Week - 4 - crash box simulation

Crash box impact analysis:

In this assignment, the student needs to simulate a crash test for a crash box for which mesh is given. A crash box is a highly energy absorbing structure that crashes on application of loads and reduces impact on other components nearby. A full-fledges crashbox is a highly sophisticated design but in this case we will go with a rectangular channel which can thought of as the most simple crashbox.

Here are the different assumptions and information required:

- The crashbox should crash into a rigidwall created using *RIGIDWALL_ keyword. Check the manual to understand and create a rigidwall.

- Material for the crashbox is steel. The simulation needs to be started using elastic material to verify its correctness and later a nonlinear material card data will be provided. Thickness of the crashbox is 1.2mm.

- Initial velocity for the crashbox should be around 50 kmph

- The units system to be used is gm-mm-ms

- The simulation should satisfy either of the two situations - (1) It crashes on the rigidwall and rebounces completely or (2) it buckles and folds in the axial direction so as to come in self-contact.

- Once the simulation is completed and results as asked for below is collected, run another simulation by increasing the thickness of the crashbox from 1.2 to 1.5mm.

Deliverables:

- Input .k file and output files (d3plot, glstat, sleout, rcforc)

- Animation of the final simulation

- Cross-sectional force generated in the middle of the crashbox (along its length)

- Acceleration plot of a node in the middle of the crashbox (along its length)

- Maximum directional stress and strain along the length of the crashbox (X strain, Y strain etc)

- Plot of all energies (total, internal, kinetic, hourglass, sliding)

- Compare the accelerations and stress/strain plots of 1.2/1.5mm crashboxes.

Objective:

To perform impact analysis on a crush tube to understand how it works and how much the thickness of the tube affects the results.

Analysis Setup:

Impact analysis:

For this analysis a crash tube was made to impact a rigid wall at 50 km/hr to understand how it deforms and how it can be used in crash structures. A crush tube is a hollow tube of rectangular cross-section used in crash structures of vehicles. This tube crushes into itself and this deformation absorbs a lot of kinetic energy of the impact reducing the impact forces experienced by the occupants in the vehicle and thereby reducing fatal injuries. A crush tube needs to deform controllably and in predictable manner in impact scenario otherwise unbalanced deformations may cause the vehicle to spin or lean to a side which might make things worse.

In this analysis first a given meshed model of a rectangular crush tube was tested with elastic material properties to make sure the analysis works fine, and then the desired material properties were added to it to finalise the analysis.

As mentioned earlier a rigid wall was created using ‘Rigidwall’ keyword to get the impact. For our convenience, the rigid wall was made to move at 50 km/hr towards a stationary and fixed at the farther end crush box, rather than the other way around by using ‘planar_moving_forces’ card from ‘Rigidwall’.

A [gm-mm-ms] unit system was used for the analysis, with a termination time of 20ms, with all the usual output cards to get the necessary data.

Procedure:

1. PART, SECTION, MAT definition:

The only part in this analysis is the tube as the wall is considered as a different keyword. The ‘shell’ section is used with a fully integrated ‘ELFORM 16’ formulation for more accurate results as there is a good chance the tube will buckle in failure. For good measures 5 integration points were employed as well. We are to compare the two cases with different thicknesses and so that is the only thing changed over the two cases.

As mentioned earlier a ‘test’ material card of ‘elastic’ formulation and the actual ‘piecewise linear plastic’ material cards were defined and switched between after the test run is done. Material properties of steel were entered for the card making sure the [gm-mm-ms] unit consistency is continued. A stress-strain curve is defined and called upon as plastic deformation is to be analysed in this example.

2. Boundary conditions and Rigid-wall definition:

In order to model a proper deformation, the tube must be kept stationary such that it doesn’t propagate as the moving rigid wall hits it. It is also necessary to keep the tube from twisting and so the farther end of the tube is fixed in all DOFs using the ‘SPC set’ card from ‘Boundary’ keyword.

A node set with all the nodes on the edge is defined and called upon in the SPC card.

A rigid wall can only be defined by defining a normal vector, which starts from the wall and propagates in the direction normal to the wall, and an edge vector ‘l’ along the length of the wall. In this case as the wall is moving towards the tube it is important to make sure the tail of the normal vector is as close as possible to the wall, as the impact will start sooner. It is also important to define the slave node set to the rigid wall as it acts as a contact formulation. We can input ‘0’ in the box and declare ‘all the nodes in the model are slave to the wall’ as well. Finally, the wall velocity for the impact and to make sure the wall is rigid, some material properties are added to it (in the same card) just to make sure the wall is stiffer than the tube model. By adding frictional coefficient ‘FRIC = 1’ we make sure there is no sliding motion between the two at the interface.

3. Contact definition:

To make sure the crush tube doesn’t penetrate itself after buckling under the impact loads, ‘Automatic single surface’ contact card is used and the tube establishes a contact with itself both as the slave and the master. Coefficients of static and Dynamic friction were added for better accuracy. We can also add the variable contact stiffness with respect to gap parameters as well as contact stiffness control which is essential in multi component contact as a result of impact such as in the case of crash test if a vehicle with multiple components made from different materials and sections. In our case the analysis is straight forward.

4. Analysis setting definition:

Using the ‘termination’ card from ‘control’ keyword, an end time of 20ms was defined to make sure the deformation can be visualised and analysed. For such an analysis with simpler material formulation, it is a good idea to keep an eye on the hour-glassing to minimise inaccurate results.

We use the ‘hourglass’ keyword to define a control policy in any case with ‘IHQ = 4’ in the stiffness from, which prevents the elements from deforming in an undesirable manner by adding stiffness.

5. Outputs definition:

Here the ‘Database’ keyword is used to request a plot data of the various result parameters such as stresses and strains using ‘Binary d3plot’ option. Similarly using the ‘ASCII’ option the nodal and elemental energy data, hourglass and sliding energy data etc. are requested as well. An output time-step -‘dt’ is defined in all these options to request the data after every ‘dt’ milliseconds of time over the total analysis time. ‘Energy’ card was toggled from ‘control’ to add hourglass and sliding energy results..

All used Keywords:

Results:

Case 1: 1.2mm thick tube:

1. Von-mises stress:

As expected the maximum Von mises stress comes out as 623.3 MPa which exceeds the yield stress limit of 450 MPa and we can see the crush tube deforming plastically. The tube buckles along its length due to the impact loads and forms a series of folds while deforming. Maximum stress concentration is observed along the corners of the tubes which undergo bending any possibly rupture in actual case.

From the plot it can be seen that the stress increases linearly once the impact is established and the tops out at around 625 MPa. It remains in that region till the end of the analysis. The small disturbances or the troughs and valleys are formed as the tube buckles and folds. As the buckled portion starts bending over, the stress goes down, and once the fold is stiff enough to not deform any more, the further part of the tube stars deforming and the stress climbs up again.

X-stress:

A higher max and minimum value but a lower average value is recorded here compared to the von-mises plot.

2. Effective strain:

As seen in the stress contour the stress concentration causes the maximum strain at the corners and on the edges of the folds where the tube deforms twice its original length. In other places the strain is very small, even within the elastic limit, but the folding of the tube essentially separates the tube into deformed boxes connected by the plastically deformed folds. The strain plot follows a similar path with some initial lag till maximum straining as the end closer to the wall deforms slowly than the rest of the tube.

3. RWall force:

This shows the resistive force experienced by the wall over the analysis. We can see the impact initiating at around 15ms as the plot breaks the zero. The negative sign is due to the direction w.r.t. global co-ordinates and can be ignored. With a maximum of 155N and average of 33N the important part of the plot is the variation of the force over time. Similar to the stress plot, these troughs and valleys are formed as the tube deforms in folds. During the bending the wall experiences less resistance as the deformation absorbs the Kinetic energy, while in other cases the stiffness of the tube resists any deformation causing the recorded force to increase.

4. Cross-sectional force:

Using the ‘sectional plane’ option from the ‘model and part’ menu, a section cut plane was established, and sectional force plot was acquired. Similar to the ‘Rwall forces’ the negative sign is directional and negligible. The Maximum force figure matches the Rwall plot as the stress wave propagates throughout the tube. The noise represents the vibrations as the tube is deforming continuously.

Around the 12ms mark the wall crosses the sectional plane, deforming the tube past it and hence the force recorded goes to zero.

5. X-acceleration:

Middle of the tube: a node is selected approximately in the middle and using its time history:

A maximum of 336 mm/s² acceleration and subsequent deceleration is recorded as the impact is established, which dies down to an average of 4.5mm/s².

6. Energy plots:

As the complete deformation of the tube isn’t recorded in the analysis time, we see the K.E. plot stopping before reaching 0 same as the I.E. plot. Their progression suggests majority of the K.E. is being converted into I.E. by deformation with minimal sliding and close to 0 hourglass energy.

Case 2: 1.5mm thick tube:

1. Von-mises stress:

Not only the values are lower but also the pattern of deformation is different in this case. Due to greater thickness, the elements are a bit stiffer and don’t deform as easily as the thinner tube. As a result the elements at the near end of the wall don not deform initially, but the elements closer to the middle do. Similar scenario is seen on the other fixed end splitting the tube into 3 parts. The middle part deforms as the wall moves forward forming the folds, and after it reaches maximum deformation, the farther part starts deforming. As the tube is short and fixed at the end, the series of folds is limited at 1 and the nearer end to the wall deforms, absorbing the energy.

The square portion around the 300 MPa mark represents the formation of the 3 parts mentioned above, the middle portion start deforming absorbing energy and almost no further stress is induced for a moment. After it folds up, and stiffens, the stress starts climbing as the other 2 parts start resisting the deformation.

Having even a bit more thickness gives the tube stiffness making the deformations stable and predictable with less chances of rupture.

X-stress:

Compared to the thinner tube there are less vibrations and perturbations in the plot showing stability in deformation. Similar trend is seen with higher values for max and min stresses with a slightly lower average.

2. Effective strain:

Significantly lower values for strain and less stress concentration can be seen. The plot is smooth and has less noise indicating controlled deformation.

3. RWall force:

Both the average resistive force and the maximum force experienced by the wall as the impact is initiated are higher than the thinner tube which implies the higher stiffness of the thicket tube.

Near the end of the analysis when the tube runs out of length to form the folded pattern, it starts to deform the nearer to the wall part. Compared to the thinner tube, the parts formed after the initial deformation at two locations as below, are larger in volume and hence can absorb a lot more energy by deforming, which explains the sudden drop in RWall force post 15 ms.

4. Cross-sectional force:

The stability in normal forces is seen here too, with minor perturbations as a result of deformation. The maximum normal force recorded is higher than the thinner tube at 200 N with almost the same average figure of 20 N. As there are fewer deformations compared to the thin tube, the force transferred to the fixed end is slightly larger, but in a controlled manner.

5. X-acceleration:

As the node is positioned in the middle, it doesn’t experience the initial jerk at the impact time as the tube deforms at 2 almost equidistant parts. Once the deformations start then a lot of vibrations are received and recorded. Even though the max, min, avg values are similar, a lot more disturbances can be seen in the plot which can be justified as the middle portion is the first one to undergo deformation by folding.

6. Energy plots:

A bit more conversion of K.E. to I.E. can be observed from the plot, with the plot not progressing linearly as the deformations aren’t very linear. We can easily distinguish the initial deformation and splitting of the tube and the final deformation as the tube runs out of length from the abrupt changes in the slope of the graphs.

Comparatively larger amount of sliding energy is recorded as the tube deforms differently as opposed to progressive linear deformation in the thinner tube. The hourglass energy is observed to be 0.

Conclusion:

1. In both the cases the acquired results are realistic and fairly accurate hence we can assume the analysis to be right. The pattern of deformation is close to realistic as well.
2. Comparing the two cases, we can conclude that even though the deformation pattern is different, due to higher stiffness the thicker tube has better and more predictable results, with almost half the strain and can be a safer option over the thinner tube with lesser chances of rupture and breakage failure. The thinner tube produces slightly higher numbers for stress and strain but has fewer vibrations under deformation due to the linear rate with which it deforms. The abruptness of the thicker tube may cause some issues but a better fixture can neutralise them.
3. At the end, it comes down to the practicality of the application where these tubes will be used, hence if the higher weight of the thicker tubes is not a problem it can do a better job, but if packaging and mass is of concern, playing around with the cross-section of the thinner tube might get good enough results too.