Week - 5 - Modelling Spotwelds

                                                                   Spotweld Failure Analysis

Aim: To analyse the deformation behaviour of a crash box joined with spotwelds as well as study the normal and shear forces acting on the spotwelds at failure. 

Geometry and spatial discretization: The model under consideration is a two-part crash box type structure. The lower part is 250mm long and 133mm wide and the upper part is 250mm long and 150mm wide. The two parts are meshed with 10011 quad elements and 10296 nodes.  The quad elements are provided a type 6 (S/R Hughes Liu) element formulation for hourglass prevention with 5 integration points across its thickness of 1.5mm.

                                                         Fig 1: Meshed part geometry under study

Spotweld definition: A series of 7 spotwelds are defined along the line shown in Fig 2 and Fig 3. The welds were defined in two ways - first by creation of beam elements using Mesh>elem gen> Beam and then by solid elements using Mesh>elem gen>Solid>shell offset. 

               Fig 2: Spotwelds created with beam elements                  Fig 3: Spotwelds created with solid elements

An element formulation of type 9 was used for the beam elements (tubular weld shape with 2mm dia) and for the solid welds a type 1 element formulation was used. This was done to ensure compatibility with the spotweld material model. 

Constitutive Material Model: For the shell elements, the MAT_024 piecewise linear plasticity model was used with the following properties:

For the weldments, MAT_100 Spotweld material model was used. The properties were the same as those used for shell elements, except for the failure criteria - a separate force-based failure for the beam and solid welds.

                                                              MAT_100 for Beam spotweld

                                                               MAT_100 for Solid spotweld

In the absence of time, strain and moment criteria, failure in spotwelds occurs when the following criterion is met:                                                    (Nrr/Nrrf)`square`+ (Nrs/Nrs)`square` + (Nrt/Nrtf)`square` = 1

Contact Definition: An Automatic_Single_Surface self contact was defined for the two parts of the box with a static coefficient of friction of 0.2. 

For the beam spotweld, an Automatic_Tied_Shell_Edge to Surface contact was defined and for the solid elements, a Spotweld contact was defined. For both these types of contact, all the weld elements (7 of them) were defined as the slave part and the two shell meshed boxes were defined as the master part. 

Boundary Conditions: A rigidwall is created at an offset of 1.5mm from the front of the box. NSID was set to zero to include all elements in the model to be slave segments to the rigidwall. 

                         Fig 4: Rigidwall definition                                           Fig 5: Initial velocity on the part

Both the parts of the box were provided with an initial velocity of 15.65mm/ms in the positive X-direction to propel it towards the rigidwall. Initial_Velocity_Generation was used for this purpose. To ensure that the box deforms a bit, instead of rebounding as it is, a small mass of 10kg is added to the boxes using Element>Mass>PartSet.

Analysis controls: The simulation is run for 3ms with binary and ASCII plots (SEFORC, SWFORC, GLSTAT, RWFORC, MATSUM) being requested at intervals of 0.1ms. Two sections are also defined to be written to the SECFORC ASCII file. 

                                                                Fig 6: Section-planes defined in the model

HGEN  and SLEN are set to 2 in Control_Energy card to request hourglass and contact energies to be computed and written to the GLSTAT file. 

Results and Discussion: The animation files show the box impacting the wall at 0.2ms after which it crumbles to a certain extent before beginning to rebound. The upper half stays in contact with the lower part as long as the spotwelds hold up. After the spotwelds fail, the upper half keeps moving in the direction of the initial velocity but with some lateral movements as well. 

The energy absorption behaviour of the two runs - beam and solid weld elements - is almost the same except for the magnitude of strain (internal) energy absorbed on impact. The model with beam elements develops 7.52e05N-mm of internal energy while that with solid weld elements absorbs 7.92e05N-mm. Kinetic Energy drops from 1.4e06N-mm to 6.34e05N-mm and 5.88e05N-mm for the beam and solid spotweld models respectively.  

          Fig 7: Energy plot for beam spotweld model                                               Fig 8: Energy plot for solid spotweld model             

Since there is not much self-contact taking place in either of the models, the sliding energy in the system is zero. No hourglass energy is observed in the beam spotweld model but in the case of the solid spotweld model, hourglass energy of 676N-mm is recorded. 

The normal force on the rigidwall is recorded to be 1.41e05N at 0.2ms for both models and drops to zero at 1.3ms and 1.5ms for the beam and solid spotweld models respectively.

              Fig 9: Rigidwall force plot for beam model                                Fig 10: Rigidwall force plot for solid model     

For the beam spotweld model, a longitudinal force of 1e05N and 4.28e03N is recorded at the lower part and upper part sections respectively. For the solid spotweld model, these values are 1.01e05N and 1.16e04N respectively. 

            Fig 11: X-force on front section of beam model                        Fig 12: X-force on front section of solid model

          Fig 13: X-force on rear section of beam model                         Fig 14: X-force on rear section of solid model

To study the intrusion speed, the acceleration at node 501658 (just behind the weld line) is recorded. The beam model records a maximum of 32.7mm/ms2 of acceleration at 1.8ms and the solid model exhibits a max acceleration of 40.5mm/ms2 @1.3. The acceleration plots also indicate severe deceleration - 45.5mm/ms2 @ 1.7ms for the beam model and 38.9mm/ms2 @ 1.9ms for the solid model. 

            Fig 15: x-acceleration for beam model                                     Fig 16: x-acceleration for solid model

For the given failure criteria, the beam spotweld elements fail between 1.27ms and 1.67ms reaching a peak axial force of 952N (element 110011). The max shear force value before failure is 497N. 

               Fig 17: Axial force on beam spotwelds                                        Fig 18: Axial force on solid spotwelds

                Fig 19: Shear force on beam spotwelds                                   Fig 20: Shear force on solid spotwelds

In the case of solid spotwelds, the maximum axial force and shear force reached before failure is 620N and 2090N respectively. Element failure here starts much earlier at 0.75ms of the run with the last element failing at 1.3ms. 

Conclusion: From the force plots of Fig 19 and 20, it can be seen that solid elements experience more shear force  - about 4 times as much - than the beam elements in spotwelds. The axial force in solid elements though is lower than in beam elements -as can be observed from Fig 17 and 18. The internal energy developed in the crashbox with solid spotwelds is also 4e04N-mm higher than the box with beam spotwelds. The maximum accelerations in both the models are observed right after the spotwelds fail and the upper part is propelled forward under its own inertia independently. For this study, a simple approximated force-based failure criterion was used. In a more complex practical setup, a time or strain or moment-based failure might be used along with or separate from the force criteria. As such, more accurate simulation results might be obtained from such a setup.