Keywords: pull-out, numerical simulation, failure analysis, plasticity.

One of the most critical and in the mean time, dangerous damage mechanisms in connections in structural steelwork is the one that corresponds to the pull-out of bolts from steel plates. Due to the great significance of this problem recently laboratory test have been recently carried out to investigate this phenomenon. Another, important reason for this investigation is that no papers were found in the literature about this phenomenon.

In the experiments force is applied increasingly to an M12 bolt until the bolt is pulled-out of a plate. "Pulling-out of the plate" means, that the material of the plate will fail at the end and the bolt becomes free. The dimensions of the plate are 120x120mm.

The results of the experiments suggest that there are two distinctive failure modes for bolt pull-out from a steel plate. When the steel plate is thin, for example 1mm, then the corner of the bolt penetrates the plate through the thickness. Later the failure of the elements propagates towards the center, which means that the corner of the bolt basically cuts up the plate. The other failure mode occurs when the plate is thick, for example the thickness is 4mm. In this case at the final, failure stage a ring separates from the plate. It is also important to note, that in this case at the corners of the bolt a pool of plastified material forms on the ring. On the other hand the failure along the sides of the bolt is a sudden fracture. In the case of plate thicknesses between 1 and 4mm the transition failure mode occurs when there is plastification at the corner of the bolts and fracture along the side of the bolt, however in this case no closed ring is formed.

Although the problem may seem very simple but it is not a traditional civil engineering analysis problem. Usually the structures or components of the structures are designed by elastic or elasto-plastic theory. However even in the case of plastic theory only limited plastic capability is considered. In this paper a problem is discussed where the experiment or numerical simulation is carried out until "full" material failure. Considering the material and geometric non-linearities several difficulties had to be solved. For the numerical analysis the LS-DYNA [1] software was used because of its capabilities, for example handling of contact and material failure.

The geometry have two axes of symmetry, therefore it is sufficient to model only one quarter of the structure for the numerical simulation. Two types of material are used in the analyses: a rigid and an elasto-plastic material. The rigid material is used for the bolt for two reasons. The first reason is that the material of the bolt has higher strength. Moreover the size effect can be considered, as the bolt head is much smaller compared to the plate, therefore it will be more rigid than the plate. The material of the plate is an elasto-plastic material with failure strain. It is important to note how the LS-DYNA [1] software handles the material failure. When the strain in a finite element reaches the 0.3 percent then the element is deleted from the mesh. This behaviour will hopefully simulate the fracture in the plate.

The load is applied to the bolt and it is transmitted to the plate through contact. The contact between the bolt and the plate is defined as an eroding contact, since the surface is continuously changing as finite elements are removed from the mesh when material failure occurs. LS-DYNA [1] is one of the programs that is capable to handle eroding contact. This was one of the main reasons to choose the LS-DYNA software for the analysis. Since even 5 mm thick plate has been investigated in the experiments therefore solid elements have been used for meshing and not shell elements. For this reason the SOLID164 hexahedron element is used from the element library of the LS-DYNA [1] program.

The finite element mesh is built up of hexahedron elements. To ensure good quality results and considering the eroding behaviour of the elements it was decided that a large number of elements are required in the plate around the edges and the corner of the bolt but in other parts of the plate coarser meshing is enough. For this reason an area is defined around the bolt points in the plate where a large number of finite elements are generated

The finite element simulation shows some promising results, for example the failure mechanism is properly simulated. However the load-displacement values determined by the finite element analysis do not correspond to the values measured in the experiments. These results show that some further considerations are necessary to simulate this phenomenon properly. Probably two of the most important features of any further analysis have to be a correct model for the material and material plastification and a better method for fracture simulation.

1

LS-DYNA User Manual, Livermore Software Technology Corporation, 2003.

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