Thomas Zacharia Metals and Ceramics Oak Ridge National Laboratory. Oak Ridge, TN (615) (FAX: )

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1 ADVANCED COMPUTATONAL RESEARCH NMATERAS PROCESSNG FOR DESGN AND MANUFACTURNG Thomas Zacharia Metals and Ceramics Oak Ridge National Laboratory Oak Ridge, TN (615) (FAX: ) 'me submctted msmrscnpt has been authored by a mntractor of the u s Go-t under contract NO. DEAC05-840R A c m r h ~ l y. the U.S G0ver-t retains a nonexdustve. royaltv-frea bcmsa to wbkh (x rewodwe the pubkshed fom of tha con-. or ahow o h to do so, foc U S Government w-" DSCLAMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thareof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. MASTER

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3 ADVANCED COMPUTATONAL RESEARCH N MATERALS PROCESSNG FOR DESGN AND MANUFACTURNG Thomas Zacharia Metals and Ceramics Oak Ridge National Laboratory Oak Ridge, TN (615) (FAX: ) ABSTRACT The computational requirements for design and manufacture of automotive components have seen dramatic increases for producing automobiles with three times the mileage. Automotive component design systems are becoming increasingly reliant on structural analysis requiring both overall larger analysis and more complex analyses, more threedimensional analyses, larger model sizes, and routine consideration of transient and non-linear effects. Such analyses must be performed rapidly to minimize delays in the design and development process, which drives the need for parallel computing. This paper briefly describes advanced computational research in superplastic forming and automotive crashworthiness. NTRODUCTON The introduction of new materials in automotive applications leads to a long development cycle because crashworthiness, durability, aging, life-time performance, and other extended lead-time factors need to be well understood prior to entering the 4to 5-year development cycle. Time constraints on vehicle development; the need for optimized components; the high cost of gearing up; and very high demands on performance, appearance, and durability indicate that new materials and processes will have a very difficult time breaking the barriers of experience and knowledge base held by traditional materials. The auto industry has identified key focus areas, including product lead times, development costs, and quality where rapid improvements in the production cycle must be made. Traditional methods for new product development involve building and testing prototype hardware. The issues of production, cost, and quality can be addressed by reducing the dependence on traditional empirical approaches and by increasing the use of accurate analytical vehicle modeling techniques. This process is based on a rational approach to minimizing the number of physical structures that would be required to be built

4 and tested to prove a design. The complexity of the numerical model requires intensive computation and large amounts of associated data. These requirements make simulations with moderate and large discretization grids intractable for singleprocessor computers. The emergence of parallel computers has revolutionized approaches to numerical solutions of large-scale engineering problems. Figure 1 shows the significant increase in performance achieved by the massively parallel machines since 1990,where the MP Linpack denotes the benchmark that is widely used for comparing performance of supercomputers [11. New algorithms are being developed by researchers in engineering and computer science in order to exploit the tremendous potential of parallel computing. Parallel computers have thus become important tools to solve complex and computationally intensive science and engineering problems. recent years, much effort has been devoted to the exploitation of parallelism for the solution of large systems of equations. Several linear finite element analysis programs implemented on different parallel computers have been proposed in recent years [3-51. Parallel algorithms are also reported for the solutions of stability problems [6], transient and dynamics problems [7-91, optimization problems [lo], and linear programming [1 11. As structures become more sophisticated, the need for efficient algorithms to accurately assess the response is growing. The use of massively parallel computers combined with the parallel domain decomposition approach has an attractive potential. The previous results [ show that the parallel computing can be successfully applied to two-dimensional static and dynamic problems in materials processing. This paper presents the results of high performance finite element simulations of superplastic forming and automotive crashworthiness, two areas critical to the design and engineering of advanced lightweight automobiles. - ::E?:+ HGH PERFORMANCE COMPUTNG, 20 0 ly YY4 1YYl ~~ ~~ 1YYS ~ Figure 1. Massively parallel performance. The recent availability of parallel computing systems has generated significant interest in the structural engineering community for development and implementation of various parallel schemes for engineering computations. Miranker [2] surveyed various parallel numerical schemes which could be used to solve a variety of engineering problems. n At ORNL, researchers have the choice of several parallel computing platforms ranging from the Kendall Square Research KSR-1 to several ntel Paragons and the ipsc/860. These parallel computers are one of two general types: shared memory (KSR-1) and distributed memory (ntel machines) multi-processors. Shared memory multi-processors allow all processors equal access to memory that has been declared global, usually through a common communication channel. This means that all of the processors can access any portion of the computer's memory. As the number of processors sharing the memory and the communication channel increases, the potential for contention between the processors for control of the memory increases. On the other hand, distributed memory multiprocessors are characterized by a network of communication channels, each of which connects a processor to another processor and memory units. Typically,each processor has a local memory of limited size. When a processor needs

5 data stored in memory other than its own, the eomput er program must explicitly request transmission of those data. The processors would send and receive messages containing the results of calculations in a single processor. Extra programming effort is required for coordinating data movement. Because communication channels are not shared in distributed memory architectures, they are more efficient than bus architectures in the use of processors and memory. Lack of equal access to memory by all processors makes the use of distributed memory computers more difficult and more limited. The finite element code DYNA3D [15] for analysis of large deformation problems in metal-forming and crashworthiness has been ported to the ntel Paragon using the Message Passing nterface (MP) standard [16]. The standard has been recently established in order to provide a stable environment for parallel program and operating system development. The variety of hardware designs and communication protocols makes porting of parallel computer programs to different computer architectures a considerable effort that does not significantly increase the value of the software. Writing a parallel program using standard conventions for communication alleviates the programming task and moves the design of communication to the domain of the operating system designer. As a principal method for exploiting concurrent processing, the domain decomposition technique has been employed in the program. The program uses the recursive spectral bisection (RSB) algorithm [171 for decomposing the problem into a number of subdomains. RSB is derived from a graph bi-section strategy and recursively divides the computational domain, as specified, into powers of 2 (2', 22, 23,24,...). Each subdomain is assigned to a specific processor. The efficiency of this computation is influenced by two factors: the computer's "load balance" and communication cost. f work is distributed unevenly, then most of the processors may be idle during much of the computation time - a waste of computer cycles. Even if work is well distributed, processors will be idle while they are waiting to receive the data from other processors needed to perform the next task. Characteristic of the domain decomposition approach is that, for a given problem size, there is a limit to the number of processors that can be effectively utilized [18]. After the computational effort, which is proportional to subdomain size, becomes comparable to communication, the program execution time cannot be further reduced by increasing the number of processors. Therefore, the communication phase of a program must be efficiently designed in order to delay performance saturation, beyond which adding processors will not reduce computational time. APPLCATONS As an example of the importance of advanced computational analysis in design and manufacturing, two problems have been selected: (1) metal-forming and (2) crashworthiness. The results from preliminary analyses are presented in the next sections, Superplastic Forming Some alloys, produced under special conditions and deformed at a carefully controlled low strain rate and high temperature, exhibit extreme ductility, called superplasticity. Superplasticity allows components typically produced by joining many pieces together into an assembly to be redesigned into a single component, lowering the manufacturing cost. Forming is accomplished using gas pressure to blow hot sheet into a die cavity or over a preform, in a process very similar to vacuum forming or blow molding of polymer sheet. Enhanced numerical simulation of material deformation during superplastic forming (SPF) of lightweight materials is an important element in achieving forming rate and cost goals for high production applications. Superplastic formability and service properties are strongly affected by strain rate, and the resulting distribution of thickness in the formed part is dependent on the part geometry and friction. Because of the high sensitivity to variations in strain rate, it is important to use a pressurization schedule during forming which will lead to acceptable formability. The ability to numerically predict forming behavior is critical to increasing forming rates and decreasing manufacturing cycle times. The models provide a means of tracking strains and strain-rates during the forming process, allowing the applied gas pressure to be adjusted to maintain the optimum SPF behavior throughout the forming process. The pressure-time

6 history predicted by the numerical model can then be applied during an actual forming process to produce the optimum SPF component in the least amount of time. Until recently, only simple shapes such as long (plane strain) and axisymmetric pans could be easily analyzed. The corners of square and rectangular pans take an extensive amount of time to completely fill the die cavity. Massively parallel high performance computers present the potential to solve complex models in a reasonable t h e period as shown in Figure 2. The results indicate a reduction in computational time from 31 days to 6 hours using 128 processors. For the 128 processors used in the analyses, the model scaled well, exhibiting - linear increase in computational speed. Calculation of Super-Plastic Forming v E 600 3p. 31 days , ,410 60, ,970 The calculated pressure schedule is presented in Figure 4. The pressure initially increases to a value of 100 psi within 500 s, and is held at that level for 1400 s beyond which the pressure is ramped up to a maximum of 420 psi to tuck in the comers. The calculated thickness profiles show good qualitative agreement with prior experimental observations on similar parts. The results are consistent with past experience that show the part failing at the corner due to over-thinning Belytschko-Tsay Shell Elements Nodal Points ia ii hours 200 '\\ i860 Nodes Figure 2.Speedup of SPF calculation with number of processors. The analysis was performed for an Aluminum 5083 alloy, processed to obtain microstructure that favors superplasticity. The pan (Fig. 3.) was formed at 525OC at a strain rate of in/in/s. The material model used in the analysis describes the yield stress by the following relationship: ay = K E" k"', where K, m, and n are material constants. For the Aluminum 5083 alloy, the strain-rate sensitivity coefficient, m, is K and n are functions of plastic strain as given in Table 1. Figure 3. Supex-plastic formed Aluminum 5083 alloy pan. Automotive Crashworthiness n order to achieve the goals of three times the fuel economy for the next generation automobile, significant weight reduction (almost one-third) must be achieved. While some weight savings can be obtained by improved design, it is clear that new materials have to be developed and used in order to achieve the necessary weight reductions.

7 B U (: : a Ln 2 a TME (seconds) Figure 4. Calculated pressure schedule. The cost of just one physical crash test can range from $50,000 to $750,000 (or more) depending upon whether the test is performed on a production model car or a prototype vehicle, respectively. The high expense of impact testing and the availability of supercomputers have motivated the development of sophisticated computer programs to model such complex physical phenomena. Many of these computational applications are highly computeintensive. n studies of crashworthiness, impact, and penetration, it is not unusual for an analysis to require several weeks of CPU time on current supercomputers despite the simplicity of the models being studied. The computational requirements for a single Belytschko-Tsay shell element with five integration points through the thickness are on the order of 3500 floating point operations per time-step and 602 words of memory. Crashworthiness models currently use 50,000 to 200,000 elements and run for about 100,000 time steps! To meet the need for greater processing speed, massively parallel computer designs have emerged that make multiple processors available to the user. Massively parallel computers, which combine several thousand processors, are able to operate concurrently on a problem. These computers provide exciting new opportunities for crashworthiness simulations by allowing the implementation of more complex databases and more realistic simulations enabling the assessment of integrated design and performance of lightweight materials in automotive applications. Recently, a car-to-car crash analysis was performed on the ORNL Paragon for the first time. A detailed finite element (FE) model of a 4door sedan was provided by the Department of Transportation [19] for evaluating the performance of crash simulation on the ORNL Paragon. The FE model of the vehicle was created by digitizing components of the vehicle, starting from external components to internal components. The front-end components from bumper to A-pillar were modeled with fine mesh while the rear half of the car had fairly coarse mesh density. Components like the bumper, front rails, upper load path beams, radiator, engine cradle, etc., were modelled to capture all significant geometric imperfections such as holes, beads, and crush initiators which play a vital role in the overall crash characteristics of a vehicle. The model used 248 material cards, defining the material models employed, an initial velocity of 35 mph, and a tire pressure of 35 psi. The analyses were performed by partitioning the problem into subdomains and assigning each subdomain to different processors. Figure 5. shows a typical decomposition of the finite element model for a single car divided into four subdomains. The decomposition algorithm assigned most of the outer body, including the engine block, of the car to a single processor. The remaining front end, requiring a fine mesh to resolve the contact problem, is partitioned into three subdomains. The model is partitioned such that the amount of calculation performed in each processor is roughly the same. Figure 6 shows the results of a 50% offset, car-to-car, frontal crash analysis performed on the ORNL Paragon. The analysis which took 48 hours on a CRAY-YMP was completed in 8 hours using 128 processors on the ntel Paragon. CONCLUSONS Massively parallel computers provide marked performance improvements over other single processor supercomputers. Applications to metal forming problems resulted in an order-of-magnitude reduction in computational time. The results indicate good scalability up to a maximum number of processors. The results of the study also confirm the applicability of massively parallel computing for crashworthiness analysis. For the first time, a car-tocar crash analysis was performed on a massivelyparallel computer. As in the case of metal forming, the results indicate significant performance gains over traditional supercomputers.

8 Figure 5. Finite element model divided into 4 sub-domains. Figure 6. 50% offset impact analysis on massiveiy parallel computer.

9 ACKNOWLEDGMENTS The authors thank Dr. B. Radhakrishnan and Dr: Srdan SimunoviC for reviewing the manuscript. The authors acknowledge the use of the ntel Paragon computers located in the Oak Ridge National Laboratory Center for Computational Sciences (CCS),funded by the Office of Scientific Computing, U.S. Department of Energy. The research was sponsored by the U.S. Department of Energy, Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies, Lightweight Materials Program, under contract DE-AC05-840R21400 with Martin Marietta Energy Systems, nc. REFERENCES 1. J. Dongarra, H. W. Meuer, and E. Strohmaier, "TOP500 Supercomputer Sites" (Technical Report RUN 40/94, University of Mannheim, Germany). 2. W. L. Miranker. "A survey of parallelism in 3. C. Farhat, E. Wilson, and G. Powess. "Solution of finite element systems on concurrent processing computers," Eng. Comput. 2, (1987). numerical analysis," SLAM Rev. 13, (1971). 4. H. Allik, S. Moore, E. O'Neil, and E. Tenebaum. "Finite element analysis on the BBN Butte,'' Cornput. Struct. 27(1), (1987). 5. D. Xois. "Parallel processing techniques for FE analysis: stiffness, loads and stresses evaluation, Comput. Struct. 28(2), (1988). ' 6. S. P. Darbhamulla, Z. Razzaq, and Storaasli. "Concurrent processing in nonlinear column stability, " Eng. Cumput. 4, (1988) Storaasli, J. Ransom and R. E. Futon. "Structural dynamic analysis on a parallel computer: the finite element machine, " Comput. Sfrzicf.26(4), (1987). 8. R. Ou and R. E. Fulton. "An investigation of parallel numerical integration methods for nonlinear dynamics," Comput. Struct. 30( 1/2), (1988), 9. C. Farhat and E. Wilson. "Anew finite element concurrent computer program architecture, nt. J. Numer. Method Eng. 24, (1987). ' 10. H. Adeli and 0. Kamal. "Parallel algorithms for structural optimization under dynamic loading," Proceedings of the Parallel Distributed Processing in Structural Engineering, ASCE National Convention, Nashville, Tenn. (ed. H. Adeli), pp (1988). 11. D. T. Nguyen and T. V. Ninh. "Parallel computations for linear programming," Proceedings of the Computer Utilization in Structural Engineering,ASCE Structures Congress '89 (ed. J.K. Neson, Jr.), pp (1989). 12. T. Zacharia, M. A. Bjerke and S. Simunovic. "High Performance Computing for Materials Process Modeling," Proceedings of the nternational Conference on Modeling and Control of Joining Processes, (ed. T. Zacharia), pp (1993). 13. T. Zacharia and G. A. Aramayo, "mpact Analysis on Massively Parallel Computer, " Proceedings of the U.S. Department of Energy Defense Programs Packaging Workshop May 6-20, P. Su, R. Fulton, and T. Zacharia. mplementation of ParallelMatrixDecomposition f o r NKE3D on K S R l S y s t e m, ORNLflM-12733, Oak Ridge National Laboratory, (1995). 15. J. 0. Hallquist, D. W. Stillman, and T. Lin, "LS-DYNA3D Users Manual," LSTC Report 1007, Rev. 2, Livermore Technology Corporation (1992). 16. Message Passing nterface Forum, "MP: A Message Passing nterface Standard" (Technical Report, University of Tennessee, 1994). 17. H. D. Simon, Computing Systems in Engineering 2, (2/3), 135 (1991).

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