Residual stresses and distortions are major obstacles against the more widespread application of wire arc additive manufacturing. Since the steep temperature gradients due to a moving localised heat source are inevitable in this process, accurate prediction of the thermally induced residual stresses and distortions is of paramount importance. In the present study, a computationally efficient thermo-mechanical model based on a semi-analytical thermal approach incorporating Goldak heat sources is developed for the process modelling of wire arc additive manufacturing. The semi-analytical thermal model makes use of the superposition principle, and thereby decomposes the temperature field into an analytical temperature field to account for the heat sources in a semi-infinite space and a complementary temperature field to account for the boundary conditions. Since the steep temperature gradients are captured by the analytical solution, a coarse spatial discretisation can be used for the numerical solution of the complementary Tˆ field. Thermal evolution is coupled to an elasto-plastic mechanical boundary value problem that computes the thermal stresses and distortions. The accuracy of the proposed model is evaluated extensively by comparing the thermal and mechanical predictions with the corresponding experimental measurements as well as the simulation results obtained by a non-linear transient model from the literature. A thin wall structure with a length of 500 mm and consisting of 4 layers is modelled. The peak normal stress along the deposition direction can be predicted with less than 10% error. Furthermore, the simulations show that the part distortions are very sensitive to the boundary conditions.

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Selective laser melting (SLM) is a widely used additive manufacturing method for building metal parts in a layer-by-layer manner thereby imposing almost no limitations on the geometrical layout of the part. The SLM process has a crucial impact on the microstructure, strength, surface quality and even the shape of the part, all of which depend on the thermal history of material points within the part. In this paper, we present a computationally tractable thermal model for the SLM process which accounts for individual laser scanning vectors. First, a closed form solution of a line heat source is calculated to represent the laser scanning vectors in a semi-infinite space. The thermal boundary conditions are accounted for by a complimentary correction field, which is computed numerically. The total temperature field is obtained by the superposition of the two. The proposed semi-analytical model can be used to simulate manufacturing geometrically complex parts and allows spatial discretisation to be much coarser than the characteristic length scale of the process: laser spot size, except in the vicinity of boundaries. The underlying assumption of linearity of the heat equation in the proposed model is justified by comparisons with a fully non-linear model and experiments. The accuracy of the proposed boundary correction scheme is demonstrated by a dedicated numerical example on a simple cubic part. The influence of the part design and scanning strategy on the temperature transients are subsequently analysed on a geometrically complex part. The results show that overhanging features of a part obstruct the heat flow towards the base-plate thereby creating local overheating which in turn decrease local cooling rate. Finally, a real SLM process for a part with an overhanging feature is modelled for validation of the proposed model. Reasonable agreement between the model predictions and the experimentally measured values can be observed.@en

Selective laser melting (SLM) wherein a metal part is built in a layer-by-layer manner in a powder bed is a promising and versatile way for manufacturing components with complex geometry. However, components built by SLM suffer from substantial deformation of the part and residual stresses. Residual stresses arise due to temperature gradients inherent to the process and the accompanying deformation. It is well known that the SLM process parameters and the laser scanning strategy have a substantial effect on the temperature transients of the part and henceforth on the degree of deformations and residual stresses. In order to provide a tool to investigate this relation, a semi-analytical thermal model of the SLM process is presented which determines the temperature evolution in a 3D part by way of representing the moving laser spot with a finite number of point heat sources. The solution of the thermal problem is constructed from the superposition of analytical solutions for point sources which are known in semi-infinite space and complimentary numerical/analytical fields to impose the boundary conditions. The unique property of the formulation is that numerical discretisation of the problem domain is decoupled from the steep gradients in the temperature field associated with localised laser heat input. This enables accurate and numerically tractable simulation of the process. The predictions of this semi-analytical model are validated by experiments and the exact solution known for a simple thermal problem. Simulations for building a complete layer using two different scanning patterns and subsequently building of multiple layers with constant and rotating scanning patterns in successive layers are performed. The computational efficiency of the semi-analytical tool is assessed which demonstrates its potential to gain physical insight in the full SLM process with acceptable computational costs.

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Selective laser melting (SLM) is a powder based additive manufacturing technique suitable for producing high precision metal parts. However, distortions and residual stresses within products arise during SLM because of the high temperature gradients created by the laser heating. Residual stresses limit the load resistance of the product and may even lead to fracture during the built process. It is therefore of paramount importance to predict the level of part distortion and residual stress as a function of SLM process parameters which requires a reliable thermal modelling of the SLM process. Consequently, a key question arises which is how to describe the laser source appropriately. Reasonable simplification of the laser representation is crucial for the computational efficiency of the thermal model of the SLM process. In this paper, first a semi-analytical thermal modelling approach is described. Subsequently, the laser heating is modelled using point, surface and volumetric sources, in order to compare the influence of different laser source geometries on the thermal history prediction of the thermal model. The present work provides guidelines on appropriate representation of the laser source in the thermal modelling of the SLM process.

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The Selective laser melting (SLM) is a powder based additive manufacturing (AM) method to produce high density metal parts with complex topology. However, part distortions and accompanying residual stresses deteriorates the mechanical reliability of SLM products. Modelling of the SLM process is anticipated to be instrumental for understanding and predicting the development of residual stress field during the build process. However, SLM process modelling requires determination of the heat transients within the part being built which is coupled to a mechanical boundary value problem to calculate displacement and residual stress fields. Thermal models associated with SLM are typically complex and computationally demanding. In this paper, we present a simple semi-analytical thermal-mechanical model, developed for SLM that represents the effect of laser scanning vectors with line heat sources. The temperature field within the part being build is attained by superposition of temperature field associated with line heat sources in a semi-infinite medium and a complimentary temperature field which accounts for the actual boundary conditions. An analytical solution of a line heat source in a semi-infinite medium is first described followed by the numerical procedure used for finding the complimentary temperature field. This analytical description of the line heat sources is able to capture the steep temperature gradients in the vicinity of the laser spot which is typically tens of micrometers. In turn, semi-analytical thermal model allows for having a relatively coarse discretisation of the complimentary temperature field. The temperature history determined is used to calculate the thermal strain induced on the SLM part. Finally, a mechanical model governed by elastic-plastic constitutive rule having isotropic hardening is used to predict the residual stresses.

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Additive Manufacturing (AM) enables fabrication of geometrically complex designs and hence offers increased freedom for designers. It has been recognized that topology optimization can serve as an ideal design tool in order to fully exploit the advantages offered by AM. However, AM processes have specific limitations which should be taken into account at the design optimization stage in order to minimize manual design adaptations and post processing cost. One such major constraint is local overheating during processing. It is evident that excessive local heating can cause defects such as melt ball formation which subsequently leads to poor surface finish and undesired mechanical properties. This paper presents a simplified thermal model inspired by the physics of additive processes and detects zones of local heat concentration i.e. `hotspots' in a geometry. Although the model emulates the boundary conditions of an AM layer and predicts the temperature field, it is not a detailed process simulation. Instead, a dedicated computationally inexpensive thermal analysis has been preferred here as it proves to be able to identify regions which are prone to overheating. The model is thus referred to as ‘hotspot detector’. A mathematical formulation is developed in order to integrate the ‘hotspot detector’ model with the density based topology optimization using adjoint sensitivity calculation method. The new method is tested and demonstrated on several numerical examples.@en