Coupled heat conduction and multiphase change problem accounting for thermal contact resistance

2020

Additive Manufacturing

Self Cite

In this contribution, a simplified macroscopic and semi-analytical thermal analysis of directed energy deposition (DED) is presented to obtain computationally efficient simulations of the entire process. Solidification and solid-state phase transitions are taken into account. The model is derived for laser metal powder directed energy deposition, although it can be simply adapted for other focused thermal energy (e.g., electron beam, or plasma arc). The gas flow used for carrying the powder significantly influences cooling conditions, which is included in the model. The proposed simulation strategy applies to multilayer composites with a wide range of shapes in the horizontal plane and arbitrary laser scanning strategies (continuous way, back and forth, etc.). The proposed work provides a simple tool to study the influence of most process parameters, design in-situ experiments and in turn develop optimization loops to reach material requirements and specific microstructures. In-situ pyrometer measurements have been compared to the model, and good agreement has been observed with 2.6% error in average. The model is used to demonstrate the effect of various process parameters for a simple cylindrical geometry and a more complex auxetic cell.

Section: Introductionsupporting

confidence: 70%

Fast simulation of temperature and phase transitions in directed energy deposition additive manufacturing

2020

Additive Manufacturing

Self Cite

“…Material parameters are listed in table 1 and the eigenstrain is given in the form of (90). This analytical form is rather arbitrary even though the quadratic evolution along the radial direction schematically corresponds to the eigenstrain analyzed in Weisz-Patrault (2017a, 2018. All tested conditions are listed in table 2.…”

Section: Resultsmentioning

confidence: 99%

Mixed analytic/energetic approach for a sliding orthotropic hollow cylinder. Application to coil sagging

International Journal of Solids and Structures

Gantier

Ehrlacher

2019

Self Cite

This paper deals with the numerical simulation of coil sagging. This problem arises within the framework of the steel making industry where strips are wound on themselves for storage. Coil sagging is a major defect that can occur for recent grades undergoing phase transitions during the coiling process. The detailed mechanisms leading to coil sagging are still not well understood, making this phenomenon very difficult to prevent. The coil is a multilayer hollow cylinder where sliding takes place at each interface and significantly contributes to the overall deformation. However, a detailed numerical simulation addressing the contact problem, considering both pressure and sliding is difficult to perform under non-axisymmetric conditions. This paper presents a simplified approach considering an orthotropic hollow cylinder instead of a multilayer coil. The anisotropy is due to contact roughness that tends to decrease the radial stiffness. The hollow cylinder is subjected to gravity and an eigenstrain representing thermal expansion, phase transitions and transformation induced plasticity. Sliding at each interface is taken into account through a continuous plastic-like shear strain that is determined through an energetic principle. The proposed solution relies on analytical developments so that computation time is compatible with parametric studies. Results are addressed in order to give a better understanding of mechanisms and conditions under which coil sagging occur.

“…There is a longbow defect at both ends of the strip. Of course, the strip cooling continues during the coiling process and the residual stresses evolve as studied in [6][7][8]. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Numerical results show that homogenous cooling conditions along the strip width tend to decrease significantly the initial residual stress profile, but cooling one surface faster than the other creates an asymmetry that is responsible for bending moments.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, numerical simulations are needed to understand and quantify all mechanisms involved in the different processes. Thus, significant efforts have been made for the simulation of the rolling process [1,2], the run out table [3][4][5] and the coiling process [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Residual stress on the run out table accounting for multiphase transitions and transformation induced plasticity

Applied Mathematical Modelling

Koedinger

2018

Self Cite

The development of harder and thinner new steel grades necessitates reasonably fast numerical simulations of forming processes in order to optimize industrial conditions through parametric studies. This paper focuses on the evolution of residual stresses of thin strips during cooling on the run out table. Since the problem involves multiphysics and non-linear processes, comprehensive and fully coupled numerical approaches may be difficult to use to design or optimize industrial conditions because of extensive computation times. Therefore, a simplified numerical simulation has been developed and consists in solving first the thermal problem coupled with multiphase transitions and then the mechanical problem accounting for thermal expansion, metallurgical deformation and transformation induced plasticity. Residual stress profiles through the strip thickness are also computed in order to evaluate classic flatness defects such as crossbow and longbow. A postprocessing is also included in order to quantify out of plane displacements that would take place if the strip were cut off the production line. It consists in computing at finite strain the relaxation of residual stresses when the tension applied by the coiler is released. The proposed numerical strategy has been tested on common industrial conditions. Highlights• Numerical strategy to simulate a non-linear and multiphysics problem: the cooling of a steel strip on the run out table.• Heat conduction strongly coupled with metallurgical transformations and an elastic-plastic calculation of residual stress evolution.• Thermal expansion, density mismatch between phases and transformation induced plasticity modeled as eigenstrain.• Significant decrease of the initial residual stress profile, but the asymmetry is responsible for bending moments• Flatness defects such as longbow and crossbow are detected.Preprint submitted to Applied Mathematical Modelling September 3, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Residual stress on the run out *Highlights AbstractThe development of harder and thinner new steel grades necessitates reasonably fast numerical simulations of forming processes in order to optimize industrial conditions through parametric studies. This paper focuses on the evolution of residual stresses of thin strips during cooling on the run out table. Since the problem involves multiphysics and non-linear processes, comprehensive and fully coupled numerical approaches may be difficult to use to design or optimize industrial conditions because of extensive computation times. Therefore, a simplified numerical simulation has been developed and consists in solving first the thermal problem coupled with multiphase transitions and then the mechanical problem accounting for thermal expansion, metallurgical deformation and transformation induced ...