Numerical modelling of impact failure of an automotive windshield glazing subjected to a dummy pedestrian headform

Highlights

• We present a numerical approach for impact failure analysis of an automotive laminated glass subjected to a dummy pedestrian headform.

• An edge-to-edge approach is proposed to tackle the contacts between glass cracks.

• Extrinsic cohesive shell elements are adaptively inserted when and where needed to represent progressive glass fracture during impact.

• The well-known tie-break algorithm is modified to model the interaction between glass and PVB.

• A series of numerical cases are performed to validate the capacity of the presented numerical algorithm in impact failure analysis of the automotive windshield laminated glass.

• Numerical studies have been conducted to investigate the influences of impact velocity, impact angle, impact location, and boundary constraint condition on head injury criterion values.

Abstract

Automotive laminated glass is normally sandwiched by two soda-lime glass layers and one polyvinyl butyral (PVB) layer. Though it is a simple composite structure, its mechanical performance including failure behaviour plays an important role in the context of pedestrian-vehicle accidents. This paper develops a numerical approach, including an extrinsic cohesive shell model and a tie-break algorithm, for impact failure analysis of automotive windshield glazing subjected to a dummy pedestrian headform. During impact, cohesive shell elements are adaptively inserted into the windshield finite element model to represent progressive glass cracking. An edge-to-edge approach is proposed to tackle the contacts between glass cracks. The interaction between glass and PVB is switched from tied connection to contact sliding after a defined fracture criterion is satisfied. The effectiveness of the developed numerical approach is validated by comparing the simulation and experimental results in terms of final fracture patterns and acceleration histories. Besides, numerical studies have been conducted to investigate the influences of impact velocity, impact angle, impact location, and boundary constraint condition on head injury criterion values.

Introduction

Nowadays, laminated glass has found widespread applications in various industries, e.g., in architectural buildings as windows [1], [2]. This paper focuses on automotive laminated glass, which is an important protective component for a vehicle. Upon impact, on one hand, the failure process, including glass fracture, can absorb some impact energies. One the other hand, most of the glass fragments can still be adhered to the plastic PVB film to avoid possible injuries caused by the flying glass shards. Therefore, laminated glass can be regarded as safety glass. Research results showed that the head of an adult pedestrian normally impacted the windshield glazing in the context of a pedestrian-vehicle accident [3], [4], which was found to be the most deadly factor for a pedestrian [5]. Therefore, it is of vital importance to investigate the impact failure and energy absorption mechanism of automotive windshield glazing, so as to protect pedestrian’s safety. In addition, Xu et al. [6] pointed out that the fracture patterns of a windshield glazing was helpful to reconstruct a traffic accident.

The New Car Assessment Programmes (NCAPs), e.g. the European NCAP [7], has considered the pedestrian head test, where a dummy headform is projected to the windshield or bonnet area, as one of the standard performance tests. The so-called head injury criterion (HIC) [8] is usually used as an indicator to evaluate the possibility of pedestrian head injury.

In laminated glass, the mechanical properties of the two components, i.e., glass and PVB, are much different. Besides, the connections between them have influences on the impact failure behavior of laminated glass [9]. Consequently, the impact failure mechanism of laminated glass is much more complicated than that of monolithic glass. Researchers have attempted to use analytical [10], [11] or experimental [12], [13], [14], [15], [16], [17] approaches to investigate the impact failure of laminated glass. Instead, a growing interest has been devoted to achieve this end by means of numerical modelling in recent decades. As addressed in [18], one needs to consider two major parts, i.e., glass fracture and the connection between glass and PVB, during impact failure of laminated glass. Up till now, there are mainly six numerical algorithms for the modelling of the major failure pattern, glass fracture. Such approaches include the well-known element deletion method [19], [20], [21], [22], [23], [24], [25], [26], the discrete element method [27], [28], the continuum damage mechanics [29], [30], the combined discrete/finite element methods [31], [32], [33], [34], [35], [36], the extended finite element method [37], [38], and the cohesive zone models [9], [39], [40], [41], [42], [43]. Regarding the connection modelling between glass and PVB, researchers usually use the share-node method [19], [22], the tied connection approach [21], [22], the tie-break algorithm [42], and the cohesive zone models [9], [35], [43], [44]. The advantages and disadvantages of these numerical approaches in impact failure analysis of laminated glass have been fully discussed in terms of glass fracture patterns and impact acceleration histories [18].

Because windshield glazing is a thin-shell laminated composite structure, it is preferable to use shell elements instead of solid elements to discretize the glass plies from the computational point of view (See [19], [20], [21], [22], [23] for examples); however, it is better to use solid elements for the PVB due to the possible large deformation. In this work, we establish a windshield finite element model by using Hughes-Liu (HL) shell elements [45] and solid elements for the discretization of glass and PVB, respectively.

Currently, the element deletion method in conjunction with shell elements is the most popular numerical technique for the modeling of glass fracture (see [19], [20], [21], [22] for examples). This numerical approach represents progressive cracking by deleting finite elements or setting the element stress values to zero, and one can also couple this approach with a damage model (e.g. [24], [46]) to describe the gradual energy dissipation. In this work, we are interested in modelling progressive glass fracture by means of cohesive zone models. Currently, cohesive zone models can be divided into two groups [47], [48], i.e., intrinsic and extrinsic models. Song et al. [46] have numerically compared the performance of the element deletion method and the cohesive zone model for dynamic fracture analysis. Their numerical results showed that: even though these two approaches suffered from mesh dependent problems, the cohesive zone model was proved to be better at capturing crack propagation and branching. Another one point is that the cohesive zone model is a better choice for fracture simulations with contact interactions between cracks, because crack growth is represented by duplicating element edges instead of deleting elements. The intrinsic cohesive models have proved to be a better approach to capture the glass fracture patterns than the element deletion method [42], [43]. Recently, several attempts have been made to simulate glass fracture using intrinsic cohesive models [40], [42], [43], where solid elements were used for the discretization of glass layers. However, previous literature has reported that the intrinsic models suffer from the so-called artificial compliance [49]. Therefore, it is better to use the extrinsic ones for the brittle cracking modelling in glass. Recently, the authors proposed an efficient cohesive shell model for brittle cracking analysis [50]. In this work, the application of the newly developed cohesive shell model is extended to progressive glass cracking in windshield glazing. Please note that, to the best of the authors’ knowledge, this is the first paper to model the major failure pattern, glass fracture, in a windshield glazing using an extrinsic cohesive shell model. An edge-to-edge (ETE) approach is developed to solve the contact interactions between glass cracks. Regarding the connection between glass and PVB, the widely-used tie-break algorithm [42] is modified to achieve the end. Several numerical simulations have been performed, where the windshield glazing is impacted by a dummy pedestrian headform with different velocities and angles, respectively. The effectiveness of the proposed numerical approach is validated by comparing the simulation and experimental results in terms of impact acceleration history and final failure patterns. Also, the effects of impact location and boundary constraint condition on HIC values are numerically investigated.

This paper is organized as follows: the presented numerical approach including the extrinsic cohesive shell model, the ETE approach for contacts between glass cracks, and the modified tie-break algorithm for impact failure analysis of windshield laminated glass is addressed in Section 2; a series of numerical cases are conducted to investigate the impact failure behavior of an automotive windshield glazing subjected to a dummy pedestrian headform using the presented numerical approach in Section 3; finally, conclusions are drawn in Section 4.