EXPLICIT SIMULATION AND HIGH-PERFORMANCE COMPUTING, APPLICATION TO A BOLT TENSILE TEST

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1 Original Article Proceedings of IDMME - Virtual Concept 2010 Bordeaux, France, October 20 22, 2010 HOME EXPLICIT SIMULATION AND HIGH-PERFORMANCE COMPUTING, APPLICATION TO A BOLT TENSILE TEST L. Adam 1, 2, A. Daidié 1, B. Castanié 1, E. Bonhomme 2 (1) : Université de Toulouse; INSA, UPS, Mines Albi, ISAE; ICA (Institut Clément Ader); 135, avenue de Rangueil, F Toulouse, France louis.adam@insa-toulouse.fr (2) : Airbus Operations SAS, 316 Route de Bayonne, Toulouse, France Abstract: The European project Maaximus (More Affordable Aircraft Structure Lifecycle through extended, Integrated & Mature numerical Sizing) aims at demonstrating the fast development and right-first-time validation of a highly optimized composite airframe. In this context, fasteners models are crucial to ensure correct structure modelling at a higher level. The present study focuses on a bolt tensile test. After a review of the state-of-the-art in this domain, the first part of the study is dedicated to explicit simulation and its specificities: resolution algorithm, mass and time scaling, comparison of energies. We also discuss about High-Performance Computing (HPC), and the need of consistency between model and computation structure. These simulation techniques are then applied to the modelling of the fastener tensile test. Experiments have been led with various fasteners diameters. We observe successful correlation between simulation and experiments both qualitatively and quantitatively. Key words: Fasteners, Simulation, Finite Elements, High- Performance Computing, Experiments. shank, screw/nut threads). Ultimate load must also be determined for several screw diameters in order to establish which laminate thickness can be tested with a considered fastener s diameter. Although a lot of papers can be found concerning stiffness of threaded assemblies or failure behaviour of riveted assemblies [B1, L1], only a few are dedicated to static failure of threaded assemblies in tension. The first part of this paper is dedicated to explicit simulation using Abaqus software, its specificities and use-cases. The concepts of High-Performance Computing (HPC) are then explained with several calculation architectures (shared memory, distributed memory), and applied to explicit simulation. Domain decomposition is widely used when studying assemblies to deal with increasingly complex models [O1]. In this study, an axisymmetric model and a three-dimensional model of a tensile test of a titanium aerospace fastener are developed. Experimental results are shown, discussed, and compared to the results of the simulation. 1- Introduction Airlines are looking for more economic, greener aircrafts, with a lower impact on the environment. In this context, the use of composite for aircraft structures can significantly decrease their mass. Assembly of composite laminates is however a complex field of study to avoid over-dimensioning of joints. A clear comprehension of transverse properties of laminates is crucial to understand the behaviour of transversely-loaded composite assemblies, as for instance in L-angle aerospace junctions (Figure 1). Several test configurations can be used to study transverse behaviour of a high-strength composite laminate. Elder [E1] uses a titanium fastener to load transversely a circularlyclamped laminate. Prior to this test, the behavior of the screw/nut feature must be precisely defined, and in particular stiffness of different regions of the joint (screw head, screw Figure 1. L-angle junction involving pull-through of fasteners 2- Explicit Simulation Two main resolution algorithms coexist in major simulation software: implicit and explicit. Initially dedicated to dynamic simulations, explicit algorithm is based on explicit central difference integration rule. This is an explicit operator in that the kinematic state at increment i+1 can be calculated from values of u and u at increment i. The computational efficiency of this algorithm is provided by the use of a diagonal mass matrix. Virtual Concept_P19-1- Copyright of IDMME - Virtual Concept

2 The explicit procedure integrates through time by using many small time increments. The central difference operator is conditionally stable and its stability limit (biggest time increment for which it is stable) is shown in equation 1. t. min min L e ( 2 ) L e : Characteristic element dimension : Material density; and µ: Lamé s coefficients. Two main observations can be done on equation 1. Firstly, critical time increment is proportional to elements size; this can lead to very small time increments for fine mesh. Secondly, it depends on the material density. This relationship will be used for mass scaling method. Although small time increment is required for dynamic applications (impact or crash for instance), which involve a short period of time (usually a few milliseconds), small time increments can rapidly lead to very long computation time for quasi-static simulations (usually a few seconds). Therefore, two solutions exist to lower computation time: time and mass scaling. Time scaling consists of increasing deformation speed to allow the displacement or loading to be applied in a shorter time period. This can only be done for rate-independent material laws (material characteristics are independent of the deformation rate). Mass scaling is available also for rate-dependent materials. The principle is to artificially increase density, thus increasing minimum stable increment, and reducing total computation time. The drawback of this method is that higher density induces higher kinetic energy. In quasi-static simulation, kinetic energy must remain significantly lower than internal energy. This point must be kept in mind when adjusting mass scaling parameter. Additional attention must be paid to artificial strain energy, totalizing the hourglass effect. To reduce computation time, Abaqus software proposes reduced-integration elements. These elements contain only one integration point by facet, which makes integral calculus easier and thus significantly reduces calculation time. For instance, a fully-integrated, second-order, 20-node three-dimensional elements requires 27 integration points, while the reduced-integration version only uses 8 points, requiring only 30% of the computation cost of the fullintegrated version. As Blanchot [B1] explains, this can lead to incorrect results for elements loaded in compression (Figure 2), as the element stiffness matrix will be rank deficient. Elements can then take the form of hourglass, giving its name to this deformation mode. This deformation does not correspond to any physical effect, and thus Abaqus software tries to prevent it by using different an hourglass control strategies. Hourglass modes are less present with second-order elements than in first-order. In this study, default hourglass control will be set up, and care will be taken to check energies. (1) Figure 2. Hourglass effect, from [B1] 3- High-Performance Computing Models are becoming increasingly large and complex. To respond to increasing computation times, research laboratories have put in common computation equipments. A few national centres are dedicated to very extensive computations as fluid mechanics or quantum physics, as the Institut du Développement et des Ressources en Informatique Scientifique (Idris) in France. For smaller models, but which are still too important for standard workstations (by calculation time and/or memory needed), regional mesocenters are efficient computation structures. This study received computation hours on the scientific structure Calcul en Midi-Pyrénées (Calmip), which regroups laboratories from Toulouse and its surroundings. Several architectures can be used for High-Performance Computing [R1]: - Shared memory: multi-processors, only one memory addressing field. Each processor can access memory on any computing node. - Distributed memory: multi-computers, several memory addressing fields (non-remote access). Each processor can access memory only on its computing node. The Calmip calculation structure has the following architecture, totalizing 1.5 Teraflop: - 2*128 processors Itanium 1.5GHz - 2*256 Go of Random Access Memory, globally shared-memory - Architecture ccnuma (cache-coherent Non- Uniform Memory Access) - Interconnection NUMAlink (fat-tree) - Linux 64-bit SuSE operating system To ensure an efficient use of computation structures, it is important to know the architecture chosen. Depending on your architecture, two parallelization techniques can be used: - Thread parallelization: light-thread runs in parallel, often in a single processor, sharing the same memory. This is therefore only usable for shared memory calculation structures. - MPI (Message passing Interface): calculations are carried out independently on several processors, and information is passed between processors using messages. Each processor is working with its own memory. This can be used on shared or distributed memory structures. Independently to machine-level parallelization techniques, two calculation-level parallelization techniques can be used in Abaqus software: - Domain parallelization: elements and nodes are Virtual Concept_P19-2- Copyright IDMME - Virtual Concept

3 divided into a number of topological domains. The analysis is then carried out independently in each domain. Information is passed between the domains in each increment as the domains share common boundaries. - Loop parallelization: Abaqus software parallelizes low-level loops in the code that are responsible for the most of the computational cost. It is less efficient than domain parallelization as some parts of the code can not be parallelized, but sometimes easier to implement. The analogy between MPI at hardware-level and domain parallelization at software-level clearly appears. This is usually the most optimized way of parallelization, and this is what is used in this study on the Calmip structure. The ratio of time needed with a single processor on time with multiple processors is called speedup. The parallelization is ideal when speedup equals the number of processors. When domain-level method is chosen, Abaqus software divides the model so that the resulting domains take approximately the same amount of computational expense. The load balance is defined as the ratio of the computational expense of the most expensive domain to that of the least expensive domain. The better the load is balanced, the higher speedup can be. Furthermore, it must be kept in mind that total (wall clock) time is separated in computation time (equation resolution inside a domain) and communication time (across domain boundaries). Thus, adding processors to carry a calculation may not decrease proportionally the computation time, and there exists an optimum in the number of processors to use. Speedups were compared on the elements-three dimensional model of this study, for loop and domain parallelization, for 2, 4 and 8 processors (Figure 3). Domain parallelization appears to be slightly better than loop parallelization for 2 and 4 processors, and the difference greatly increases for 8 processors. Speedup for 2 processors is about 1.7, which is a good efficiency. For 4 processors, speedups are exactly the same as for 2 processors. This can be explained by the fact that the nut/screw contact area cannot be divided upon several domains. The domain containing this zone is therefore requiring extensive calculation, while the others wait for interface messages at each increment, cancelling any benefit of having 2 processors more. The interesting speedup of 3.9 for 8 processors is due to a better load balance between domains, even though the contact zone stays in a unique domain. Loop parallelization does not appear to be a competitive method as it always gives worse results than domain parallelization, even with a unique contact area. Being given these results, the best compromise seems to be a 2 processors - 2 domains parallelization, as the waiting time in the calculation queue will be significantly lower for 2 processors than for 8. Speedup 4,50 4,00 3,50 3,00 2,50 2,00 1,50 1,00 0,50 0,00 Domain parallelization Loop parallelization Number of cpus Figure 3. Speedups for domain and loop parallelization As a conclusion, the choice of a number of processors depends on the number of degrees of freedom of the model and of the distribution of contact zones. 4- Models Two models were created to represent this experimental study, a first axisymmetric, to understand global phenomena, and a three-dimensional to evaluate more precisely the behaviour in the vicinity of the recess. As Abaqus/Explicit allows element removal, exact failure patterns can be obtained and compared to post-mortem observations. Explicit simulation was also chosen to study parallelisation efficiency, to prepare for larger models as for transverse loading of composite laminates Material properties Several studies exist on constitutive models for titanium alloys. To deal with plasticity, most of them use Johnson- Cook model [J1], presented in equation 2, as it is readily available in most common numerical packages and presents accurate correlation with experimental data. Plastic properties of titanium alloys were compared from several authors, including Calamaz [C1] and Daboussi [D1], showing minor differences. The study from Daboussi has the advantage of giving coefficients at quasi-static deformation rate. n * m A B 1 C ln T * 1 Daboussi also proposes correlation coefficients to be used with Johnson-Cook damage model [J2], using quasi-static and dynamic punch tests. Considering quasi-static * simulation, is set to 1 s-1, both transition and instantaneous temperatures are set to ambient temperature and elevation of temperature during tensile test is neglected. Daboussi finds failure strain (D1) to be equal to 0.5 for the titanium alloy. Table 1 regroups coefficients used for plasticity and fracture modelling. Material A (MPa) B (MPa) N C m D1 Ti-6Al-4V Table 1: Johnson-Cook properties of Ti-6Al-4V3 Nut is made of 8740 steel (40NiCrMo2), oil quenched and tempered. Elastic properties were taken from the literature. Approximate plastic properties were extrapolated from tensile strength and elongation. Holding parts and cylinders (2) Virtual Concept_P19-3- Copyright IDMME - Virtual Concept

4 are made of 35NiCrMo16, oil quenched and tempered. Elastic properties were taken from the literature. Considering the heat treatment and low stresses present in these parts, material is considered purely elastic. Table 2 regroups elastic and plastic constants for these steels. Material E Re Rm A (GPa) (-) (MPa) (MPa) (%) 8740 Steel NiCrMo Table 2. Elastic and plastic properties of steels 4.2. Axisymmetric model Model is created with Abaqus software, in explicit, using 4- node bilinear axisymmetric quadrilateral, reduced integration, hourglass control elements (CAX4R). Thread geometries are taken from AS-8879, UNJF-3A for the screw and UNJF-3B for the nut. As shown by Zhao [Z1], the helix angle has negligible effect on the load distribution so an axisymmetric model can be used. Exact geometry of the nut is complex, as the threads are not circular. The top view (Figure 4) shows three lobes that deform during screwing and play the role of a self-locking feature. The axisymmetric model neglects this particular shape and supposes a circular one. Figure 4 depicts this model, composed of cylinders, holding parts and the bolt. Three contact areas are defined (denoted A, B and C on Figure 5). All these interactions are kinematic, pure slave/master, hard contact with a friction coefficient taken arbitrarily equal to 0.1. Simulation takes approximately 7min on a classical workstation with a time increment of 10-6s. As explained before, special care must be taken concerning energies in explicit simulation (Figure 6). Kinetic energy (blue curve) stays clearly below internal energy (green curve), which confirms explicit simulation can be used for this quasi-static test. Both energies are oscillating after a time of 0.09s, which corresponds to the breakage time. System is then instable. Attention must also be paid to artificial strain energy (in red), which corresponds to hourglass energy, and must remain clearly lower than internal energy. Energy (J) 8,E+03 6,E+03 4,E+03 2,E+03 0,E+00 Internal energy Kinetic energy Evolution of energies with time Artificial strain energy 0 0,02 0,04 0,06 0,08 0,1 Time (s) Figure 6. Comparison of energies for axisymmetric model Revolution axis Upper cylinder Upper holding part Figure 4. Top view of the nut Nut A B 4.3. Three-dimensional model Geometry of the recess was precisely defined via direct measurement and introduced in the three-dimensional model, using Abaqus software. The recess is composed of a hexagonal shape (used to fit the wrench), and a circular prehole of a slightly smaller diameter, that goes slightly deeper than the hexagonal shape. Due to this recess, the smallest sector that can be considered for symmetry is a 30 sector as shown in Figure 7. The same assumption than for axisymmetric model was taken concerning the helix angle. Thus, it is neglected and threads considered cylindrical. Screw C Model overview Bolt detail Thread close-up Figure 5. Axisymmetric model Threads of cylinders and holding part are not represented in a first approximation. The two parts are jointed by a tie constraint. Compliances of the holding parts were determined with axisymmetric model, allowing only the screw and the nut to be represented. Axial displacement is imposed to the bearing side of the nut, while the head of the screw is restrained along the z-axis on its bearing side. Considering the chamfer of the steel holding part is large enough compared to screw under-head radius, only the flat area of the bearing side of the screw is restrained. Displacement along the θ-axis is blocked for faces perpendicular to θ-axis (symmetry condition). Materials are identical to those of the axisymmetric model. To improve calculation time, the damage model for titanium is only applied to the threaded part of the screw. Simulation Virtual Concept_P19-4- Copyright IDMME - Virtual Concept

5 takes approximately 1h10min on a classical workstation with a time increment of 10-5s. Kinetic and hourglass energies stay significantly below internal energy, validating quasi-static simulation. System is oscillating after screw failure. Normalized load 1 0,75 Typical load-displacement curve 0,5 I II III 30 sector 0,25 Top view of the threaded part of the screw 0 0,00 0,25 0,50 0,75 1,00 Normalized displacement Figure 8. Typical load versus displacement curve z θ r Figure 7. Three-dimensional model Global conclusions regarding these data are that tests are highly reproducible within a type of fastener, and that behaviour is similar for both diameters in the linear part. Average ultimate load is about 30% higher for larger fasteners. Variation in ultimate load is also linked to nut position on the screw: the more the nut is screwed, the higher the ultimate load is Linear part 5. Experimental study Experimental test rig Experimental test rig was specially designed for this test series. It is composed of two holding features, one for the head of the screw and the other for the nut. In order to fasten the nut on the screw, a special part was designed to block the nut in rotation while screw was manually torqued via its hexagonal recess. Cylinders are manufactured in high-strength steel 30NCD16 heat-treated 1300MPa (oil quenching and tempering). Screws used for this experimental study are titanium (TiAl-6V) Hi-Lite of diameters 4.8 mm (3/16 in.) and 6.35 mm (1/4 in.). An Instron extensometer is fixed on the screw s shank to obtain deformation in the shank of the screw and thus an estimate of the Young modulus of the titanium. Tests were conducted on an Instron 8675 traction machine, load-controlled at a speed of 10kN/min. The machine is equipped with a 100kN load sensor Experimental results Figure 8 represents a typical load versus displacement experimental curve. Three different phases can be distinguished (marked I, II and III on the figure). Phase I, approach, corresponds to the establishment of contacts and play compensation in the global assembly. Phase II, the linear part, represents the domain of use of the assembly. Focus will be given to this part, studying compliances of different elements of the assembly. The last part, phase III, regroups non-linear behavior and failure of the bolt. Different breakage configurations will be noticed and interpreted. The linear part corresponds to the elastic deformation of the joint. Several compliances play a role in the elastic behavior. A 10mm-Instron extensometer was used to measure the deformation of the screw shank. Strain-stress curves were plotted for several tests in order to evaluate the Young modulus of the titanium. Experimental values of the Young modulus are consistent with values obtained by Calamaz [C1]. The small scattering existing on the Young modulus can be explained by the measure uncertainty of both the extensometer and the load sensor. Screws for a given diameter came from the same material batch and material properties scattering is judged significantly lower than measure uncertainty Inflexion point towards breakage At a given displacement, an inflexion is observed, marker of the beginning of part III. A loss of stiffness occurs, usually seen as an external sign of plasticity. Considering material used, heat treatment done and size of the holding parts, it seems unrealistic that plasticity occurs in these parts. With this assumption, plasticity is likely to come from the screw (head and/or shank), the nut and/or the nut/screw threads. Comparison of machine displacement and extensometer elongation with increasing force shows that extensometer elongation increases linearly with force. However, machine displacement stops to be linear after a given force. This and the fact that imposed stress is lower than elastic limit of titanium show that screw s shank stays in elastic domain throughout the test. This inflexion in load versus displacement curve can come from head plasticity (umbrella-shape) or plastic threads deformation. Virtual Concept_P19-5- Copyright IDMME - Virtual Concept

6 Breakage Several breakage scenarios occur. For 4.8mm specimens, we observe two different breaking patterns. The first one is thread stripping, the second one is more unusual: it is a conical failure initiating at the first thread engaged and throughout the hexagonal recess. Figure 9 presents these different breaking patterns Fracture Axisymmetric model brings a first approximation on damage initiation. Conical failure is happening in certain conditions, as in experiments. First element failure occurs in the screw s thread root, propagating up and to the centre of the screw, creating the characteristic conical shape (Figure 11). First element failure After conical failure Figure 11. Conical breakage patterns with axisymmetric model Conical failure Thread stripping Figure 9. Fasteners breakage patterns For 6.35mm specimens, we only observe the typical thread stripping. Conical failure only happens when nut is not completely screwed. The reduction of section involved by the hexagonal recess seems to introduce a stress concentration, causing this type of failure. Load repartition between threads in a classical nut explains the localisation of the fracture in the root of the first thread. 6- Model validation using experimental data Linear part Load (kn) Load versus displacement curve of the tensile test Experiment Simulation 0 0,2 0,4 0,6 0,8 Adimensional displacement (-) Figure 10. Experimental and simulated tensile behaviour Displacement of holding parts was compared for test results and simulation, with a 6.35mm fastener (Figure 10). Experimentally measured by two lever-type dial comparators, it was compared only in the linear part (which is the main area of interest for this study). Elastic behaviours are very similar in the range considered. Error on assembly stiffness is of about 6%. A batch of simulations was performed both for axisymmetric and three-dimensional models, to try to obtain the different breakage scenarios depending on the nut position on the 4.8mm screw. Simulations were numbered 1 to 7, standing for which screw thread the first thread of the nut is engaged in. Number 1 corresponds to a fully screwed nut. A significant loss of tensile strength can be observed when nut is not fully screwed, especially when nut axial position is near to the hexagonal recess. Simulation data were compared to available experimental data for diameter 4.8mm fasteners (Figure 12). Breakage scenarios were identical (thread strip (T) for number 1, conical type (C) for number 4 and 5). We observe a good correlation between simulation data and experimental ones, which are furthermore quite dispersed. This scattering can be a result of the rounding of the first thread engaged: due to the helix angle, the first thread engaged depends on the angle at which screw is observed. The number of revolution the nut has done to meet its final position is therefore considered as an integer number in the simulation, which is not the case in real experiments. We observe significant slope changes on the maximum forces, which corresponds to a change from thread stripping to conical failure and vice versa. Thread 4 is a transition point, as it corresponds to a mixed mode in axisymmetric model (initiation of conical failure, which transforms in thread stripping), and is the first conical failure in threedimensional model. This can also explain scattering at this point for experiments, which correlates sometimes with axisymmetric model and sometimes with three-dimensional one. Virtual Concept_P19-6- Copyright IDMME - Virtual Concept

7 Normalized Ultimate Load (-) 1,00 0,80 0,60 0,40 Evolution of ultimate load depending on the position of the nut Axisymmetric model (-) Experimental (-) Three-dimensional model (-) Threads Conical Threads First thread engaged Figure 12. Max tensile load in function of first thread engaged (4.8mm fastener) Experimental result for fully screw nut is lower than simulation as nut was torqued in the thread run-out of the screw. computation platform. Paralleling methods are discussed, depending on the calculation architecture and model complexity. Breakage scenarios are defined, depending on the position of the nut on the screw, using both axisymmetric and three-dimensional models. Experimental results are then presented and explained, using a polyvalent tensile test rig. Experimental and simulated results show a good correlation, both qualitatively and quantitatively. 8- Acknowledgments The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/ under grant agreement n The authors wish to thank Calmip organization for allowing us calculation hours and for their continuous support. Figure 13. Comparison of experimental and simulated breakage patterns Subgroups can be made for conical failures. Depending on the position of the nut, three different patterns occur, both from experimental and simulated results (Figure 13). For a nut screwed until thread number 4, fracture crosses the screw from a thread root to the bottom of the circular hole, resulting in a one-shot conical pattern. For little less screwed nut (to thread number 5), a first part of the pattern is diagonal to reach the axial point corresponding to the bottom of the circular hole, another one is horizontal to complete the fracture to the circular hole. For both of these patterns, the fracture reaches the bottom of the circular hole, so that the crystallised coating present at the bottom of the hexagonal recess is visible on the nut. For the last pattern (thread 6), fracture goes from a thread root to the bottom of the hexagonal recess, so that crystallised coating is not visible anymore on nut but on screw. 7- Conclusion As a first step to a better understanding of transverse behaviour of composite laminates, this study presents a model of a tensile test of a titanium aerospace fastener. Principles of the High-Performance Computing are first presented and applied to the actual model via the Calmip 9- References [B1] Blanchot, V. and Daidie, A. Riveted assembly modelling: Study and numerical characterisation of a riveting process. In Journal of Materials Processing Technology, 180(1): , [C1] Calamaz, M. et al. Toward a better understanding of tool wear effect through a comparison between experiments and SPH numerical modelling of machining hard materials. In International Journal of Refractory Metals and Hard Materials, 27(3): , 2009 [D1] Daboussi, W. and Nemes, J.A. Modelling of ductile fracture using the dynamic punch tests. In International Journal of Mechanical Sciences, 47(8): [E1] Elder, D.J. and Verdaasdonk, A.H. Fastener pullthrough in a carbon fibre epoxy composite joint. In Composite Structures, 86(1): , 2008 [J1] Johnson, G.R. and Cook, W.H. A constitutive model and data for metals subjected to large strains, high strains rate and high temperatures. In Proceedings of 7 th internation symposium on ballistics, 1983 [J2] Johnson, G.R. and Cook, W.H. Numerical approach for assessment of dynamic strength for riveted joints. In Aerosp. Sci. Technol, 3(1): , 1999 [L1] Langrand, B. et al. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, and pressures. In Engineering Fracture Mechanics, 21(1):31 48, 1985 [O1] Odièvre, D. et al. A parallel, multiscale domain decomposition method for the transient dynamic analysis of assemblies with friction. In Comput. Methods Appl. Mech. Engrg., 199(1): , 2010 [R1] Renon, N. Introduction à l optimisation de codes sur les systèmes HPC. Calmip training material, 2009 [Z1] Zhao, H. Stress concentration factors within bolt nut connectors under elasto-plastic deformation. In International Journal of Fatigue, 20(9): , 2009 Virtual Concept_P19-7- Copyright IDMME - Virtual Concept