Characteristics of windshield cracking upon low-speed impact: Numerical simulation based on the extended finite element method

Abstract

Windshield glass crack characteristics are of great interest to vehicle manufacturers, safety engineers, and accident investigators, because they contain important information on energy mitigation, pedestrian protection, and accident reconstruction. We use the extended finite element method (XFEM) to analyze the model problem of low-speed head impact on a windshield plate. Both the radial crack and circumferential crack propagations are characterized. A parametric study is carried out to investigate the effects of impact speed, head mass, initial material flaw, material fracture criterion, etc., and correlate them with the crack direction and length. It is found that the critical accident information, such as the impact speed or damage stress, can be deduced from the crack pattern characteristics. A qualitative bridge can be established between numerical simulation result and real-world accident via the crack growth mechanism. Our study shows that XFEM is a useful tool for simulating several types of cracks that appear during quasi-static indentation or low-speed impact of foreign objects on windshield materials.

Introduction

The standard windshield material used in automotive industry comprises of a PVB interlayer sandwiched by two mono soda-lime glass sheets. The impact resistance and fracture characteristics of the windshield are widely recognized as one of the most important factors in automotive crashworthiness [1], [2], [3], [4], particularly because it plays an important role when pedestrians, cyclists, or another vehicle collide with the automobile. According to a traffic accident annual census, about 5094 (or 13.67%) of the total deaths are pedestrians or cyclists in US in 2008 [5], and the relevant number is 25,308 (or 34.04%) in China in the same year [6]. Head injury is identified as the primary cause of death of pedestrians [7], and among them, almost half (42.78%) of the cases were resulted from the impact between human head and windshield [4]. After the head impacts on the windshield material, cracks including radial crack and circumferential crack appear in the glass material [4] owing to the hoop and radial stresses, respectively (Fig. 1). The crack profiles (e.g. length, pattern, etc.) on the windshield material contain critical information for impact speed (which is extremely useful for accident reconstruction), vehicle crashworthiness, and insights for improving pedestrian and passenger protection. This motivates us to study the characteristics of low-speed head impact-induced crack propagation on the windshield glass material.

In the past studies of impact on windshield glass, due to the intrinsic complexity of numerical analyses of cracking, researchers in automotive engineering often avoid explicit simulation of crack propagation. For example, Zhao et al. [8], [9], [10] established a continuum damage mechanics model and simulated the damage and failure of the windshield upon model head impact, without explicitly considering crack propagation. Timmel et al. [11] used a smeared model based on an explicit finite element solver to compute the dynamic response of the windshield before and after fracture; again crack growth was not simulated. Sun and Khaleel [12] suggested a constitutive model based on continuum damage mechanics to study the stone-impact resistance of windshield, and the crack pattern was simplified by damage distribution; they also calculated the initial failure and strength degradation of borosilicate glass at high strain rate using the same model [13]. Moreover, Ismail et al. [14] suggested a combined approach of continuum damage mechanics and fracture mechanics to study the static indentation of glass by spherical indenter, where only the stress and damage distribution were analyzed. Although no explicit information of crack propagation in windshield was included in these previous works, the relevant information of damage evolution may provide useful hints on fracture initiation characteristics.

Meanwhile, there were numerous theoretical and numerical studies on the crack propagation in bulk brittle materials (including bulk glass) under static indentation or low-speed impact [15]. Several profiles of indentation cracks and their initiation mechanisms were discussed by Cook and Pharr [16]. The evolution of median/radial crack was described by the classic theory developed by Lawn et al. [17]. An improved understanding of indentation cracking was established based on finite element analyses, for radial and half-penny cracks [18] as well as lateral cracks [19]. For glass, the propagation of cone cracks in layered glass (with different shapes of projectiles) was studied by Chai and Ravichandran [20]. The effect of impact angle of steel ball on cone crack length in glass was studied by Suh et al. [21]. Despite useful information such as the crack propagation path, angel and speed, these previous studies were limited to thick bulk materials, thus cannot be directly applied to thin plate-like windshields. Moreover, the previous indentation/impact cracking studies typically focus only on one type of crack (such as cone cracks in most previous low-speed impact studies), whereas in windshields both radial and circumferential cracks are involved (Fig. 1). The present study aims to close the aforementioned gap by studying the crack propagation characteristics (including both radial and circumferential cracks) when a model windshield undergoes low-speed impact.

The numerical investigation of multiple crack propagation is based on the extended finite element method (XFEM) [22], [23] in this study. Comparing with other numerical techniques such as the cohesive element method [24], [25] and element deletion method [14], [26], XFEM is arguably more efficient since it does not require remeshing during crack propagation. The additional degrees of freedom (DOFs) associated with the nodes intersected by the crack geometry are implemented in XFEM, eliminating the need of crack boundary (geometric discontinuity) conformation [27]. XFEM has been successfully applied to simulate dynamic fracture, fatigue, and various crack patterns in brittle materials [28], [29], [30], [31], [32], [33], and it is employed to study the low-speed impact-induced cracking in brittle plates in the present paper. Upon head impact, the interaction between the stress field and the initiation and propagation of the radial and circumferential cracks are computed using XFEM. The effects of various impact conditions and sensitivity to initial flaw are discussed. The findings may provide useful insights on crack patterns resulted from low-speed impact of pedestrian head on windshield, and thus helpful for accident reconstruction, pedestrian protection, and vehicle crashworthiness analysis.