Directed energy deposition (DED) is a class of additive manufacturing (AM) processes using a moving focused heat source to melt feed-stock material simultaneously deposited by a moving nozzle. Both single and multi-track scanning strategies can be performed to build multilayer thin-walled structures and massive parts alike. Process parameters have a significant influence on microstructure [1] and residual stresses [2], which mainly depend on temperature history.

However, although fast numerical approaches have been developed for thermal analysis and phase transitions [3,4], efficient computation of residual stresses remains challenging. Indeed, 3D/2D finite elements method (FEM) involves meshing along the layer thickness and/or height, which implies a very fine discretization along the print direction as the elements should not be too elongated to avoid conditioning issues [5].

To avoid such a fine mesh density, an enriched 1D model immersed in the 3D space named QuadWire is proposed. Reducing dimension (e.g., from 3D to 2D/1D) and increasing the number of degrees of freedom (DOF) enables significantly shorter computation time while still capturing complex stress fields in the part and ensuring good accuracy [6].

In the proposed model, layer thickness and layer height are internal parameters independent of mesh size, which in turn can be coarser along print direction. At each material point, 4 displacement vectors are introduced leading to 12 DOFs. Thus, kinematic conditions between a bead and its 4 neighbors (i.e., right, left, top and bottom) may be simply written. The model derivation through the virtual work principle will be broached, and a linear thermo-elastic behavior will be derived.

This contribution focuses on a FE implementation of this extended 1D model, and several analytic calculations of multilayer structures representing both single and multi-track scanning strategies will be derived and used as exact references for validation and convergence analysis. In addition, material parameters will be identified to match 3D computations on various test cases.

This extended 1D approach enables numerical optimization of process parameters [7] to control residual stress.

References

[1] M. Manjaiah, J. Y. Hascoët, and M. Rauch; Materials Science and Engineering, 2020, 259, 114583.

[2] E. R. Denlinger, J. C. Heigel, P. Michaleris, and T. A. Palmer; Journal of Materials Processing Technology, 2015, 215, 123-131.

[3] D. Weisz-Patrault; Additive Manufacturing, 2020, 31, 100990.

[4] A. Edwards, D. Weisz-Patrault, and E. Charkaluk. Additive Manufacturing 2023, 61, 103300.

[5] D. Weisz-Patrault, P. Margerit, and A. Constantinescu, Additive Manufacturing, 2022, 56, 102903.

[6] J. F. Caron, A. Diaz Diaz, R. P. Carreira, A. Chabot, and A. Ehrlacher, Composites Science and Technology, 2006, 66, 755-765.

[7] M. Boissier, G. Allaire, and C. Tournier, Structural and Multidisciplinary Optimization, 2020, 61, 2437-2466.