Structural adhesives are recognized by the automotive industry as a powerful alternative solution... more Structural adhesives are recognized by the automotive industry as a powerful alternative solution to traditional fastening methods such as welding or riveting. As a new technological solution, they introduce requirements in terms of the evaluation of their mechanical performance. In particular, enhanced safety guarantee requires not only to know the material performance in standard laboratory tests but to be able to predict it under real conditions, in particular for complex shaped parts. This may be done by finite element simulation. Nevertheless, the small thickness and the specific material behavior of the joint make modeling difficult using available numerical tools. This work focuses on the assessment of structural adhesive joints up to their maximal strength using finite element analysis. A complete methodology is proposed which addresses the implementation of a specific non-linear elasto-plastic material constitutive model which is accurate to describe the joint behavior under multi-axial loadings. Experimental tests and an original strategy for the identification of material parameters based on inverse identification are proposed. Finally computational efficiency is addressed using specific interface elements which makes the constitutive model convenient for the simulation of large industrial problems.
An elastomeric material was investigated with a bubble inflation rheometer, and its mechanical be... more An elastomeric material was investigated with a bubble inflation rheometer, and its mechanical behavior was modeled as a rubbeer-like solid. Classical strain energy functions were considered and the hyper-elastic were calculated by a direct identification procedure from simple uniaxial and equibiaxial extension test data, and the reults are compared against those obtained by an inverse method from matching the meaured response to a finite element to a finite element analysis solution, which dependent on the unknown material parameters. The optimised employed the Levenberg-Marquardt algorithm and Abaqus software to compute the cost function and its gradients. The constants so obtained were further used in finite element analysis, and the numerical results were compared with experiments. This study showed that the inverse method, used to estimate the material parameters, is a good alternative to the direct identification, especially since the latter often requires homogeneous strain state, which is very difficult to obtain.
The biaxial rheological behavior of materials such as elastomers or polymers can be obtained usin... more The biaxial rheological behavior of materials such as elastomers or polymers can be obtained using a bubble-inflation-technique. A circular membrane is clamped at the rim and expanded under gas pressure. The inflation of the circular membrane is recorded using a CCD video camera and the blowing pressure by a pressure sensor. Then, from elongation and curvature radius measurement at the pole of the bubble, one can deduce equibixial stress-strain data. This study describes the optimization of a bubble-inflation rheometer. The most sensitive point of the technique is the estimation of the elongation at the bubble pole, deduced from video camera measurements. A direct measurement of the bubble thickness was performed using a magnetic probe in order to validate rheometer results. Such a validation has evidently never been carried out before. Results of quasi-static equibiaxial characterisation of elastomers are presented and analyzed.
The explicit dynamic algorithm commonly used to solve sheet metal forming problems, has been appl... more The explicit dynamic algorithm commonly used to solve sheet metal forming problems, has been applied to solve two plastic transformation processes: blow molding and thermoforming. Constitutive laws which properly represent polymer at processing temperature have been considered. We have compared the thickness and stress distributions for hyperelastic and viscoelastic models. Two examples on blow molding and thermoforming have been studied and the numerical results have been compared with experimental data.
In tube hydroforming, some local thinning can be observed on industrial components. When low carb... more In tube hydroforming, some local thinning can be observed on industrial components. When low carbon steels are concerned, the process is stopped broadly after reaching the plastic instability (strain localization) while having an acceptable part. In numerical simulation, the classical elastic-plastic models reach their limits when the plastic instability occurs, the process simulation becomes very sensitive to numerical parameters which leads to poor prediction of post-localization behaviour. Consequently, a full understanding of post-localization is important for the formability prediction purpose. In this work, various numerical simulations were carried out on both tensile and hydroforming tests. The classical Prandtl-Reuss model is first investigated and the obtained results clearly show that this model is not appropriate to predict the post-localization behaviour. Then, some regularization techniques such as material rate dependence and the introduction of gradient-based internal variable in the constitutive relations were evaluated. In the light of the obtained results, the rate-dependent model seems to be well adapted to predict the post-localization behaviour in tube hydroforming simulation. Thus, the rate-dependent approach was adopted and the basic model was enhanced to fit some experimental data from tensile tests. Finally, the hydroforming Corner Fill test was simulated and the numerical results were compared with measurements to validate the proposed approach. This comparison shows that the rate-dependent model greatly improves the accuracy of the predictions.
Journal of Shanghai Jiaotong University (science), 2011
The high temperature gradients experienced during fusion welding lead to a local dilatation and m... more The high temperature gradients experienced during fusion welding lead to a local dilatation and metallurgical transformations that generate inhomogeneous plastic deformation, residual stresses and distortions in the welded parts which can affect the service life of the structures. To predict such residual stresses and distortions, finite element analysis is nowadays widely used. This work reports a 3D finite element model for welding simulation. The proposed model is based on semi coupled thermo-mechanical analysis using a double ellipsoidal model of heat source. Firstly, a disk heated in its central zone is investigated. Secondly the validation concerns the simulation of a fully 3D two pass butt weld. The idea in this work concerns the calibration of the heat source parameters with the help of the inverse analysis to improve the heat flow predictions. For the stress analysis, an annealing temperature is introduced to force the material to lose its hardening memory above a given temperature. The predicted residual stresses as well as the predicted distortions are found to be sensitive to the annealing temperature.
The problem of appropriately defining the First Indenter-Sample Contact (FISC) is known to be a m... more The problem of appropriately defining the First Indenter-Sample Contact (FISC) is known to be a major problem in hardness measurement and particularly in nano-indentation. Another difficulty arises from the determination of the real indentation area when a piled up occurs near the indentation print. This phenomenon is known as the Indentation Size Effect (ISE). The indentation piles up can be particularly heavy for low loads which affects the nano-indentation measurements. The Loading Displacement Curves (LDC) with ISE can be modelled by the PSR law (Proportional Specimen Resistance). We show that an error on the FISC validates PSR law even if no ISE occurs meaning that it is illusory to quantify the ISE with only one loading curve. To overcome this difficulty, a statistical protocol is proposed that consists in simultaneously analysis a fixed number of loading curves. With this approach, a new equation of LDC is proposed that allows determination of Hardness, ISE coefficient and the FISC position on each curve (98 LDC are recorded from a fused silica standard). The uncertainty on each coefficient is determined by a bootstrap protocol.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2008
Ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical ma... more Ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical machines. As the blanking process deeply affects the material mechanical state near the cut edge, it also involves degradations of magnetic properties like loss of permeability. In this context, full understanding of the shearing process is needed and a predictive model can be helpful for the design of rotating electrical machines. With such a model, the designer can easily assess the influence of the blanking process parameters on the reliability of the designed machines. For this purpose, the constitutive equation used for the blanking process modelling is a key point since accurate predictions are required. In this paper, a rate-dependent constitutive model for the blanking process investigation is used to improve the accuracy of the predictions. Material testing and characterization are carried out in order to fit the constitutive model parameters to experimental data. The identified model is then used for numerical simulation of various blanking tests and the obtained numerical results are compared with measurements for validation purposes. The strain rate effect was found to be relevant for the blanking process.
International Journal of Mechanical Sciences, 2009
Cite this article as: A. Ben Ismail, M. Rachik, P.-E. Mazeran, M. Fafard and E. Hug, Material cha... more Cite this article as: A. Ben Ismail, M. Rachik, P.-E. Mazeran, M. Fafard and E. Hug, Material characterization of blanked parts in the vicinity of the cut edge using nanoindentation technique and inverse analysis,
___________________________________________________________________ RÉSUMÉ : Nous présentons quel... more ___________________________________________________________________ RÉSUMÉ : Nous présentons quelques schémas numériques explicites pour la résolution de problèmes non linéaires en mécanique des structures. Dans les algorithmes présentés, le pas d'intégration en temps est ajusté de manière à obtenir la précision souhaitée tout en optimisant le coût de calcul. Une technique de pas adaptatif et de prolongement de la solution dans le cas d'une méthode de Runge-Kutta d'ordre quatre a été adoptée. Dans les procédés de mise en forme tels que le soufflage des plastiques ou l'hydroformage des tôles, la solution peut présenter des instabilités qui se traduisent par des points limites sur les courbes charges-déplacements. Des techniques de pilotage ont été développées afin d'adapter l'algorithme aux problèmes présentant des points limites. Les résultats obtenus sur des exemples de membranes sous pression attestent d'une économie notable en temps de calcul en comparaison avec d'autres schémas itératifs tel que la méthode classique de Newton-Raphson. Enfin, on montre que l'intérêt de ces méthodes est encore accru dans le cas de problèmes faisant intervenir des conditions de contact évolutives. ABSTRACT : This paper presents some numerical schemes for non-linear structural mechanic problems. The proposed algorithms are non-iterative and are associated with technics for time step size and error control. We treat the discrete equilibrium relation as a system of ordinary differential equations. This system is then solved with a fourth order Runge-Kutta method. In order to use these algorithms for numerical simulation of sheet forming processes where instabilities occur we have developed a prescribed displacement technique analysis. The results obtained on bulge test and thermoforming examples show a great computational cost economy in comparison with the iterative Newton-Raphson method. MOTS-CLÉS : résolution de problèmes non-linéaires, schémas explicites, méthode d'intégration de Runge-Kutta, mise en forme de matériaux, points limites, pilotage. KEY-WORDS : non-linear problems, explicit schemes, Runge-Kutta method, instabilities, prescribed displacement analysis. ___________________________________________________________________
The ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrica... more The ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical machines. However, the optimization of the designed machines depends on full understanding of the shearing process. The material mechanical state and magnetic properties near the cut edge depend on various parameters like geometric configuration (shape of the tools, punch blade radius), clearance, frictional contact at the interfaces and the punch speed. Several studies of the blanking process have been proposed to assess the influence of these parameters, but only a few are concerned with the punch velocity. In this paper we use a rate dependent constitutive model for the blanking process investigation to improve the accuracy of the predictions. A 0.65 mm thickness sheet of a non-oriented full-process FeSi (3 wt.%) steel is used. The material testing and the characterization are carried out in order to fit the constitutive model parameters to the experimental data. Classical tensile tests and video-tensile tests are combined to establish the sheet metal constitutive law. The identified model is, then, used for numerical simulations (which are performed using ABAQUS/Explicit software) of various blanking tests: the clearance is ranging from 3.8% to 23%, punch velocity of 23 mm/s and 123 mm/s. In order to validate this work the numerical results obtained are compared to the measurement. The comparisons relate to the punch force and the punch penetration at fracture that are affected by the clearance and the strain rate.
In this paper, we present a comprehensive experimental and numerical study of the sheet metal bla... more In this paper, we present a comprehensive experimental and numerical study of the sheet metal blanking process. Various blanking tests involving different materials and geometry are investigated and the numerical results are compared with experimental data. For the numerical aspects of this study, the main topics discussed are sheet metal constitutive model, the numerical integration algorithm and mesh adaptivity. Taking into account the complexity of the blanking process, we chose an explicit ®nite element code to overcome the convergence problems. Our numerical model is thus based on a dynamic explicit scheme associated with the ALE formulation for mesh adaptivity. Since the choice of the sheet metal constitutive model is important to achieve the product shape prediction and the burr height estimation, we compare the Parndtl±Reuss plasticity model with Gurson±Tvergaard±Needleman coupled plasticity-damage model. The comparisons between numerical results and measurements show that the maximum punch force is strongly related to the plastic¯ow but that the burr height estimation requires damage modelling. In addition, Gurson's modi®ed model greatly improves the punch force prediction. #
Structural adhesives are recognized by the automotive industry as a powerful alternative solution... more Structural adhesives are recognized by the automotive industry as a powerful alternative solution to traditional fastening methods such as welding or riveting. As a new technological solution, they introduce requirements in terms of the evaluation of their mechanical performance. In particular, enhanced safety guarantee requires not only to know the material performance in standard laboratory tests but to be able to predict it under real conditions, in particular for complex shaped parts. This may be done by finite element simulation. Nevertheless, the small thickness and the specific material behavior of the joint make modeling difficult using available numerical tools. This work focuses on the assessment of structural adhesive joints up to their maximal strength using finite element analysis. A complete methodology is proposed which addresses the implementation of a specific non-linear elasto-plastic material constitutive model which is accurate to describe the joint behavior under multi-axial loadings. Experimental tests and an original strategy for the identification of material parameters based on inverse identification are proposed. Finally computational efficiency is addressed using specific interface elements which makes the constitutive model convenient for the simulation of large industrial problems.
An elastomeric material was investigated with a bubble inflation rheometer, and its mechanical be... more An elastomeric material was investigated with a bubble inflation rheometer, and its mechanical behavior was modeled as a rubbeer-like solid. Classical strain energy functions were considered and the hyper-elastic were calculated by a direct identification procedure from simple uniaxial and equibiaxial extension test data, and the reults are compared against those obtained by an inverse method from matching the meaured response to a finite element to a finite element analysis solution, which dependent on the unknown material parameters. The optimised employed the Levenberg-Marquardt algorithm and Abaqus software to compute the cost function and its gradients. The constants so obtained were further used in finite element analysis, and the numerical results were compared with experiments. This study showed that the inverse method, used to estimate the material parameters, is a good alternative to the direct identification, especially since the latter often requires homogeneous strain state, which is very difficult to obtain.
The biaxial rheological behavior of materials such as elastomers or polymers can be obtained usin... more The biaxial rheological behavior of materials such as elastomers or polymers can be obtained using a bubble-inflation-technique. A circular membrane is clamped at the rim and expanded under gas pressure. The inflation of the circular membrane is recorded using a CCD video camera and the blowing pressure by a pressure sensor. Then, from elongation and curvature radius measurement at the pole of the bubble, one can deduce equibixial stress-strain data. This study describes the optimization of a bubble-inflation rheometer. The most sensitive point of the technique is the estimation of the elongation at the bubble pole, deduced from video camera measurements. A direct measurement of the bubble thickness was performed using a magnetic probe in order to validate rheometer results. Such a validation has evidently never been carried out before. Results of quasi-static equibiaxial characterisation of elastomers are presented and analyzed.
The explicit dynamic algorithm commonly used to solve sheet metal forming problems, has been appl... more The explicit dynamic algorithm commonly used to solve sheet metal forming problems, has been applied to solve two plastic transformation processes: blow molding and thermoforming. Constitutive laws which properly represent polymer at processing temperature have been considered. We have compared the thickness and stress distributions for hyperelastic and viscoelastic models. Two examples on blow molding and thermoforming have been studied and the numerical results have been compared with experimental data.
In tube hydroforming, some local thinning can be observed on industrial components. When low carb... more In tube hydroforming, some local thinning can be observed on industrial components. When low carbon steels are concerned, the process is stopped broadly after reaching the plastic instability (strain localization) while having an acceptable part. In numerical simulation, the classical elastic-plastic models reach their limits when the plastic instability occurs, the process simulation becomes very sensitive to numerical parameters which leads to poor prediction of post-localization behaviour. Consequently, a full understanding of post-localization is important for the formability prediction purpose. In this work, various numerical simulations were carried out on both tensile and hydroforming tests. The classical Prandtl-Reuss model is first investigated and the obtained results clearly show that this model is not appropriate to predict the post-localization behaviour. Then, some regularization techniques such as material rate dependence and the introduction of gradient-based internal variable in the constitutive relations were evaluated. In the light of the obtained results, the rate-dependent model seems to be well adapted to predict the post-localization behaviour in tube hydroforming simulation. Thus, the rate-dependent approach was adopted and the basic model was enhanced to fit some experimental data from tensile tests. Finally, the hydroforming Corner Fill test was simulated and the numerical results were compared with measurements to validate the proposed approach. This comparison shows that the rate-dependent model greatly improves the accuracy of the predictions.
Journal of Shanghai Jiaotong University (science), 2011
The high temperature gradients experienced during fusion welding lead to a local dilatation and m... more The high temperature gradients experienced during fusion welding lead to a local dilatation and metallurgical transformations that generate inhomogeneous plastic deformation, residual stresses and distortions in the welded parts which can affect the service life of the structures. To predict such residual stresses and distortions, finite element analysis is nowadays widely used. This work reports a 3D finite element model for welding simulation. The proposed model is based on semi coupled thermo-mechanical analysis using a double ellipsoidal model of heat source. Firstly, a disk heated in its central zone is investigated. Secondly the validation concerns the simulation of a fully 3D two pass butt weld. The idea in this work concerns the calibration of the heat source parameters with the help of the inverse analysis to improve the heat flow predictions. For the stress analysis, an annealing temperature is introduced to force the material to lose its hardening memory above a given temperature. The predicted residual stresses as well as the predicted distortions are found to be sensitive to the annealing temperature.
The problem of appropriately defining the First Indenter-Sample Contact (FISC) is known to be a m... more The problem of appropriately defining the First Indenter-Sample Contact (FISC) is known to be a major problem in hardness measurement and particularly in nano-indentation. Another difficulty arises from the determination of the real indentation area when a piled up occurs near the indentation print. This phenomenon is known as the Indentation Size Effect (ISE). The indentation piles up can be particularly heavy for low loads which affects the nano-indentation measurements. The Loading Displacement Curves (LDC) with ISE can be modelled by the PSR law (Proportional Specimen Resistance). We show that an error on the FISC validates PSR law even if no ISE occurs meaning that it is illusory to quantify the ISE with only one loading curve. To overcome this difficulty, a statistical protocol is proposed that consists in simultaneously analysis a fixed number of loading curves. With this approach, a new equation of LDC is proposed that allows determination of Hardness, ISE coefficient and the FISC position on each curve (98 LDC are recorded from a fused silica standard). The uncertainty on each coefficient is determined by a bootstrap protocol.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2008
Ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical ma... more Ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical machines. As the blanking process deeply affects the material mechanical state near the cut edge, it also involves degradations of magnetic properties like loss of permeability. In this context, full understanding of the shearing process is needed and a predictive model can be helpful for the design of rotating electrical machines. With such a model, the designer can easily assess the influence of the blanking process parameters on the reliability of the designed machines. For this purpose, the constitutive equation used for the blanking process modelling is a key point since accurate predictions are required. In this paper, a rate-dependent constitutive model for the blanking process investigation is used to improve the accuracy of the predictions. Material testing and characterization are carried out in order to fit the constitutive model parameters to experimental data. The identified model is then used for numerical simulation of various blanking tests and the obtained numerical results are compared with measurements for validation purposes. The strain rate effect was found to be relevant for the blanking process.
International Journal of Mechanical Sciences, 2009
Cite this article as: A. Ben Ismail, M. Rachik, P.-E. Mazeran, M. Fafard and E. Hug, Material cha... more Cite this article as: A. Ben Ismail, M. Rachik, P.-E. Mazeran, M. Fafard and E. Hug, Material characterization of blanked parts in the vicinity of the cut edge using nanoindentation technique and inverse analysis,
___________________________________________________________________ RÉSUMÉ : Nous présentons quel... more ___________________________________________________________________ RÉSUMÉ : Nous présentons quelques schémas numériques explicites pour la résolution de problèmes non linéaires en mécanique des structures. Dans les algorithmes présentés, le pas d'intégration en temps est ajusté de manière à obtenir la précision souhaitée tout en optimisant le coût de calcul. Une technique de pas adaptatif et de prolongement de la solution dans le cas d'une méthode de Runge-Kutta d'ordre quatre a été adoptée. Dans les procédés de mise en forme tels que le soufflage des plastiques ou l'hydroformage des tôles, la solution peut présenter des instabilités qui se traduisent par des points limites sur les courbes charges-déplacements. Des techniques de pilotage ont été développées afin d'adapter l'algorithme aux problèmes présentant des points limites. Les résultats obtenus sur des exemples de membranes sous pression attestent d'une économie notable en temps de calcul en comparaison avec d'autres schémas itératifs tel que la méthode classique de Newton-Raphson. Enfin, on montre que l'intérêt de ces méthodes est encore accru dans le cas de problèmes faisant intervenir des conditions de contact évolutives. ABSTRACT : This paper presents some numerical schemes for non-linear structural mechanic problems. The proposed algorithms are non-iterative and are associated with technics for time step size and error control. We treat the discrete equilibrium relation as a system of ordinary differential equations. This system is then solved with a fourth order Runge-Kutta method. In order to use these algorithms for numerical simulation of sheet forming processes where instabilities occur we have developed a prescribed displacement technique analysis. The results obtained on bulge test and thermoforming examples show a great computational cost economy in comparison with the iterative Newton-Raphson method. MOTS-CLÉS : résolution de problèmes non-linéaires, schémas explicites, méthode d'intégration de Runge-Kutta, mise en forme de matériaux, points limites, pilotage. KEY-WORDS : non-linear problems, explicit schemes, Runge-Kutta method, instabilities, prescribed displacement analysis. ___________________________________________________________________
The ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrica... more The ferromagnetic sheet metal blanking is widely used for the manufacturing of rotating electrical machines. However, the optimization of the designed machines depends on full understanding of the shearing process. The material mechanical state and magnetic properties near the cut edge depend on various parameters like geometric configuration (shape of the tools, punch blade radius), clearance, frictional contact at the interfaces and the punch speed. Several studies of the blanking process have been proposed to assess the influence of these parameters, but only a few are concerned with the punch velocity. In this paper we use a rate dependent constitutive model for the blanking process investigation to improve the accuracy of the predictions. A 0.65 mm thickness sheet of a non-oriented full-process FeSi (3 wt.%) steel is used. The material testing and the characterization are carried out in order to fit the constitutive model parameters to the experimental data. Classical tensile tests and video-tensile tests are combined to establish the sheet metal constitutive law. The identified model is, then, used for numerical simulations (which are performed using ABAQUS/Explicit software) of various blanking tests: the clearance is ranging from 3.8% to 23%, punch velocity of 23 mm/s and 123 mm/s. In order to validate this work the numerical results obtained are compared to the measurement. The comparisons relate to the punch force and the punch penetration at fracture that are affected by the clearance and the strain rate.
In this paper, we present a comprehensive experimental and numerical study of the sheet metal bla... more In this paper, we present a comprehensive experimental and numerical study of the sheet metal blanking process. Various blanking tests involving different materials and geometry are investigated and the numerical results are compared with experimental data. For the numerical aspects of this study, the main topics discussed are sheet metal constitutive model, the numerical integration algorithm and mesh adaptivity. Taking into account the complexity of the blanking process, we chose an explicit ®nite element code to overcome the convergence problems. Our numerical model is thus based on a dynamic explicit scheme associated with the ALE formulation for mesh adaptivity. Since the choice of the sheet metal constitutive model is important to achieve the product shape prediction and the burr height estimation, we compare the Parndtl±Reuss plasticity model with Gurson±Tvergaard±Needleman coupled plasticity-damage model. The comparisons between numerical results and measurements show that the maximum punch force is strongly related to the plastic¯ow but that the burr height estimation requires damage modelling. In addition, Gurson's modi®ed model greatly improves the punch force prediction. #
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Papers by Mohamed Rachik