Computational welding mechanics using equivalent simplified modelling

Welding is a widely used joining technique that enables the realization of many machine components, civil engineering works and pressure equipment. During the welding process, metallic materials are exposed to extreme temperature gradients, with high thermal expansion and microstructural changes in the Heat Altered Zone. These severe conditions determine distortions and residual stress in the welded zone. Residual stress can be added to those acting on the joint during the normal operation, and the total stress state can result in unforeseen stress conditions. Moreover, distortions could make it difficult to assemble components after the welding. Computational welding mechanics is a branch of engineering aimed at simulating welded joints according to analytical and numerical approaches to determine the evolution of temperature, distortions and residual stresses during and after the welding process. Currently, the most widely used approach for thermal and structural analysis of welded components, in both industry and academia, is the finite element method. In order to simulate the mechanical effects of the welding process, two distinct kinds of Finite Element Analysis are generally needed. In the first stage, a transient thermal analysis is necessary to simulate the welding torch effects and determine temperature trends over the welding process. The resulting degree of freedoms of the thermal analysis, i.e. nodal temperature, is provided in input in the second stage of simulation, that is the steady state mechanical FEA. Best Finite Element modelling is obtained when using solid elements for thermo-structural simulations. However, in detailed simulations of multi-pass welds the use of conventional 3D models is time-consuming, and can be unfeasible in large and complex welded structure. For these reasons, a new equivalent parametric model for the simulation of longitudinal multi-pass welds on plane structures, such as plates and rectangular hollow sections with a low computational burden has been introduced. The new Weld Equivalent Model (WEM) here proposed is made with single and multilayer shell, link and beam elements and utilizes thermal and structural constraint equations. Moreover, it has been realised an evolution of the WEM, called Weld Equivalent Constraint Equation Model (WECEM). This second model is realised only by shell elements thermally and structurally connected through constraint equations. The equivalent models are generated by automatic subroutines, also acting on a pre-existing FE shell model. Solid brick models of the plates are used as a benchmark for the equivalent models in thermal and mechanical simulations. Ad hoc subroutines have been created for the implementation of these simulations, too. The parametric solid brick models developed help to simulate multi-pass butt weld of shell or tubes in full detail, with no time consuming manual pre-processing operations. Thanks to the parametric models, the accurate geometry modelling and meshing in the toe and the root zone of the weld seam, permit to adequately simulate fatigue behaviour of the welded joint analysed. Welding residual stresses generally occur in the joints and can affect their fatigue life. Fatigue life assessment of some numerical case studies of welded butt-joints has been deepened using different approaches. A complete comparison between the nominal stress, the notch stress and the strain-life methods has been achieved by taking into account the welding residual stresses and the mean stress influence. The correct determination of temperature trends during the welding process simulation is essential for the subsequent mechanical FEA. In order to obtain the above-mentioned temperature trends, the calibration of the modelled heat flux source must be carried out. Generally, a large number of trial simulations must be performed in order to obtain the correct calibration. However, manual trial and error calibrations are often complex and optimum results are not always achieved. To overcome such difficulties, in this thesis it is reported a combined analytical and numerical method to automatically determine the parameters of the most used heat source model, i.e. the double-ellipsoidal heat source. The functioning of this method is based on the genetic algorithm NSGA-II. The first-attempt parameters are obtained through the solution of the Fachinotti analytical formulation. This first stage requires a restricted set of experimental data, such as weld pool extension and one temperature trend in the proximity of the seam. Afterwards, first-attempt parameters and experimental data are used to determine the final parameters by means of a set of 2D numerical thermal simulations guided through the genetic algorithm optimization. This thesis is composed of six chapters. Chapter 1 introduces computational welding mechanics with an overview of the state of the art. Chapter 2 outlines the parametric equivalent models in thermal and structural configurations. The structure of the models, the elements and the effective constraint equations used are illustrated in detail. The Weld Equivalent Model has been implemented in Ansys and in Abaqus programs through MAPDL and Python scripts, respectively, to test the real applicability of the parametric method in the two main commercial finite element software. Several numeric case studies have been reported. A modal comparison between the WEM and a 3D brick model of a plate has been achieved to prove the correct structural behaviour of the equivalent model. Thermal and structural results of both the WEM and a solid brick model have been compared in two different butt-weld plate simulations. One of these plates has been simulated through the WECEM as well, in order to obtain a complete comparison between the WEM, the WECEM and the solid model. Besides, a butt weld of a hollow square duct has been simulated with the WEM and the solid model to verify the innovative model results in a more complex simulation. Chapter 3 contains the description of the 2D/3D parametric model realised. This model permits the thermal-structural simulation implementing the moving double ellipsoidal heat source model, too. An experimental bead-on-plate welding, present in literature, has been replicated with the 3D parametric model in order to preliminary test the model and the developed moving heat source script. A complete simulation of an experimental multi-pass girth weld of a tube, reported in the literature, has allowed to validate the 3D parametric model also in the structural analysis. Chapter 4 describes the innovative semi-analytical method developed to automatically determine the geometric parameters of the double-ellipsoidal heat source. A first test of the solution part of the MATLAB code realised has been implemented directly to calculate the thermal field and to obtain the shape of the weld pool of an experimental bead-on-plate welding. The whole method has been applied in a preliminary numerical simulation and in two experimental bead-on-plate welding processes to determine the best heat source parameters. Chapter 5 introduces the three methods used in the fatigue assessment of four numerical butt-weld plates subject to zero-tension and fully reversed cycles. Nominal, notch and strain-life approaches have been investigated and compared. The Smith-Watson-Topper (SWT) equation has been used in the strain-life approach to correctly take into account welding residual stress in the fatigue assessment. Chapter 6 focuses on the experimental fatigue tests conceived in this thesis and that will be realised shortly. Hourglass-shaped test specimens have been made in order to test the fatigue life of the multipass girth welds using the rotating bending machine at the University of Rome “Tor Vergata”.