Gotowa bibliografia na temat „Visco-plasticity Model”

Considering the rheological mechanical characteristics of rock mass, a viscous-plastic model of rock mass which can describe the acceleration creep stage of rock mass was proposed. Moreover, combining with viscous-elastic shearing rheological model of rock mass in series, a new constitutive model of visco-elasticity-plasticity considering the rheology was constructed. Due to the shearing rheological curves of granite, the model of visco-elasticity-plasticity considering the rheology was identified and the rheological parameters of the model were obtained. The comparison between the viscous-elastic-plastic rheological model of rock mass and experimental result of granite shows that the accelerating rheological properties of rock mass can be depicted effectively by the constitutive model of visco-elasticity-plasticity considering the rheology.

As a contact of vibrational rotary forging is highly nonlinear, the contact area and boundary between rotary toolhead and workpiece had more accurate calculation, made the contact boundary more tally with the actual situation. For a surface effect is of complexity for vibrational rotary forging, a vibrational rotary forging visco-elasticity plasticity model was built, and the visco-elasticity spatial matrix and the visco-plasticity spatial matrix were derived by the generalized Hooke's law in elasticity theory and the increase theory in mechanics of plasticity, then by the finite element founction of MATLAB for the surface effect analyzed during the vibrational rotary forging deformation, it is shown as blow: the surface effect should be appeared with high frequency vibration or low frequency vibration, but there are some conditions for surface effect produced during plastic process, and then the hypothesis that the friction vector is reversal of deformation load, and it is benefit to deformation process during the part of time in vibration period is validated.

As lack of a efficiency theoretical approximate solution for the surface effect mechanism analyzed during continuing and local vibrational plastic deformation process, according to vibrational rotary forging deforming characters, a three-dimension visco-elasticity plasticity constitutive equation was built by Kelvin model and Liewei-Mises model. After this constitutive equation was to be matrixing and to be introduced to tetrahedral solid elements, a visco-elasticity spatial stiffness matrix and a visco-plasticity spatial stiffness matrix were respectively derived. According to experimental parameters given, some simulation experimental projects were designed, a FEM models were established, and some FEM experiments were done on condition that amplitude and vibrational frequency were respectively changed, then different normal load-time curves were obtained. It is shown from experiment results that surface effect will appear during vibrational rotary forging forming process with little amplitude, the surface effect is related to the amplitude and the frequency, and this effect generation should be in special conditions, then preparatory research of surface effect mechanism of continuing and local vibrational plastic deforming process.

In order to reflect the tertiary rheological characteristics of hard rocks at the high stress states, a new nonlinear visco-elastic-plastic model is proposed on the basis of linear visco-elastic-plastic model and nonlinear visco-elastic-plasticity. And then the corresponding constitutive model are deduced, which can be used for describing rocks’ long-term strength characteristics and their creep deformational behavior and time-dependent damage under interaction of coupled seepage-stress field in rock engineering. At last, considering the time effect of rock damage in the process of tertiary creep, a coupled seepage -stress creep damage model for investigating the whole creep deformation behavior, including tertiary creep failure process is established, and the related equations governing the evolution of stress, creep damage and rock permeability along with the creep deformation of rock is introduced.

We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted for through canonical combinations of Scott-Blair elements to construct a series of well-known fractional linear viscoelastic models, such as Kelvin–Voigt, Maxwell, Kelvin–Zener, and Poynting–Thomson. We also consider a fractional quasi-linear version of Fung’s model to account for stress/strain nonlinearity. The fractional viscoelastic models are combined with a fractional visco-plastic device, coupled with fractional viscoelastic models involving serial combinations of Scott-Blair elements. We then develop a general return-mapping procedure, which is fully implicit for linear viscoelastic models, and semi-implicit for the quasi-linear case. We find that, in the correction phase, the discrete stress projection and plastic slip have the same form for all the considered models, although with different property and time-step-dependent projection terms. A series of numerical experiments is carried out with analytical and reference solutions to demonstrate the convergence and computational cost of the proposed framework, which is shown to be at least first-order accurate for general loading conditions. Our numerical results demonstrate that the developed framework is more flexible and preserves the numerical accuracy of existing approaches while being more computationally tractable in the visco-plastic range due to a reduction of 50% in CPU time. Our formulation is especially suited for emerging applications of fractional calculus in bio-tissues that present the hallmark of multiple viscoelastic power-laws coupled with visco-plasticity.

The computation of the macroscopic response of polycrystalline aggregates from the properties of their single-crystal is a main problem in materials mechanics. During the mechanical deformation processing, all the grains in the polycrystalline material sample are reoriented. A crystallographic texture may thus be developed which is responsible for the material anisotropy. Therefore, the modeling of the texture evolution is important to predict the anisotropy effects present in industrial processes. The formulation of polycrystals plasticity has been the subject of many studies and different approaches have been proposed. Ahzi and M'Guil developed a viscoplastic phi-model. This model takes into account the grains interaction effects without involving the Eshelby inclusion problems.In this thesis, the phi-model was applied to different crystallographic structures and under different loading conditions. The mechanical twinning has been taken into account in the model. The FCC rolling texture transition from copper-type to brass-type texture is studied. The shear tests in FCC metals are also studied. The predicted results are compared with experimental shear textures for a range of metals having a high SFE to low SFE. For BCC metal, we compare our predicted results with those predicted by the VPSC model. We study the slip activities, texture evolutions and the evolution of yield loci. We also present a comparison with experimental textures from literatures for several BCC metals under cold rolling tests. The model has also been extended to HCP metals. We predict the deformation behavior of the magnesium alloy for different interaction strengths. We also compare our predicted results with experimental data from literatures. We show that the results predicted by the phi-model are in good agreement with the experimental ones.

L'objet de ce projet de recherche est de prédire la durée de vie d'éléments mécaniques qui sont soumis à des phénomènes de fatigue cyclique. L'idée est de développer un schéma numérique novateur pour prédire la rupture de structures sous de tels chargements. Le modèle est basé sur la mécanique des milieux continus qui introduit des variables internes pour décrire l'évolution de l'endommagement. Le défi repose dans le traitement des cycles de chargement pour la prédiction de la durée de vie, particulièrement pour la prédiction de la durée de vie résiduelle de structures existantes. Les approches traditionnelles de l'analyse de la fatigue sont basées sur des méthodes phénoménologiques utilisant des relations empiriques. De telles méthodes considèrent des approximations simplificatrices et sont incapables de prendre en compte aisément des géométries ou des charges complexes associées à des problèmes d'ingénierie réels. Une approche basée sur la description de l'évolution thermodynamique d'un milieu continu est donc utilisée pour modéliser le comportement en fatigue. Cela permet de considérer efficacement des problèmes d'ingénierie complexe et la détérioration des propriétés du matériau due à la fatigue peut être quantifiée à l'aide de variables internes. Cependant, cette approche peut être numériquement coûteuse et, par conséquent, des approches numériques sophistiquées doivent être utilisées.La stratégie numérique sur laquelle ce projet est basé est singulière par rapport aux schémas incrémentaux en temps usuellement utilisés pour résoudre des problèmes élasto-(visco)plastique avec endommagement dans le cadre de la mécanique des milieux continus. Cette stratégie numérique appelée méthode LATIN (Large Time Increment method) est une méthode non-incrémentale qui recherche la solution de manière itérative sur l'ensemble du domaine spacio-temporel. Une importante innovation de la méthode LATIN est d'incorporer une stratégie de réduction de modèle adaptative pour réduire de manière très importante le coût numérique. La Décomposition Propre Généralisée (PGD) est une stratégie de réduction de modèle a priori qui sépare les quantités d'intérêt spacio-temporelles en deux composantes indépendantes, l'une dépendant du temps, l'autre de l'espace, et estime itérativement les approximations de ces deux composantes. L'utilisation de l'approche LATIN-PGD a montré son efficacité depuis des années pour résoudre des problèmes élasto-(visco)plastiques. La première partie de ce projet vise à étendre cette approche aux modèles incorporant de l'endommagement.Bien que l'utilisation de la PGD réduise les coûts numériques, le gain n'est pas suffisant pour permettre de résoudre des problèmes considérant un grand nombre de cycles de chargement, le temps de calcul peut être très conséquent, rendant les simulations de problèmes de fatigue intraitables même en utilisant les techniques LATIN-PGD. Cette limite peut être dépassée en introduisant une approche multi-échelle en temps, qui prend en compte l'évolution rapide des quantités d'intérêt lors d'un cycle et leur évolution lente au cours de l'ensemble des cycles. Une description type « éléments finis » en temps est proposée, où l'ensemble du domaine temporel est discrétisé en éléments temporels, et seulement les cycles nodaux, qui forment les limites des éléments, sont calculés en utilisant la technique LATIN-PGD. Puis, des fonctions de forme classiques sont utilisées pour interpoler les quantités d'intérêt à l'intérieur des éléments temporels. Cette stratégie LATIN-PGD à deux échelles permet de réduire le coût numérique de manière significative, et peut être utilisée pour simuler l'évolution de l'endommagement dans une structure soumise à un chargement de fatigue comportant un très grand nombre de cycles
The motivation of the research project is to predict the life time of mechanical components that are subjected to cyclic fatigue phenomena. The idea herein is to develop an innovative numerical scheme to predict failure of structures under such loading. The model is based on classical continuum damage mechanics introducing internal variables which describe the damage evolution. The challenge lies in the treatment of large number of load cycles for the life time prediction, particularly the residual life time for existing structures.Traditional approaches for fatigue analysis are based on phenomenological methods and deal with the usage of empirical relations. Such methods consider simplistic approximations and are unable to take into account complex geometries, and complicated loadings which occur in real-life engineering problems. A thermodynamically consistent continuum-based approach is therefore used for modelling the fatigue behaviour. This allows to consider complicated geometries and loads quite efficiently and the deterioration of the material properties due to fatigue can be quantified using internal variables. However, this approach can be computationally expensive and hence sophisticated numerical frameworks should be used.The numerical strategy used in this project is different when compared to regular time incremental schemes used for solving elasto-(visco)plastic-damage problems in continuum framework. This numerical strategy is called Large Time Increment (LATIN) method, which is a non-incremental method and builds the solution iteratively for the complete space-time domain. An important feature of the LATIN method is to incorporate an on-the-fly model reduction strategy to reduce drastically the numerical cost. Proper generalised decomposition (PGD), being a priori a model reduction strategy, separates the quantities of interest with respect to space and time, and computes iteratively the spatial and temporal approximations. LATIN-PGD framework has been effectively used over the years to solve elasto-(visco)plastic problems. Herein, the first effort is to solve continuum damage problems using LATIN-PGD techniques. Although, usage of PGD reduces the numerical cost, the benefit is not enough to solve problems involving large number of load cycles and computational time can be severely high, making simulations of fatigue problems infeasible. This can be overcome by using a multi-time scale approach, that takes into account the rapid evolution of the quantities of interest within a load cycle and their slow evolution along the load cycles. A finite element like description with respect to time is proposed, where the whole time domain is discretised into time elements, and only the nodal cycles, which form the boundary of the time elements, are calculated using LATIN-PGD technique. Thereby, classical shape functions are used to interpolate within the time element. This two-scale LATIN-PGD strategy enables the reduction of the computational cost remarkably, and can be used to simulate damage evolution in a structure under fatigue loading for a very large number of cycles

Cogliati, Belén. (2011). Modelos viscosos em mecânica dos solos: análise de uma equação visco-hipoplástica. Dissertação de Mestrado, Escola Politécnica da Universidade de São Paulo, São Paulo. Esta dissertação estuda o comportamento de um modelo visco-hipoplástico proposto por Niemunis (2002), com as funções constitutivas da equação hipoplástica de Nader (2003). Para entender o papel da viscosidade no comportamento do solo são discutidos o adensamento secundário, a influência da velocidade de deformação na resistência não-drenada e a variação do coeficiente de empuxo com o tempo. Como etapa preliminar, são apresentados os modelos reológicos simples em uma dimensão, formados por um só elemento (modelos de Hooke, Newton e Saint-Venant) e modelos compostos pela combinação desses elementos (modelos de Maxwell, Bingham, Kelvin- Voigt, sólido linear padrão e visco-plástico com endurecimento). São deduzidas as equações de fluência e relaxação para todos esses modelos. Em três dimensões, são apresentadas as formulações do modelo visco-hipoplástico de Niemunis (2002) com as funções constitutivas de Nader (2003). São deduzidas as expressões simplificadas desse modelo para ensaios triaxiais. Em seguida, as equações são aplicadas à simulação de ensaios de compressão isotrópica e compressão não-drenada, com o objetivo de investigar a relaxação e a fluência bem como para analisar a influência dos parâmetros na resposta do modelo.
This thesis studies the behavior of the visco-hypoplastic model proposed by Niemunis, using Nader\'s hypoplastic constitutive equations. To understand the importance of viscosity in soil behavior the following topics are first examined: secondary consolidation, strain rate effects on undrained strength and the time variation of the coefficient of lateral pressure at rest. As a preliminary step, the present work discusses one-dimensional rheological models formed by a single element (Hooke\'s, Newton\'s and Saint-Venant\'s models) or by the combination of these elements (Maxwell\'s, Bingham\'s, Kelvin-Voigt\'s models; the standard linear solid model and the visco-plastic hardening model). For all the rheological models creep and relaxation are investigated. Niemunis\' visco-hypoplastic model with Nader\'s constitutive equations is presented next. First, simplified expressions of this model for triaxial test are deduced. Then the equations are applied to the simulation of isotropic compression and undrainded compression tests, with the aim of investigating relaxation and creep as well as of analyzing the influence of each parameter on the model response.

Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response. In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route. Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is highly non-linear and solving them requires the employment of numerical techniques. Had the interest been limited only to problems with nicely behaved continuous field variables, the finite element method (FEM) could have been a natural choice for solving the governing PDEs. Keeping in mind the limitations of the FEM in discretizing such large deformation problems and in handling discontinuities, a smooth particle hydrodynamics (SPH) formulation for the micro-inertia driven visco-plasticity model is undertaken in this thesis. The visco-plasticity model is then exploited to simulate ductile damage by suitably coupling the discretized SPH equations with an existing damage model. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic strain/ damage parameters and thus the numerical implementation avoids a computationally intensive return mapping. Our current approach therefore provides for an efficient numerical route to simulating impact dynamics problems. However, implementation of the SPH equations demands some additional terms such as artificial viscosity to arrive at a numerically stable solution. Using such stabilizing terms is however bereft of a rational or physical basis. The choice of artificial viscosity parameters is ad-hoc -an inappropriate choice leading to unphysical solutions. In order to circumvent this, the micro-inertia driven visco-plasticity model is reformulated using peri dynamics (PD), a more efficacious scheme to treat shock waves/discontinuities within a continuum model. Remarkably, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of non-local interaction. Exploiting the present model, we also explore the determination of conservation laws based on a variational formulation for dissipative visco-plastic solids wherein the system variables are appropriately augmented with those describing the time-reversed dynamics. This in turn enables us to undertake symmetry analyses on the resulting Lagrangian to assess, for instance, material resistance to crack propagation. Specifically, our results confirm that materials with higher rate sensitivity tend to offer higher resistance to fracture. Moreover, it is found that the kinetic energy of the inertial forces contributes to increased plastic flow thereby reducing the available free energy for crack propagation. This part of the work potentially opens a model-based route to the design of micro-defect structures for optimal fracture resistance.

A service-aged P91 steel was used to perform an experimental programme of cyclic mechanical testing in the temperature range of 400°C to 600°C, under isothermal conditions, using both saw-tooth and dwell (inclusion of a constant strain dwell period at the maximum (tensile) strain within the cycle) waveforms. The results of this testing were used to identify the material constants for a modified Chaboche, unified visco-plasticity model, which can deal with rate-dependant cyclic effects, such as combined isotropic and kinematic hardening, and time-dependent effects, such as creep, associated with visco-plasticity. The model has been modified in order that the two-stage (non-linear primary and linear secondary) softening which occurs within the cyclic response of the service-aged P91 material is accounted for and accurately predicted. The characterisation of the cyclic visco-plasticity behaviour of the service-aged P91 material at 500°C is presented and compared to experimental stress-strain loops, cyclic softening and creep relaxation, obtained from the cyclic isothermal tests.

Abstract. A comprehensive 3D visco-elasto-plasto-damage constitutive model of concrete is proposed to analyze its behaviour under long-term and cyclic loadings. This model combines the visco-elasticy and plasticity theories together with damage mechanics. The work aims at providing an efficient model capable of predicting the material behaviour, taking into account time-dependent effects at the mesoscale. The visco-elastic part is modeled within the framework of the linear visco-elasticity theory. The creep function is evaluated with the aid of the B3 model by Bažant and Baweja, and implemented via the exponential algorithm. The modified Menétrey-Willam pressure-dependent yield surface, and a non-associated flow rule are used for the plastic formulation of the model. The damage part of the model considers two exponential damage parameters: one in tension, and one in compression, that account for a realistic description of the transition from tensile to compressive failure. After discussing the numerical implementation, the proposed model is calibrated, and numerical results at the mesoscale level are compared to experimental results.

Sheet metals usually exhibit a certain degree of plastic anisotropy because of the rolling effect. To characterize the anisotropic behavior in simulations related to large deformation, strain-rate independent phenomenological models are frequently used in quasi-static conditions. Two functions are generally included in such a model, i.e. the yield function and the plastic potential. The former limits the stress state within the yield surface while the latter determines the direction of the plastic strain increment. Traditional plasticity models mostly assume associated flow rule, in which the two functions mentioned above are identical. With the enhanced demand of accuracy, the forms of the associated models become too complex with more and more parameters to achieve an easy calibration procedure. Alternatively, in the past decade the non-associated models were increasingly used for sheet metals. Separate functions for the two aspects of plasticity lead to efficient characterization and convenient calibration. In numerical study of dynamic loading cases, how to characterize strain-rate dependence of plasticity is an important issue. Some visco-plastic models were developed to take the rate effect into account, e.g. Johnson-Cook and Cowper-Symonds models, where the isotropic J2 flow theory was commonly used. However, when the material is severely anisotropic, this approach is very likely to be insufficient, and a model including both anisotropy and rate dependence would be needed. Extending a non-associated anisotropic model to be rate-dependent is a promising approach which has not been published in open literature to the best knowledge of the authors. Objective of the present study is to develop an applicable model for characterizing dynamic mechanical behavior of a typical high-strength steel sheet. Two steps are performed. The material is investigated under quasi-static loading firstly. Tensile test results show an obvious anisotropy which cannot be described by traditional associated models. So the non-associated Hill48 model is chosen and calibrated. Accuracy of the model is verified by a quasi-static punching test. Thereafter the dynamic material properties are obtained by conducting tensile tests at quite a few strain-rate levels covering 0.0004–1200s−1. To characterize the positive strain-rate effect in strength, the non-associated Hill48 model is extended to be visco-plastic after checking two rate-dependence formulations in existing isotropic models. With implementing the extended model into a user subroutine of ABAQUS/explicit, simulations of the dynamic tension tests are run and compared to the real experiments. A good agreement between the simulated and the experimental result is achieved using the VUMAT.

In this paper, FEM is employed to investigate the effects of nose radius and edge radius on the turning of AISI4140. The tool material used is Carbide and Johnson-Cook plastic model is employed to model the workpiece due to its capability of modeling large strains, high strain rates, and temperature dependent visco-plasticity. Different nose radii and edge radii are used to explore the effects of the nose radius and edge radius on the machining temperature, cutting forces, and power. This model provides a fundamental understanding of cutting mechanics of the turning operation of AISI 4140.

ABSTRACT: The object-oriented software concept is applied to material mechanics calculations. The result is a comprehensive predictor-corrector which has been employed to solve virtually all of the constitutive exercises in a mature, general-purpose, finite element program. In addition to updating internal variables consistent with global inputs (corrector), the software also produces consistent material tangents (predictor), without resort to formulae. Coupled mechanical-thermal-porous flow problems are addressed as well as compound mechanical responses: creep-plasticity, creep-damage, etc. Material and spatial coordinate transformations are incorporated as well as transformation to and from local material axes. Internal calculations may be undertaken in either spatial or material coordinates, depending upon the native definition. Even viscoelasticity and hyper-viscoelasticity, via Prony series, are efficiently handled by the sparse solver. A tool to exercise any material model, simulating global inputs, is incorporated. Historical plots may be produced and inputs may be cyclical or otherwise simulate complex histories. This is accomplished by using PostScript operators. 1 INTRODUCTION It is perhaps most common in commercial modeling software that each constitutive model is self-contained, that is, each solves the responses and forms the material tangents (algorithm-oriented software design). There is much advantage to be gained by employing a uniform solution/tangent formation strategy for all material models. Indeed, this is the subject of this communication. At first examination, this may seem incongruous considering the different solution strategies employed for different models. For example visco-elasticity, via a prony series, is most often solved by a recursive solution scheme, whereas plasticity would be solved via a Newton-Raphson scheme. Of course, for simplified versions of these models, a forward difference integration scheme is employed, Flac3d, for example. If the constitutive model is algorithmically nonlinear, it is tacitly assumed that any path dependence is captured by taking small time/load steps. The highly nonlinear nature of strain-hardening models, however, generally requires iteration at the constitutive level. This is generally not supported in forward difference programs so the material models in these codes tend to be relatively simple.

This paper describes high temperature cyclic and creep relaxation testing and modelling of a high nickel-chromium material (XN40F) for application to the life prediction of superplastic forming (SPF) tools. An experimental test programme to characterise the high temperature cyclic elastic-plastic-creep behaviour of the material over a range of temperatures between 20°C and 900°C is described. The objective of the material testing is the development of a high temperature material model for cyclic analyses and life prediction of superplastic forming (SPF) dies for SPF of titanium aerospace components. A two-layer visco-plasticity model which combines both creep and combined isotropic-kinematic plasticity is chosen to represent the material behaviour. The process of material constant identification for this model is presented and the predicted results are compared with the rate-dependent (isothermal) experimental results. The temperature-dependent material model is furthermore applied to simulative thermo-mechanical fatigue (TMF) tests, designed to represent the temperature and stress-strain cycling associated with the most damaging phase of the die cycle. The model is shown to give good correlation with the test data, thus vindicating future application of the material model in thermo-mechanical analyses of SPF dies, for distortion and life prediction.

Titanium alloys are classified as hard-to-cut materials due to high chemical reactivity and low thermal conductivity. In this paper, the Finite Element Method (FEM) is used to model and simulate effects of cutting speeds and too-chip frictional coefficients in orthogonal machining of Titanium alloy (Ti-6Al-4V). Johnson-Cook plastic model is used to model the workpiece due to its capability of modeling large strains, high strain rates, and temperature dependent visco-plasticity. The tool material is Carbide. Three different cutting speeds (70m/min, 150m/min, and 190m/min) and four different frictional coefficients (0.3, 0.5, 0.7, and 1.0) are used to explore the effects of the cutting speeds and frictional coefficients on the cutting temperature, cutting forces, and chip morphology. This model provides fundamental understanding of cutting mechanics of the orthogonal cutting of Titanium alloy (Ti-6Al-4V).

Abstract Nickel-base superalloys (NBSAs) are extensively utilized as the design materials to develop turbine blades in gas turbines due to their excellent high-temperature properties. Gas turbine blades are exposed to extreme loading histories that combine high mechanical and thermal stresses. Both directionally solidified (DS) and single crystal NBSAs are used throughout the industry because of their superior tensile and creep strength, excellent low cycle fatigue (LCF), high cycle fatigue (HCF), and thermomechanical fatigue (TMF) capabilities. Directional solidification techniques facilitated the solidification structure of the materials to be composed of columnar grains in parallel to the <001> direction. Due to grains being the sites of failure initiation the elimination of grain boundaries compared to polycrystals and the alignment of grain boundaries in the normal to stress axis increases the strength of the material at high temperatures. To develop components with superior service capabilities while reducing the development cost, simulating the material’s performance at various loading conditions is extremely advantageous. To support the mechanical design process, a framework consisting of theoretical mechanics, numerical simulations, and experimental analysis is required. The absence of grain boundaries transverse to the loading direction and crystallographic special orientation cause the material to exhibit anisotropic behavior. A framework that can simulate the physical attributes of the material microstructure is crucial in developing an accurate constitutive model. The plastic flow acting on the crystallographic slip planes essentially controls the plastic deformation of the material. Crystal Visco-Plasticity (CVP) theory integrates this phenomenon to describe the effects of plasticity more accurately. CVP constitutive models can capture the orientation, temperature, and rate dependence of these materials under a variety of conditions. The CVP model is initially developed for SX material and then extended to DS material to account for the columnar grain structure. The formulation consists of a flow rule combined with an internal state variable to describe the shearing rate for each slip system. The model presented includes the inelastic mechanisms of kinematic and isotropic hardening, orientation, and temperature dependence. The crystallographic slip is accounted for by including the required octahedral, cubic, and cross slip systems. The CVP model is implemented through a general-purpose finite element analysis software (i.e., ANSYS) as a User-Defined Material (USERMAT). Uniaxial experiments were conducted in key orientations to evaluate the degree of elastic and inelastic anisotropy. The temperature-dependent modeling parameter is developed to perform non-isothermal simulations. A numerical optimization scheme is utilized to develop the modeling constant to improve the calibration of the model. The CVP model can simulate material behavior for DS and SX NBSAs for monotonic and cyclic loading for a range of material orientations and temperatures.

Abstract Gas turbine blades are subjected to complex mechanical loading coupled with extreme thermal loading conditions which range from room temperature to over 1000°C. Nickel-base superalloys exhibit high strength, good resistance to corrosion and oxidation, long fatigue life and is capable of withstanding high temperatures for extended periods of time. Consequently, Ni-base superalloys (NBSAs) are highly suitable as blading materials. The cyclic strains due to mechanical as well as thermal cycling leads to Thermomechanical fatigue (TMF). Damage from TMF takes the form of microstructural material cracking which consequently lead to the failure of the component. In order to increase the service life and reliability and reduce operating costs, development of simulations that accurately predict the material behavior for TMF is highly desirable. To support the mechanical design process, a framework consisting of theoretical mechanics, experimental analysis and numerical simulations must be used. Capturing the effects of thermomechanical fatigue is extremely important in the prediction of the material behavior and life expectation. Single crystal (SX) Ni-base superalloys exhibit anisotropic behavior. A modeling framework which is capable of simulating the physical attributes of the material microstructure is essential. Crystallographic slip along the slip planes controls the microstructural evolution of the material Crystal Visco-Plasticity (CVP) theory captures anisotropic behavior as well as the slip along the slip planes. CVP constitutive models can capture rate-, temperature, and history-dependence of these materials under a variety of conditions. Typical CVP formulations consist of a flow rule, internal state variables, and parameters. The model presented in the current study includes the inelastic mechanism of kinematic hardening and isotropic hardening which are captured by the back stress and drag stress, respectively. Crystallographic slip is accounted for by the incorporation of twelve octahedral six cubic slip systems. An implicit integration scheme which uses Newton-Raphson iteration method is used to solve the required solutions. The CVP model is implemented through a general-purpose finite element analysis software (i.e., ANSYS) as a User-Defined Material (USERMAT). A small batch of uniaxial experiments were conducted in key orientations (i.e., [001], [011], and [111] to assess the level of elastic and inelastic anisotropy. Modeling parameters are expressed as temperature-dependent to allow for simulation under non-isothermal conditions. An optimization scheme based in MATLAB utilizes this experimental data to calibrate the CVP modeling constants. The CVP model has the capability to simulate material behavior for monotonic and cyclic loading coupled with in phase and out phase temperature cycling for a variety of material orientations, strain rates, strain and temperature ranges. A CVP model that predicts SX behavior across various rates, orientations, temperatures and load levels have not been presented before now.