Metal additive manufacturing is the most rapidly developing branch of additive manufacturing technology, which has been widely used in aerospace, energy and power and other fields, and the development of related numerical simulation technology is of great academic and engineering significance for in-depth understanding of its complex physical processes and optimization of process parameters.
Different from the traditional material processing methods of subtractive manufacturing (cutting, grinding, etc.) and equal material manufacturing (casting, forging, etc.), metal additive manufacturing is based on three-dimensional computer-aided design (CAD) data, and the discrete materials (powder, wire, etc.) are accumulated layer by layer to manufacture physical components through light sources or high-energy heat sources, which is a "free manufacturing" process of bottom-up superposition of material forming, which is expected to become a key technical way to realize the cross-generational improvement of high-end industrial equipment structures such as aero engines.
In this issueValley. ColumnThe article "Development of Numerical Simulation Technology for Metal Additive Manufacturing" published in the journal Aviation Power, Issue 4, 2023 will be shared.
Overview of metal additive manufacturing**
According to the material feed mode, metal additive manufacturing technology can be mainly divided into two categories: powder bed fusion (PBF) and directed energy deposition (DED), the former including laser selective melting technology and electron beam selective melting technology, etc., and the latter includes laser powder feeding additive manufacturing technology, electron beam wire feeding additive manufacturing technology and arc wire feeding additive manufacturing technology (see Figure 1). However, at this stage, metal additive manufacturing technology still has deficiencies in the forming accuracy and mechanical properties of components, which has become a bottleneck restricting its wide industrial application. The main reason is that metal additive manufacturing involves the melting of materials, the flow and solidification of the molten pool, the formation of microstructure and the evolution of internal stress and strain, etc., which is a very complex multi-scale and multi-physics coupling process, and the basic problems such as metallurgical defect formation mechanism, microstructure evolution law, part warping deformation and cracking, surface quality and forming dimensional accuracy control have not been fully broken through. Relying solely on experimental testing technology to carry out micro-scale observation in the process of additive manufacturing, there are shortcomings such as poor stability, poor repeatability, limited resolution and observable area, and at the same time, due to the huge number of parameters involved in the process, the optimal process parameter window of the "trial-and-error method" has the shortcomings of low efficiency, long cycle and high cost.
Fig.1 Technical principle of metal additive manufacturing.
In recent years, the development of numerical simulation technology has provided a powerful tool for the in-depth understanding of the complex physical processes and the optimization of process conditions for metal additive manufacturing. The numerical simulation technology of metal additive manufacturing is mainly divided into two categories: micro-scale simulation and macro-scale simulation, the former aims to reveal the formation mechanism of metal additive manufacturing defects and the evolution law of microstructure, and the related research work is concentrated in universitiesThe latter focuses on the residual stress and warpage deformation of metal additive manufacturing parts, which has been integrated by a number of commercial additive manufacturing simulation software, which can effectively improve the first-time printing success rate of engineering parts.
Microscale simulation
Essentially, metal additive manufacturing is the process in which raw materials are sequentially converted from solid (powder, wire) to liquid (molten pool) and then to solid (parts) under the action of a moving heat source, in a predetermined layer-by-layer scanning sequence. The microscopic scale of the above process by using high-fidelity numerical simulation method is the key means to reveal the formation mechanism of metal additive manufacturing defects and optimize the process parameters. According to the different focus of the physical problems studied, the microscale simulation methods of metal additive manufacturing can be roughly divided into three categories: heat-flow coupling, heat-structure interaction, and heat-fluid-structure interaction, as shown in Figure 2.
Fig.2 Schematic diagram of three microscale simulation methods.
l Thermal-fluid coupling
The thermal-flow coupling simulation method focuses on the flow and heat transfer process of molten metal in the molten pool, and usually uses the finite volume method, the arbitrary Lagrangian-Euler method and the lattice Boltzmann method to solve the problem, regardless of the solid mechanics problems involved. This method is mainly used to study the formation mechanism of metallurgical defects in the forming process, and can be used as the input of microstructure numerical simulation algorithms (such as phase field method, etc.) to realize the remelting of microstructure in the process of material melting and the nucleation and growth of grains in the process of solidification.
lThermal-solid interaction.
The thermal-solid interaction simulation method focuses on the temperature distribution of the cladding deposited material and substrate and the deformation process of internal stress related to temperature change during the forming process, and usually uses the finite element method to solve the problem without considering the flow and convective heat transfer in the molten pool. Combined with appropriate simplification, this method can be applied to the simulation of large and complex parts at the macro scale.
lThermal-fluid-structure interaction.
The thermal-fluid-structure interaction method simulates the thermal melting, flowing, and solidification of raw materials, as well as the interaction between raw materials and molten pools and substrate materials under the same description framework.
Macro-scale simulations
Metal additive manufacturing is to melt and solidify raw materials such as powders and wires into preset part shapes layer by layer with the assistance of heat sources such as laser, electron beam and arc, which is accompanied by cyclical, intense and unstable heating and cooling, and it is easy to generate complex thermal stress fields and thermal load processes in the parts. Similar to the welding process, this will create huge residual stresses within the part, causing the part to crack or warp and deform, resulting in part manufacturing failure. Due to the extreme complexity of modeling and the high computational cost, the above-mentioned micro-scale numerical simulation methods can only solve the problem of finite passes and finite layer scales, and cannot carry out the analysis of larger-scale additive manufacturing processes. In order to realize part-level simulation, it is necessary to rationally simplify the problem from the aspects of equivalent and layer-by-layer efficient discretization of part deposition process and solution of material mechanical behavior.
lThe deposition process is equivalent.
At present, the numerical simulation of metal additively manufactured parts is based on the finite element method, and the "life and death unit" setting is used to realize the layer-by-layer printing process. Due to the large number of deposition layers involved in the part, it is difficult to perform detailed thermal-mechanical coupling simulations for each deposition layer (about a few tens of microns in height). By introducing the concept of "super layer", it is an effective way to solve the above problem by equating multiple adjacent deposited layers with similar temperature history into one layer, and activating each "super layer" in the printing order from bottom to top during the simulation process, so as to avoid explicitly describing the specific scanning process of each deposited layer. This method has been widely used in a variety of commercial additive manufacturing** software.
It should be noted that the heat source scanning method in the process of metal additive manufacturing is the key factor that causes the anisotropy of the mechanical properties of the material (such as elastic modulus, yield strength, etc.) of the part.
lEfficient discretization layer by layer.
When using the "life and death cell" to simulate the layer-by-layer printing process of metal additively manufactured parts, the 3D model of the part needs to be evenly sliced in the printing direction (each layer is a "super layer") and the finite element discretization is performed layer by layer. However, the existing finite element meshing strategy is only applicable to parts with simple regular shapes, and for parts with complex profiles (such as aero engine turbine blades), when slicing in layers, the horizontal section cuts the blade edge plate and the blade root arc transition, which inevitably forms a large number of geometric features such as small angles (close to 0°) and small thickness (close to 0mm), resulting in the degradation of the quality of the finite element mesh and even the failure of meshing, as shown in Fig. 3(a).
Fig.3 Layer-by-layer efficient discrete approach.
The voxel-based finite element meshing method provides an effective means for the layer-by-layer discretization of complex parts in metal additive manufacturing. A voxel is an extension of a pixel in three-dimensional space, and its shape is a fixed-size square, which is the smallest unit representing a three-dimensional object. Based on this concept, a 3D geometry that was originally described by patch or volume information can be converted into a model described by voxel information (i.e., voxelized), and then each voxel can be converted into finite element hexahedral elements. Since all voxels have the same size, each layer of voxels can be used directly as a "super layer". As shown in Fig. 3(b), the smaller the voxel size, the higher the degree of conformity between the discrete finite element model and the actual geometric model, and the greater the corresponding computational cost.
lMechanical behavior solving.
The accurate solution of the mechanical behavior of each layer of materials in the process of metal additive manufacturing is the key link of residual stress and warping deformation of the first part, and the premise is to understand the mechanism of residual stress, and then use the thermal-mechanical coupling method or inherent strain method to solve the problem.
Thermal-mechanical coupling method At present, it is generally believed that the residual stress in metal additive manufacturing parts is mainly in three aspects, as shown in Figure 4. One is the temperature gradient, in the heating process, the solid material at the boundary of the molten pool is heated and expands outward, and due to the existence of the temperature gradient, the above-mentioned expansion is limited by the surrounding lower temperature material, so that compressive stress is generated in the high-temperature solid material at the boundary of the molten pool, with the movement of the heat source, the previously formed molten pool is rapidly cooled and solidified, and the molten pool material shrinks and is limited by the surrounding material, resulting in tensile stress. The second is cooling shrinkage, the most important feature of metal additive manufacturing is layer-by-layer deposition, the post-deposited layer shrinks during the cooling process and is constrained by the previous deposited layer, which leads to tensile stress in the post-deposited layer and additional compressive stress in the previous deposited layer, that is, for the parts deposited layer by layer, the internal is residual compressive stress, and the outer surface is tensile stress. The third is the solid-state phase transformation, in which some metal materials will undergo solid-state phase transformation during the cooling process, resulting in additional strain, which will loosen the residual stress in the deposited parts and even reverse the phenomenon. For metal additive manufacturing, the cyclic heating-cooling (heat) of each layer of material and the deformation constraints (forces) between each layer are the most important factors affecting the residual stresses, so the layer-by-layer thermal-mechanical coupling simulation of the part is the most direct way to solve the mechanical behavior of the material. The method is now integrated into commercial additive manufacturing** software, and its basic process is as follows: first, based on the "super layer" and voxelized sub-network technology, the finite element mesh model of the part is establishedThen, the "life and death unit" technology was used to activate the "super layer" layer by layer according to the printing order, and the transient thermal analysis was carried out at the same time to obtain the temperature distribution of each layer and its evolution in the manufacturing processFinally, the temperature of each layer is used as the input, combined with the high-precision thermoelastoplastic constitutive relationship of the material (if necessary, the solid phase transformation effect should also be considered), and the deformation and stress of the part during the layer-by-layer printing process are calculated. This method assumes that the thermal gradient in the printing direction has a much greater effect on the deformation of the part than the thermal gradient in the direction within each layer, so the "super layer" can be activated as a whole (assuming the initial temperature is the melting point) without considering the scanning movement of the heat source within each layer during the simulation. To simplify the calculation process, for powder bed fusion additive manufacturing, the thermal boundary conditions between the printed part and the surrounding powder are simplified to equivalent convective heat transfer coefficients, thus avoiding the need to model the powder.
Fig.4. Mechanism of formation of residual stress in metal additive manufacturing.
lIntrinsic strain method.
The intrinsic strain method was first proposed by the Japanese scholar Ueda (UEDA) and is widely used in the torsion and residual stress of large welded structures**. Due to the ability to quickly realize residual strain and twist deformation of large and complex parts**, intrinsic strain is now the mainstream method for part-level additive manufacturing simulation and has been integrated into a variety of commercial additive manufacturing simulation software. There are two main methods to obtain intrinsic strain in metal additive manufacturing simulation: microscale simulation and standard part deformation calibration. The steps of the microscale simulation are to establish a high-resolution microscale thermal-mechanical coupling model based on the actual additive manufacturing process conditions, and to solve the elastoplasticityThen, according to the microscale simulation results, the intrinsic strain tensor was extracted based on different strategiesFinally, the extracted intrinsic strain tensor is used as the initial strain and applied layer by layer to the finite element model of macro-scale parts, and the residual stress and twisting deformation are **. It is important to note that metal additive manufacturing, although still welded in nature, affects the deformation and stress distribution of the post-deposited layer due to its layer-by-layer printing physical characteristics, and likewise the shrinkage of the post-deposited layer is limited due to the constraints of the previous deposited layer. The interaction between the layers makes the internal stress-strain variation of the part more complex, and there are large errors in the residual stress and twisting deformation of the additively manufactured parts directly according to the original intrinsic strain theory. To solve this problem, Liang Xuan of the University of Pittsburgh proposed a modified intrinsic strain method suitable for additive manufacturing, which introduces the cumulative contribution of the evolution of elastic strain caused by the shrinkage of the post-sediment layer during cooling to the intrinsic strain. The deformation calibration of standard parts is to use the specified process parameters, print the standard parts (generally select cantilever beams with toothed supports), test the twisted deformation of the standard parts after removing the substrate, compare with the numerical simulation results based on the assumed intrinsic strain, and iteratively optimize the intrinsic strain tensor with the goal that the twist deformation error is lower than the threshold value, as shown in Figure 5.
Fig.5. The intrinsic strain is determined based on the deformation calibration of the cantilever beam.
Wrapping up
Numerical simulation is an important means to understand the complex physical process of metal additive manufacturing and realize the optimal process conditions, which can be roughly divided into two categories: micro-scale simulation and macro-scale simulation. The microscale simulation method focuses on simulating the melting-solidification process of materials under the action of moving heat sources, aiming to reveal the formation mechanism and microstructure evolution law of metal additive manufacturing defectsThe macro-scale simulation method focuses on simulating the residual stress and warpage deformation of metal additive manufacturing parts, simplifies the deposition process by using the "super layer" technology, realizes the efficient discretization of the model layer by layer by voxel finite element method, and solves the mechanical behavior of materials through the unidirectional thermal-mechanical coupling algorithm or the intrinsic strain method, especially the intrinsic strain method, which has been integrated by a number of commercial additive manufacturing simulation software because it can quickly realize the residual strain and twist deformation of large and complex parts.
In the early stage, the China Aero Engine Research Institute has carried out the development of three-dimensional numerical software for aero engines, including aerodynamics, heat transfer, combustion and strength, among which the strength analysis module has the basic functions of finite element pre- and post-processing, solving, etc.
In view of the complexity of the problems involved in metal additive manufacturing and the urgency of the demand, the authors believe that the research and development of metal additive manufacturing modules should be carried out in the order of macro first and then micro. In the first stage, priority is given to the development of additive manufacturing numerical modules for parts (such as blades, discs, blisk blade rings and combustion chambers, etc.), which are mainly used for the warping deformation and cracking of large-scale additive manufacturing parts, surface quality and forming dimensional accuracy control, etc., to improve the success rate of one-time printing, it is necessary to add functions such as "life and death unit", voxel-based finite element meshing, intrinsic strain optimization algorithm, and additive manufacturing template on the basis of the existing finite element strength analysis module. In the second stage, the multi-field coupling simulation of metal additive manufacturing oriented to the micro scale is mainly used to analyze the formation mechanism of metallurgical defects, the evolution law of microstructure, etc., optimize the process parameters, and provide support for the improvement of the accuracy of the part-level simulation in the first stage.
This article was originally published in Aviation Power, Issue 4, 2023.
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