Configurational Forces in Cutting Processes of Microstructured Titanium

The micro cutting process of microstructured material is influenced by the heterogeneity of the microstructure. In case of cp-titanium an hcp crystal structure is present. Therefore the material response is described with elastic anisotropy and crystal plasticity with the prismatic and basal slip systems of cp-titanium. Also self and latent hardening are considered. The rate dependency is taken into account by a visco-plastic evolution law. In order to investigate a micro cutting process the concept of configurational forces for standard dissipative media is used. Within the finite element method an example illustrates the effects of the heterogeneity and the grain boundary on the configurational force. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laminate-based modelling of microstructure and switching in ferroelectrics

The purpose of the work is the thermodynamics-based modelling of the polarisation and the deformation microstructure in the ferroelectric single crystal with the help of a laminate-based approach. The incremental variational-based rate-dependent macroscopic model for dissipative ferroelectric material [1] and the laminate-based microscopic model [2] established in the literature are taken as basis and shall be further extended to a single crystal laminate structure dependent on the loading frequency based on the coupled electromechanical framework taking the effect of polarisation into account. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Phase Field Approach for Martensitic Transformations and Crystal Plasticity

This work is motivated by cryogenic turning which allows end shape machining and simultaneously attaining a hardened surface due to deformation induced martensitic transformations. To study the process on the microscale, a multivariant phase field model for martensitic transformations in conjunction with a crystal plastic material model is introduced. The evolution of microstructure is assumed to follow a time-dependent Ginzburg-Landau equation. To solve the field equations the finite element method is used. Time integration is performed with Euler backward schemes, on the global level for the evolution equation of the phase field, and on the element level for the crystal plastic material law. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On physics-based crystal plasticity models: Application to virtual material testing of sheet metals

It is possible to pursue a multi-scale modeling approach for sheet forming simulations by applying the concept of virtual material testing to determine the yield surface from the microstructure of a given material. Full-field simulations with phenomenological crystal plasticity models are widely used for this kind of investigations. However, recent developments focus on incorporating physical quantities like dislocation density into these models. In this work, a dislocation density based crystal plasticity model is used to investigate the plastic anisotropy of the deep drawing steel DC04. In particular, we focus on the prediction of R-values, which can be used to calibrate macroscopic plasticity models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale modelling and simulation of micro machining of titanium

The microscale morphology of micro machined component surfaces is directly connected to the heterogeneous microstructure. The deformation depends on the crystal structure, in case of the considered cp-titanium, the hcp crystal structure. In a first approach the crystal plastic deformation is modeled with isotropic hardening. A visco-plastic evolution law accounts for the rate dependency. The concept of configurational forces is used with the framework of crystal plasticity to model the cutting process of cp-titanium. The setting is implemented into the finite element method. The examples show the effect of the material heterogeneity on the deforamtion behavior and on the related configurational forces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of microstructural pattern formation in crystal plasticity

The mechanical behavior of most materials is dictated by a present or emergent underlying microstructure which is a direct result of different, even competing physical mechanisms occurring at lower length scales. In this work, energetic microstructure interaction via different non-convex contributions to the free energy in metals is modeled. For this purpose rate dependent gradient extended crystal plasticity models at the glide-system level are formulated. The non-convex energy serves as the driving force for the emergent microstructure. The competition between the kinetics and the relaxation of the free energy is an essential feature of the model. Non-convexity naturally arises in finite-deformation single-slip crystal plasticity and the results of the gradient model for this case are compared with an effective laminate model based on energy relaxation. Similarities as well as essential differences are observed and explained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical creep model for pure copper

A Unit Cell made of copper is simulated and investigated under creep conditions within the framework of micromechanics. Geometrical 3D model of the copper microstructure is represented as a Unit Cell with grains of random crystallographical orientation and geometry. Such simulation enables algorithm of Voronoi tessellation. The stress-strain behavior of grains in the general case is anisotropic due to the ordered crystalline structure. The anisotropic model for a material with a cubic symmetry is implemented in Abaqus and used to assign behavior of grain interior in elastic and creep regions. Material parameters for elastic model are taken from elastic tests of single crystal copper [1]. Power law material parameters for creep model are taken from creep test performed for single crystal copper [2]. The model parameter ξ is validated numerically. Creep results are presented for the case of proportional loading during the primary and secondary creep. Statistical analysis of creep curves received for 55 different realizations of Unit Cell geometry is carried out. As a result confident interval and mathematical expectation of creep data are calculated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of microstructure in a Cosserat continuum using relaxed energies

We develop a nonlinear incompressible multiphase material model in a Cosserat continuum with microstructure. The free energy of the material is enriched with an interaction potential taking into account the intergranular kinematics at the continuum scale. As a result the total energy becomes non-convex, thus giving rise to the development of microstructural phases. To guarantee the existence of minimizers an exact quasi-convex envelope of the corresponding energy functional is derived. As a result a three phase material energy appears, among them two of the phases are with microstructure in the translational motion (displacment field) and micromotion (microrotation field), whereas the third phase is without internal structure. The corresponding relaxed energy is then used for finding the minimizers of the two field minimization problem corresponding to a Cosserat continuum. Results from a numerical example predicting the development of microstructure in the material are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on statistically similar RVEs for real microstructures based on different statistical descriptors

A method for constructing statistically similar representative volume elements (SSRVEs) for a real dual-phase (DP) steel microstructure is presented in this contribution. The advantageous material properties of such kind of steels originate from the interaction of the microstructure constituents of the material on the microscale. In order to capture these effects directly in the material modeling, the FE² method is a suitable tool, where an RVE representing the microstructure of a material is used in the microscopic boundary value problem, which is solved at each Gauss-point of the macroscopic boundary value problem. However, RVEs based on real microstructures typically implicate high computational expenses due to the complexity of the underlying microstructure and its discretization. SSRVEs, which have a lower complexity than conventional RVEs but are still able to represent the material, can be used instead. Here, different statistical measures for the construction of SSRVEs and their comparison are the main focus. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Configurational Forces in Crystal Plasticity

The surface morphology of micro machined surfaces depends on the heterogeneous microstructure. A crystal plasticity model is used to describe the plastic deformation in cp-titanium with its hcp crystal structure. Therefore the basal and prismatic slip systems are taken into account. Furthermore, self and latent hardening are considered. The rate dependency is motivated by a visco plastic evolution law. The cutting process of cp-titanium is modeled within the concept of configurational forces for a standard dissipative media. This framework is implemented into the finite element method. An example illustrates the effects of the microstructure on plastic deformation and configurational forces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Phase Field Modeling of Laminate Deformation Microstructure in Finite Gradient Crystal Plasticity

The macroscopic mechanical behavior of many materials crucially depends on the formation and evolution of their microstructure. In this work, we consider the formation and evolution of laminate deformation microstructure in plasticity. Inspired by work on the variational modeling of phase transformation [5] and building on related work on multislip gradient crystal plasticity [9], we present a new finite strain model for the formation and evolution of laminate deformation microstructure in double slip gradient crystal plasticity. Basic ingredients of our model are a nonconvex hardening potential and two gradient terms accounting for geometrically necessary dislocations (GNDs) by use of the dislocation density tensor and regularizing the sharp interfaces between different kinematically coherent plastic slip states. The plastic evolution is described by means of a nonsmooth dissipation potential for which we propose a new regularization. We formulate a continuous gradient-extended rate-variational framework and discretize it in time to obtain an incremental-variational formulation. Discretization in space yields a finite element formulation which is used to demonstrate the capability of our model to predict the formation and evolution of laminate deformation microstructure in f.c.c. Copper with two active slip systems in the same slip plane. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and numerical simulation of multiscale behavior in polycrystals via extended crystal plasticity

The purpose of this work is to exploit the algorithmic formulation of models for multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The models for extended crystal plasticity are based on the formulation of rate potentials whose form is determined by (i) energetic processes via the free energy, (ii) kinetic processes via the dissipation potential, and (iii) the form of the evolution relations for the internal-variable-like quantities upon which the free energy and dissipation potential depend. Examples for these latter quantities are the inelastic local deformation or dislocation densities as GNDs. Different algorithmic implementations are discussed, namely the algorithmic variational approach and the dual mixed approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro-mechanical analysis of creep behavior in a multipass weld

A method of evaluating creep response of the multipass weld based on the micro-macro mechanics approach is introduced. Multipass weld microstructure that consists from columnar, coarse and fine grained zones is considered. Materials of these constituents assumed to be isotropic. Weld metal properties of inelastic behavior have general type of symmetry and are described by the anisotropic creep constitutive model. To model the microstructure of the multipass weld metal the representative volume element (RVE) is created for CAE Abaqus. Material properties of weld metal grain type zones are taken from the experiments. Numerical tests on uniform loading of the RVE are performed. Creep material properties for equivalent weld material are found for welds with different number of passes. The symmetry type of the creep material properties of multi-pass weld are evaluated for the equivalent weld material. As an example of macro model analysis of the welding, the creep calculation of the cylindrical shell with the welding under the uniform inner pressure is performed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Construction of Statistically Similar RVEs for 3D Microstructures

This contribution presents a method to construct three-dimensional Statistically Similar RVEs (SSRVEs) for the simulation of dual phase steel (DP steel). Since the microstructure of DP steel strongly influences the overall material properties, it should be incorporated in numerical calculations. For this purpose the FE² method can be applied and for an efficient computation SSRVEs with a reduced complexity compared to the real microstructure have to be defined, which still represent the mechanical response of the material accurately. The construction method is based on the minimization of a least-square functional considering suitable statistical measures describing the inclusion morphology of a given real microstructure. The mechanical response of the SSRVEs is compared to the response of the real microstructure in virtual mechanical tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Methods of Micro–Macro Transitions in Nonlinear Elasticity

Continuum micromechanics deals with idealized materials where the macroscopic material response is modelled in an averaged or homogenized sense based on the information of the heterogeneous microstructure. In general, an efficient treatment of multiscale systems requires the application of equivalent structural problems where the constituents are governed by overall properties. The key contribution of this paper is the computational exploitation of variational methods for a numerical upper and lower bound estimation of the effective material response. We present aspects for the formulation of an appropriate minimizing principle yielding the displacement fluctuations on the microstructure and the local effective constitutive variables of the macrostructure depending on the choice whether we apply linear displacement, traction or periodic boundary conditions to the displacement fluctuations on the boundary of the microstructure. The proposed concept will be demonstrated in the scope of some representative model problems.     

Designing Statistically Similar RVEs for 3D Dual Phase Steel Microstructures

This contribution presents a method for the construction of three-dimensional Statistically Similar Representative Volume Elements (SSRVEs) for dual phase steels (DP steels). From such kind of advanced high strength steels, enhanced material properties are observed, which originate in the interaction of the individual constituents of the material on the microscale. Our aim is to directly incorporate the microstructure in the material modeling, which can be accomplished by applying i. e. the FE² method. A RVE representing the real material is used in the microscopic boundary value problem, which is solved at each macroscopic integration point. Since such RVEs usually exhibit a high complexity due to the underlying real microstructure, high computational costs are a drawback of the approach. We replace this RVE with a SSRVE, which has a lower complexity but which is still able to represent the mechanical behavior of the RVE and thus of the real microstructure. Virtual experiments show the performance of the method. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)