Study Of Efficient Numerical Methods For Coupled Thermal-mechanical Process Of Additive Manufacturing

Additive manufacturing(AM)is an advanced rapid prototyping technology,which has the advantages of flexible material selection,short production cycle and high material utilization.Additive manufacturing technology of metal materials can take into account the forming requirements of complex structure and high-performance components,and has been widely used in aerospace,medical,automobile and other fields,filling the gap of traditional manufacturing technology.However,the metal components undergo rapid heating cycles due to the scanning of the high-energy beam for a long time in additive manufacturing process,the resulting local thermal stress can easily induce severe distortion and even cracking of the components.Therefore,developing highly efficient and accurate numerical methods for this problem is of great significance to optimize the manufacturing parameters and to improve the quality of the manufactured components.So far the finite element method(FEM)is the main numerical tool to simulate the coupled thermal-mechanical process of additive manufacturing.It can quickly reproduce the evolution of temperature and stress fields of metal components in the manufacturing process,and has been applied in various researches of the additive manufacturing technology.However,there is still a lot of room for improvement in the computational efficiency and accuracy of the finite element analysis of AM.On one hand,large variation in temperature exists in AM and the thermophysical parameters such as heat conductivity change dramatically in AM process.Hence,heat transfer in AM is typically nonlinear.The commonly used traditional predictioncorrection method in dealing with this nonlinear problem requires excessive number of iteration steps and thus is computationally inefficient.On the other hand,due to the heating of the moving high-energy beam,the spatial gradient of the temperature field is high and the conventional(linear)FEM cannot capture such high gradients accurately.This may not only lead to inaccurate results in temperature,but also produce large errors in the results of distortion.In this thesis,the coupled thermal-mechanical process of additive manufacturing of metal materials is studied,and the purpose is to develop efficient numerical methods for such manufacturing process.Aiming at the problem of insufficient accuracy and efficiency of coupled thermal-mechanical simulation of AM,a tangent stiffness algorithm for heat transfer in AM process is proposed.The consistent Element-free Galerkin method(EFG)and the generalized finite element method(GFEM)using second order approximation are introduced into this field.An adaptive coarsening algorithm is established according to the layer-by-layer deposition process and the simulation of additive manufacturing process of complex components is realized with improved accuracy and efficiency.The influence of manufacturing parameters such as scanning strategy and preheating temperature on forming quality are analyzed in-depth.The work of this thesis is summarized as follows:First,the tangent stiffness algorithm for nonlinear heat transfer process of additive manufacturing is proposed.The thermophysical parameters of metal vary dramatically in additive manufacturing process,which introduces high nonlinearity.However,the conventional prediction-correction iterative algorithm used in heat transfer analysis of additive manufacturing is directly generalized from the linear heat transfer algorithm,which ignores the thermal conductivity gradient term in the stiffness.It leads to a large number of iterative steps,terrible convergence and poor robustness.In this thesis,the tangent stiffness of nonlinear heat transfer is obtained by considering the thermal conductivity gradient in the linearization of the weak form of nonlinear heat transfer governing equation.Numerical results show that the number of iterative steps of the tangent stiffness algorithm is only about half of that of the conventional algorithm,which significantly accelerates the convergence of the predictioncorrection iterative algorithm.For problems with high gradient of the thermal conductivity,the conventional algorithm diverges whereas the tangent stiffness algorithm still shows quite good convergence.This demonstrates that the tangent stiffness algorithm possesses excellent robustness.In the simulation of nonlinear heat transfer process of additive manufacturing,the convergence and computational efficiency of tangent stiffness algorithm are much better than the conventional algorithm.It can reduce the simulation time by half and the computational efficiency of heat transfer in additive manufacturing is improved remarkably.Then,the consistent EFG method for coupled thermal-mechanical process of additive manufacturing is developed.The nodal shape function of EFG method does not depend on elements.Therefore,it is convenient to add/delete nodes locally and to construct high-order approximation functions.By taking full use of these merits,the EFG method is applied to simulate the additive manufacturing process.A simple and effective adaptive algorithm to coarsen nodes layer-by-layer is established according to the layer-by-layer deposition process,and a corresponding consistent integration scheme is also constructed.In this way,the adaptive consistent EFG method for coupled thermal-mechanical process of additive manufacturing is developed.On the basis of above work,an efficient adaptive analysis of coupled thermalmechanical process in additive manufacturing is implemented and the evolution of temperature and deformation fields are obtained.Subsequently,the influence of laser heat source power and scanning speed on the size of molten pool and the impact of scanning mode on the distortion are further investigated.Numerical results also show that the developed consistent EFG method is not only more accurate than the conventional FEM,but also faster than the stanadard EFG method.Finally,an adaptive generalized finite element method(GFEM)for coupled thermalmechanical process of additive manufacturing is established.In the course of simulating the coupled thermal-mechanical problem of additive manufacturing by the EFG method,we find that although the EFG method has the advantage of high accuracy,its shape function does not satisfy the interpolating property.This complicates the data mapping which is required by the computational modeling of the AM process.Considering the fact that the GFEM without extra degrees of freedom(i.e.extra-dof-free GFEM)is convenient to introduce versatile enrichment functions at nodes and possesses the interpolating property,we introduce this method to the modeling of additive manufacturing process.The technique of constraint on degrees of freedom(DOF)is employed to implement the layer-by-layer adaptive mesh coarsening in extra-dof-free GFEM.Numerical results show that this method is able to simulate the additive manufacturing process of complex structures such as motor rotor.In addition,the temperature field with high gradients near the molten pool is computed accurately.Based on numerical simulation,the mechanism of influencing the distortion of components by preheating and manufacturing thickness are exposed.Furthermore,the developed method is significantly more accurate than the conventional FEM in temperature and distortion fields.According to the research in this thesis,the following conclusions could be drawn: the tangent stiffness for nonlinear heat transfer can effectively improve the computational efficiency of the prediction-correction method and about 40% of the CPU time can be saved.Moreover,the adaptive mesh coarsening in accordance with the characteristics of additive manufacturing process reduces more than 90% nodes without reducing the accuracy.This remarkably improves the computational efficiency.Compared with the conventional FEM,high order numerical methods such as GFEM are more accurate in predicting the distortion of components builded by AM.For instance,in the example of additive manufacturing of Titanium alloy wall,the error in distortion resulting from GFEM is only about 1/5 of that from FEM.The structure of the thesis is as follows: Chapter 1 describes the research background and related development.Chapter 2 introduces the coupled thermal-mechanical model of metal additive manufacturing.In chapter 3,the tangent stiffness algorithm for nonlinear heat transfer in additive manufacturing process is proposed.The consistent EFG method and the adaptive GFEM for modeling the coupled thermal-mechanical process in AM are presented in chapter 4and 5,respectively.Conclusion and future work are summarized in Chapter 6.All the algorithms presented in this thesis are implemented in Fortran90 language and the design of the computer program is described in the Appendix.