FEA Information Engineering Journal

Transcription

1 ISSN Volume 3, Issue 6, June 2014 FEA Information Engineering Journal Electromagnetics

2 FEA Information Engineering Journal Aim and Scope FEA Information Engineering Journal (FEAIEJ ) is a monthly published online journal to cover the latest Finite Element Analysis Technologies. The journal aims to cover previous noteworthy published papers and original papers. All published papers are peer reviewed in the respective FEA engineering fields. Consideration is given to all aspects of technically excellent written information without limitation on length. All submissions must follow guidelines for publishing a paper, or periodical. If a paper has been previously published, FEAIEJ requires written permission to reprint, with the proper acknowledgement give to the publisher of the published work. Reproduction in whole, or part, without the express written permissio of FEA Information Engineering Journal, or the owner of of the copyright work, is strictly prohibited. FEAIJ welcomes unsolicited topics, ideas, and articles. Monthly publication is limited to no more then five papers, either reprint, or original. Papers will be archived on For information on publishing a paper original or reprint contact editor@feaiej.com Subject line: Journal Publication Cover Figure 3 Visualization results for the TEAM 12 problem. Coupling of the EM Solver with Mechanical and Thermal Shell Elements Pierre L Eplattenier - Julie Anton - Iñaki Çaldichoury Livermore Software Technology Corporation 2 Fea Information Engineering Journal June 2014

3 FEA Information Engineering Journal TABLE OF CONTENTS Publications are to 13th LS-DYNA International Users Conference, 2014 A Simple Weak-Field Coupling Benchmark Test of the Electromagnetic-Thermal- Structural Solution Capabilities of LS-DYNAÒ Using Parallel Current Wires William Lawson and Anthony Johnson General Atomics Electromagnetics Coupling of the EM Solver with Mechanical and Thermal Shell Elements Pierre L Eplattenier, Julie Anton, and Iñaki Çaldichoury Livermore Software Technology Corporation Further Advances in Simulating the Processing of Composite Materials by Electromagnetic Induction M. Duhovic, M. Hümbert, P. Mitschang, M. Maier Institut für Verbundwerkstoffe GmbH, Erwin- P. L Eplattenier, I. Çaldichoury Livermore Software Technology Corporation Numerical Simulations to Investigate the Efficiency of Joint Designs for the Electro- Magnetic Welding (EMW) of the Ring-shaft Assembly H. Kim,, J. Gould - Edison Welding Institute J. Shang - American Trim, A. Yadav 3, R. Meyer - Caterpillar Inc Pierre L'Eplattenier - Livermore Software Technology Corporation 4 All contents are copyright to the publishing company, author or respective company. All rights reserved. 3 Fea Information Engineering Journal June 2014

4 13 th International LS-DYNA Users Conference Session: Electromagnetic A Simple Weak-Field Coupling Benchmark Test of the Electromagnetic-Thermal-Structural Solution Capabilities of LS-DYNA Using Parallel Current Wires William Lawson and Anthony Johnson General Atomics Electromagnetics Abstract To begin learning the coupled field capability of LS-DYNA and validate results, a simple simulation of parallel wires carrying current was run. The magnitude of the current in the wires is such that the coupling between the electromagnetic (EM), thermal and structural fields is weak, in the sense that the coupling is taken to be one way. That is, there is no feedback amongst the three field solutions. This allows us to compare LS-DYNA code and known analytical results for code validation to build confidence that the code is being correctly used. LS-DYNA results are also compared to ANSYS results when no analytical results are valid. In addition, this simulation allowed us to test the transfer of EM generated Ohmic heating to the thermal field, and the transfer of EM generated forces to the structural field, a necessary process for coupling fields. Furthermore, to be able to compare the code and analytical results, temperature-dependent material properties have not been included - a decent approximation with the low currents used. The set-up of the coupled field model is discussed. Comparison of the LS-DYNA code and analytical results show good agreement where applicable. Comparison with ANSYS results is also good. Introduction With EM-thermal-structural coupled field capability, pulsed current simulations can be run entirely within LS-DYNA by applying a single current versus time load. Field coupling is achieved by first transferring the EM Ohmic loads to the thermal solver as thermal input loads. Then the calculated thermal loads, along with the already calculated EM Lorentz forces, are transferred over to the structural solution as structural input loads, thereby completing the 3-field coupling (1-way) process. Figure 1 illustrates the load coupling transfer process. Solid lines in the figure represent the load transfer used in this paper. The dashed lines represent capability (full 2-way feedback) that exists in LS-DYNA but is not tested in this paper. Figure 1. Result Transfer between Electromagnetic, Thermal and Structural Solvers. The solid lines represent result transfer tested in this paper. The dashed lines represent capabilities that exist in LS-DYNA but are not tested by the problem simulated in this paper. 1-1

5 Session: Electromagnetic 13 th International LS-DYNA Users Conference To learn the setup of an EM-thermal-structural simulation, and to verify that it was done correctly, two LS-DYNA simulations of parallel current carrying wires were run. This scenario is pictured in Figure 2. Two versions of this analysis were conducted with different boundary conditions. The first simulation applied current through finite length parallel wires. The second simulation approximated infinite length parallel wires and applied the same current through both wires. The details of the differences between these two simulations will be described later. Results of both simulations were compared to analytic calculations, which are presented in the next section. Where an exact analytic calculation did not exist, the LS-DYNA simulations were compared to the same problem solved in ANSYS. Figure 2. Parallel Wires Carrying Current and Current Profile Versus Time It is important to note that the reason for running a simulation of parallel, current carrying wires is that many of the results can be compared to basic analytic calculations for all three fields (electromagnetic, thermal and structural). This allows for one simulation to benchmark all three fields and their associated coupling. Verifying the code-generated results of a simple model against analytical results is always wise as a means to build confidence in both the use of the code and in the code results, before moving onto something more complicated, since in general no such analytical results exists for comparison. Only a few keyword cards are required to set up the LS-DYNA EM simulation. *EM_CONTROL was used to enable the eddy current solver and set the number of cycles between updates of the EM-FEM and EM-BEM matrices. Both of these were set such that the matrices are only calculated at the beginning of the simulation since displacements were expected to be small and EM material properties did not include temperature dependence. *EM_CONTROL_TIMESTEP was used to select automatic time step calculation Two *EM_CIRCUIT cards, one for each wire, tell the solver where the current goes in, where it goes out, and how it varies with time *EM_MAT_001 was used to define each wire as a conductor and define the electrical conductivity. The properties for wire 1 and wire 2 are the same, but they need to be defined as two different materials for the EM solver 1-2

6 13 th International LS-DYNA Users Conference Session: Electromagnetic The setup of the thermal simulation also requires only a few keyword cards. *CONTROL_SOLUTION was used to select a coupled thermal-structural analysis *CONTROL_THERMAL_SOLVER was used to select the solver type and convergence tolerance *CONTROL_THERMAL_TIMESTEP was used to select a constant time step size *INITIAL_TEMPERATURE_SET was used to initialize both wires to room temperature *MAT_THERMAL_ISOTROPIC was used to set the thermal conductivity and specific heat capacity of the wires The setup of the structural solution includes keyword cards that will be familiar to most LS-DYNA users. These cards won t be discussed here for that reason, and since the keyword deck is included at the end of this paper. Analytic Calculations For the case of two parallel wires carrying a DC current, analytic solutions can be written down for all three fields as well as the net effect of the coupling between the fields. This section will summarize these analytical equations. In the EM-field solution, element force densities are calculated and converted to nodal forces applied in the structural field. The electromagnetic Lorentz force per unit length w between the wires (infinite in length) is given by the equation below, where I is the current and d is the distance between the wire centers. It is assumed that the distance between the wire centers is much greater than the radii of the wires so that the finite wire thickness can be neglected. Under this assumption we obtain for w 1-3

7 is the material electrical resistivity, L is the wire length and A is the wire cross sectional area. Session: Electromagnetic 13 th International LS-DYNA Users Conference Additionally in the EM-field solution, Ohmic heating is calculated and later applied in the thermal field solution as an input. The Ohmic heat rate Power on a wire is given below, where I is the current, 1-4

8 13 th International LS-DYNA Users Conference Session: Electromagnetic mesh of the two wires and a large volume of air surrounding the wires. The LS-DYNA mesh is created from the Workbench mesh by unselecting the air and converting the wire nodes and elements to the LS-DYNA keyword format with ANSYS Parametric Design Language code within ANSYS. The LS-DYNA solver automatically models the air mesh with boundary elements. The geometry and mesh including the air are shown in Figure 4 and Figure 5, respectively. Twelve hexahedron elements are used to model each wire diameter as depicted in Figure 6. The length of the wire is modeled with 100 hexahedron elements. Figure 4. Finite Length Model Geometry Including Air 1-5

9 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 5. Finite Length Model Entire Mesh Including Air 1-6

10 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 6. Finite Length Model Detail of Wire Mesh The ANSYS and LS-DYNA models are shown in Figure 7. The most obvious difference between the two models is the large box of air surrounding the wires in the ANSYS model. The ANSYS model also includes EM boundary conditions on the box exterior faces, but the air volume is intended to be large enough that the air volume looks approximately infinite so that the magnetic field runs tangent to the air walls. As expected, the ANSYS model has more elements as a result of the air enclosure, but this does not necessarily equate to longer EM solution times, since the LS-DYNA air boundary element matrix is denser than the ANSYS air finite element matrix. The advantage of the boundary element method used in LS-DYNA comes in easier meshing and the ability to simulate large structural deflections. 1-7

11 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 7. ANSYS (a) and LS-DYNA (b) finite length wires models Listed in Table 1 are the geometry, material and load inputs for both the LS-DYNA and ANSYS models. Geometry Wire Radius (m) Wire Length (m) 0.5 Center-to-center Distance Between Wires (m) 0.1 Material Wire Young's Modulus (N/m^2) 1.250E+11 Wire Density (kg/m^3) 8900 Wire Specific Heat Capacity (J/kg K) 385 Wire Thermal Conductivity (W/m-K) 390 Wire Electrical Resistivity (Ohm-m) 2.00E-08 Wire Electrical Conductivity (S/m) 5.00E+07 Load Max Current (A) Current Rise Time (s) 0.01 Table 1. Finite Length Wires Simulation Inputs Since the current profile includes a rise time, it is important to consider the diffusion skin depth and ensure that the mesh has at least 2-3 elements per skin depth to accurately model the current diffusion at early times. When current is applied quickly, it initially flows within 1 skin depth of the surface and gradually diffuses through the thickness of the conductor with increasing time. The equation for calculating the skin depth is given below. Observe that the skin depth (δ) decreases, thus requiring a smaller element thickness to capture the current behavior correctly, as the current frequency (f) increases (rise time decreases) and as the electrical conductivity (σ) of the material increases. m is the permeability of the wires and is taken to be that of free space and remains constant. 1-8

12 13 th International LS-DYNA Users Conference Session: Electromagnetic 1-9

13 Session: Electromagnetic 13 th International LS-DYNA Users Conference a primary contributor to the lower total forces per unit length for the code results (as compared to the analytical calculations) depicted in Figure 8. It is also clear that the 2% difference in total force between the LS-DYNA and ANSYS simulations is mostly due to differences in force at the wire ends. Agreement away from the ends is much better than 2%. Figure 9. Attractive Force per Unit Length between Finite Length Wires along Wire Length at Maximum Current The total wire heat generation rate in the LS-DYNA simulation was calculated by summing the heat generation rate of all the elements in each wire. The LS-DYNA simulation under-predicts the analytical heat generation rate at maximum current by 2.1%. The analytical calculation used the actual cross sectional area of the finite element mesh. A finite element mesh can t perfectly represent a circle, and as a result has a slightly lower area than a perfect circle 1.1% lower for the mesh used in this simulation. This lower cross sectional area leads to a greater wire resistance, which leads to a greater heat generation rate as compared to a perfect circular cross section wire. The ANSYS simulation result (not shown in the plot) is a near perfect match with the analytical calculation, differing by less than 0.01% at maximum current. 1-10

14 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 10. Time History of Heat Generation Rate in One Finite Length Wire The average wire temperature was calculated from the LS-DYNA simulation by summing all the nodal temperatures in each wire and then dividing by the number of nodes. This is a reasonable average temperature approximation for this model given the relatively uniform mesh and relatively uniform temperature distribution. This method would not be as accurate for models with highly non-uniform meshes, localized temperatures and/or diffusion. The wire average temperature rise at the end of the simulation under-predicts the analytic calculated temperature rise by 2.3%, which is nearly consistent with the simulation underpredicting the heat generation rate by 2.1%. The under-prediction in temperature rise and heat generation rate should be identical, and the minor difference is likely due to the nodal temperature averaging technique used to calculate the average temperature. Like the heat generation rate analytic calculation, the average temperature calculation uses the actual geometry from the finite element model. The modeled cross sectional area and mass are both 1.1% lower than the ideal geometry, and reducing these 2 numbers increases the expected temperature change. The ANSYS average temperature was calculated by taking the volume averaged temperature over each wire. The ANSYS temperature time history is not shown in Figure 11 since it lies nearly on top of the analytical calculation time history. The ANSYS simulation temperature rise is 0.2% greater than the analytic calculation. 1-11

15 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 11. Time History of Finite Length Wire Average Temperature The results of the LS-DYNA coupled field simulation are in good agreement with analytic calculations and the ANSYS coupled field simulation. The LS-DYNA calculated total attractive force between the wires is 2% lower than the force calculated with the ANSYS coupled field simulation. The LS-DYNA and ANSYS force distribution along the length of the wire is a very good match away from the wire ends. At the wire ends, the LS-DYNA calculated forces are lower than the ANSYS calculated forces. There is no reason to believe that either simulation is more accurate than the other. The fact the total force, and force distribution along the length of the wires, is very similar between the two codes is encouraging. The LS-DYNA calculated heat generation rate and temperature rise are 2% lower than the analytic calculated values. One possible source of this difference is the convergence tolerances used in the implicit EM and thermal solvers. However, from the perspective of designing and simulating a pulsed current device, the difference between the LS-DYNA code generated results and the analytic calculations is small and more than acceptable. Deflection results have not been presented for the finite length wires simulation since there is no basic analytic calculation for the non-uniform applied load. Deflection results will be presented in the next section for the semi-infinite wires simulation, as they are necessary for verification that the Lorentz forces are properly applied in the structural solution. Stress has also been omitted since there is no basic analytic calculation for the non-uniform loading applied to the finite length wires, and since a high number of through thickness elements are required to accurately predict the bending stress in the wires. 1-12

16 13 th International LS-DYNA Users Conference Session: Electromagnetic Semi-Infinite Wires Simulation As stated earlier in this paper, the analytic calculation for force per unit length between parallel wires carrying current neglects end effects, or in other words, assumes very long wires. End effects were clearly significant for the finite length wires simulation presented in the previous section as seen in Figure 9. In fact, the length over which the end effects act can be approximated from Figure 9. Due to the expected end effects, a valid comparison between the LS-DYNA Lorentz force and the analytically calculated Lorentz force could not be made. Also, because of the non-uniform Lorentz force distribution along the length of the wire, the structural deflection of the wire mid-point could not be checked using the textbook formula for a uniformly loaded beam. The LS-DYNA and ANSYS simulations presented in this section model semiinfinite length wires so the code generated forces and deflections can be compared to the analytical solutions. The LS-DYNA semi-infinite length wires model was created by adding 0.75 meter rigid wires to each end of the 0.5 meter elastic finite length wires model as shown in Figure 12. These rigid wires were structurally constrained in all degrees of freedom. The long rigid wires were used to accomplish a few things. First, they are long enough to keep the end effects away from the elastic center section, resulting in the uniform load on the elastic section that is needed to validate Lorentz force and the wire mid-point deflection. The rigid wires also constrain the ends of the elastic section, which is necessary to provide the fixed boundary condition assumed by the wire mid-point deflection calculation. Finally, the rigid wires were used to minimize the structural solution CPU time. Both the center and the ends of the wires were modeled using identical thermal and electromagnetic material models. In ANSYS, a semi-infinite length model was created with two 0.5 meter long wires surrounded by air. In this model the air ends where the wires end in the wire axis direction, and EM boundary conditions were used to simulate the wires as infinite length. This was accomplished by enforcing flux parallel boundary conditions on all of the outer boundaries of the air volume. Figure 12. Semi-Infinite Wires Model Geometry for Ansys (a), and LS-DYNA (b) The force per unit length calculated by the LS-DYNA simulation is 0.7% greater than the force per unit length calculated in the ANSYS simulation (averaged over the length of the wire). This comparison was made at the end of the simulation, with the maximum current applied to the 1-13

17 Session: Electromagnetic 13 th International LS-DYNA Users Conference wires. The LS-DYNA simulation also has a slight (±1.2%) variation in force over the length of the wire. Both simulations show forces per unit length within 1% of the nominal analytic calculation, which used the wire center-to-center distance for the force calculation. Figure 13. Attractive Force per Unit Length between Semi-Infinite Wires along Wire Length at Maximum Current The analytically calculated wire midpoint deflection shown in Figure 14 assumes zero dynamic amplification, so the LS-DYNA and ANSYS calculated deflections are expected to oscillate about the analytic calculated time history. The LS-DYNA wire midpoint deflection at full current is oscillating about a value 3% above the analytic calculated deflection, which is 3% more than expected since the LS-DYNA force per length is within 0.1% of the analytic calculated nominal value. Interestingly, the natural frequency measured in the LS-DYNA simulation is about 3% higher than the analytically calculated value. So, the wire has a higher natural frequency (implying high stiffness) and higher deflection (implying low stiffness) than calculated analytically, which is not expected. Sorting out these minor differences likely calls for a mesh sensitivity study. The ANSYS simulation uses 20 implicit structural load steps (each diamond marker in the ANSYS wire midpoint deflection time history curve is a load step). The ANSYS calculated midpoint deflection is oscillating near the analytically calculated midpoint deflection, but the time stepping is too coarse to accurately simulate the structural response. 1-14

18 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 14. Semi-Infinite Wire Midpoint Deflection Time History The force results of the LS-DYNA semi-infinite wires simulation compare well with the ANSYS and analytical calculations. The wire midpoint deflection is 3% higher than expected, but close enough to conclude that the Lorentz forces are being properly applied. Combined with the finite length wires simulation, all LS-DYNA results are within 2-3% of the ANSYS and analytical results (where applicable). Certainly additional simulations could be run to understand the minor differences between the LS-DYNA, ANSYS and analytical calculations. One simulation on that list would better approximate the analytical calculation zero thickness wire assumption and reduce the wire radii relative to the center-to-center distance between the wires. Another set of simulations could examine the sensitivity of the results to mesh density. However, a 2-3% difference between the LS-DYNA, ANSYS and analytical calculations is close enough for most applications to proceed with simulating more complicated devices in the LS-DYNA coupled field code. Keyword Input The LS-DYNA keyword input for the finite length wires model is shown in this section with the exception of the *node, *element and *set listings. Figure 15 summarizes the node, element and segment sets referenced in the keyword input. 1-15

19 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 15. LS-DYNA Set and Part Numbers Used in Keyword Input 1-16

20 13 th International LS-DYNA Users Conference Session: Electromagnetic 1-17

21 Session: Electromagnetic 13 th International LS-DYNA Users Conference 1-18

22 13 th International LS-DYNA Users Conference Session: Electromagnetic 1-19

23 Session: Electromagnetic 13 th International LS-DYNA Users Conference 1-20

24 13 th International LS-DYNA Users Conference Session: Electromagnetic Coupling of the EM Solver with Mechanical and Thermal Shell Elements Pierre L Eplattenier Julie Anton Iñaki Çaldichoury Livermore Software Technology Corporation 7374 Las Positas Road Livermore, CA Abstract The Electromagnetics (EM) solver of LS-DYNA has recently been extended to shell elements, in order to solve coupled EM/mechanical/thermal problems on thin plates, which appear in Magnetic Metal Forming and Welding experiments. Due to the magnetic diffusion of the EM fields through the thickness of the plate, which is a very important phenomenon that needs to be precisely solved, the EM part of the simulation still needs a solid mesh with several through thickness elements. This solid mesh, underlying the shell mesh is thus automatically built during the simulation and is used to solve the EM equations. The EM fields are then averaged or summed through the thickness in order to compute equivalent EM fields on the shells, and in particular an equivalent Lorentz force and Joule Heating which are used by the mechanical and thermal solvers. The model is presented and illustrated on some academic and industrial examples. Comparisons between solid and shells are presented. In a last part of this paper, a different new feature of the EM solver, the computation of magnetic field lines in and around the conductors is presented. 1-1

25 are evenly spread on a segment [, nsol new nodes Session: Electromagnetic 13 th International LS-DYNA Users Conference Purpose of conducting shells versus conducting solids The Electromagnetism (EM) module was introduced a few years ago in LS-DYNA [1]. Some important applications of the module and its coupling with the Mechanical and Thermal solvers of LS-DYNA concern the Magnetic Metal Forming (MMF) and Welding (MMW) of thin conductor plates. Up to now, the only way to do such simulations was to use solid elements to model the thin plates since the EM solver only could handle these elements. One of the reasons for such a limitation was that in general MMF and MMW processes, the current rise time and electrical conductivity of the workpiece are such that the diffusion of the EM fields through the thickness of the workpiece happens at the same time as its mechanical deformation and thermal heating. Solving correctly this diffusion process is capital to get correct EM forces and Joule Heating. For example, if this diffusion is too fast (which happens when the conductor has a low electrical conductivity or the current rise time is too slow), the workpiece will act like a strainer and let most of the magnetic pressure go through it without moving much. In order to correctly solve this EM diffusion through the thickness of the workpiece, we still need to use, on the EM side, solid elements with at least a few elements through the thickness. On another hand, shell elements often have better mechanical and thermal behavior when modeling thin plates. We thus decided to build a solid mesh which is used to solve the EM equations, underlying the shell mesh used for the thermal and mechanical equations. We will first present in more details the model just introduced, and then show some examples with some comparisons between using only solid elements for the mechanics, thermal and EM (old method); and using shells for the mechanics and thermal and solid elements for the EM (new method). Presentation of the Model For each part, we can specify the number of solid element nsol in the shell thickness in the *EM_MAT_004 card. The solid mesh is then built the following way: For each original node shell, 1-2

26 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 1 Sketch showing how new solid elements are generated from the initial shell elements Validation of the model on the TEAM 12 model In order to validate the implementation of conducting shells, we used an academic EM mechanical problem where the deformations are not too important so that the mechanical differences between shells and solids are minimized. The so-called TEAM 12 problem consists of a clamped beam placed in a uniform magnetic field [2] (See Figure 2). The magnetic field has a first component exponentially decaying with time that generates an induced current in the beam that in turn, interacts with the second constant component of the field and creates a Lorentz force which causes the beam s movement. The TEAM 12 experiments were performed with four different values for this constant field : 0.2, 0.5, 0.7 and 0.9 T. This problem has already been used for validating the EM solver and presented in [3]. In the present case, the objective is not so much to compare against the experiment but to ensure that the beam keeps a consistent behavior when modelled with solid elements (the classic way) or with shells elements (the new way). Results for the beam s oscillations are shown of Figure 3 and Figure 4. As one can see the results are very similar for the two methods. A slight phase difference can be observed the reason for which is unknown at this time which may be due to the different mechanical behavior of shells and solids. Figure 2 Sketch of the TEAM12 problem 1-3

27 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 3 Visualization results for the TEAM 12 problem. Comparison between using shells or solids for the beam. Figure 4 Maximum beam displacements for different Magnetic flux amplitudes (0.2, 0.5, 0.7 and 0.9 T) [2]. 1-4

28 13 th International LS-DYNA Users Conference Session: Electromagnetic Illustration on a typical metal forming case We now present a typical magnetic metal forming simulation using shell elements. The simulation represents the free forming of an aluminum plate by a spiral coil and is very similar to the case presented in [1]. Comparison is again made against the equivalent solid element case. It appears clearly on Figure 5 that both behaviors are similar and consistent. When looking into more details, some small differences can be observed but those can be explained by the fundamental and intrinsic different characteristics of shell and solid elements on the structure side, since this case presents very large deformations. Figure 5 Results for the forming test case. Comparison between using shells and solids for the workpiece. Update and future developments on shells for EM The EM solvers 1 (Eddy Current) and 3 (Resistive heating) are now coupled with shells, soon to be extended to solver 2 (Inductive heating). One can combine shells (e.g. for the workpiece) with solid elements (e.g. for the coil). This works in SMP and MPP. More options may be added for the through thickness distribution of the solids in order to better represent the skin depth. 1-5

29 Session: Electromagnetic 13 th International LS-DYNA Users Conference Magnetic field lines in the air A new feature has been implemented in order to display magnetic field lines at a given time in both the conductors and the surrounding air. This feature is important since the use of the BEM method does not allow the visualization of the EM fields in the air. However, it does not change anything in the way the EM fields are solved; those field lines only aim at giving visual additional information to the user. Consequently, a new card has been added, *EM_DATABASE_FIELDLINE which can be used to trigger and control the calculation of these field lines. Basically, the user needs to provide one point which will be used as a starting point for the field line. He also needs to specify how many points he wants on the field lines and the frequency of computation of these lines. There are two optional cards. The first one allows the user to define the type of integration scheme used to compute the lines (Runge Kutta 4 or Dormand Prince 853) [4]. The other one allows the user to define the method used to compute the field B which is the second member of the field lines equations. One has to be aware that the computation of the magnetic field lines could be time consuming especially when some points are close to the structure. What actually drives the cost of the magnetic field lines computation is the calculation of the second member. The direct method is accurate but shouldn't be used systematically. Two methods of approximation are available: the multipole method [5] and the multicenter method. The latter one has been developed at LSTC. Calculation methods Integration scheme The magnetic field lines are useful for visually representing the strength and the direction of the magnetic field 1-6

30 13 th International LS-DYNA Users Conference Session: Electromagnetic the contributions of all the source currents inside the conductors. This is often time consuming. However, one could also use the fact that the target is often far away from the charge distribution to compute an approximate contribution rather than the exact one. Based on this idea, two methods, the multipole and multicenter methods are currently being investigated. More information on the multipole method can be found at [5]. Examples Torus Let s consider a torus in which one an electric current circulates which generates a magnetic field B around it. The torus is split into 900 solid elements. The magnetic field lines are shown on Figure 7. Figure 6 Torus mesh Figure 7 Magnetic field lines for the torus case 1-7

31 Session: Electromagnetic 13 th International LS-DYNA Users Conference Time performances: Method Initialization time Computation time Total computation time Multicenter 13s 24ms 68ms 13s 92ms Multipole 1s 54ms 1s 22ms 2s 76ms Direct - - 3mn 30s Coil sections plus Plate Let s now consider the section of a coil plus a plate. This could represent part of an MMF simulation (See Figure 8). An electric current circulates into the 3 tubes which induces a current in the plate. An electromagnetic field turns around the 3 tubes and is compressed around those tubes due to the plate. The tubes and the plate are split into solid elements. The magnetic field lines can be seen on Figure 9. Figure 8 Mesh of the coil plus plate case 1-8

32 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 9 Magnetic field lines for the coil plus plate case Time performances: Method Initialization time Computation time Total computation time Multicenter 13smn 11s 35s 13mn 46s Multipole 22s 1mn 19s 1mn 41s Direct - - 6h 31mn Conclusion and future developments on magnetic field lines As can be observed from the previous tables, the advantages of the multipole and multicenter methods versus the direct method are evident regarding computational time. Further research will be undertaken on those two methods which, if proven successful, could be used during the assembly of the BEM matrices and maybe the solution of the BEM system thus reducing the computational time of the whole EM run. 1-9

33 Session: Electromagnetic 13 th International LS-DYNA Users Conference Bibliography [1] P. L'Eplattenier, J. Imbert and M. Worswick, "Introduction of an Electromagnetism Module in LS-DYNA for Coupled Mechanical-Thermal-Electromagnetic Simulations," Steel Research Int, vol. 80, no. 5, [2] L. R. Turner, Q. T. H and S. Y. Lee, "Analysis of the Felix experiments with cantilevered beams and hollow cylinders," in Fourth Eddy current Seminar Rutherford Appleton. [3] I. Çaldichoury and P. L'Eplattenier, "Validation Process of the Electromagnetism (EM) Solver is LS-DYNA R7 : the TEAM cases," in 12th International LS-DYNA Users Conference, Detroit, [4] E. Hairer, G. Wanner and S. P. Norsett, Solving Ordinary Differential Equations, Springer, [5] V. Rokhlin, "Rapid Solution of Integral Equations of Classic Potential Theory," J. Computational Physics, vol. 60, pp , [6] P. M. L'Eplattenier and I. J. Çaldichoury, LS-DYNA EM Theory Manual, LSTC,

34 13 th International LS-DYNA Users Conference Session: Electromagnetic Further Advances in Simulating the Processing of Composite Materials by Electromagnetic Induction M. Duhovic, M. Hümbert, P. Mitschang, M. Maier Institut für Verbundwerkstoffe GmbH, Erwin-Schrödinger-Str., Building Kaiserslautern, Germany P. L Eplattenier, I. Çaldichoury Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA Abstract Continuous induction welding is an advanced material processing method with a very high potential of providing a flexible, fast and energy efficient means of joining together thermoplastic composites to themselves and metal alloys. However, optimization of the process is very difficult as it involves the interaction of up to four different types of physics. In the previous installments of this work, static plate heating and continuous induction welding simulations of carbon fiber reinforce thermoplastic (CFRTP) plates were presented looking in particular at point temperature measurements and 3D surface plots of the in-plane temperature distribution across the entire width of the joint on the top as well as the joining interface of the laminate stack. In this paper, static plate heating tests are once again revisited and the importance of through the thickness temperature behavior is considered. For a single plate, the through thickness temperature profile follows a predictable pattern when using an induction frequency producing a skin depth of the same thickness as the plate. For two stacked but unconnected plates, the temperature profile becomes less obvious, in particular for plate stacks of different thicknesses. By correctly simulating the through thickness temperature profile the heating behavior can be ultimately controlled via top surface air-jet cooling together with other induction equipment parameters giving an optimum heating effect at the joining interface. In addition, further developments in the induction heating electromagnetism module available in LS-DYNA R7 are examined including the inclusion of an orthotropic electromagnetic material model as well as electrical contact and its resulting contact resistance and effect on the overall heating behavior. 1-Introduction As the aerospace industry pushes the use of composite materials in commercial aircraft to beyond 50% of the total structural weight (Boeing 787 and Airbus A350), the automotive industry can catch a glimpse as to what is in store for them in the near future. Carbon fiber reinforced thermoplastic plastics (CFRTPs) combined with advanced metal alloys represent the next logical step in material selection in order to meet future energy efficiency goals and lightweight design criteria. An important part of the vehicle body construction is joining. Joining methods for metallic passenger cells and chassis components include automated robotic spot and seam welding of prestamped parts along with glueing in some areas mainly for providing water sealing properties. For the use of fiber reinforced thermoplastic parts to be accepted in the automotive industry, the 1-1

35 Session: Electromagnetic 13 th International LS-DYNA Users Conference ability for the material to be joined quickly and efficiently by robotic means in a controlled manner giving excellent bond strength between the connected parts needs to exist. All the aforementioned features can be provided by induction welding technology. 2-Short overview of induction welding Induction welding is a materials joining process that uses an oscillating electromagnetic field to generate a contact-free heating. The subsequent fusion bonding which occurs in the case of thermoplastic composite joints is supported by applying pressure and allowing enough time for intermolecular diffusion to take place. Thermoplastic composite to metal joints are also possible utilizing similar processing conditions, although the bond in this case is created through different adhesion mechanisms. During the process, an induction coil, connected to a high frequency oscillating current source (usually in the khz MHz range) creates an alternating current in the coil. This current in turn produces a time-variable magnetic field of the same frequency in the near surroundings of the coil as illustrated in Figure 1. I in I out Magnetic field Induction coil Top CFRTP laminate Eddy currents Bottom CFRTP laminate Figure 1: Working principle of induction heating in weave structured CFRTP sheet materials (image courtesy of Mrs. Mirja Didi IVW GmbH) The alternating magnetic field induces oscillating eddy currents in a work piece when placed in close proximity to the coil. Heat energy is generated via the Joule effect as a result of the induced eddy currents flowing through the electrically conductive material [1, 2]. For composite materials containing glass fiber reinforcements, no Joule heating can occur and a susceptor material in the form of a steel mesh or electrically conductive polymer film, for example, is required between the materials to be joined. Composites containing carbon fibers in certain configurations (weaves) however, produce a significant Joule heating effect and can be utilized to achieve the necessary heating effect. During a finite element simulation of the induction welding process of thermoplastic composites, it is precisely the Joule heating phenomena which is of primary interest and is simulated. 1-2

36 13 th International LS-DYNA Users Conference Session: Electromagnetic 3-Static plate through thickness heating experiments In order to investigate the through thickness temperature distributions during induction heating and more importantly induction welding, static plate heating experiments have been performed. Although the findings cannot be directly transferred to the continuous heating (moving coil) case, they can provide a useful insight into joule heating phenomena for different plate thicknesses and the possible effects of a contact resistance between the plates. For all the experiments, carbon fiber reinforced polyphenylene sulfide (CF-PPS) was used. The experimental setup for static plate heating measurements is shown in Figure 2. Induction coil Coupling distance Laminates Thermocouples (T 1, T 2, T 3 ) Figure 2: Schematic of double laminate static heating test performed using 2x1 and 2x2 mm thick CF-PPS plates A pancake type coil identical to that used in previous works [3, 4] was again used to heat either a fully connected (consolidated) or unconnected stack of two CF-PPS laminates. In order to measure the temperature, three thermocouples were used, one on top of the upper laminate (temperature T 1 ), one between the two laminates (temperature T 2 ) and one on the bottom of the lower laminate (temperature T 3 ). The experiments were carried out for laminates with a thickness of 1 mm and 2 mm. Moreover three different generator powers (10%, 20%, 30%) and two different coupling distances (5 and 10 mm) were used. The results for an unconnected stack of two laminates with a thickness of 1 mm at a coupling distance of 10 mm are shown in Figure 3. The specimens were always heated until the top laminate reached 250 C. The experiments confirmed the previously assumed temperature distribution. The top laminate is heated the most and the temperature drops with increasing distance to the coil. A similar behavior was observed when the coupling distance was reduced to 5 mm as shown by the results in Figure

37 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 3: Static heating results for two laminates with a thickness of 1 mm and a coupling distance of 10 mm Figure 4: Static heating results for two laminates with a thickness of 1 mm and a coupling distance of 5 mm A comparison of the heating times shows that a reduction of the coupling distance by 50% can lead to a reduction in heating time of up to approximately 75%. At a power of 10% the heating times was reduced from 120 s to 30 s. The reason for this lies in the fact that the magnetic field intensity drops with increasing distance to the coil as predicted by the Biot-Savart law. Moreover it can be observed, that the difference in temperature between the top of the upper laminate and the two other measuring points decreases when either the coupling distance is increased or the power is decreased. 1-4

38 13 th International LS-DYNA Users Conference Session: Electromagnetic The results of Figures 3 and 4 can be compared to the case where two 1 mm plates have been fully consolidated together, in effect representing a single uniform 2 mm thick plate. Figure 5 shows this for a coupling distance of 10 mm. It can be seen compared to Figure 3 that the time required to heat the top laminate to 250 C is now slightly lower at all powers. In addition, a strange effect in the order of the temperatures can be observed where the T 2 thermocouple in the center of the laminate measures a lower temperature that thermocouple T 3 on the bottom surface. This can be explained by the fact that the thermocouples cannot be placed in the exact same position through the thickness and may coincide exactly or be slightly away from a junction (fiber crossover) heating location. It is also believed that regardless of the Biot-Savart law, the low electrical conductivity of the material results a skin depth giving a fairly uniform volumetric heating. Figure 5: Static heating results for a single laminate with a thickness of 2 mm and a coupling distance of 10 mm In Figure 6, with a coupling distance of 5 mm, the switch in the expected trend between the T 2 and T 3 thermocouples is amplified since the same specimen was used to perform the test. The results highlight the difficulty in measurement due to the discontinuous in-plane temperature pattern that results (particularly at high powers and small coupling distances) from closely spaced junction heating zones defined by the carbon fiber reinforcement yarn size and weaving pattern. Further experiments are required to be able to assess any additional joule heating influence due to a contact resistance perhaps using a very finely woven carbon fiber reinforcement mesh. From the current results, it can be seen that the overall impact on the Joule heating effect due to an additional contact resistance between the plates should not be very high. 1-5

39 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 6: Static heating results for a single laminate with a thickness of 2 mm and a coupling distance of 5 mm The resulting heating curves from the induction heating of two unconnected laminates with a thickness of 2 mm at a coupling distance of 5 mm are shown in Figure 7. Figure 7: Static heating results for two laminates with a thickness of 2 mm and a coupling distance of 5 mm 1-6

40 13 th International LS-DYNA Users Conference Session: Electromagnetic In this case, it was observed that the temperature T 1 on the top laminate appears to be overtaken by the temperature T 2 between the laminates. It can also be seen that T 3 is now much lower and that a volumetric type heating that was somewhat the case in the 2 x 1 mm tests now no longer occurs. The same trend but with a lower spread between the T 1 T 3 temperature curves occurs for a coupling distance of 10 mm albeit over a longer heating time. Using a new specimen now consolidated into a single 4 mm thick plate, the heating experiments were once again performed for the different coupling distances of 5 and 10 mm as are shown in Figures 8 and 9 respectively. Figure 8: Static heating results for a single laminate with a thickness of 4 mm and a coupling distance of 5 mm Just as was observed for the 2 x 1 mm case, the overall heating time to 250 C in the unconnected 2 x 2 mm specimen compared to a single 4 mm specimen appears to be longer by 20-30%. This seems to be a consistent observation overall in all the experiments and may suggest a kind of electromagnetic shielding effect coupled with a poor thermal conductivity barrier at the interface of the two unconnected laminates. The latter seems unlikely as the thermal conductivity through the thickness of the laminate is already very poor (values used in this work of 0.32 W/m.K as calculated by Moser [5] and which have been measured for such materials by Schuster [6]). While shielding type explanations seem plausible, the reason as to why for the thicker laminate cases, the top laminate temperature T 1 is overtaken by T 2 and even T 3 in the case of 10 mm coupling distance is baffling. Material related effects can be counted out as the same phenomenon has been observed in many different specimens. Equipment and thermocouple effects could be responsible, although regarding the equipment, some changes in the machine parameters during the test cannot account for the switch in temperature order observed. 1-7

41 Session: Electromagnetic 13 th International LS-DYNA Users Conference Thermocouple errors are another possibility due to the influence of the magnetic field, however this has also been studied quite closely and the effects are predictable and can be minimized for certain thermocouple types. Some help through the use of finite element electromagnetic simulations using LS-DYNA R7 as performed in the following section may help shed some light on these issues. Figure 9: Static heating results for a single laminate with a thickness of 4 mm and a coupling distance of 10 mm Modelling induction heating in LS-DYNA R7 4-1 The inductive heating solver in LS-DYNA The Electromagnetism (EM) solver included in release R7 of LS-DYNA solves the Maxwell equations in the Eddy current (induction-diffusion) approximation [7-9]. This is suitable for cases where the propagation of electromagnetic waves in air (or vacuum) can be considered instantaneous which is the case in most industrial magnetic metal welding, forming or inductive heating applications. The EM solver is strongly coupled with all the other solvers available in LS-DYNA allowing truly multi-physics phenomena to be simulated. EM fields are solved using a Finite Element Method (FEM) for the conductors and a Boundary Element Method (BEM) for the surrounding air/insulators therefore eliminating the need for a surrounding air mesh. An inductive heating solver was introduced in order to solve the computer cost issue arising when high frequency currents, therefore very small time steps, were combined with long simulation runs (typically, an AC current with a frequency ranging from khz to MHz and a total

42 13 th International LS-DYNA Users Conference Session: Electromagnetic time for the process in the order of a few seconds). The induction heating solver works by assuming a current which oscillates very rapidly compared to the total time of the process. A full eddy-current problem is solved over two full periods with a "micro" EM time step where the EM fields as well as the joule heating is computed. It is then assumed that the properties of the material (heat capacity, thermal conductivity, magnetic permeability) and mostly the electrical conductivity which drives the flow of the current and the joule heating do not change for the next periods of the current within the macro EM time step (or overall solution time step) chosen. The calculated averaged joule heating term is then added many times over to the thermal solver. If the material properties change significantly affecting the EM fields or more accuracy is desired, then more recalculations of the macro EM time step can be performed over the entire solution time. 4-2 Material properties A large number of material properties need to be collected in order to setup the simulations. A summary of the properties used in the LS-DYNA finite element models can be found elsewhere in previous works by Duhovic et al. [10]. Free convection heat transfer coefficients are also taken into account on exposed faces of the plates and are input as tabulated values with respect to temperature (for a range of C). Typical average values for free convection are 7.83 W/(m 2.K) for the horizontal upside surface, 5.94 W/(m 2.K) for the horizontal downside surface and W/(m 2.K) for the vertical faces. The skin effect is an electromagnetic phenomenon whereby the flow of current concentrates itself on the outer surface of the conducting body. The skin depth is automatically calculated using the formula given in Equation (1), which is a function of the specified electromagnetic material properties. It can be seen that the calculated value may be significant in the present work as the skin depth is quite close to the overall thickness of the laminate stack, i.e. 5.8 mm at 540kHz for CF-PPS. where 2r r d =» 503 (1) (2pf )( m m ) m f o r r δ = the skin depth in meters (calculated using Eq. 1 as 5.8 mm for pancake coil (540 khz) for CF-PPS) μ r = the relative permeability of the medium (1 used for CF-PPS, reference [5]) μ o = the magnetic permeability of free space (4 π 10-7 H/m) ρ = the resistivity of the medium in Ω m, also equal to the reciprocal of its conductivity: ρ = 1 / σ (for CF-PPS, ρ = Ω m, reference [5]) f = the frequency of the current in Hz 1-9

43 Session: Electromagnetic 13 th International LS-DYNA Users Conference 5-Static plate through thickness induction heating simulations 5-1 Single and double plate induction heating models Comparisons to the experiments performed in section 3 can be made for both the single and double plate induction heating cases. Figures 10 a) and b) show example models of the single and double (100 x 100 x 2 mm) CF-PPS static plate induction heating simulations respectively and their corresponding temperature measurement locations which are equivalent to those used in the physical experiments. Note that in the images presented in Figure 10, the models have been cut in half in order to better visualize the through thickness temperatures. a) Air gap b) Figure 10: LS-DYNA R7 FEM/BEM simulation model set-up for a) single 2 mm and b) double 2 x 2 mm plate through the thickness temperature investigations and their corresponding point temperature measurement points 1-10

44 13 th International LS-DYNA Users Conference Session: Electromagnetic In Figure 10 b) it can be seen that a small gap has been left between the plates in the double plate model. For this EM simulation case the interaction between three EM bodies is considered without the use of the EM contact card which is still currently in the beta development phase. In order for the EM solver to converge, the size of the gap must be no smaller than the thickness dimension of the solid finite elements used (i.e. the BEM element size adjacent to the gap). When the EM contact card is used, then no gap is required for convergence since the contact resistance is considered as part of the EM circuit. In this case, an extra Joule heating term according to Holm s equation [11] defining a contact resistance can also be implemented. Point temperature heating results for the single plate model shown in Figure 10 a) are given in Figures 11 and 12. Note that the node locations (Node 1, Node 2, Node 3) shown in Figure 10 correspond to the location of thermocouples (T1, T2, T3 on the graph legend) used in the physical experiments presented in section 3. The heating of two plates is of more interest than one but adds further complications as it involves an extra load contributor (i.e. an extra plate) in the electromagnetic circuit. The eddy currents developed in the top plate are now also affected by the presence of the bottom plate as well as the coil. In the double plate simulation case, the temperatures at Nodes 2 and 3 are averaged in order to estimate the experimental temperature T2 at the joining interface. Figure 11: Comparison between experiments and LS-DYNA simulation results for a 2 mm thick CF-PPS plate at 10 mm coupling distance for 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz 1-11

45 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 12: Comparison between experiments and LS-DYNA simulation results for a 2 mm thick CF-PPS plate at 5 mm coupling distance for 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz Based on the results from the simulations, the following comments can be made regarding the accuracy of the heating predictions for the single 2 mm plate (Figures 11 and 12). For the discussion it should be noted that in the current simulations a constant value of electrical conductivity was used. For a coupling distance of 10 mm, it can be seen that the predictions are good at the beginning but tend to get worse over a larger temperature range and longer heating times. The reason for this could be the fact that the code uses a sinusoidal approximation for the shape of the oscillating current wave form when in fact the actual waveform deviates significantly from this shape. A solution to this is already planned via the implementation of an actual two-period current waveform, implemented as a curve based input replacing the current and frequency parameters in the EM_Circuit card. The actual two-period current versus time waveform (the same as required for the full eddy current solver) occurring on the coil can be measured using special electronic equipment and an oscilloscope and can then be output as a data file for use in the simulations. Another deviation in the prediction is the spread in the temperature curves T1- T3. This is briefly discussed in section 5.2 in terms of the implementation of a non-linear temperature dependent electrical conductivity which is also possible in the code via an equation of state (EOS) in the EM_MAT card. The EOS id in the EM_MAT card then links to a curve defining the electrical conductivity versus temperature. 1-12

46 13 th International LS-DYNA Users Conference Session: Electromagnetic For the closer coupling distance and shorter heating time results shown in Figure 12, the implementation of a non-liner electrical conductivity is believed to be more important as the through thickness temperature gradients are much larger. In Figure 12, it can be seen that the top surface (T1) temperature predictions are good but that the temperatures in the other two locations are over predicted. In Figure 13, the results from the simulations of the 2 x 2 mm plate stack using the model shown in Figure 10 b) are compared with the experiments. Only the most relevant temperature location, T2, at the bonding interface has been compared for clarity. It can be seen that the prediction is again initially good but begins to deviate more and more at lower power levels and longer heating times. Figure 13: Comparison between experiments and LS-DYNA simulation results for a 2 x 2 mm thick CF-PPS plate at 5 mm coupling distance for T2 only at 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz The full set of simulation results for the 2 x 2 mm plate is given in Figure 14. A direct comparison can be made with the experimental curves obtained for the same parameter set shown earlier in Figure 7. Here it can be seen that the temperature at locations T1 and T3 are highly overestimated if the experimental results are assumed to be 100% correct. Further simulation versus experimental comparisons of a single 4 mm thick CF-PPS plate at 5 and 10 mm coupling distances were also performed. In this case, Figures 15 and 16 show very good overall predictions of the temperatures but again no sign of any non-linear type temperature rise in T1 or switching of the highest temperature location as was observed in the experiments. 1-13

47 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 14: LS-DYNA simulation results for a 2 x 2 mm thick CF-PPS plate at 5 mm coupling distance for all thermocouple locations T1- T3 at 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz Figure 15: Comparison between experiments and LS-DYNA simulation results for a single 4 mm thick CF-PPS plate at 5 mm coupling distance for 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz 1-14

48 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 16: Comparison between experiments and LS-DYNA simulation results for a single 4 mm thick CF-PPS plate at 10 mm coupling distance for 10% (163 A), 20% (231 A) and 30% (283 A) power and coil frequency of 540kHz It is very interesting to observe that in the simulations of 2 x 2 mm plates using the gap approach and no consideration of any contact resistance between the laminate stack, that the heating of the 2 x 2 mm material stack compared to a single 4 mm plate at the same coupling distance occurs faster. The difference however is small (21.9 sec versus 20.2 sec to 253 C for the 4 mm and 2 x 2 mm tests respectively) but is likely to be within the margin of error of the results. Preliminary implementation of the EM contact resistance card with Joule heating effect show much higher temperature predictions but still no kinking in the T1 temperature curves as observed experimentally for all tests but more prominently for the thicker material cases both connected and unconnected. 5-2 Influence non-linear electrical conductivity and orthotropic material input In general, using a constant value of electrical conductivity over-predicts the heating effect over a wider temperature range as can be seen in Figures By defining a non-linear electrical conductivity dependent on temperature, both the temperature spread through the thickness and the predictions over a large temperature range can be improved. This improvement however, comes at the expense of computing time as the electromagnetic fields must be recalculated enough times to capture the non-linearity. Initial simulations performed to assess the significance of orthotropic electrical conductivity tend to suggest no difference in the heating behavior when the material is 1-15

49 Session: Electromagnetic 13 th International LS-DYNA Users Conference considered electrically orthotropic as opposed to isotropic. In an isotropic case, the material is assumed to have an electrical conductivity equivalent in all directions to that measured in the inplane directions. It can only be presumed that the large order of magnitude difference (~1000) between the in-plane and through the thickness electrical conductivity, combined with the large skin depth (more that the entire thickness of the laminate stack, see Eqn. 1) results in an insensitivity to the through thickness value of electrical conductivity. This means that a simpler (isotropic) electromagnetic material model can in this case be applied. 6-Conclusions The following work has demonstrated further developments in the induction heating solver available in LS-DYNA R7. Focus was given here to the prediction of the through thickness temperature distribution in single and stacked CF-PPS thermoplastic composite plates of 1 and 2 mm thicknesses. At present the overall predicted Joule heating is good but several peculiarities which occur experimentally are not reproduced in the simulations. These are effects including the temperature on the plate surface closest to the coil becoming lower than the temperature measured in the middle or the non-coil side of the single laminate or laminate stack after a significant heating time at a temperature well below the melting temperature of the PPS polymer. It was suspected and discussed that material, temperature measurement and induction equipment effects may be responsible for the behavior. In order to help understand why the experiments deviate from the simulation in this respect, further experimental investigations using a very fine reinforcement structure will be performed together with two different types of induction heating equipment and temperature measurements with thermocouples and non-contact laser pyrometers. At present the simulations do not consider electrical and thermal contact between unconnected plates however this is currently being implemented to see what such effects then have on the through thickness heating behavior. References [1] D. Grewell, A. Benatar and J. Park. Plastics and Composites Welding Handbook. Hanser, München, [2] V. Rudnev, D. Loveless, R. Cook and M. Black. Handbook of Induction Heating. Marcel Dekker, New York, USA, [3] M. Duhovic, L. Moser, P. Mitschang, M. Maier, I. Caldichoury, P. L Eplattenier. Simulating the Joining of Composite Materials by Electromagnetic Induction. In: Proceedings of the 12th International LS-DYNA Users Conference, Electromagnetic (2), Detroit, [4] M. Duhovic, I. Caldichoury, P. L Eplattenier, P. Mitschang, M. Maier. Advances in Simulating the Joining of Composite Materials by Electromagnetic Induction. In: Proceedings of the 9th European LS-DYNA Users Conference, Manchester, [5] L. Moser. Experimental Analysis and Modeling of Susceptorless Induction Welding of High Performance Thermoplastic Polymer Composites, PhD thesis, Institute für Verbundwerkstoffe GmbH, Kaiserslautern, Germany, [6] J. Schuster, D. Heider, K. Sharp, M. Glowania, Thermal conductivities of three-dimensionally woven fabric composites, Composites Science and Technology, Volume 68, Issue 9, July 2008, Pages [7] LS-DYNA Theory Manual, LSTC. 1-16

50 13 th International LS-DYNA Users Conference Session: Electromagnetic [8] P. L Eplattenier, G. Cook, C. Ashcraft, M. Burger, A. Shapiro, G. Daehn, M. Seith, Introduction of an Electromagnetism Module in LS-DYNA for Coupled Mechanical-Thermal-Electromagnetic Simulations, 9th International LS-DYNA Users conference, Dearborn, Michigan, June [9] P. L Eplattenier, G. Cook, C. Ashcraft, Introduction of an Electromagnetism Module in LS-DYNA for Coupled Mechanical-Thermal-Electromagnetic Simulations, Internatinal Conference On High Speed Forming 08, March 11-12, 2008, Dortmund, Germany. [10] M. Duhovic, I. Caldichoury, P. L Eplattenier, P. Mitschang, M. Maier. Advanced 3D finite element simulation of thermoplastic carbon fiber composite induction welding. ECCM-16-16th European Conference on Composite Materials, Seville, Spain, June 22-26, [11] R. Holm, Electrical Contacts-Theory and Applications, 4th ed., Springer Verlag, New York,

51 13 th International LS-DYNA Users Conference Session: Electromagnetic Numerical Simulations to Investigate the Efficiency of Joint Designs for the Electro-Magnetic Welding (EMW) of the Ring-shaft Assembly H. Kim 1, J. Gould 1, J. Shang 2, A. Yadav 3, R. Meyer 3, Pierre L'Eplattenier 4 1 Edison Welding Institute, 1250 Arthur E. Adams Drive, Columbus, Ohio , U.S. 2 American Trim, 999 West Ground Ave., Lima, Ohio 45801, U.S. 3 Caterpillar Inc., Peoria, Illinois , U.S. 4 Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA Abstract In this study, numerical simulations on electro-magnetic welding (EMW) were conducted for dissimilar materials joint of the ring-shaft assembly. LS-DYNA electromagnetism module was adopted to simulate the EMW process. Simulation results were correlated with the EMW experimental works with two different joint designs, single and double flared lap joint. Two different materials, aluminum 6061-T4 and copper, C40, were used for the driver ring material on the stationary steel shaft. LS-DYNA simulation model was used to investigate the effects of impact angle and velocity on surface-layer bonding and joining efficiency of the driver ring on a steel shaft. Analytical modeling was also conducted to estimate the magnetic pressure between the coil and the ring. Experimentally, a 90-KJ machine was used at different energy levels. From these experiments, the double flared lap joint showed better joint efficiency and the copper showed better adhesion than aluminum at same energy levels. The performance of joint was evaluated by push-off testing. A double flared copper ring at 45-KJ gave the best performance of joint, and exceeded the required axial thrust load requirement. From the metallographic analysis, the interface of joint did not show the metallurgical bonding, however, strong mechanical interlocking was achieved. This study demonstrates the viability of EMW process for dissimilar material joining. KEYWORDS Electro-magnetic welding (EMW), Dissimilar materials joining INTRODUCTION Electro-magnetic welding (EMW) is a high-speed process used for joining tubular structures. EMW is applicable to a nominally lap-type joint of tube-to-tube or tube-to-bar configurations. EMW uses the magnetic repulsion between two opposing magnetic fields to drive a conductive metal. The energy stored in a capacitor bank is discharged usually within 20 ms, through an induction coil that encompasses the parts to be joined. The magnetic field produced by the coil crosses the workpiece, generating eddy currents in the workpiece. This current produces its own magnetic field. These two opposing magnetic fields at the coil and workpiece induce a repulsion force between the coil and the workpiece. The theory behind this repulsion is well explained by Lenz s law. This repulsion causes the outer workpiece to drive and impact the inner workpiece at very high velocity (Figure 1). These 1-1

52 Session: Electromagnetic 13 th International LS-DYNA Users Conference impact velocities, combined with an appropriate impact angle, are sufficient to create localized deformation and subsequent bonding. Figure 1. EMW System (Left) and the Configuration of Coil/Workpieces (Right) The resulting bond occurs with a morphology quite similar to that of explosion bonding. The process has shown particular promise for dissimilar materials joining that is usually hard to obtain by arc welding. Given the short cycle times, as well as the capability to join dissimilar material combinations, the process has attracted considerable attention in a range of industrial applications the aerospace, automotive, and electronics industries. OBJECTIVE The objective of this study is to reliably predict the effects of impact angle and velocity on surface-layer bonding and joining efficiency of the driver ring on a steel shaft. Figure 2 shows the required assembly design. A ring has to be welded on the steel shaft and this ring played as a mechanical stopper in actual service condition. Conventionally, this joint was made by arc welding. However, the joint strength is required to meet to a minimum 20-KN axial thrust load in service condition. Figure 2. The Ring-Shaft Assembly (all units are in mm) DESIGNS FOR WELD JOINT AND TOOLING Baseline components and process requirements for EMW were designed to join the ring-shaft assembly. Two different designs (single- and double-flared rings and associated concentrator) were conceived to accelerate the ring during EMW process, as show in Figures 3 and 4, respectively. Single-flared ring was designed to have almost zero gap in radius between the steel bar and the ring. Double-flared ring was designed to have a 2-mm gap on radius. Increasing the gap can increase the impact speed of ring during EMW, but it is not appropriate for the single-flared ring, because it can cause unnecessary plastic deformation of 3-mm straight section (Figure 3) and this can result in the loss of discharging energy. 1-2

53 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 3. Schematic of Designs of Field Shaper and Ring Object (all units are mm) The inclined angle of flared section of ring, namely attack angle, was recommended to be 15 degrees from extensive experimental work of EMW [Kojima et al., 1989 and Masumoto et al., 1985]. Figure 4. Schematic of Designs of Field Shaper and Double-Flared Ring Object (all units are mm) Two different materials, aluminum (Al 6061-T4) and chromium copper alloy (C18200) were used for ring. Al 6061-T6 tubes with 49.5-mm outer diameter and 3.5-mm-thick were machined to 10.7-mm long, and then heat treated to Al 6061-T4 condition. After heat treatment, the rings were flared to have 15-degree attack angle with a forming die in the hydraulic press. Copper rings were heat treated at 650ºC for 1½ hour and quenched to water. The yield strength and tensile strength of Al 6061-T4 are 45 and 241-MPa, respectively. The yield strength and tensile strength of C18200 are 352-MPa and 365-MPa. The bars and rings were polished with sand papers, and then cleaned with acetone. The double-flared samples were directly machined, because of difficulties in forming flares. Figure 5 showed both single- and double-flared samples. Figure 6 shows the initial position of double-flared ring into the halves of copper concentrator. 1-3

54 Session: Electromagnetic 13 th International LS-DYNA Users Conference Figure 5. Single- and Double-Flared Aluminum and Copper Samples Figure 6. Double-Flared Ring and the Split Halve of Copper Concentrator EXPERIMENTAL WORK The welding experiments were conducted in a MAGNEFORM 90-KJ magnetic pulse welder. The machine is equipped with 30 capacitors, and each capacitor has capacitance of 60-mF. The charging voltage over the capacitor bank is up to 10-kV. The main coil, a copper concentrator, and fixture are shown in Figure 7. The split halves of the concentrator are assembled around the ring. This sub-assembly is inserted into the bore of the filed shaper. All pieces in the assembly are insulated from each other with the use of Kapton tape. The completed assembly is then inserted into the bore of the single turn coil. Figure 7. The Split Halves of the Copper Concentrator (Left) and EMW Experimental Setup (Right) Welding trials were conducted in an iterative manner and the detailed test conditions are given in Table 1. The welded samples were selectively inspected by cutting the ring and checking if the ring was easily separated from steel bar. Push-off test and metallography were used to evaluate weld quality. The push-off test was conducted by using the 66.7-kN Instron Machine with the ram speed of mm/min. To hold the welded part during the testing, the annual fixture was used to fix a steel bar during the test. The maximum load and the displacement at the maximum load were measured from the machine. 1-4

55 13 th International LS-DYNA Users Conference Session: Electromagnetic Table 1. Testing Conditions. Ring Material Al 6061-T4 C18200 Joint Design Single flared Double flared Single flared Double flared Voltage (KV) 4.47/5.20/6.32/ 7.75/8.94/ /6.32/7.07/ 7.75 Energy (KJ) 18/24/30/36/ 72/81 24/36/45/54 EXPERIMENTAL RESULTS In EMW tests, most of the single-flared ring samples showed relatively weak joint with steel bar compared to the double-flared ring samples. Aluminum ring samples showed local melted edge as the discharge energy was increased, while the chromium copper alloy ring did not show any local melting at same or even higher levels of energy. Figure 8 shows double-flared aluminum samples tested at 24-KJ and 30-KJ. Figure 9 shows the doubleflared copper sample tested at 45-KJ. Figure 8. Aluminum Ring Samples Joined to Steel Bars Figure 9. Copper Ring Sample Joined to Steel Bars at 45-KJ Push-off test results are summarized in Table 2. Double-flared copper samples No.35 and No.37 tested at 45-KJ showed the maximum load to be about 80-kN and 62-kN, respectively. 1-5

56 Session: Electromagnetic 13 th International LS-DYNA Users Conference Table 2. Push-Off Testing Results. Micrographs at the joint interface were taken to inspect the weld line. However, there are no clear metallurgical bonding observed between steel and aluminum that are marked as CS and Al in Figure 10. The copper ring sample also did not show any metallurgical bonding and after cutting the ring samples from joint, it was easily separated from steel bar. With these micrographic results, most of the joints were made by mechanical fitting without metallurgical bonding. Interestingly, this mechanical fitting showed significantly higher joint strength in push-off tests. Figure 10. Micrographs of EMW Joint Area ANALYTICAL RESULTS Magnetic pulse pressure, P m, was calculated by using the analytical equation (1) [Gourdin 1989 and Daehn 2005]. Pm = m n f I t 2 2 ls ( ) (1) Where m 0 = magnetic permeability, n = the number of coil turn, l s=coil length, f 2 =the coupling factor between the primary and the secondary currents. This analytical model does not consider any efficiency loss of current while it transfers from the main coil-tocopper concentrator and ring. The measured time-current curves were used to calculate the magnetic pulse pressures. Figure 11 and Figure 12 show the measured curves for the aluminum ring sample at 30.6-KJ and the copper ring sample at 45-KJ. The maximum magnetic pressure was calculated as 2.39-GPa for the aluminum ring sample and 4.05-GPa for the copper ring sample. 1-6

57 13 th International LS-DYNA Users Conference Session: Electromagnetic Figure 11. Measured Time-Current Profile for Aluminum Ring Tested at 30.6-KJ. Figure 12. Measured Time-Current Profile for Copper Ring Tested at 45-KJ. LS-DYNA SIMULATION RESULTS Figure 13 is the 3D FEM model built by LS-DYNA. It can be seen that this model is actually axisymmetric. To save the computational time, a 2D axisymmetric model was built to simulate the forming of double-flared rings, shown in Figure 14. Figure 13. 3D FEM model of double-flared rings with coil and field shapers 1-7

58 Session: Electromagnetic 13 th International LS-DYNA Users Conference (a) Steel rod Field shaper 1 Field shaper 2 Coil Double-flared ring (b) Figure 14. 2D FEM model of double-flared rings with coil and field shapers (a) whole 2D model; (b) closer view The AISI 4140 steel rod was set as rigid material with shell elements. The double-flared rings of Al T4 and C18200 were modeled using Johnson-Cook strength model, which is listed in Table 2. Table 2. Parameters of Johnson-Cook strength model for Al 6061-T6 Al 6061-T4 (Johnson, 1983) Cu (Johnson, 1985) A (MPa) B (MPa) C n m Tm (K) Figure 15 shows the simulation results of the 2D simulation for the case of Cu double-flared ring EM formed at 45-KJ. The measured current profile in Figure 12 was set as the input for the simulation. The simulation results indicated that the Cu double-flared ring began to move at 2.80-µs. The middle section of the ring impacted the steel rod at µs with the velocity of 282-m/s, shown in Figure 15 (3). The two ends of the Cu ring continued to move forward after the middle section impacted the steel rod. The two ends impacted the steel rod at µs with the velocity of 396-m/s. It should be noted that the simulation results indicated that the impact angle was small (around 1~3 degree), shown in Figure 15 (3), (4) and (5). The small impact angle made the impact welding hard to achieve. The 2D simulation for the case of Al6061-T4 double-flared ring EM formed at 30.6-KJ. The measured current profile in Figure 11 was set as the input for the simulation. The simulation results showed the middle section of Al6061-T4 double-flared ring impacted the steel rod at the velocity of 403-m/s, and the two ends of the Al6061- T4 ring impacted the steel rod at the velocity of 538-m/s. Similar as the Cu double-flared ring, the impact angle was small, around (3~5 degree), which also made the impact welding hard to achieve. 1-8

59 13 th International LS-DYNA Users Conference Session: Electromagnetic (1) (2) (3) (4) (5) (6) Figure 15. Double-flared Cu ring at different time frame (EM formed at 45-kJ) (1) t=0-µs; (2) t=10.19-µs; (3) t=18.40-µs; (4) t=19.00-µs; (5) t=20.20-µs; (6) t=21.20-µs FINDINGS The following findings can be summarized from this study: The single- and double-flared ring samples with a zero gap did not show any reliable joint in test. To increase the kinetic energy for welding, the ring-shaft gap was increased to 2-mm and the double-flared ring samples with 2-mm gap showed the improved retentions between the ring and the shaft, but no welding was obtained. The double-flared with 2-mm gap showed the best performance in terms of the maximum push-off load. Finite-element analysis (FEA) simulation predicted the impact velocity of Cu double-flared ring was at the range of 282-m/s to 396-m/s, and the impact velocity of Al 6061-T4 double-flared ring was at the range of 403-m/s to 538-m/s. Finite-element analysis (FEA) simulation predicted the impact angles for both the Cu and Al6061-T4 double-flared ring were small, which made the impact welding hard to achieve. The diameter/thickness ratio ~12.0 was found to be difficult to weld for EMW because of small impact angle and thermal damage and melting as the current levels increased. DISCUSSIONS 1-9