INTERACTION OF STRAIN RATE AND NECKING ON THE STRESS-STRAIN RESPONSE OF UNIAXIAL TENSION TESTS BY HOPKINSON BAR

Abstract The effect of the necking combined to that of the strain rate is analysed in dynamic split Hopkinson bar (SHTB) tests, by both experiments and finite elements. Experiments from the literature by Noble et al. are considered here together with other tests ran at the University of Catania. Two different characterization procedures are used for modeling the materials, leading to strain and strain rate-dependent flow stress according to the Johnson-Cook model for the Remco Iron by Noble et al., and to an MLR-based calibration for the FeN steel implemented by fortran subroutines, respectively. After satisfactory validation of the finite elements results and of the dynamic hardening models via comparison to the experimental stress-strain, a detailed investigation on the way the necking perturbation of the stress interacts with the strain rate is carried out, expecially investigating how the ratio of the flow stress/true stress evolves with the strain and the strain rate. Special modifications are introduced to the subroutine modeling the strain rate-promoted dynamic amplification of the stress; the related response from finite elements confirms the outcomes of previous papers, unveiling a new feature of the dynamic stress in SHTB tests and providing new information about the suitability and the accuracy of the modern procedures for the dynamic stress-strain characterization

Crashworthiness assessment considering the dynamic damage and failure of a dual phase automotive steel

Analyzing crash worthiness of the automotive parts has been posing a great challenge in the sheet metal and automotive industry since several decades. The present contribution will focus on one of the most urging challenges of the crash worthiness simulations, namely, an enhanced constitutive formulation to predict the failure and cracking of structural parts made from high strength steel sheets under impact. A hybrid extended Modified Bai Wierzbicki damage plasticity model is devised to this end. The material model calibrated using the experimental data covering high strain rate deformation, damage and failure successfully predicted the instability and subsequent response of the crash box under impact. Simulation results provide the deformation shape and deformation energy in order to predict and evaluate the vehicle crashworthiness. The simulations further helped in discovering the irrefutable impact of strain rate and stress state on the impact response of the auto-body structure. The strain rate is found to adequately affect the energy absorption capacity of the crash box structure both in terms of impact load and fold formation whereas the complex stress state has a direct association to the development of instability within the structure and early damage appearance within the folds

Oscillation Flow Induced by Underwater Supersonic Gas Jets from a Rectangular Laval Nozzle

AbstractIn present work, direct measurements of the interfacial behavior of water-submerged gas jets, with nozzle operated in over-expansion to highly under-expansion conditions, were performed using high-speed digital photography. The experimental results show that the two low-frequency oscillations, which are so called jet necking/bulging and necking/back-attack phenomenon, are also found in the region near present rectangular nozzle exit.As the nozzle pressure ratio increased, two distinct flow regimes can be observed: One that showed unstable gas/water interfacial characteristics for nozzle pressure ratio, NPR or Po/Pa≤ 10.17 when the jet pattern showed similar shape as the one issuing from axisymmetric nozzles, and the other with stable jet pattern for NPR > 18.48 when a 3D cross-like cross section jet gas/water boundary started to form and grow from the nozzle exit. Finally, numerical analysis on shockwave structures of the experimental nozzle models was carried out, and the submerged jet gas/water interface characteristics show good agreement with the jet boundaries predicted by numerical simulations. The numerical results indicate that the over-expanded flow in the four corner regions as well as the recompression shock wave may play a dominant role in the interface instability to result in necking/bulging and necking/back-attack phenomenon during over-expanded to slightly under-expanded conditions

High Strain-Rate and Temperature Behaviour of Metals: Advanced Testing and Modelling

The purpose of the thesis was the prediction of the dynamic behaviour of metals. In order to investigate the mechanical response of metals in dynamic conditions, different experimental techniques were developed and used. The experimental data were analyzed through different procedures with the aim to provide consistent methodologies suited to extract sets of model parameters usable in the commercial FE codes

Stratégies efficaces en caractérisation des matériaux et calibration de modèles mécaniques pour la conception virtuelle des tôles métalliques

The mechanical design of sheet metal forming parts tends to be more virtual, reducing delays and manufacturing costs. Reliable numerical simulations can also lead to optimized metallic parts using accurately calibrated advanced constitutive models. Thus, the aim of this thesis is to improve the representation of the mechanical behavior of the material in the numerical model, by developing efficient and accurate methodologies to calibrate advanced constitutive models. A recent trend in material characterization is the use of a limited number of heterogeneous mechanical tests, which provide more valuable data than classical quasi-homogeneous tests. Yet, the design of the most suitable tests is still an open question. To that extent, an overview of heterogeneous mechanical tests for metallic sheets is provided. However, no standards exist for such tests, so specific metrics to analyze the achieved mechanical states are suggested and applied to four tests. Results show that the use of various metrics provides a good basis to qualitatively and quantitatively evaluate heterogeneous mechanical tests. Due to the development of full-field measurement techniques, it is possible to use heterogeneous mechanical tests to characterize the behavior of materials. However, no analytical solution exists between the measured fields and the material parameters. Inverse methodologies are required to calibrate constitutive models using an optimization algorithm to find the best material parameters. Most applications tend to use a gradient-based algorithm without exploring other possibilities. The performance of gradient-based and -free algorithms in the calibration of a thermoelastoviscoplastic model is discussed in terms of efficiency and robustness of the optimization process. Often, plane stress conditions are assumed in the calibration of constitutive models. Nevertheless, it is still unclear whether these are acceptable when dealing with large deformations. To further understand these limitations, the calibration of constitutive models is compared using the virtual fields method implemented in 2D and 3D frameworks. However, the 3D framework requires volumetric information of the kinematic fields, which is experimentally difficult to obtain. To address this constraint, an already existing volume reconstruction method, named internal mesh generation, is further improved to take into account strain gradients in the thickness. The uncertainty of the method is quantified through virtual experiments and synthetic images. Overall, the impact of this thesis is related to (i) the importance of establishing standard metrics in the selection and design of heterogeneous mechanical tests, and (ii) enhancing the calibration of advanced constitutive models from a 2D to a 3D framework.O projeto mecânico de peças por conformação de chapas metálicas tende a ser mais virtual, reduzindo atrasos e custos de produção. Simulações numéricas confiáveis também podem levar a peças optimizadas usando modelos constitutivos avançados calibrados com precisão. Assim, o objetivo desta tese é melhorar a representação do comportamento mecânico do material no modelo numérico, através do desenvolvimento de metodologias eficientes e precisas para a calibração de modelos constitutivos avançados. Uma tendência recente na caracterização de materiais é o uso de um número limitado de ensaios mecânicos heterogéneos, que fornecem dados mais valiosos do que os ensaios clássicos quase-homogéneos. No entanto, a concepção de ensaios mais adequados ainda é uma questão em aberto. Este trabalho detalha os ensaios mecânicos heterogêneos para chapas metálicas. No entanto, não existem ainda normas para estes ensaios, pelo que métricas específicas para analisar os estados mecânicos são sugeridas e aplicadas a quatro ensaios. Os resultados mostram que o uso de várias métricas disponibiliza uma boa base para avaliar ensaios mecânicos heterogéneos. Devido ao desenvolvimento de técnicas de medição de campo total, é possível utilizar ensaios mecânicos heterogéneos para caracterizar o comportamento dos materiais. No entanto, não existe uma solução analítica entre os campos medidos e os parâmetros do material. Metodologias inversas são necessárias para calibrar os modelos constitutivos usando um algoritmo de otimização para encontrar os melhores parâmetros do material. A maioria das aplicações tende a usar um algoritmo baseado em gradiente sem explorar outras possibilidades. O desempenho de vários algoritmos na calibração de um modelo termoelastoviscoplástico é discutido em termos de eficiência e robustez do processo de otimização. Frequentemente, são utilizadas condições de estado plano de tensão na calibração de modelos constitutivos, hipótese que é questionada quando se trata de grandes deformações. A calibração de modelos constitutivos é comparada usando o método de campos virtuais implementado em 2D e 3D. No entanto, a implementação 3D requer informações volumétricas dos campos cinemáticos, o que é experimentalmente difícil de obter. Um método de reconstrução volúmica já existente é melhorado para considerar os gradientes de deformação ao longo da espessura. A incerteza do método é quantificada através de ensaios virtuais e imagens sintéticas. No geral, o impacto desta tese está relacionado com (i) a importância de estabelecer métricas na seleção e concepção de ensaios mecânicos heterogéneos, e (ii) promover desenvolvimentos na calibração de modelos constitutivos avançados de 2D para 3D.La conception mécanique des pièces métalliques tend à être plus virtuelle, réduisant les délais et les coûts de fabrication. Des simulations numériques fiables peuvent conduire à des pièces optimisées en utilisant des modèles mécaniques avancés calibrés avec précision. Ainsi, l’objectif de cette thèse est d’améliorer la représentation du comportement mécanique du matériau dans le modèle numérique, en développant des méthodologies efficaces et précises pour calibrer des modèles de comportement avancés. Une tendance récente dans la caractérisation des matériaux est l’utilisation d’un nombre limité d’essais mécaniques hétérogènes, qui fournissent des données plus riches que les essais classiques quasi-homogènes. Pourtant, la conception des tests les plus adaptés reste une question ouverte. Ce tra- vail détaille les essais mécaniques hétérogènes pour les tôles métalliques. Cependant, aucune norme n’existe pour de tels tests, ainsi des métriques spécifiques pour analyser les états mécaniques sont suggérées et appliquées à quatre tests. Les résultats montrent que l’utilisation de diverses métriques fournit une bonne base pour évaluer des essais mécaniques hétérogènes. L’utilisation des essais mécaniques hétérogènes pour caractériser le com- portement des matériaux est rendue possible par des mesures de champ. Cependant, aucune solution analytique n’existe entre les champs mesurés et les paramètres du matériau. Des méthodologies inverses sont nécessaires pour calibrer les modèles de comportement à l’aide d’un algorithme d’optimi- sation afin de déterminer les meilleurs paramètres de matériau. Un algorithme basé sur le gradient est très fréquemment utilisé, sans explorer d’autres pos- sibilités. La performance de plusieurs algorithmes dans la calibration d’un modèle thermoélastoviscoplastique est discutée en termes d’efficacité et de robustesse du processus d’optimisation. Souvent, des conditions de contraintes planes sont supposées dans la cal- ibration des modèles, hypothèse qui est remise en cause dans le cas de forte localisation des déformations. La calibration de modèles de comporte- ment est comparée à l’aide de la méthode des champs virtuels développée dans les cadres 2D et 3D. Cependant, le cadre 3D nécessite des informations volumétriques des champs cinématiques, ce qui est expérimentalement dif- ficile à obtenir. Une méthode de reconstruction volumique déjà existante est encore améliorée pour prendre en compte les gradients de déformation dans l’épaisseur. L’incertitude de la méthode est quantifiée par des expériences virtuelles, à l’aide d’images de synthèse. Dans l’ensemble, l’impact de cette thèse est lié à (i) l’importance d’établir des métriques dans la sélection et la conception d’essais mécaniques hétérogènes, et (ii) à faire progresser la calibration de modèles de comportement avancés d’un cadre 2D à un cadre 3D.Programa Doutoral em Engenharia Mecânic

A combined experimental and modeling study of low velocity perforation of thin aluminum plates

This work conducts a combined experimental and modeling study of low velocity projectile perforation of thin AA5083-H116 aluminum plates. Experiments were performed in order to characterize the candidate material and calibrate simple and easy to implement empirical models for both the material response and ductile failure behavior. Quasi-static tensile tests were performed in order to investigate the Portevin-Le Chatelier effect common to 5xxx series aluminum as well as to calibrate a Ramberg-Osgood representation for the material stress-strain curve. The material response at strain rates up to and exceeding 104 s-1 was investigated by means of an electromagnetically driven ring expansion test, characterizing the potential strain rate sensitivity of the material. Additionally, the failure behavior and potential damage accumulation of the material were evaluated using an interrupted, multiple loading path strain-to-failure test, validating a Johnson-Cook failure model for use in numerical simulation. Low velocity ballistic impact and perforation experiments, investigating several specific mechanisms of deformation and failure, were conducted and modeled by implementing the developed material and failure model in 3D finite element simulations.Aerospace Engineerin

Microdevices for extensional rheometry of low viscosity elastic liquids : a review

Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations

Identification of viscoplastic parameters and characterization of Lüders behaviour using digital image correlation and the virtual fields method

In this study, tensile loading experiments are performed on notched steel bars at an average applied strain rate of 1s-1. Displacement fields are measured across the specimen by coupling digital image correlation (DIC) with imaging using high speed CCD cameras (4796 fps). Results from the experiments indicate the presence of local strain rates ranging from 0.1 to 10s-1 in the notched specimens. The heterogeneity of the strain rate fields provides suitable conditions for determining simultaneously all the elasto-visco-plastic constitutive parameters governing the material behavior. For that, the whole stress fields are reconstructed in the specimen using the full-field deformation measurements. This reconstruction is repeated with different constitutive parameters until the average stress in the specimen matches the one measured with the load cell response. Perzyna’s model is firstly considered for the reconstruction of stresses but it is shown to be unsuited for providing the drop in the average stress that is systematically detected at the onset of plasticity by the load cell. This drop is attributed to the sudden occurrence of plasticity in the material due to Lüders effect. A modified model for elasto-visco-plasticity taking account of Lüders behavior in the material is considered afterwards. It yields a better agreement between the reconstructed stresses and the load cell response, and a more accurate identification of the parameters driving the visco-plastic model. Eventually, it is shown how to use DIC measurements for replacing the load cell measurements when the transient effects in the test reach the resonance frequency of the load cel

Parameter identification of a mechanical ductile damage using Artificial Neural Networks in sheet metal forming.

In this paper, we report on the developed and used of finite element methods, have been developed and used for sheet forming simulations since the 1970s, and have immensely contributed to ensure the success of concurrent design in the manufacturing process of sheets metal. During the forming operation, the Gurson–Tvergaard–Needleman (GTN) model was often employed to evaluate the ductile damage and fracture phenomena. GTN represents one of the most widely used ductile damage model. In this investigation, many experimental tests and finite element model computation are performed to predict the damage evolution in notched tensile specimen of sheet metal using the GTN model. The parameters in the GTN model are calibrated using an Artificial Neural Networks system and the results of the tensile test. In the experimental part, we used an optical measurement instruments in two phases: firstly during the tensile test, a digital image correlation method is applied to determinate the full-field displacements in the specimen surface. Secondly a profile projector is employed to evaluate the localization of deformation (formation of shear band) just before the specimen’s fracture. In the validation parts of this investigation, the experimental results of hydroforming part and Erichsen test are compared with their numerical finite element model taking into account the GTN model. A good correlation was observed between the two approaches

Stress-Strain Relationship Characterization of Armoured Graded Aluminium and Steel Alloys Using a Digital Image Correlation Technique

The need for better and lighter armoured concepts is ever increasing. Weather due to the challenges of the modern theatre of war, which require the vehicles to easily move in dense urban areas and in vast soft grounded deserts, or by the nature of the increasingly ingenious threats, traditional armour solutions fail to provide adequate protection. The current work is part of a project intended to develop an armour solution that incorporates cork in its composition. This work focuses on the study of metal alloys and their mechanical characterization at low strain rates. For this purpose, a look is taken into the history and evolution of armoured vehicles and the characteristics of the different materials adopted in the course of armour development. The basic concepts associated with metal alloys loading and deformation behaviour are described as well as the methodology usually employed when preforming mechanical characterization of metals. In order to determine the material constants required to create the strain hardening parameter of the Johnson-Cook constitutive material model, quasi-static tests are conducted in 45 specimens composed of three rolling directions (0º, 45º and 90º) of 5 mm and 10 mm thick AW- 5083-H111 aluminium alloy and 2.2 mm thick Ramor 500 steel alloy. The strain data is processed through strain gauges applied in the specimens’ surface and an in-house integrated digital image correlation technique. The experimental results show that the digital image correlation technique employed in this study offers good results compared to both the strain gauge data and the similar examples from the literature. It is also possible to note the difference in behaviour in the three cutting directions in both alloys. Dynamic strain aging and instabilities of high frequency oscillation phenomena are recorded on the aluminium alloy, just as expected from high magnesium content alloys. The strain hardening constants and the Cockcroft-Latham failure criterion are successfully extrapolated and compared to similar materials. As a general conclusion, this work creates a good foundation for the full material characterisation on the larger spectrum of strain rates and will allow for the future research necessary for the main project.A necessidade para melhores e mais leves conceitos de blindagens é sempre crescente. Quer devido às dificuldades do campo de batalha moderno, que requerem que os veículos se movam facilmente nas densas áreas urbanas e em vastos desertos de terreno macio, quer pela natureza crescentemente engenhosa das ameaças, as blindagens tradicionais falham em fornecer proteção adequada. O presente trabalho, faz parte de um projeto com o propósito de desenvolver uma solução de blindagem que incorpore cortiça na sua composição. Este estudo irá focar-se em ligas metálicas e a sua caracterização mecânica a baixas taxas de deformação. Para este fim, é feita uma breve revisão da história e evolução de veículos blindados e as características dos diferentes materiais empregados no desenvolvimento de blindagens. Os conceitos básicos associados com o comportamento de carregamento e deformação de ligas metálicas são descritos assim como a metodologia normalmente utilizada aquando da execução da caracterização mecânica de metais. A fim de determinar as constantes do material necessárias para a criação do parâmetro de endurecimento de deformação do modelo constitutivo de material de Johnson-Cook, são realizados testes quase estáticos em 45 provetes compostos pelas três direções de rolamento (0º,45º e 90º) de alumínio AW-5083-H111 de 5 mm e 10 mm de espessura e aço Ramor 500 de 2,2 mm de espessura. Os dados da deformação são processados a partir de extensómetros aplicados na superfície dos provetes e por uma técnica de correlação digital de imagem caseira. Os resultados experimentais mostram que a técnica de correlação digital de imagem empregada neste estudo oferece bons resultados quando comparado com os dados dos extensómetros e com exemplos de materiais semelhantes da literatura. Também é possível denotar o comportamento diferenciado nas três direções de corte em ambas as ligas. Os fenómenos de envelhecimento dinâmico da deformação e instabilidades de oscilação de elevada frequência são registados na liga de alumínio, tal como esperado de ligas de elevado teor de magnésio. As constantes do endurecimento da deformação e do critério de falha de Cockcroft-Latham são extrapoladas com sucesso e comparadas com materiais semelhantes. Como conclusão geral, este trabalho cria uma boa fundação para a completa caracterização dos materiais num maior espetro de velocidades de deformação e vai permitir realizar a investigação necessária para o projeto principal