Scipedia: Journal Papers

On the constitutive modeling of coupled thermomechanical phase-change problems

Mar��a Jes��s Samper — Wed, 03 Apr 2019 11:24:22 +0200

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.

On the numerical modeling of frictional wear phenomena

Mar��a Jes��s Samper — Thu, 25 Jul 2019 12:42:26 +0200

The evolution of the contact surfaces wear may become particularly important in the definition of the frictional behavior, in particular for frictional contact problems involving large slips, typically in sheet metal forming and bulk forming operations. Despite this fact, most of the current applications reported in the literature are restricted to a standard Coulomb law, using a constant friction coefficient. Such simple models may represent only a limited range of tribological situations and it appears to be necessary to develop a class of models which incorporate the state conditions and their evolution at the contact surfaces, taking into account the influence of complex phenomena such as wear, lubrication and chemical reactions, among others, see Oden and Martins [1].

In this paper a simple numerical model for the simulation of frictional wear behavior, within a fully nonlinear setting, including large slip and finite deformation, is presented. The model relies on the introduction of an internal variable related to the state conditions at the contact surface. Here, two possible definitions of this internal variable have been considered. The fully nonlinear frictional contact formulation, entirely derived first on a continuum setting by Laursen and Simo [2–6], has been extended here to accomodate the characterization of the wear frictional behavior.

Within the computational aspects, two families of robust time stepping algorithms, arising from an operator split of the constrained frictional evolution equations, are discussed.

Finally, following current approaches, see Lassen [9], Lassen and Bay [10], Owen et al. [11], de Souza et al. [12], Stromberg et al. [13] and Stromberg [14], a long-term tools wear prediction is given by introducing an a priori wear estimate derived from Archard's law, Archard [15].

The numerical model has been implemented into a enhanced version of the computational finite element program FEAP. Numerical examples show the suitability of the proposed model to capture the essential features of the frictional behavior at the contact interfaces and to provide a prediction of tool wear in forming operations.

On the formulation of coupled thermoplastic problems with phase-change

Mar��a Jes��s Samper — Tue, 02 Apr 2019 11:50:28 +0200

This paper deals with a numerical formulation for coupled thermoplastic problems including phase-change phenomena. The final goal is to get an accurate, efficient and robust numerical model, allowing the numerical simulation of solidification processes in the metal casting industry. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. The constitutive behavior has been defined by a thermoelastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. A brief summary of the thermomechanical frictional contact model is included. The numerical model has been implemented into the computational Finite Element code COMET developed by the authors. A numerical assessment of the isentropic and isothermal operator splits, regarding the nonlinear stability behavior, has been performed for weakly and strongly coupled thermomechanical problems. Numerical simulations of solidification processes show the performance of the computational model developed.

Thermo�\mechanical analysis of industrial solidification processes

Mar��a Jes��s Samper — Thu, 28 Mar 2019 10:20:50 +0100

The paper presents an up�\to�\date finite element numerical model for fully coupled thermo�\mechanical problems, focussing in the simulation of solidification processes of industrial metal parts. The proposed constitutive model is defined by a thermo�\visco�\elasto�\(visco)plastic free energy function which includes a contribution for thermal multiphase changes. Mechanical and thermal properties are assumed to be temperature�\dependent, and viscous�\like strains are introduced to account for the variation of the elastic moduli during the cooling process. The continuous transition between the initial fluid�\like and the final solid�\like behaviour of the part is modelled by considering separate viscous and elasto�\plastic responses as a function of the solid fraction. Thermo�\mechanical contact conditions between the mould and the part are specifically considered, assuming that the heat flux is a function of the normal pressure and the thermal and mechanical gaps. A fractional step method arising from an operator split of the governing equations is used to solve the non�\linear coupled system of equations, leading to a staggered product formula solution algorithm suitable for large�\scale computations. Representative simulations of industrial solidification processes are shown, and comparison of computed results using the proposed model with available experimental data is given.

Numerical analysis of coupled thermomechanical frictional contact problems. Computational model and applications

Mar��a Jes��s Samper — Thu, 25 Jul 2019 16:59:15 +0200

In this paper a numerical model for the analysis of coupled thermomechanical multi-body frictional contact problems at finite deformations is presented. The multi-body frictional contact formulation is fully developed on the continuum setting and then a spatial (Galerkin projection) and temporal (time-stepping algorithm) discretization is applied. A contact pressure and temperature dependent thermal contact model has been used. A fractional step method arising from an operator split of the governing equations has been used to solve the coupled nonlinear system of equations, leading to a staggered solution algorithm.

The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of coupled thermomechanical frictional contact problems.

A new frictional time integration algorithm for large slip multi-body frictional contact problems

Mar��a Jes��s Samper — Thu, 25 Jul 2019 16:49:10 +0200

In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the simple context of a model problem: the sliding motion of a particle onto a rough surface. Time integration of frictional traction is performed introducing a new slip path parametrization, which is defined independently traction is performed introducing element parametrization used in the spatial triangularization. The key point of the algorithm is that now, in presence of large slips, problems associated with slip motions such that a full incremental slip path is not within a single surface element, are completed bypassed. Remarkably, the algorithm is defined on the solely basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization. Geometrically, the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path. The algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a Newton-Raphson iterative solution scheme. The algorithm can easily be extended to large slip multi-body frictional contact problems, involving finite strains.

Comparative study on sheet metal forming processes by numerical modelling and experiment

Mar��a Jes��s Samper — Fri, 18 Jan 2019 11:00:16 +0100

In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell formulation.

Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation

Mar��a Jes��s Samper — Tue, 11 Dec 2018 13:29:40 +0100

In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.

Plastic and viscoplastic flow of void�\containing metals. Applications to axisymmetric sheet forming problems

Mar��a Jes��s Samper — Tue, 11 Dec 2018 13:19:31 +0100

A formal analogy between the equations of pure plastic and viscoplastic flow theory for void�\containing metals and those of standard non�\linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.

Challenges to be tackled in the computational modeling and numerical simulation of FSW processes

Mar��a Jes��s Samper — Fri, 26 Jul 2019 11:37:51 +0200

The computational modeling and numerical simulation of Friction Stir Welding (FSW) processes is an extremely challenging task due to the highly nonlinear and coupled nature of the physical problem and the complex computational issues that need to be properly tackled in the numerical model.

Numerical analysis of the manufacturing processes of a mock-up of the ITER NHF First Wall Panel

Mar��a Jes��s Samper — Fri, 26 Apr 2019 12:29:32 +0200

The objective of ITER is to build a new Tokamak, with the goal of demonstrating the scientific and technical feasibility of fusion power. The First Wall Panels are the inner component of the reactor, built with different materials that must support high heat flux levels inside the vacuum vessel. The manufacturing processes of the First Wall are a complex procedure including bending, hipping and cutting procedures which, in general, lead to residual stresses and distortions of the fabricated component. In this work, the analysis of the thermo-mechanical response of a simplified prototype of the ITER NHF First Wall Panel is presented from the numerical point of view. The experimental procedure within each phase of the whole manufacturing process is described. Residual stresses and distortions have been measured and analyzed. The numerical simulation of the manufacturing process includes the description of the main hypothesis, the applied loads and the boundary conditions assumed at every stage of the process. Special attention is paid to the simulation of machining and cutting by means of an ad-hoc element deactivation strategy. The numerical results are compared with the experimental evidence to show the prediction capability and the limitations of the proposed numerical model.

Conserving algorithms for frictionless and full stick friction contact dynamic problems using the direct elimination method

Mar��a Jes��s Samper — Fri, 26 Jul 2019 11:25:38 +0200

In this paper, conserving time�\stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy�\momentum–preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty�\based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time�\stepping algorithm is shown.

A fast and accurate two-stage strategy to evaluate the effect of the pin tool profile on metal flow, torque and forces during friction stir welding

Mar��a Jes��s Samper — Wed, 10 Apr 2019 10:32:32 +0200

Pin geometry is a fundamental consideration in friction stir welding (FSW). It influences the thermal behaviour, material flow and forces during the weld and reflects on the joint quality.

This work studies four pin tools with circular, triflute, trivex, and triangular profiles adopting a validated model of FSW process developed by the authors. The effect of the rotating tool geometry on the flow behaviour and process outcomes is analysed. Additionally, longitudinal and transversal forces and torque are numerically calculated and compared for the different pin shapes. The study is carried out for slip and stick limiting friction cases between pin and workpiece.

The main novelties of the paper are a “speed-up” two-stage simulation methodology and a piecewise linear version of the constitutive model, both of them conceived for the use in real case industrial applications, where the achievement of accuracy with affordable simulation times is of importance.

The Norton-Hoff constitutive model is adopted to characterize the material behaviour during the weld. The piecewise linear version of the model developed by the authors greatly facilitates the convergence of the numerical solution ensuring both computational efficiency and accuracy. A two-stage computational procedure is applied. In the first stage, a forced transient is carried out; in the second one, the magnitudes of interest are computed.

The study shows that the proposed modelling approach can be used to predict and interpret the FSW behaviour for a specific pin geometry. Moreover, the reduction of the simulation time using the two-stage strategy can be up to 90%, compared to a standard single stage strategy.

Local�Cglobal strategy for the prediction of residual stresses in FSW processes

Mar��a Jes��s Samper — Tue, 09 Apr 2019 12:38:28 +0200

This work describes the local–global strategy proposed for the computation of residual stresses in friction stir welding (FSW) processes. A coupling strategy between the analysis of the process zone nearby the pin tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW. As a first step, the local problem solves the material stirring as well as the heat generation induced by the pin and shoulder rotation at the heat affected zone. The Arbitrary Lagrangian Eulerian (ALE) formulation is adopted to deal with the rotation of complex pin shapes. A thermo-rigid-viscoplastic constitutive law is employed to characterize the viscous flow of the material, driven by the high-strain rates induced by the FSW process. A mixed temperature–velocity–pressure finite element technology is used to deal with the isochoric nature of the strains. The output of this local analysis is the heat generated either by plastic dissipation or by friction, and it is used as the power input for the welding analysis at structural (global) level. The global problem is tackled within the Lagrangian framework together with a thermo-elasto-viscoplastic constitutive model. In addition, in this case, the mixed temperature–displacement–pressure format is introduced to deal with the deviatoric nature of the plastic strains. The outcomes of this analysis are the distortions and the residual stresses after welding. The material used in this work is stainless steel 304 L; however, the methodology presented is applicable to a wide range of materials. The proposed numerical strategy is validated by the experimental evidence.

Challenges in thermo-mechanical analysis of Friction Stir Welding processes

Mar��a Jes��s Samper — Tue, 09 Apr 2019 10:52:25 +0200

This paper deals with the numerical simulation of friction stir welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of essential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat affected zone (HAZ). The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools. A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced. To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations induced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework). At global level, the material behavior is characterized by a thermo–elasto–viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermo–visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton–Hoff, Carreau or Sheppard–Wright, among others are tested. To better understand the material flow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results. A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.

Software Solutions for ICME

Mar��a Jes��s Samper — Fri, 26 Jul 2019 10:52:06 +0200

The Integrated Computational Materials Engineering expert group (ICMEg), a coordination activity of the European Commission, aims at developing a global and open standard for information exchange between the heterogeneous varieties of numerous simulation tools. The ICMEg consortium coordinates respective developments by a strategy of networking stakeholders in the first International Workshop on Software Solutions for ICME, compiling identified and relevant software tools into the Handbook of Software Solutions for ICME, discussing strategies for interoperability between different software tools during a second (planned) international workshop, and eventually proposing a scheme for standardized information exchange in a future book or document. The present article summarizes these respective actions to provide the ICME community with some additional insights and resources from which to help move this field forward.

Numerical modeling of the electron beam welding and its experimental validation

Mar��a Jes��s Samper — Tue, 09 Apr 2019 12:26:00 +0200

Electron Beam Welding (EBW) is a highly efficient and precise welding method increasingly used within the manufacturing chain and of growing importance in different industrial environments such as the aeronautical and aerospace sectors. This is because, compared to other welding processes, EBW induces lower distortions and residual stresses due to the lower and more focused heat input along the welding line.

This work describes the formulation adopted for the numerical simulation of the EBW process as well as the experimental work carried out to calibrate and validate it.

The numerical simulation of EBW involves the interaction of thermal, mechanical and metallurgical phenomena. For this reason, in this work the numerical framework couples the heat transfer process to the stress analysis to maximize accuracy. An in-house multi-physics FE software is used to deal with the numerical simulation. The definition of an ad hoc moving heat source is proposed to simulate the EB power surface distribution and the corresponding absorption within the work-piece thickness. Both heat conduction and heat radiation models are considered to dissipate the heat through the boundaries of the component. The material behavior is characterized by an apropos thermo-elasto-viscoplastic constitutive model. Titanium-alloy Ti6A14V is the target material of this work.

From the experimental side, the EB welding machine, the vacuum chamber characteristics and the corresponding operative setting are detailed. Finally, the available facilities to record the temperature evolution at different thermo-couple locations as well as to measure both distortions and residual stresses are described. Numerical results are compared with the experimental evidence.

3D numerical models of FSW processes with non-cylindrical pin

Mar��a Jes��s Samper — Mon, 08 Apr 2019 13:48:51 +0200

Friction stir welding (FSW) process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the arbitrary Lagrangian–Eulerian formulation, remeshing or the orthogonal sub-grid scale method. It is shown that these two formulations essentially deliver the same results.

A direct elimination algorithm for quasi-static and dynamic contact problems

Mar��a Jes��s Samper — Fri, 26 Jul 2019 10:30:38 +0200

This paper deals with the computational modeling and numerical simulation of contact problems at finite deformations using the finite element method. Quasi-static and dynamic problems are considered and two particular frictional conditions, full stick friction and frictionless cases, are addressed. Lagrange multipliers and regularized formulations of the contact problem, such as penalty or augmented Lagrangian methods, are avoided and a new direct elimination method is proposed. Conserving algorithms are also introduced for the proposed formulation for dynamic contact problems. An assessment of the performance of the resulting formulation is shown in a number of selected benchmark tests and numerical examples, including both quasi-static and dynamic contact problems under full stick friction and frictionless contact conditions. Conservation of key discrete properties exhibited by the time stepping algorithm used for dynamic contact problems is also shown in an example

3D numerical models of FSW processes with non-cylindrical pin

Mar��a Jes��s Samper — Mon, 08 Apr 2019 12:59:31 +0200

Friction stir welding process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the Arbitrary Lagrangian Eulerian formulation, remeshing or the Orthogonal Sub-Grid Scale method. It is shown that these two formulations essentially deliver the same results.