Knowledge Based Cloud FE Simulation of Sheet Metal Forming Processes

The use of Finite Element (FE) simulation software to adequately predict the outcome of sheet metal forming processes is crucial to enhancing the efficiency and lowering the development time of such processes, whilst reducing costs involved in trial-and-error prototyping. Recent focus on the substitution of steel components with aluminum alloy alternatives in the automotive and aerospace sectors has increased the need to simulate the forming behavior of such alloys for ever more complex component geometries. However these alloys, and in particular their high strength variants, exhibit limited formability at room temperature, and high temperature manufacturing technologies have been developed to form them. Consequently, advanced constitutive models are required to reflect the associated temperature and strain rate effects. Simulating such behavior is computationally very expensive using conventional FE simulation techniques. This paper presents a novel Knowledge Based Cloud FE (KBC-FE) simulation technique that combines advanced material and friction models with conventional FE simulations in an efficient manner thus enhancing the capability of commercial simulation software packages. The application of these methods is demonstrated through two example case studies, namely: the prediction of a material's forming limit under hot stamping conditions, and the tool life prediction under multi-cycle loading conditions.


Introduction
Finite Element (FE) simulations have become a powerful tool for optimizing process parameters in the metal forming industry. The reliability of FE simulation results is dependent on the accuracy of the material definition, input in the form of flow stress data or constitutive equations, and the assignment of the boundary conditions, such as the friction coefficient and the heat transfer coefficient. In the past few years, advanced FE simulations have been developed via the implementation of user-defined subroutines, which have significantly broadened the capability of FE software.
The use of such advanced FE simulations in the design of forming processes for structural components has been investigated by both the aviation and automotive industries, with the intention of producing lightweight structures that reduces operating costs and CO 2 emissions. Particular focus has been placed on the replacement of steel components with lower density materials, such as aluminum alloys and magnesium alloys. However, these alloys, especially the stronger variants, offer limited formability at room temperature and thus complexshaped components cannot be manufactured using the conventional cold stamping process. Therefore, advanced high temperature forming technologies, such as warm aluminum forming [1][2][3][4] , hot stamping of aluminum alloys [5][6][7][8][9] and hot stamping of high strength steels 10 , have been developed over the past decades to enable complex-shaped components to be formed. In general, high temperature forming processes involve significant temperature variations, strain rate and loading path changes 11 , which would, for instance, cause inevitable viscoplastic and loading history dependent responses from the work piece materials. These are intrinsic features of high temperature forming processes and may be difficult to represent using conventional FE simulation techniques. Another desirable feature would be the ability to predict the tool life over multiple forming cycles in such processes, since they require low friction characteristics achieved through coatings that degrade with each forming operation. To represent all these features via the implementation of user-defined subroutines would be computationally very expensive. Moreover, the development and implementation of multiple subroutines would require excessive multi-disciplinary knowledge from an engineer conducting the simulations.
In the present work, a novel Knowledge Based Cloud FE (KBC-FE) simulation technique is proposed, based on the application of modules on a cloud computing environment, that enables an efficient and effective method of modeling advanced forming features in conjunction with conventional FE simulations. In this technique, data from the FE software is processed at each cloud module, and then imported back into the FE software in the relevant consistent format, for further processing and analysis. The development of these modules and their implementation in the KBC-FE is detailed.

Development of a High Temperature Forming Limit Prediction Model
1. Laser cut the specimens for formability tests from the aluminum alloy AA6082 sheets (1.5 mm thickness) into the selected geometries 12 .
2. Etch a grid pattern, composed of 0.75 mm diameter circular points with a regular spacing of 1 mm, on the surface of the specimens using an electrolytic method 13 . 3. Manually apply graphite grease as a lubricant on the non-etched side. 4. Assemble the dome test rig in a high rate hydraulic press 12 . Use a 250 kN hydraulic universal testing machine. 5. Heat up the dome test rig to a testing temperature and set the punch at a constant moving speed. Then initiate the test.
Note: The testing temperatures are 300, 400, and 450 °C, respectively. The testing speeds include 75, 250, and 400 mm/s. 6. Stop the test at the first occurrence of necking.
Note: The press stroke (i.e., final specimen height) is set such that necking is just observed on the formed specimen. 7. Measure the final specimen height using a height gauge, and calculate the strains and maximum strain rates (the rate of change of strain with respect to time) using an optical 3D forming analysis system. Analyze the changes in the grid spacing to compute the strains at each point of the formed specimen. 8. Ensure that the optical 3D forming analysis system includes a camera, the formed specimen, and calibration scale bars 14 .
Note: The specimen is placed at the center of a turntable and enclosed with the scale bars, and their relative positions are kept fixed for the duration of the analysis. 9. Set the camera at a fixed elevation (e.g., 50 cm) and angle (e.g., 30, 50, or 70°) to the specimen, and take pictures over a complete rotation (360°) of the turntable, in increments of 15°. Note: In the present work, three sets of images were acquired from multiple camera elevations and angles in order to map the strains over the entire specimen 15 . 10. Load the images into the optical 3D forming analysis software, and proceed to compute the strains. Do this by clicking on the 'compute ellipses and bundle' function, which detects the grid points, followed by clicking the 'compute 3D points and grid' function which builds up the grid. Note: Calculate the strains and visualize it in the evaluation mode. 11. Output the strain distributions to determine the limit strains for each specimen based on ISO 12004 16 , and plot the forming limit diagrams for different forming speeds and forming temperatures. 12. Calibrate a material model for AA6082 at different temperatures from 300 to 500 °C and strain rates from 0.1 to 10 s -1 .
Note: The material model and its constants for AA6082 are detailed in reference 17 .
13. Implement and unify the Hosford anisotropic yield function 18 , Marciniak-Kuczynski (M-K) theory 19 and the material model in step 1.12 into an integration algorithm so as to formulate the forming limit prediction model. Note: The model is described in reference 11 . 14. Calibrate and verify the developed model for step 1.13 using the experimental results obtained in step 1.11. 15. Predict the forming limits through the verified model 11 from step 1.14.
Note: Figure 1 shows the resulting model predictions at different temperatures, at a forming speed of 250 mm/s, or equivalently, a strain rate of 6.26 s -1 .

Development of an Interactive Friction/Wear Model
1. Perform ball-on-disc tests for coated (disc) specimens 1. Prepare titanium nitride (TiN) coatings on bearing steel GCr15 disc using cathode arc and mid-frequency magnetron sputtering, with the deposition parameters given in reference

Develop the interactive friction model
1. Characterize the overall friction coefficient µ by combining the initial friction µ α with the ploughing friction of hardware particles µ Pc (as shown in Eq.(1)) 20 . (1) 2. Combine the ploughing friction between the ball and substrate (µ Ps ) with the instantaneous coating thickness (h) to model the coating breakdown induced sharp increase of the ploughing friction µ Pc (Eq.(2)). Note: In this case, µ Pc equals µ Ps when the remaining coating thickness is zero (indicating the complete breakdown of the hard coating).
(2) whereλ 1 and λ 2 are model parameters introduced to represent the physical meaning of the wear process. λ 1 describes the influence of large entrapped wear particles, and λ 2 represents the intensity of the ploughing friction effect, which is characterized by the slope of the friction coefficient. 3. Use a time based integration algorithm to obtain the evolution of the remaining coating thickness and model the accumulated wear under varying contact conditions. Update the coating thickness in each calculation loop by Eq. (3).
where h 0 is the initial coating thickness and is the time dependent wear rate of the coating. 4. Modify Archard's wear law 22 (Eq. (4)) and implement it in the present model.
where K is the wear coefficient, P is the contact pressure, v is the sliding velocity, and H c is the combined hardness of the coating and the substrate. 5. Use Korsunsky's model to calculate the combined hardness (Eq. (5)).

(5)
where H s is the hardness of the substrate, α is the hardness ratio between coating and substrate and β is the influence coefficient of the thickness. 6. Represent the load dependent parameters λ 1 and K by power law equations.
where κ λ1 , κ K , Ν λ1 and Ν K are material constants related to the evolution of friction 20 . 7. Fit the interactive friction model to the experimental results using an integration algorithm developed in the authors' group to determine the model parameters.

KBC-FE Simulation Case Studies
1. KBC-FE simulation case study 1: prediction of forming limit under hot stamping conditions 1. Create and name a new simulation project in the FE simulation software. Select the process as 'Stamp hot forming' and the solver type as 'PAM-AutoStamp' when saving the project. 2. Import the door inner die by clicking on the 'Import tools CAD' and then 'Import & transfer' the door inner 'IGS' geometry file into the FE simulation software graphic interface. Select the 'Hot forming' strategy for meshing of tools. Name the imported object as 'Die'.

KBC-FE Simulation for Necking Prediction
In a hot stamping process, the use of a shape-optimized blank will not only save material cost but also help to reduce the presence of defects, such as necking, cracking, and wrinkling. The initial blank shape affects the material flow significantly during forming, and hence a sensible design of the blank shape is critical to the success of the hot stamping process and quality of the final products. To reduce the efforts of trialand-error experiments to determine the optimal blank geometry, KBC-FE simulation was proven to be a highly efficient and effective method for minimizing the areas with necking. Using this technique, each simulation takes approximately 2 hours, while the parallel cloud module computation for necking prediction is completed within 4 hours. Figure 4 shows the evolution of the blank shape used in the hot stamping, an example of automotive door inner component. The initial blank shape, adopted from a conventional cold stamping process, was first used in the KBC-FE simulation. Experimental results in Figure 4(a) show that large failure (cracking or necking) areas are visible after the hot stamping. After one iteration of the blank shape optimization, it can be seen in Figure 4(b) that an almost fully successful panel is formed with much less necking, compared to using the initial blank shape. It can be seen that there is still an indication of necking at the pockets in the top right and left corners of the panel. After further optimization in Figure 4(c), the optimized blank shape was finally obtained with no visible necking on the panel. The optimized blank shape determined by the KBC-FE simulation was verified experimentally through hot stamping trials conducted on a fully automated production line offered by a production system manufacturer.

Discussion
The KBC-FE simulation technique enables advanced simulations to be conducted off site using dedicated modules. It can run functional modules on a cloud environment, that link up nodes from different specializations, to ensure that process simulations are conducted as accurately as possible. The critical aspects in the KBC-FE simulation may involve independency of the FE codes, efficiency of the computation, and accuracy of the functional modules. The realization of each advanced function in a module would rely on the development of a new model and/or a novel experimental technique. For example, the forming limit module is developed based on the new unified forming limit prediction model 11 , and the friction tool life prediction module has currently been developed by the implementation of the interactive friction model 20 . The KBC-FE simulation technique also offers the function of selective computation, i.e., only the elements fulfilling the selection criteria are selected for further evaluation in the individual modules. For instance, the tool life prediction module automatically selects the elements for which the hard coating tends to breakdown, by ranking the wear rate of all the elements in the 1st forming cycle, thus usually less than 1% of the elements will be selected for further tool life evaluations under multi-cycle loading conditions. In the present research, the tool life prediction after 300 forming cycles can be completed within 5 min.
By conducting the relevant tests and calibrating accordingly, the forming limit model could be applied to forming process simulations to consequently determine the optimal parameters for producing a component from such alloys successfully, and with no incidences of necking. The forming limit prediction model was developed as a cloud module that was independent of the FE software being utilized, and could be applied to any FE software to assess the formability of a material during forming, without complicated subroutines 17 . By importing the relevant data into the model, calculations could be carried out to determine whether failure would occur, in regions of the component that the user could specify, saving on computational resources. However, it should be noted that as the stress-strain curves are input into the FE software through a simple look-up table, it may be difficult to fully represent the material properties at various temperatures and strain rates during simulation.
In the tool life prediction module, the frictional behavior during forming can be predicted by importing the required deformation history data into the verified friction module 20 , and then importing the discrete data points calculated by the cloud module for each element back into the FE software. This ensures that the advanced friction module can be used by all FE codes, regardless of their ability to incorporate user-subroutines. Additionally, the module could be run in parallel to further reduce the computation time. The interactive friction/wear model assumed the absence of wear particles during initial sliding, and as a result, it would be reasonable to expect a constant initial value of friction coefficient 0.17 20 . Although this model revealed the evolution of friction distribution, the frictional behavior during a forming process is very complicated, and it is difficult to completely integrate the complex frictional behavior from the cloud module into the FE simulation.
As a future technology, the KBC-FE simulation will rely on the development of dedicated and robust internet based FE simulation software packages, which would require a highly profitable, but completely different business model to be established by the software developers. In addition, a dedicated internal network needs to be built within the collaborative parties to ensure data security and the control reliability of the industrial system.

Disclosures
The authors have nothing to disclose.