Week - 5 - Modelling Spotwelds

Spot-welds Simulation and study:

Objective: To study and simulate how a spot-weld joint is formed and used in a crash analysis by comparing results for a solid element spot-welded crush box with a beam element spot-welded crush box.

Analysis Setup:

Spot-weld joints: Used to model a spot-welded sheet metal component generally in a crash analysis. Simply put an element is used to mimic the ‘spot’ of the welded joint, to which appropriate material properties and a section property with a high integration point element formulation is assigned. Using special contact cards, the two sheets/ components are ‘tied’ to each other and the analysis is performed. If the outputs parameters overcome the limiting parameters for axial force, shear forces and moments as well as torsion specified in material card for the ‘weld’ element, the spot fails, the element is deleted and the cycle is repeated for every weld element at every time step.

A rigid wall was created using ‘Rigidwall’ keyword to get the impact. For our convenience, the rigid wall was made to move at 100 km/hr towards a stationary and fixed at the farther end crush box model, rather than the other way around by using ‘planar_moving_forces’ card from ‘Rigidwall’.

In this analysis first a given meshed model of a rectangular crush tube was tested with failure time of 6 ms ‘TFAIL’ in material properties – MAT_Spotweld 100 to get an idea for the above mentioned limiting parameters, and then the same material properties were added and the failure time option was disabled to finalise the analysis.

In actual case these limiting parameters namely EFAIL – Effective plastic strain at failure, NRR – Maximum axial stress at failure, NRS – Maximum shear stress at failure, NRT – Resultant stress at failure, MSS,MTT – Moment resultants, MRR – Torsional Moment resultant are to be acquired from an actual shear test for the given material spot welds. The objective of this simulation is to study the method hence the data is gathered the other way. To make the simulation better as mentioned in the question, the time step and the limiting parameters were tweaked for the failure of welds to be postponed to the middle of analysis time.

A [gm-mm-ms] unit system was used for the analysis, with a termination time of 13 ms, with all the usual output cards to get the necessary data.

Procedure: CASE 1: Beam elements spot-weld:

1. PART, SECTION, MAT definition:

Three parts namely the 2 brackets/tubes and the spot-welds are defined. The brackets/tubes have a 2D section with ELFORM – 16 a fully integrated 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 with a 1.2 mm shell thickness. This part will have the same section and material properties over both the cases.

MAT - 24 - ‘piecewise linear plastic’ material cards was defined for the bracket. Material properties of steel were entered for the card making sure the [gm-mm-ms] unit consistency is continued. We use the effective strain-stress parameters along with ‘C’ and ‘p’ to define the plastic nature of the material as plastic deformation is to be analysed in this example.

The parameters were taken from 'Dynaexamples' spotweld tutorials.

https://www.dynaexamples.com/introduction/intro-by-j.-reid/crashbox

For the spot-weld elements, a specific card – ‘MAT 100’-‘Spotweld’ was defined. As mentioned, all the failure limiting parameters were input here as per the requirement of failure midway simulation.

2. Boundary conditions and Rigid-wall definition:

In order to model a proper deformation, the other bracket must be kept stationary such that it doesn’t propagate as the moving rigid wall hits it. It is also necessary to keep the brackets 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.

According to the cases, the ‘Prescribed velocity’ figure of the rigid wall is altered to see the spot-weld failure over the simulation time. To test things out, the wall was placed on both the front and rear of the bracket to make sure we get consistent results.

3. Spot-welds definition:

Using the geometry option, lines were drawn using the ‘point to point’ setting where the spot-weld is to be defined. These lines are the ‘Projected’ to ‘closest projection’ i.e. the inner bracket to get a set of lines for each face.

Using the ‘spot-welding’ option with the ‘by position or line’ setting, one by one each line was used to form ‘beam’ element - ‘welds’ between the two ‘parts’. To keep things simple only few spots were formed.

This part was then assigned the ‘section’ and ‘material’ properties required.

4. 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.

To establish the spot-weld, we use ‘tied’ contact in this case the ‘tied-edge-to-surface contact’ where we define the part containing all the spot-welds in this case beams as slaves and a set of the brackets as ‘part-set’ as the master. By doing this we make sure there is no penetration of weld-elements in the brackets, and establish a welded joint.

4. Analysis setting definition:

Using the ‘termination’ card from ‘control’ keyword, an end time of 13 ms 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.

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. A specific output ‘swfor’ – which gives the spot-weld forces and moments is enabled to investigate upon any uncertainties. 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.

Case 1:

1. Spot-welds failure:

As the given model lacked the geometrical stiffness of a closed rectangular crush box, It couldn’t give similar results and the comparison of any output parameters with the crush box was pointless. The limiting parameters were not legitimate too as mentioned before, hence only the parameters responsible for the failure of the beam elements were of interest.

https://drive.google.com/file/d/1Yr1aiCfMd0BKwjb-ObRrl2Xj7Da3f4Hn/view?usp=sharing

https://drive.google.com/file/d/1NGjzDF9GyRWJi-BXtySV3w169_0sMESZ/view?usp=sharing

https://drive.google.com/file/d/1ruZPDVmhVHJFIfQX88C5f_Ae3PCbMAxf/view?usp=sharing

For the beam element simulations, in both the cases, the beams failed under the resultant – Axial and shear forces and got deleted as soon as the figures closed to the 10k limit . It is evident from the ‘Axial resultant force’ contour data in the d3plot which was enabled using ‘Binary D3THDT’ card.

1. Failure of the beam-spots on top:

2. Beam-elements at the corners and below:

3. Elements on the shoulder:

4. Elements on the sides:

5.The bottom-most elements:

6. The failure of elements and the respective axial forces can be co-related by the graphs gathered from ‘SWFORC’ card from the ‘ASCII’ data:

a. Axial force data:

b. Resultant force:

c. Failure time data:

The results were similar in the case where the rigid-wall was made to approach the model from the other end:

https://drive.google.com/file/d/1YIq5AQKoTOs2xXKNOQnMELALFlHjbU4l/view?usp=sharing

https://drive.google.com/file/d/1aG1Ahkkq4xrYmz9qnrMCwkFZwaQashJS/view?usp=sharing

1. Failure of the beam-spots on top:

2. Beam-elements at the corners and below:

3. Elements on the shoulder:

4. Elements on the sides:

5. The bottom-most elements:

• Axial force data:

• Resultant force:

• Failure time data:

Case 2: Solid spot elements:

In this case instead of drawing a line and forming beam elements along it, using the ‘edit elements’ option, ‘Hex’ elements were created by selecting 8 nodes, 4 from each bracket, such that a single ‘Hex’ solid element, connects 2 ‘Shell’ elements, 1 from each bracket. To keep things simple, the number of elements again was kept low.

A solid section with ‘ELFORM’ – 1 was used as it is the only compatible and computationally reasonable solid element.

Similar to case 1, the material properties of the spot-weld solid elements were tweaked, with a lot higher values for the limiting parameters due to the better element formulation.

As a ‘Hex’ element is has more nodes and hence ability to undergo deformation in more dimensions it is more suitable for such examples especially in case of torsional and moment loads. A 1D element like the beam or even a 2D element is not suitable for loads normal to the thickness of the element and a solid or 3D element is a better choice. It can be seen in this case as contrary to 1^st case, the elements fail in torsional and moment loads, while the axial forces do reach the limiting parameters but not over.

In both the case the element and the section are the only different parameters and hence all the steps mentioned above were repeated for this case as well.

Simulation results:

https://drive.google.com/file/d/1SDhGy-WBOe0iAaoC4iZFLl_XR0j29MAr/view?usp=sharing

1. All except 1 the other solid spot elements fail under resultant moment condition.

1. Failure of the solid-spots element on side:110013

As the ‘spot weld forces’ cannot be visualised using ‘d3’ plot, the ‘timeline’ function of the plot is used to see in real time how the parameter varies, as the straight red line moves over the timeline. The solid element ‘110013’ fails first which can be seen from the plot and the timeline.

2. Solid Spot-elements on the other side fails:110016

As mentioned, the solid or 3D element is better suited for applications where a lot of bending and torsional loads are to be induced during the analysis.

3. Solid element on top fails:110020

More elements on the top side and the elemental stiffness of a 3D element means the top element spots fail later in the simulation unlike case 1.

4. Bottom most element on one side – 110015:

5. Another element on the top fails:110019

6. Solid-spot element fails under Torsion - 110012:

Solid spot element -‘110012’ failed under torsion as per the plot. While all other elements show significant torsional loading, their failure was due to the resultant moment reaching its limit. For this element, given its position on the side edge where the outer bracket overlaps and bends inwards, the torsional loads take over.

7. Final element on the top – 110017:

Fails at the very end as all other spot-welds being failed means all the forces get concentrated on one joint.

2. The results were a bit different in case where the wall was made to approach the other way. 3 of the 7 spot-elements survive the simulation as none of the loads overcome the limiting parameters. The geometric stiffness of 3D elements, and the density of elements to distribute the loads and the direction of loading which deforms the brackets in a suitable manner were the reasons.

https://drive.google.com/file/d/1T28shx8RMTAqUOhFcdTE2mhD7wEc-_UO/view?usp=sharing

1. Consecutive failures of solid elements on side: 110020

110016:

Both 110020 and 110016 failed around 6 second mark and were placed on the top and side of the bracket respectively. The directional change of loading caused the brackets to deform in a different way, so instead of getting overlapped by the outer bracket and then getting pulled along the length, here, the elements were pushed into the outer bracket and over the 8.5 second mark were just along the ride.

2. Top surface element failure: 110019

3. Bottom most element failure: 110015

4. Un-Failed elements:

As seen in the animation and graphs, the surviving elements are the least loaded elements due to previously mentioned reasons. After the 8ms mark, there is not much deformation in the inner bracket and the outer bracket starts deforming and buckling. As a result the elements simply get displaced along the length with the rigid wall without any loads, the exception being 110013 which was placed on the top surface and due to the deformation experiences loading.

As one of the sides got deformed more than the other, the elements there failed earlier (110016, 110020, 110015) and twisted the bracket further. This resulted in the significantly less loads on the elements on the opposite side of the bracket(110017, 110012) and helped them survive.

Conclusion:

1. From the results of both the cases, it is evident that the type of element used along with its element formulation and properties plays a major role in getting the right results hence the expected behaviour of the components after deformation should also be studied before running the simulation to help with element selection.
2. Usually in complicated analysis scenarios such as crashworthiness analysis, the spot-weld deformation and behaviour is not of interest and the computation cost and time of 3D weld element is not an option, as a result beam elements are used. In any analysis, the area of focus should get the most attention and everything else should be a compromise.
3. The material properties of the spot-weld material determine its performance, hence for better results, experimental data should be preferred.

Drive link with all the files and animations:

https://drive.google.com/drive/folders/1Ao0wFVGdS_pBBG5dlNCjVQHVd2TH9NrR?usp=sharing