MODELING FLEXIBLE PACKAGE/GRANULAR MATERIAL INTERATION THROUGH COMBINATION OF DISCRETE ELEMENT METHOD (DEM) AND FINITE ELEMENT METHOD (FEM)

Transcription

1 MODELING FLEXIBLE PACKAGE/GRANULAR MATERIAL INTERATION THROUGH COMBINATION OF DISCRETE ELEMENT METHOD (DEM) AND FINITE ELEMENT METHOD (FEM) Wenbo Xu, Pavan Valavala, Mark Mirgon, Sam Crabtree, Lori Kardos, and Didem Oner- Deliormanli Materials Siene and Engineering, Corporate R&D Tehnial Servie and Development (TS&D), Pakaging and Speialty Plastis The Dow Chemial Company Abstrat A variety of appliations use flexible film for shipping solid granular materials. The film/pakages must have suffiient toughness and/or strength to endure impat during shipping and handling. Pakage performane is ommonly evaluated using a drop test typially from a ertain height speified by ASTM and/or ISTA standards. One limitation of the drop test is that it an only qualitatively determine whether a pakage will survive. In order to better understand impat type loading whih an lead to pakage failure, more quantitative information suh as stresses/strains developed during the drop tests is required. We have developed a model to simulate drop tests of a flexible pakage ontaining solid partiles. The model utilized some of the apabilities available in Abaqus software pakage, suh as Abaqus/Expliit, Finite Element Method (FEM), and Disrete Element Method (DEM) to apture the interation between the flexible pakage and a large amount of solid partiles inside. Preliminary results ompare well with drop tests arried out in our laboratory. Introdution Flexible pakages are widely used to pakage solid granular material, e.g. pet food and onstrution material, as shown in Figure. These pakages typially weighs about 0 to 0 kg. Figure. Flexible pakages for granular materials. As a basi performane requirement, these flexible pakages must maintain their mehanial integrity if they are aidentally dropped. The pakage must also have suffiient toughness and strength to endure expeted ollision or impat during shipping and handling. The drop resistane of the pakage is ommonly evaluated by dropping a pakage from a speified height. One limitation of the drop test is that it an only qualitatively determine whether a pakage will survive. In order to better understand how pakage failure is initialized during drop impat, we need more quantitative information suh as how the stresses/strains develop during the drop. The objetive of this study is to apply Finite Element Analysis (FEA) and Disrete Element Method (DEM) to model drop tests of flexible pakages ontaining granular materials. The model is useful for understanding the pakage failure mode during drop tests, helping identify key variables ontrolling the drop resistane of pakages, and eventually guiding resin seletion to meet performane requirements. Experiments Drop tests were onduted using 6.8 kg (5 lb) dog food pakages purhased from loal supermarket, to gain some basi understanding of pakage performane. For eah test, one bag of pet food was dropped from.5 m and the pakage fell on its bottom side. The pakage was dropped repeatedly until failure ourred. High speed videos of the drop proess were taken and used for omparison with simulation predition. Tensile samples ut from undamaged areas of the broken pakages were sent for tensile testing to obtain the stress-strain urve of the pakage film. Figure shows several still photos of the drop test taken from high speed video. After the pakage hit the floor, it started to bulge as pet food pellets started pushing from inside the pakage. Meanwhile, the top part of the pakage shows folding. As pakage deformation reahes a threshold point (at 5 ms), failure was initialized at a spot on the seam where the two faes of the pakage join together (red arrow in Figure ). The failure then propagated along the seam, leading to the final damage of the pakage. SPE ANTEC Anaheim 07 / 08

2 Figure. High speed photos of the drop test. Figure 3 shows the failure surfae of one tested pakage. The failure origin was lose to the base of the pakage. The failure then propagated along the edge of a seam where the two faes join together. As noted by the red arrows, the failure surfae shows the film has been strethed and peeled off along the seam surfae, though no extensive strething was found in the adjaent seal. Figure 4. Shematis of the model for pakage drop test Simulation Steps A DEM simulation typially begins with one step to settle partiles. As shown in Figure 5(a), a olletion of pellets are first plaed inside the pakage without ausing any overlap among them. Then eah pellet starts to fall freely under gravity and interat with other pellets and the pakage wall (Figure 5(b)). Eventually all partiles an find their stable loations, providing an initial pakage onfiguration for subsequent analysis, as shown in Figure 5(). Figure 3. (a) Broken pet food pakage; (b)-() Magnified view of region B and region C in (a). Model Development Although FEA is widely used for strutural analysis of ontinuum solids, it would be impratial to model eah pet food pellet with FEA due to extremely high omputational ost. DEM provides an ideal solution to model events involving a large number of solid pellets. The model ombines both methods so that the interation between pet food pellets and pakage film an be taken into aount. Figure 4 shows the floor and the pakage in the model, whih are simulated with shell elements. The pet food pellets are simulated with speial DEM elements available in Abaqus/Expliit. Eah pellet is simulated as a rigid sphere using a single node element loated at the sphere enter. More details about the DEM tehnique in Abaqus/Expliit are disussed in a following setion. Figure 5. Settlement of pellets in the model of drop tests (ross-setion view) Given the limited spae inside the pakage, it is diffiult to plae the required amount of pellets in one settlement step without ausing overlap. An alternative solution is to add a seond settlement step so that more pellets an be added to bring their total amount lose to SPE ANTEC Anaheim 07 / 09

3 that of a real pet food pakage, as shown in Figure 5(d)- (f). The pellets settlement steps determine the shape of a filled pakage and the stable loations of eah pellet inside, providing an initial ondition to simulate drop tests. The simulation starts from the moment when the pakage initially makes ontat with the floor. The pakage and the pellets have a predefined initial veloity v o, whih depends on the drop height h as v o gh, where g is the gravity onstant. For a pakage drop from.5 m, its initial veloity v o=5.465 m/s. The rigid floor remains fixed throughout the simulation. Modeling Pet Food Pellets with DEM The DEM tehnique in Abaqus/Expliit models eah individual pellet as a rigid sphere with a speified radius and density. It uses a single node element (element type: PD3D) to represent the sphere enter. Despite being a rigid sphere, the ompliane of pellets an be indiretly defined by speifying a proper soft ontat model between pellets, as well as between pellets and other surfaes. A typial ontat model for DEM elements inludes normal and tangential ontat. In the tangential diretion, a frition oeffiient an be defined (0.3 is used here). The normal ontat model is represented by a spring and dashpot model shown in Figure 6. Figure 6. Contat model between partiles in DEM where E and E, and are the Young s modulus and Poisson s ratio, respetively, of the two ontating spheres. In Abaqus/Expliit, the normal ontat fore between partiles an be defined using data tables of ontat fore versus penetration distane to repliate the Hertz solution. Damping oeffiient ontrols kineti energy loss when partiles ollide with other objets. The loss of kineti energy an be quantified using the oeffiient of restitution, e, defined as: V V e (4) where V and V are the relative veloity at the ontat point before and after ollision. Coeffiient of restitution is related to damping oeffiient. For a speial ase where a partile ollides with a flat surfae, the oeffiient of restitution e is related to the damping oeffiient as follows 3 : e exp ( / ) ( / ) where is the ritial damping oeffiient orresponding to the ase where the partile does not rebound, i.e. e=0. For a partile of mass m, it an be derived as mk using the spring and dashpot model shown in Figure 6. A benhmark study was onduted using DEM in Abaqus/Expliit to alulate the oeffiient of restitution for a single sphere olliding with a flat surfae. Figure 7 verifies that the damping oeffiient for partile ontat atually obeys Equation 5 in Abaqus/Expliit. In this study, the ontat damping is defined in terms of the fration of ritial damping /. (5) Contat stiffness K determines the normal ontat fore F as a funtion of penetration distane (=R +R - d) as K df / d. The Hertz ontat model is used in this study 3-4, whih alulates the ontat fore F as: 4 * 3 F E R () 3 RR R () R R E * (3) E E Figure 7. Coeffiient of restitution as a funtion of damping oeffiient. SPE ANTEC Anaheim 07 / 0

4 Given the lak of data for ontat stiffness and ontat damping of pet food pellets, a parameter study was performed over a wide range of pellet stiffness and ontat damping oeffiients. Comparison between the predition and drop tests identifies the optimal parameter values with the losest agreement. The spherial shape of DEM elements is different from the irregular shape of typial pet food pellets. In the model, the sphere radius is set equal to 5 mm, whih is lose to the maximum dimension of a pet food pellet. The total number and weight of pellets are also lose to that of the 6.8 kg pet food pakage. The number of pellets added by the two stage settlement is about 5,800, whih is lose to the amount of pellets inside a 6.8 kg pet food pakage (~3,000 pellets, based on weight measurement of individual pellets). The intrinsi density of pellets is set equal to 50 kg/m 3 so the total pellet weight in the FEA model is about 6.8 kg (5 lb). Modeling Flexible Pakages with FEM detailed features, suh as the wrinkles of the deformed pakage. Figure 8. Predited pakage deformation vs. high speed photo of drop tests (front view). The 0.4 mm thik plasti pakage is modeled with deformable shell elements (element type: S4R and S3R). It is assumed the pakage film is isotropi and exhibits no strain rate dependene. The film is then modeled as a monolayer using the isotropi, elasti-plasti model in Abaqus/Expliit. Stress-strain data were obtained by testing samples ut from tested pet food pakages along their vertial diretions. The tests were onduted at loading rate of 5.4 mm/min. In the model, the film has Young s modulus E=74.5 MPa and Poisson ratio =0.39. The material model assumes that isotropi hardening begins after yield (0 MPa). Results and Disussion Predited Pakage Deformation during Test This model simulates the drop test of a 6.8 kg pet food pakage from.5 m. It uses stress-strain data from the pakage film as input for its mehanial properties. The number and weight of pellets are similar to that of a real pet food pakage. The ontat stiffness and ontat damping of pellets have been tuned to obtain the best qualitative math between predition and tests. Figure 8 and Figure 9 ompare the predited pakage deformation with the high speed drop test video. It is lear that the model an qualitatively apture the general trend of pakage deformation after the drop impat fairly well. After the pakage touhes the floor, its lower portion starts to bulge as the pellets inside ollide on the pakage wall and push it outward. Meanwhile, the top edge of the pakage bends and tends to fold. Consequently, the pakage develops a pear-like shape as shown by the side view in Figure 9. The model an also apture very Figure 9. Predited pakage deformation vs. high speed photo of drop tests (side view). Despite the qualitative agreement on the trend of deformation, the predited deformation still shows some deviations from experiments. The deviation is assoiated with the fat that the initial pakage onfiguration in the simulation, i.e. pakage shape, pellet shape and pellet volume, is not exatly the same as the real pakage. This an be attributed to the settling of pellets into the pakage in the model, as well as the limitation that spherial pellets are used by the DEM in Abaqus/Expliit. Development of Stresses during Drop Test Figure 0 shows the distribution of von Mises stress in the pakage. The stresses are normalized by the maximum stress developed after drop impat. Signifiant stresses start to develop from the base of the pakage instantly after the impat and propagate upward toward the adjaent material. Several high stress regions are identified along the seams where neighboring faes join SPE ANTEC Anaheim 07 /

5 one another. The maximum von Mises stress is loated in several spots along the seams (denoted by red arrows). Material in the high stress region exhibits higher risks of yielding and premature failure. The high stresses are assoiated with loalized deformation due to film wrinkling and ollision with partiles inside the pakage. Figure. Dissipation of kineti energy Conlusions A FEA model has been developed to simulate drop test of a flexible pakage ontaining granular material. The model applies Disrete Element Method to simulate solid pellets, whih inorporates the interations between pellets, as well as the ontat between pellets and the plasti pakage, into the finite element strutural analysis. Figure 0. Stress distribution in pakage after drop impat. The drop tests show that the pakage tends to fail along the seam where neighboring faes join together. This is exatly where the model predits high stresses should our. Yielding will first happen to the material along the seam, leading to the initialization of failure. Dissipation of Kineti Energy The total kineti energy of a 6.8 kg pet food pakage dropped from.5 m is about 03 J. As shown in Figure (a), the total kineti energy of the pakage dereases rapidly following the drop impat. Meanwhile, the flexible pakage deforms, resulting in an inrease in the elasti and plasti strain energy as shown in Figure (b). By omparing the strain energy with the initial kineti energy, only a small portion (<0%) of the kineti energy is dissipated via the plasti and elasti strain of the pakage. A majority of the kineti energy is dissipated by frition and damping between disrete partiles. The model was applied to simulate the drop test of 6.8 kg (5 lb) pet food pakages from.5 m. Validation of the FEA model was done by omparing the predited pakage deformation with deformation observed in the drop test. Preliminary FEA results show a good qualitative agreement with drop tests. The predited pakage deformation agrees qualitatively with the high speed video of drop tests. The predited stress distribution agrees with the failure mode observed in drop tests. Stresses first develop from the base of pakage and then propagate upward. FEA shows high stresses our in the area lose to pakage base and along the pakage seam, whih oinides with the loation of pakage failure initialization during the tests. Referenes. Abaqus Analysis User s Guide (V6.4), Session 5... Website of Dow Chemial (valid on De 0 06): 3. Kevin Franis Malone, Bao Hua Xu, Partiuology, 6 5, (008). 4. H. Kruggel Emden, E. Simsek, S. Rikelt, et al., Powder Tehnology, 7, 57, (007). SPE ANTEC Anaheim 07 /