### Computational Welding Mechanics: Thermomechanical and Microstructural Simulations

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The test bench setup for the homogeneous base material models can be seen in Fig. Welding distortions and temperature curves are measured via displacement transducers and thermocouples. In case of the Al-Cu overlap joints, welding distortions are determined optically, based on stochastically distributed grey value patterns on the topside of the specimens Fig. Test bench setup for the validation ofthe base material models; a experimental setup ofe.

Cu-ETP base material welding experiments; b schematic illustration; support ofsheet metal specimens for base materials. Test bench setup for Al-Cu overlap joints; a positions ofthermocouple measurement; b applied stochastically distributed pattern for optical measurement ofwelding distortions; c scheme: position ofthermocouple for Al-Cu overlap joint configuration. Different weld seam lengths are produced, having a total length from 15mm to 60mm at different focal diameters df.

A summary of the experimental welding parameters for the base materials and overlap joints is shown in Tab. Table 1. Summary ofwelding parameters for welding experiments ofA To predict residual stresses and welding distortions accurately, information about the temperature field distribution within the heat affected zone is crucial.

For structural analysis sequentially coupled thermo-mechanical Finite Element analyzes are performed. The exact physical modeling of the welding process is still a challenging task due to highly nonlinear couplings of different physical domains, thus the complex fluid dynamic processes are often simplified by a heat conduction problem Eq. Heat sources are used to model the heat input for laser beam welding.

Defined in Eq. These models are superimposed multiple times for the temperature field analysis of the Al-Cu overlap joints Fig 3. Heat source models; a double ellipsoidal and conical heat source model in accordance to Goldak [3, 4] applied for temperature field reconstruction; b heat source model combination for base materials e.

For the mechanical analysis the governing equation is given by the momentum balance. Neglecting intertia forces, this leads to the formulation in Eq. The constitutive equation incorporates an incrementally formulated isotropic elasto-plastic material model. The total incremental strain consists of an elastic, plastic and thermal part Eq. Effects of thermal dilation are included into the constitutive equation Eq. Using von Mises J plasticity Eq. With ctf being the temperature dependent yield strength, 5 and d. Within the framework of FEM the weak formulation of the governing equations is used.

For detailed derivations of corresponding equations, it shall be refered to Cardona [2] or to literature, Bathe [1], Lindgren [6] and Radaj [9]. Hardness measurements Fig. To model the material's softening a methodology similar to Ossenbrink [8] is applied, i. The material data has been determined experimentally by means of a Gleeble testing machine for characteristic laser welding heating and cooling rates.

Softening of base materials A For thermal simulation thermo-physical material data is implemented into the numerical model. The FE models contain temperature dependent material properties for thermal conductivity, heat capacity and latent heat. A constant convective heat transfer coefficient is assumed for the outer surfaces while cooling. The thermo-physical material data of the Al-Cu overlap joint are derived, based on micrographs, i.

The resulting thermal conductivity values are obtained via linear interpolation between the base material data values. Both welding parameters in Tab.

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Additionally, thermal and mechanical contact formulation is applied for the numerical modeling of Al-Cu overlap joint gap or penetration behavior. The temperature field is reconstructed via heat source models, see Fig. The boundary conditions are defined equivalent to the experimental fixations. The FE models include transducer positions TP as well as checkpoints P to compare measured and numerically determined welding distortions at discrete points.

Finite-Element models for welding simulation, i. In this work a phenomenologicalmaterial modeling approach on macro scale is chosen to simulate the mechanical response of the dissimilar material connections in overlap joint. The formation of brittle intermetallic phases is at first neglected and therefore not included.

The goal of the study is to compute welding distortions mainly and finally to compare them to welding experiments.

### Acknowledgement

A generic material model approach is selected for the Al-Cu weld seam section, based on the approach of Johnson-Cook Eq. Here A, B, C, n and m are phenomenological material parameters. Tmeit and Ttrans are the melting and the transition temperature. The parameter values of the Johnson Cook model are determined inversely via a parameter identification process Fig. The Johnson-Cook parameters represent the weld seam section's material properties for the cooled down state after welding.

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Shear tests of the overlap joints form the experimental database for the parameter identification. The Johnson-Cook parameters are calibrated to the ascending force-displacement curves Fig. The parameter identification neglects the residual stresses caused by welding. The applicablitiy of the methodology is verified numerically by additional 2D Al-Al overlap joint shear test simulations. Here the thermo-mechanical simulation has been performed prior to the shear test simulation, thus taking into account residual stress state.

The resulting curves Fig. The comparison in Fig. It can be concluded that residual stresses have minor influence, whereas neglecting damage modeling can explain why higher deviations to the experimental results occur. Heat source models are calibrated, using micrographs of the base materials weld seam cross section area and additional thermocouple measurements Fig.

For A Heat source model calibration on the example ofA On basis of the temperature field results, welding distortions are computed in a subsequent mechanical analysis. The stress-strain data according to Fig. Comparison oftransducer displacements and FE results for A Besides experimental validation by means of welding distortions, additional measurements of residual stresses and textures are performed. The world is heavily dependent on reliable weld joints, including in ships, power plants, building, bridges, cars, etc.

The CWM-platform developed, with its integrated hardware, software, and methodologies, models consistent and representative weld induced stress and strain fields in welded components and structures. The methodologies developed cohere to continuums mechanics, the finite element method, and constitutive material modelling, and make use of realistic weld heat flux, thermo-mechanical boundary conditions, and base and weld material data extracted from a specific welding procedure qualification record.

This all for the purpose of ensuring consistent, conservative, and realistic finite element simulation results. Where seaworthiness and FFS assessment methods constitutes fundamental knowledge in the field of maritime science e. The CWM-platform is defined as the systems-engineering [3] solution that successfully integrates hardware, software, and methodology to be used for thermo-mechanical Finite Element weld simulations.

## GEONX | Software

Arc weld processes [4] are characterised by transient thermal behaviour, leading to rapid changes in material properties and a dynamic interaction between weld and base material. The complexity of this expansion and contraction process is described in [5]. Finite element analyses FEA of arc weld processes present quasi-dynamic, multi-physical problems that should be simulated through the use of a powerful platform. Therefore, the platform presented here has been under continuous development and improvement since [6], with an emphasis on the use of realistic material and weld process data [7 â€” 8].

The accumulated thermal and mechanical influences from the first weld pass to the final run are brought forward in one and the same meshed geometrical model. Described first are the hardware and software configuration of the platform, as well as the material used in the model.

The final section presents the boundary conditions used. The core speed is up to 2. In this case, simulation results are written to that disk and the remaining four GB hard drives are used for project storage and post- processing of simulation results. The non-linear finite element analysis methodologies used by the code, such as the Lagrangian-, the Eularian- and the arbitrary Lagrangian-Eulerian formulations, are extensively described in [13]. The theoretical foundations of the inelastic material modelling, with its numerical formulation and implementation, are described in [14].

The mathematical modelling of macroscopic volume elements behaviour, and the physics underlying these phenomena are presented in [15 - 16].

This assumes that, first, the entire transient thermal simulation has been solved, and second, the transient mechanical simulation has been solved using the temperature field solution obtained from the thermal simulation, see Figure 1. Figure 1 Schematic description of a sequentially coupled thermo-mechanical FE- weld simulation [24] In the platform presented here, a thermo-mechanical staggered coupled method is used.

This implies that the transient thermal and mechanical simulations are solved in parallel with each other and the two FEA-processes provide essential input data to each other. Typically, three thermal time steps will be calculated between each mechanical time step, see Figure 2. The first version of the model was presented in [32].

The current production version of the material models are found in [33 â€” 34]. A general description of its prerequisites and use is given in [35].

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## Computational Welding Mechanics

Both the thermal and mechanical material models are designed to model the base and weld material and simulate the intricate combination of the thermal, elastic, and plastic strains on the plastic strain hardening and the formation of residual stress fields. The plastic strain hardening and the residual stress are released as a function of the residual stress release temperature.

Also described by the material models is the weld material that will be activated in the later sequence of a multi-pass weld simulation, or the so- called quiet material. The strain hardening is defined by the use of yield surfaces. Two different types of hardening models isotropic and kinematic and the effect of those on the yield surfaces are described in Figure 3; the effect is further elaborated in [36 â€” 38]. A detailed description of the equations that govern the material model is given in [34].

The weld material is present from the very first simulation sequence and is gradually activated during the time it takes for the thermal energy to heat up the weld material between its solidus- TS and liquidus temperatures TL.