Greater pedestrian protection thanks to XFEM glass breakage simulation

Scenarios such as a pedestrian's head hitting a windscreen are calculated and simulated during vehicle development. This is intended to give a realistic analysis of pedestrian safety to provide a basis for further optimisation. However, glass breakage caused by head impact on a windscreen continues to be difficult to recreate with existing calculation methods. TECOSIM has now extended its existing FLD glass breakage simulation model to include XFEM, further improving the procedure as a result.

The automotive industry primarily uses laminated safety glass in windscreens and panorama roofs. This material is also growing in importance in vehicle development as the industry increasingly focuses more closely on pedestrian protection. Crash scenarios such as a "head hitting a windscreen" are calculated and simulated during design. The results are intended to give a realistic analysis of their influence on pedestrian safety to serve as a basis for further optimisation. However, glass breakage caused by head impact on a windscreen continues to be difficult to recreate with existing calculation methods.

Modelling and simulation of laminated safety glass

TECOSIM has been taking a close look at laminated safety glass in cooperation with automotive and glass manufacturers for a few years now. The specialist in computer-aided engineering has been a permanent guest in the "Laminated glass" working group at German Research Association of Automotive Technology since 2011. TECOSIM has developed an extended laminated glass model in close cooperation with Ford as part of a research project. This model closely examined the different material properties of glass and polyvinyl butyral film (PVB), such as the behaviour of glass under pressure and tensile load and the shear strength of the PVB film. The research also investigated other parameters such as pre-tensioning in the glass layers, the meshing technique and mesh density. Attention was also paid to avoiding negative influences on calculation times and manageability since the extended model also needed to provide full vehicle crash calculations and not be limited to detailed studies of components.

Crack formation and its representation

Crack formation in laminated glass can be divided into two stages: first, cracks emerge in a star shape radiating out from the point of contact. These appear on the interior surface of the windscreen, away from the impact object. Ring-shaped cracks then develop in concentric circles around the point of contact, starting from the star-shaped cracks.

A conflict in objectives emerged in the crack formation analyses at the initial stage of the research project. Although the model displayed a good match until the first crack was formed, it then proved to be impossible to map the stress concentration at the tip of cracks realistically. There was a need to find a method which was suitable for modelling both the high failure limit when crack formation starts and the reduced failure level during the second stage. Tecosim developed an optimised windscreen model in several steps based on what is known as a forming limit diagram (FLD). The forming limit diagram allows the correlation to be mapped between the failure of a material and the ratio between principal and secondary strain. Layered shell elements were used to reproduce both the brittle failure of the two glass layers with subsequent crack formation and the elastic stress condition and consequent behaviour of the PVB film bridging over the cracks. There was considerable improvement to the crack model produced.

Ford has been using this extended simulation model as standard for modelling laminated glass since the research project was completed in 2011.

Method further developed: eXtended finite element method

In 2013, TECOSIM started to develop the glass breakage simulation model even further based on the research project findings since using the eXtended finite element method – XFEM for short – generated additional optimisation potential for crack reproduction. This simulation needed to be improved to map break behaviour more accurately and more realistically. The meshing technology, i.e. the use of rectangular or triangular elements, also needed to be investigated since these elements affect the fracture pattern greatly.

XFEM extends the finite element method to include special functions, thus adding extra scope for finite element nodes. A jump function has been added to all nodes whose area of influence is divided by a crack.  XFEM offers the advantage that cracks can be mapped by elements. This increases the accuracy and gives a significantly more realistic representation since elements which are no longer whole fail and thus "cut a swathe" through the windscreen equal to the width of the element. This is because a real crack does not have a width initially.

The CAE specialists use XFEM for modelling and also take different meshing densities and techniques into account for glass breakage simulation. The results were closely compared with one another in a number of analyses. The representation with rectangular elements at four millimetres gave the best result: the breakage image produced was very close to a real breakage. More than anything, this was due to the fact that cracks can now also be mapped through a single element. Extending the element form function further enhanced the simulation method, thus optimising the representation of cracks and fractures.

The XFEM model was studied using the explicit solver RADIOSS. XFEM implementation was optimised in close cooperation with software manufacturer Altair and modified for the required practical uses. As a result, TECOSIM has now found an excellent method for mapping brittle components which are subjected to loads beyond their failure limit and whose behaviour has significant influence after breakage. The eXtended finite element method is eminently suitable for providing a sufficiently precise image of crack formation without undue negative influence on the time required for simulation and the work involved for modelling.

The laminated safety glass model enhanced by XFEM enables engineers to use a computer to predict the effects of a head impact and thereby reduce the risk of injury considerably.