To analyze and compare different cases with various contact types and different parameters as well as notch positions to compare the results

Objective: To analyze and compare different cases with various contact types and different parameters as well as notch positions and compare the results for the same boundary conditions.

Given model is a crash tube with hollow square configuration meshed with all Quad QEPH 24 shell elements. Two halves of the tube are joined with a weld contact (Type 2). The face of tube has several notches placed symmetrically. An initial velocity about 50km/hr is applied at the top of the tube with the help of rigid body.The boundary conditions are such that only translation in Z axis i.e. vertical direction is allowed. The aim of this exercise is to find the effects of notches on outputs.

CASE 1: The Crash tube model is run as it is. Default parameters for the contacts. Type 7 contact defined as to prevent penetration(due to crushing).

https://drive.google.com/open?id=1L2Nm_RrivLhnZaVvqGc15K4O4KU640NO

Contact interfaces:

Results: 1.Rigid wall forces:

The peaks in rigid wall force are seen after valley as the crumbling of tube divides the tube in two parts momentarily ,which consumes some energy and hence less force is generated on wall. The continuation of force as velocity pushes the upper part into lower causing it to become single unit again. This process repeats itself till the whole tube is crushed into a small dense box. After peaking at 28ms no further transmission of force is seen as the thick crushed tube below the rigid body node resists further compression. A significantly higher force is required to flatten the crushed tube.

The same is reflected in K.E. Plot.

2.Forces:

The initial velocity applied being 13.3m/s or around 50km/h the steel material tube with Plas_john material card undergoes elasto-plastic deformation.

Max von mises stress is recorded at 26ms. 696N/mm2 . Like the plastic strain, Von mises stress are maximum on the corner edges of the tube as the faces undergo bending and crushing.

The contact forces are low till 26ms and go up after. 

3.Energies:

As described in the previous slides the Internal energy of the system is mirroring K.E. Plot. The contact energy which represents contact forces is 0 till 20ms. As there isn’t room for further absorption of energy the whole crushed tube acts as a block undergoing compression. The type 7 contact keeps nodes from penetrating segments of the tube and is reflected in the energy plot.

Case:2 ‘Inacti=6’ to compensate for initial penetrations:

In this case an option'Inacti' which deals with initial penetration is set to 6 which compensates the gap for such contact is any.

https://drive.google.com/open?id=1KVrLcix8_iBsdh5Hutkge6TafuLSGDcJ

Results: 1.Rigidwall forces:

The Inacti =6 setup is only influential when there are any initial penetrations. As in our case the contact defined is type-7 self contact, no any changes in any output are seen.

2.Forces:

The same outputs as in case 1 are seen here.

3.Energies:

The same nature of energy plot is seen here as in case 1.

Case 3: Add a Type 11 contact and recommended parameters for better coverage:

The recommended parameters are defined for the already present type-7 contact.Type-11 edge to edge contact (self contact here)with similar parameters is defined for better coverage. The gap minimum is kept lower in type-11 than that in type-7 to compensate for bigger the element size.

https://drive.google.com/open?id=1IwLPjOGoOSmlj4HXlxtyPBm12k4lQUXj

Results: 1. Rigid wall Forces

The nature of the Rigid wall plot is same as Case-1 till 20ms afterwards no dips and peaks are seen as in case-1 and the plot climbs steadily till a peak of 1.5MN a good 100 KN more than case 1. The added parameters and additional contact type-11 gets better details of the analysis. The internal energy plot gets a bit steeper for the same time window.

2.Stresses and  Forces:

The max. Von Mises stress comes out to be a little less than that in Case 1

The significant difference is seen in the contact force analysis. The peak value is 317.7 KN compared to 93KN for case-1 with concentration at the type-2 contact site.

As seen previously the jump is experienced from 20ms onwards where the tube is acting more like a crush box.

3.Energies:

Even though the plot nature of the energies is almost the same as case-1, there is small differences in peak values, specially in contact energy plot. The noticeable difference is seen post 20ms mark

Case: 4- Removing notches and boundary conditions on node.

The notches are removed with the help og ‘align node’ option. The boundary conditions(DOFs) applied on the rigid node at the upper end are removed as shown.

https://drive.google.com/open?id=1wwUL8lcVR2dTGvI4xttQt6i4-8bsyDVd

Results:1. Rigid wall Forces:

As seen from the plot due to the absence of notches the crushing of tube is random and hence uncontrolled. This gives sharp spikes as output here. The usual climb around 20ms is a bit delayed in this case and after that a significantly lower peak value of 13MN is achieved. A rough estimate being non-concentrated stresses due to absence of notches means random loading and hence random straining and may cause failure in case of surface defects.

2.Stress and forces:

As suggested, except the difference between the contact forces all other outputs are similar to the analysis of a notched surface.

The crumbling pattern was also different as there isn’t a notch to initiate.

3. Energies:

The plots are almost similar the only difference being the slopes for internal energy and K.E. Are a bit steeper on the notched tube post 20ms compared to zero notched tube. The reason if nitpicked the initial delay in crumbling of the tube due to absence of notch.

Case 5: Adding a notch on one of the faces at the middle:

Using the ‘move node’ option a square set of nodes was pushed inwards on one of the faces approximately in the middle of the lower part of tube. All the other analysis parameters and inputs were kept the same.

https://drive.google.com/open?id=1Rw9b6m3417Xr61KE5oJ5I5FnFg5iGuyW

Results:1. Rigid wall Forces:

As stated previously the notches dictate crushing procedure of the tube. The notch is the first part of the tube that undergoes bending and bulges of such bent metal are formed on either side of the notch. The placement of notch along the length of the tube divides the tube in two parts such that the lower part gets crushed first as it is transmitting the load into wall. If such a divided lower part is big enough, al large bulge on each end of the part is formed. This bulge or bent metal is out of the line of force and doesn’t undergo compression initially as the tube continues to crush. When the tube is  compressed into a block around 18ms, these series of bulges get in contact with each other and undergo compression as they now come into line of action, till the tube is completely crushed to a plate. The peaks on valleys in Rigid-wall plot post 18ms is due to the compression of such bulges. In a no notch tube the bulge size is almost random and hence the spikes in the plot. A carefully placed notch makes sure the bulges formed get compressed right away  and smoothens the plot.

2.Stress and forces:

As there is a node on only one face a non-uniform compression is recorded. Similar to the no notch case the contact forces are high due to forces in vertical direction pulling the type-2 contact elements apart. 

A minor difference in von mises stress and max. rigid wall force is seen.

3. Energies:

Due to the presence of notch the first compression is recorded immediately and is shown by the high slope in I.E. Plot. The magnitudes in both the plots for single notch and zero notch tubes are almost the same with smaller variations in the slopes and nature of the graphs after the initial 7ms.  

Case 6: Another notch is added to the opposite face with same setup:

Similar to the previous case another notch is added to the opposite face of the tube using ‘move node’ option. The notches are randomly placed around the middle of the lower half of the tube.

Results:1. Rigid wall Forces:

The placement of the notch dictates how the bulges due to bending of metal tube faces occurs. In this case the notch is a bit too near the bottom and so instead of 2 only a single bulge is formed and the bottom end collapses unfavourably causing a spike around 6ms. Similarly the bulge formed above the notch is too near the top. As the usual climb initiates at 17ms the smaller portion of the tube above the top bulge first collapses into it at 19ms causing a sharp valley after which the whole crushed tube acts like a box and further compresses as seen previously.

2.Stress and forces:

The contact forces are significantly lower than a single notched tube as even though the placement could be better, two notches result in a more uniform compression and bending of the tube.

Other outputs are similar to single notched tube

3. Energies:

There is close to no difference between the single and two notches tube energy plots, similar immediate compression around the notch is recorded.

A comparison across the cases:

No.	Contact forces	Max. Rigid wall force	Max. Von mises
Well defined notched tube.	317.7KN at 26ms.	1.5 MN	643N/mm2 @ 30
Notched tube without B.C.	324KN. At 26ms	1.5MN	648N/mm2 @ 30
No notches no B.C.	251KN at 27ms	1.29MN	669N/mm2 @30
No notches with B.C.	251KN @ 27	1.3MN	645N/mm2 @29
Single notch no B.C.	-	-	-
Single notch with B.C.	417KN @26	1.41MN	639N/mm2 @26
2 notches no B.C.	373KN @26	1.41MN	613N/mm2  @25
2 notches with B.C.	331KN @26	1.41MN	600N/mm2  @27
Mid notch without B.C.	307 KN @ 26	1.41MN	634N/mm2 @ 30
Mid notch with B.C.	303KN @26ms	1.4MN	646N/mm2  @26

Conclusion:

• In the case of single notch tube without any B.C. due to the excessive crushing action of only one face, the vertical force due to initial velocity applied act as a leaverage firsh pushing the tube sideways at 13ms., and finally rotating the whole tube about at around 17ms. before the complete crushing of tube is done. Hence no maximum forces and stresses are acquired.This can be one of the disadvantages of having single notch or even poorly positioned notch and isn't recommended.
• Summing up the results given in the previous slide a zero notched tube with boundary conditions gives out the least outputs for contact forces, however the compression and stresses are non-uniform.
• The plastic strain across the cases is within limit as no deletion of elements is recorded.
• A notched tube results in higher contact forces but a smoother transmission of load is seen. When placed carefully a symmetrically notched tube can undergo predictable compression with similar sized bulges to prevent any spikes in loads.
• When input with recommended parameters, a zero notched crash tube with both type-7 and type-11 contact interfaces gives out best/realistic results.

A folder with all the files and a ppt with:

https://drive.google.com/open?id=1c2jHIDihVfl5CVtj9mpWgiI3vZIlxgF9

The ppt:

https://drive.google.com/open?id=1gfGDIFWAJNAJIkmPgCfo1Vyj7XDOmmG0