Residual Stress and Deformation Modelling for Metal Additive Manufacturing Processes

Transcription

1 Proceedings of the World Congress on Mechanical, Chemical, and Material Engineering (MCM 215) Barcelona, Sain July 2-21, 215 Paer No. 245 Residual Stress and Deformation Modelling for Metal Additive Manufacturing Processes Heng Liu, Todd Sarks, Frank Liou Missouri University of Science and Technology/ Deartment of Mechanical Engineering Rolla MO 6549, USA David M. Dietrich Missouri University of Science and Technology/ Deartment of Systems Engineering Rolla MO 6549, USA Abstract Metal additive Manufacturing has gained increasing attention in the area of raid manufacturing and reairing. This rocess involves extremely high thermal gradients and heat and cooling rate, resulting in residual stresses and distortion. This aer resents a 3D sequentially couled thermo-mechanical finite element model to redict residual stresses and deformations. The temerature distribution, thermal stress field and geometry deformation across domain are illustrated. The effect of deosition arameters on residual stress and deflections are also exlored. A set of validation exeriments for mechanical effects were conducted using laser dislacement sensor. The comarisons between the simulated and exerimental results show good agreement. Keywords: Residual stress, deformation, additive manufacturing, finite element analysis, exerimental validation 1. Introduction Highly localized heating and cooling during direct metal deosition (DMD) rocess may roduce nonuniform thermal exansion and contraction, resulting in comlicated distribution of residual stresses in the heat affect zone and unexected distortion in the whole structures as shown in Fig. 1. The residual stresses may romote fracture and fatigue and induce unredictable buckling during the service of deosited arts and the distortion is often detrimental to the dimensional accuracies of structures. Therefore, it is vital to redict the behaviour of materials after DMD rocess and otimize the design/manufacturing arameters to control the residual stresses and distortion. Fig. 1. A metal deosition rocess may roduce nonuniform thermal exansion and contraction, resulting in distribution of residual stresses in the heat affect zone. The focus of this aer is to investigate both the thermal and mechanical behaviour of DMD rocess of Stainless Steel 34. Based on finite element analysis ackage ABAQUS, a 3-D sequentially couled 245-1

2 thermo-mechanical model is develoed to simulate the transient temerature field, residual stress and final deformation. A laser dislacement sensor is used to record the deflection of the substrate caused by thermal stresses during the deosition rocess. By comaring exeriment results with simulation results, the numerical model is validated. 2. Residual Stress and Distoration Residual stresses are those stresses that would exist in a body if all external loads were removed. When a material is heated uniformly, it exands uniformly and no thermal stress is roduced. But when the material is heated unevenly, thermal stress is roduced (Masubuchi, 198). Highly localized heating and cooling during the DMD rocess roduces non-uniform thermal exansion and contraction, which results in a comlicated distribution of residual stresses in the heat affect zone and unexected distortion across the entire structure. The residual stresses may romote fractures and fatigue and induce unredictable buckling during the service of deosited arts. This distortion often is detrimental to the dimensional accuracies of structures; therefore, it is vital to redict the behaviour of materials after the DMD rocess and to otimize the design/manufacturing arameters in order to control the residual stresses and distortion. 3. Overall Simulation and Exeriment Aroach Based on the finite element (FE) analysis ackage ABAQUS, a 3-D, sequentially couled, thermomechanical model was develoed to simulate the transient temerature field, residual stress and final deformation involved in the DMD rocess. The numerical modelling involved two main stes and the solution rocesses are shown in Fig. 2. In the first ste, a transient thermal analysis was carried out to generate the temerature history of the entire work iece. In the second ste, mechanical analysis was conducted to calculate the residual stress and deformation of work iece, and the load for this ste is the temerature field file generated in revious ste. Fig. 2. Flow Chart Showing the Process of Numerical Modelling 245-2

3 In order to validate the case study, an exeriment was conducted by using a laser dislacement sensor to record the deflection of the substrate caused by thermal stresses during the deosition rocess. By comaring the exerimental results with simulation results, the numerical model was validated. This validated model can be extended to multi-layer laser aided DMD rocess of stainless steel under various rocess arameters and further to other materials. 4. Finite Element Modelling Of Residual Strss and Distorsion Governing Equations In the DMD rocess, the stress/deformation field in a structure would largely deend on the temerature field, but the influence of the stress/deformation field on the temerature field is negligible. Thus, a heat transfer analysis not couled with mechanical effect is considered. The transient temerature field T( x, y, z, t ) throughout the domain was obtained by solving the 3-D heat conduction equation, Eq. (1), in the substrate, along with the aroriate initial and boundary conditions (Reddy, 21). T T T T C k k k Q t x x y y z z (1) Where T is the temerature, is the density, C is the secific heat, k is the heat conductivity, and is the internal heat generation er unit volume. All material roerties were considered temeraturedeendent. Q Initial and Baundary Conditions The initial conditions alied to solve Eq. (1) were: T( x, y, z,) T (2) T( x, y, z, ) T (3) Where T is the ambient temerature. In this study, T was set as room temerature, K. The boundary conditions including thermal convection and radiation, are described by Newton s law of cooling and the Stefan-Boltzmann law, resectively. The internal heat source term, Q in Eq. (1), also was considered in the boundary conditions as a surface heat source (moving laser beam). The boundary conditions then could be exressed as (Reddy, 21): K c hc T T T T T n (4) Q h T T T T where k, T, T and Q bear their revious definitions, n is the normal vector of the surface, h c is the heat convection coefficient, is the emissivity which is.9 in the case study as described in Section 5 of this aer, is the Stefan-Boltzman constant which is W / m K, reresents the surfaces of the work iece and reresents the surface area irradiated by the laser beam

4 4. 3. Adjustments and Assumtions Accurate modelling of the thermal rocess results in highly nonlinear couled equations. To simlify the solution rocess and reduce the comutational cost, the following adjustments and assumtions were considered Energy Distribution of the Laser Beam In the exeriment, a circular shaed laser beam shot onto the substrate vertically with a constant and uniform ower density. Thus, the heat source term constant and uniformly distributed surface heat flux defined as: Q in Eq. (1) was considered a P Q 2 r (5) Where is the absortion coefficient, P is the ower of the continuous laser, and r is the radius of the laser beam. In the case study, was set as.4 according to numerous exerimental results, and r 1.25 mm Movement of Laser Beam The motion of the laser beam was taken into account by udating the osition of the beam s center R with time as follows: t t t t t t t R x udt y vdt z wdt 1 2 (6) where x, y, and z are the satial coordinate the laser beam center, u, v, and w are the continuous velocities the laser beam travels along x, y, and z direction Powder Addition In modelling, the continuous owder addition rocess is divided into many small time stes. Using the Model Change (Simulia, 211), in each time ste, a set of elements was added onto the substrate to form rectangular deosits along the centerline of the substrate. The width of the deosits was assumed to be the same as the diameter of the laser beam, and the thickness of the deosits was calculated from the seed at which the laser travelled and the owder feed rate with an efficiency of.3 in the case study. The geometry of the deosits was udated at the end of each ste to simulate corresonding boundary conditions Latent Heat of Fusion The effect of the latent heat of fusion during the melting/solidification rocess was accounted for by modifying the secific heat. The equivalent secific heat c is exressed as (Toyserkani et al., 24): * * c T c T T m L T (6) * Where c T is the modified secific heat, c T is the original temerature-deendent secific heat, L is the latent heat of fusion, T m is the melting temerature, and T is the ambient temerature. In 245-4

5 the case study, the values of the latent heat of fusion, solidus temerature and liquidus temerature of SS 34 (Ghosh, 26) aear in Table 1. Table. 1. Latent Heat of Fusion for Stainless Steel 34 Latent Heat of Fusion (J/kg) Solidus Temerature (K) Liquidus Temerature (K) Marangoni Effect The effect of Marangoni flow caused by the thermocaillary henomenon significantly imacts the temerature distribution so it must be considered in order to obtain an accurate thermal field solution (Alimardani et al., 27). Based on the method roosed by Lama et al. (Lama et al., 1997), artificial thermal conductivity was used to account for the Marangoni effect: k m T k T T T 2.5k T T T liq liq (7) Where km T is the modified thermal conductivity, k T maintain their revious definitions. T liq is the liquidus temerature, and T and Combined Boundary Conditions The boundary conditions shown in Eq. 4 can be rewritten as: K hc hrt T Q h h T T T n (8) c r Where h r is the radiation coefficient exressed as: r 2 2 h T T T T (9) Eq. (8) indicates that convection was dominant at low temeratures, while radiation made a major contribution to heat loss at high temeratures. Because Eq. (9) is a 3rd-order function of temerature T, a highly nonlinear term was introduced by the radiation coefficient, thus greatly increasing the comutational exense. Based on exerimental data, an emirical formula combining convective and radiative heat transfer was given by Vinokurov (1977) as: h h T T T T T c (1) Where h is the combined heat transfer coefficient which is a lower order function of temerature T comared with h r. The associated loss in accuracy using this relationshi is estimated to be less than 5% (Labudovic and Kovacevic, 23). In ABAQUS, a user subroutine FILM is written to simulate heat loss as follows: SUBROUTINE FILM(H,SINK,TEMP,KSTEP,KINC,TIME,NOEL,NPT, 245-5

6 1 COORDS, JLTYP, FIELD, NFIELD, SNAME, NODE, AREA) INCLUDE 'ABA_PARAM.INC' DIMENSION H(2),TIME(2),COORDS(3),FIELD(NFIELD) CHARACTER*8 SNAME SINK= H(1)=.2169*(TEMP**1.61) H(2)=.34921*(TEMP**.61) 3 RETURN 4 CONTINUE END! Sink temerature! Film coefficient! Rate of change of the film coefficient Material Proerties Temerature-deendent thermal hysical roerties, including density, secific heat, thermal conductivity and latent heat, should be used as inuts Element Selection The tye and size of elements used to aroximate the domain were determined on the basis of comutational accuracy and cost. In transient heat transfer analysis with second-order elements, there is a minimum required time increment. A simle guideline is (Simulia, 211): 6c k 2 t l (11) t Where c, ρ and k are as reviously defined, is the time increment, and is a tyical element dimension. If the time increment is smaller than this value, nonhysical oscillations may aear in the solution. Such oscillations are eliminated with first-order elements (Simulia, 211) but can lead to inaccurate solutions (Reddy, 21). Considering the stability along with the comutational time and accuracy, first-order 3-D heat transfer elements (C3D8) with h-version mesh refinement (refine the mesh by subdividing existing elements into more elements of the same order) were used for the case study. Fine meshes were used in the deosition zone, and the mesh size gradually increased with the distance from the deosits. In regions more searated from the heat affect zone, coarser meshes were utilized. 5. Case Study A clamed cantilever beam when deosit material in the middle of the beam as shown in Fig. 3 is used an examle here elements were created due to numerical convergence within 1% error to model this case. The residual stress distribution within the final deosits is shown in Fig. 4 (a quarter of deosits is hidden to show internal residual stress). Normal stresses σ 11, σ 22, σ 33 along three satial directions are shown in Fig. 4(a)-4(c) resectively and the Von Mises stress is shown in Fig. 4(d). It can be seen that comressive residual stress exists in the to free surface of deosits. This is caused by the stee temerature gradient. The temerature gradient in x and y direction can be as high as 45 K/mm and 14 K/mm resectively. The exansion of hotter to layer is inhibited by underlying material, thus introducing comressive stress in to surface. Residual stresses in lower art of deosits are mostly tensile stresses due to cool-down hase of the molten layers (Mercelis and Kruth, 26). After the deosition is finished and laser is turned off, the remelted lower art of deosits begin to shrink and this shrinkage is restricted by the underling material, thus tensile stresses are induced. l 245-6

7 Fig. 3. The meshing scheme of a clamed cantilever beam when deosit material in the middle of the beam. (a) σ11 (b) σ22 (c) σ33 (d) Von Mises stress Fig. 4. Contour lots of residual stress field within deosits During DMD rocess, the substrate will continuously exerience exansion and shrinkage and finally kee a deformed shae. In this aer, deflection in y direction, shown in Fig. 5, is the main deformation under consideration and is observed by both exeriments and simulations shown below

8 Fig. 5. Deflection of substrate in y direction An exerimental validation was also conducted. The substrate is clamed at the left end to revent rigid body motion as shown in Fig 5. Keyence s LK-G5 series laser dislacement sensor is ut right below the right end of the substrate to record the dislacement of the free end in y direction with frequency of 25 Hz during the rocess. The exerimental setu is shown in Fig 6. Fig. 7 shows the comarisons of deflection of substrate between exeriment and simulation results for both cases. It can be seen from these lots that the trend of the deflection calculated from the simulation matches very well with the exeriment results. For each deosition layer, the substrate firstly bends down due to thermal exansion on the to surface and then bends u due to thermal shrinkage during the cooling rocess. After comletely cooled down, the substrate kees the deformed shae. Fig. 6. Exerimental Setu (a) Deflection in Case 1 (b) Deflection in Case 2 Fig. 7. Simulation and exeriment results of deflection of substrate The differences of final deflection value between simulation and exeriment are 28.5% and 24.6% for case 1 and 2 resectively. There are several reasons could be resonsible for these differences. Firstly, errors exist in exeriment set u. In the simulation, laser beam travels exactly along the centerline of substrate. However, this cannot be erfectly accomlished in exeriments. These offsets would affect the deflection to a large extent since the deflection is sensitive to the osition of heated zone and measuring oint

9 Secondly, the laser dislacement sensor does not track the dislacement of one articular node. It works by sensing the signal reflected by obstacle so the ositions it monitors is always changing as the substrate kees deforming. The simlifications and assumtions considered in both thermal and mechanical analysis are also imortant factors contributing to the differences. 6. Conclusion A sequentially couled thermo-mechanical finite element model is develoed and validated by exeriment. The results show the characteristics of temerature distribution, residual stress and deformation within formed deosits and substrates. Finite Element modelling can be used to redict the resulting mechanical behaviour of materials after DMD rocesses effectively. More efforts are needed to exlore more comlicated situations in industry and to otimize design/manufacturing arameters to control the residual stress and distortion. Acknowledgements This work was artially funded through NASA s Fundamental Aeronautics Program, Fixed Wing Project, under NRA NNX11AI73A, Boeing, and Rolls Royce. The authors would like to acknowledge William J. Seufzer and Karen Taminger of NASA Langley Research Center for their critical advice and mentorshi. Suort from Missouri S&T s Intelligent Systems Center, Material Research Center, and Manufacturing Engineering rogram is also greatly areciated. References Alimardani, M., Toyserkani, E., & Huissoon, J. P. (27). A 3D Dynamic Numerical Aroach For Temerature And Thermal Stress Distributions In Multilayer Laser Solid Freeform Fabrication Process. Otics and Lasers in Engineering, 45(12), Ghosh, S. (26). Process Modeling for Solidification Microstructure and Transient Thermal Stresses in Laser Aided DMD Process. Unublished Doctor of Philosohy, University of Missouri--Rolla. Labudovic, M., Hu, D., & Kovacevic, R. (23). A Three Dimensional Model For Direct Laser Metal Powder Deosition And Raid Prototying. Journal Of Materials Science, 38(1), Lama, C., Kalan, A. F., Powell, J., & Magnusson, C. (1997). An Analytical Thermodynamic Model Of Laser Welding. Journal of Physics D: Alied Physics, 3(9), Liou, F. (28). Raid Prototying and Engineering Alications: A Toolbox for Prototye Develoment (Dekker Mechanical Engineering). CRC Press, 28, ISBN-1: , ISBN-13: Heng, L., Sarks, T. E., Liou, F., Dietrich, D. M. (213). Numerical Analysis of Thermal Stress and Deflection in Multi-Layer Laser Metal Deosition Processes. Proceedings of the 24th Solid Freeform Fabrication Symosium. Masubuchi, K. (198). Analysis Of Welded Structures: Residual Stresses, Distortion, And Their Consequences. Oxford, United Kingdom: Pergamon ress. Mercelis, P., & Kruth, J. (26). Residual Stresses In Selective Laser Sintering And Selec- Tive Laser Melting. Raid Prototying Journal, 12(5), Reddy, J. N., & Gartling, D. K. (21). The finite element method in heat transfer and fluid dynamics, CRC PressI Llc, Boca Raton, FL Simulia, D. (211). ABAQUS 6.11 Analysis User's Manual., Toyserkani, E., Khajeour, A., & Corbin, S. (24). 3-D Finite Element Modeling Of Laser Cladding By Powder Injection: Effects Of Laser Pulse Shaing On The Process. Otics and Lasers in Engineering, 41(6), Vinokurov, V. A. (1977). Welding Stresses and Distortion: Determination and Elimination. British Library Lending Division