper alloys 0.1mm-thick are considered, with more than 20 grains through the thickness. Consequently, both model approaches are valid on theoretical ground. The phenomenological models’ performance was conditioned by the experimental database used for parameter identification. The CP approach was more robust with respect to parameter identification, while allowing for a less flexible description of kinematic hardening, at the cost of finer mesh and specific grain-meshing strategies. The conditions for accurate springback predictions with CP-based models are investigated, in an attempt to bring these models at the robustness level required for industrial application.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/140562016-01-01T00:00:00ZADZIMA, FrancisMANACH, Pierre-YvesTABOUROT, LaurentTOUTAIN, SébastienDIOT, Jean-LucBALAN, TudorMicro-forming of ultra-thin sheet metals raises numerous challenges. In this investigation, the predictions of state-of-the-art crystal plasticity (CP) and phenomenological models are compared in the framework of industrial bending-dominated forming processes. Sheet copper alloys 0.1mm-thick are considered, with more than 20 grains through the thickness. Consequently, both model approaches are valid on theoretical ground. The phenomenological models’ performance was conditioned by the experimental database used for parameter identification. The CP approach was more robust with respect to parameter identification, while allowing for a less flexible description of kinematic hardening, at the cost of finer mesh and specific grain-meshing strategies. The conditions for accurate springback predictions with CP-based models are investigated, in an attempt to bring these models at the robustness level required for industrial application.Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
http://hdl.handle.net/10985/10654
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/106542016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
http://hdl.handle.net/10985/11856
Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The present study focuses on the development of a relevant numerical tool for predicting the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118562017-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, Farid The present study focuses on the development of a relevant numerical tool for predicting the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.