# Soft impact responses of laminated glass simulated with the combined finite-discrete element method

## Abstract

### Purpose

This paper aims to investigate the responses of laminated glass under soft body impact, including elastic impact and fracture/fragmentation consideration.

### Design/methodology/approach

The simulation uses the combined finite-discrete element method (FDEM) which combines finite element mesh into discrete elements, enabling the accurate prediction of contact force and deformation. Material rupture is modelled with a cohesive fracture criterion, evaluating the process from continua to discontinua.

### Findings

Responses of laminated glass under soft impact (both elastic and fracture) agree well with known data. Crack initiation time in laminated glass increases with the increase of the outside glass thickness. With the increase of Eprojectile, failure mode is changing from flexural to shear, and damage tends to propagate longitudinally when the contact surface increases. Results show that the FDEM is capable of modelling soft impact behaviour of laminated glass successfully.

### Research limitations/implications

The work is done in 2D, and it will not represent fully the 3D mechanisms.

### Originality/value

Elastic and fracture behaviour of laminated glass under soft impact is simulated using the 2D FDEM. Limited work has been done on soft impact of laminated glass with FDEM, and special research endeavours are warranted. Benchmark examples and discussions are provided for future research.

## Keywords

#### Citation

Chen, X. and Chan, A. (2018), "Soft impact responses of laminated glass simulated with the combined finite-discrete element method", *Engineering Computations*, Vol. 35 No. 3, pp. 1460-1480. https://doi.org/10.1108/EC-10-2017-0386

### Publisher

:Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

## 1. Introduction

With the increase of single and laminated glass applications as structural members in automotive industry and civil engineering structures, it is deemed important to understand the behaviour of glass fractures, as cracking may occur when glass is under impact loading (Masters *et al.*, 2010). Projectiles, particularly for high-rise buildings, usually come from windborne debris, such as metal fragments, roof shingles and wooden blocks.

Based on the material characteristics of projectiles, impact can be classified as hard impact and soft impact. When the deformation of a projectile is negligible, the impact is termed as “hard impact”. For hard impact, projectiles such as steel balls are of a high elastic modulus and rigidity, and the contact time during impact is very short. Fracture behaviour of glass and laminated glass under hard body impact has been extensively investigated in the past decades (Flocker and Dharani, 1997; Knight *et al.*, 1977; Sun *et al.*, 2005). Recently, a comprehensive review (Chen *et al.*, 2017) was presented on the computational failure modelling of automotive laminated glass under hard impact. On the other hand, projectiles undergo extensive deformation which is comparable with their characteristic sizes in soft impact. The contact duration between the impactor and target is much longer over that in hard impact. By virtue of these characteristics, the behaviour of soft impact is quite different from that of hard impact, and special research endeavours are warranted.

There are some analytical and experimental analysis performed on the impact characteristics of glass under soft impact (Pacio *et al.*, 2011; Schneider and Wörner, 2001) where pendulum tests were performed to evaluate the impact resistant strength of glass. As the tests are time demanding and cost intensive, computational approaches are desired by many researchers. However, investigations on the computational analysis of damage mechanisms of glass and laminated glass subjected to soft impact are limited, and almost all of them are based on finite element method (FEM).

In automotive industry, focus is given to the head impact onto the laminated windshield or side windows, rendering a better design guidance ensuring occupants or pedestrians from further injury (Untaroiu *et al.*, 2007). To help understand the crack initiation and further fracture behaviour of glass and laminated glass under head impact, a series of work on the computational modelling has been performed (Xu and Li, 2009; Zhao *et al.*, 2005, 2006a, 2006b). A failure model based on a critical energy threshold was proposed by Pyttel *et al.* (2011), and crack growth is determined by the maximum stress criterion. The implementation of the model was completed within the explicit finite element solver PAM-CRASH, and head impacts onto both flat as well as curved parts of windshield were simulated and validated with experiments. In Peng *et al.* (2013), mechanical behaviour of laminated windshield under pedestrians’ head impact was investigated with LS-DYNA, and different combinations of glass and PVB plies were modelled.

In civil engineering, typical soft projectiles could be windborne wood blocks or other hyper-elastic materials. Shetty *et al.* (2012) analysed the impact damage of laminated glass subjected to large wood cylinders with both round and flat noses. They found that a thinner outer glass ply would result in a better pre-failure stress distribution, whereas a thicker interlayer produces a lower stress field in the failure area. In Dharani and Yu (2004), fracture initiation in glass panels impacted by collapsed trees or ceiling wood was investigated, and an energy release rate criterion was developed for determining the crack initiation time and location. Dharani *et al.* (2005) indicated that Hertzian cone crack is not observable in the case of Douglas fir cylinder impact on glass. Three possible damage regions were presented, and it was pointed out that the maximum tensile stress may cause the surface flaw to extend in a laminated glass under soft impact. The vulnerability of laminated glass window subjected to windborne wood block impact was also computationally analysed by Zhang *et al.* (2013). They suggested that the interlayer thickness plays a crucial role in the penetration resistance capacity of laminated windows.

Besides wood impacts, drop tests with a silicon rubber cylinder nose were performed with velocities ranging from 0.5 to 3.5 m/s. Finite element simulations were conducted with ABAQUS/explicit, and fracture behaviours of laminated glass with TPU, PVB and SGP interlayer materials were examined. In addition to the low velocity impact, deformation and damage mechanisms of laminated glass under high velocity (100-180 m/s), bird strike were also studied for the safety of aviation (Mohagheghian *et al.*, 2017).

Although the FEM is capable of predicting crack initiation and propagation in glass and laminated glass, it is difficult to accommodate further fragmentation. As a matter of fact, damage of glass under soft impact is highly discontinuous, and the use of a discrete approach is necessary. This paper uses the combined finite-discrete element method (FDEM). The FDEM is a special branch of the discrete element method (DEM) and is developed since 1990s (Munjiza, 1992; Munjiza *et al.*, 1995). It combines finite element mesh into discrete elements and overcomes the limitations of both the FEM and DEM. The Munjiza–NBS contact detection algorithm (Munjiza and Andrews, 1998) is employed to make sure the computational time is linear to the number of elements. A combined single and smeared crack model (Munjiza *et al.*, 1999) is implemented into the FDEM and its mesh sensitivity can be avoided should employed elements are fine enough (Munjiza and John, 2002). Some generic development of the FDEM can be referred to the monographs of Munjiza and his co-workers (Munjiza, 2004; Munjiza *et al.*, 2011; Munjiza *et al.*, 2015). Though there are some applications of the FDEM on fracture investigations of engineering materials such as concrete and rock (Guo *et al.*, 2015; Liu *et al.*, 2013), little attention has been given to hard and soft impact damage of laminated glass (Munjiza *et al.*, 2013). Previous research of the present authors (Chen, 2009; Chen *et al.*, 2016; Chen and Chan, 2018) successfully simulated the impact fracture and fragmentation of single and laminated glass under hard body impact using the combined FDEM, with the acquisition of reasonable crack patterns, e.g. flexural and Hertzian cone cracks, and it would be a good attempt to extend research to soft impact.

The purpose of this paper is to investigate the elastic and fracture responses of laminated glass under soft body impact using the 2D FDEM. The theory of FDEM is explained briefly and computational material model is addressed. Two cases, one for elastic and the other for fracture consideration, are presented, and results are validated with data from ABAQUS and other literature. A further study on the influence of impact velocity, Young’s modulus of projectile and contact surface on fracture behaviour of laminated glass is performed. It is found that responses of laminated glass under soft impact differs significantly from hard impact. Conclusions are reached in the final section that the FDEM is capable of modelling soft impact responses of laminated glass.

## 2. Basic theories

In this section, theories including the FDEM and the material models used in this paper are briefly introduced. The FDEM considers solid a combination of both continua and discontinua, and the status of glass from continua to discontinua is evaluated by a Mode I-based cohesive crack model from the authors’ earlier work (Chen *et al.*, 2016).

### 2.1 Finite-discrete element method

It is known that the FDEM, which combines finite element mesh into discrete elements, is a special branch of DEM family. The introduction of finite elements enables the structural deformation and contact forces be predicted accurately. Both translational and rotational motions of a single discrete element *i* are computed explicitly in accordance with Newton’s second law:

*m*is the mass of discrete element

_{i}*i*;

*r*is the position;

_{i}*I*is the moment of inertia;

_{i}*ω*is the angular velocity;

_{i}*F*and

_{i}*T*are net external force and torque, respectively. Referring to equations (1) and (2), velocity and position of each element can be determined at any arbitrary time step.

_{i}Contact algorithm, which can be classified as contact detection and interaction, is key to the FDEM. Munjiza–NBS algorithm is used in the FDEM to evaluate contact detection. Its computational time is linear to the number of discrete elements, and details can be referred to Munjiza and Andrews (1998) and Munjiza (2004). Contact interaction law determines the contact force, which is also crucial in the FDEM. Contact forces in the FDEM are formulated in terms of the overlapping area *S* (Figure 1). Elemental penetration area *dA* on *S* results in an infinitesimal contact force *d***f**, where:

Subscripts “t” and “c” denote the target and the contactor, respectively. *d***f**_{t} and *d***f**_{c} in equation (3) can be further written in the form of:

*and P*

_{c}*are points that sharing the same coordinate on*

_{t}*S*;

*φ*and

_{c}*φ*are potentials defined by FDEM;

_{t}*E*is a contact penalty parameter, and is usually a large value;

_{p}*grad*represents the gradient. Integrating

*dA*over

*S*, contact force

**f**is obtained as:

It is worth mentioning that contact force in FDEM can be accurately predicated regardless of the rigidity of different materials in contact, which introduces great convenience in modelling very soft projectile impact onto hard laminated glass surface.

### 2.2 Material models

It is widely held that fracture will not occur in the projectile and the interlayer. Consequently, only rupture of glass and glass-interlayer interface is considered in this paper. In FDEM, cracks are assumed to occur coincide with element edges, and material rupture is achieved by element disassociation. Currently, only three-node constant strain triangular elements are available in the 2D FDEM computer code “Y” (Munjiza, 2000), and line interfaces (or joints, Figure 2) are used to evaluate the material rupture. Fracture models are implemented in these line interfaces, and the status from continua to discontinua is determined by the deformed separation *δ* of each joint interface. Separation *δ* is also termed with “crack width” in the context.

Referring to Chen *et al.* (2016), a Mode I-based cohesive fracture model is used for glass fracture. Before bonding stress *σ* reaches the tensile strength *f _{t}*, material is within elasticity, and this stage is named with “strain hardening”. The point when

*σ*reaches

*f*is the onset of damage. After that,

_{t}*σ*is assumed to decrease gradually with the increase of crack width

*δ*. When

*δ*reaches a critical value

*δ*,

_{c}*σ*drops to zero and the cracking process is completed. The stage that

*σ*drops with the increase of

*δ*is defined as “strain softening”. Softening behaviour is depicted through a descending

*σ*-

*δ*curve, where the area under the curve equals to the fracture energy

*G*as:

_{f}In the FDEM, no pre-existing crack or notch is needed, and crack initiation and propagation are determined directly by the actual stress and deformation distributions within the material.

Note that *δ _{p}* is the onset separation which is also the elastic limit, and

*δ*is the critical separation when

_{c}*σ*= 0. Following Munjiza (2004), the complete relation between

*σ*and

*δ*is presented in equation (8):

*z*is a heuristic parameter:

In equation (9), *D* is a fracture damage index within [0, 1]. When *δ _{p}* <

*δ*≤

*δ*,

_{c}*D*= (

*δ*−

*δ*)/(

_{p}*δ*−

_{c}*δ*); when

_{p}*δ*>

*δ*,

_{c}*D*= 1, leading to total disassociation and free movement of two adjacent elements.

*δ*is calculated from the elastic modulus and the tensile strength while

_{p}*δ*is obtained from the fracture energy. It is verified by Chen

_{c}*et al.*(2016) that for the fracture of glass, parameters

*a*= 1.2,

*b*= −1.0 and

*c*= 1.0 can be adopted for equation (9) and a corresponding normalised smooth bilinear glass softening curve is plotted in Figure 3. Further introduction on the glass fracture model can be referred to Chen

*et al.*(2016).

For glass-interlayer interface, there is no specific value on the adhesive properties in standards or existing literature, as research on its characterisation is limited. As similar cohesive fracture models also have been used (Pelfrene *et al.*, 2014) for the consideration of interface debonding, the smooth bilinear descending softening relation in Figure 3 is deemed acceptable and used for the rupture of glass-interlayer interface in this paper as:

in a single impact, the laminated glass mainly experiences Mode I failure; and

with different combinations of

*f*and_{t}*G*, the glass-interlayer interfacial behaviour can be well characterised._{f}

## 3. Results and discussions

In this section, two cases are presented and discussed to validate the applicability and effectiveness of the FDEM in simulating soft impact responses of laminated glass. Results from the FDEM simulation show that good agreement is achieved with data from the FEM.

### 3.1 Elastic impact

#### 3.1.1 Verification with ABAQUS.

Consider a 1-m long 0.022-m thick laminated glass beam with both ends clamped [Figure 4(a)]. The thicknesses of outside and inside glass plies are *h*_{o} = *h*_{i} = 0.01 m, and the thickness of interlayer is *h*_{inter} = 0.002 m. The centre of the laminated glass beam is subjected to the impact of a 0.01-m radius ball. To simulate soft impact behaviour, Young’s modulus of the ball is set to be *E*_{projectile} = 1 GPa. 9180 triangular elements are meshed for the laminated glass body. Elements with a characteristic size of 0.001 m are used in the middle impact effective area, while in the far field coarse mesh is accurate enough in accordance with the Saint-Venant’s principle. The boundary of the ball is meshed with 0.0005 m (characteristic size) triangular elements to make sure a reasonably circular shape can be guaranteed, and the inside is meshed with 0.001 m elements so that potential large deformation can be modelled. Material parameters for the analysis are tabulated in Table I. Time step is 0.5 × 10^{−9} s. The impact velocities are set to be *v* = 0.3 and 0.6 m/s, and no fracture occurs in the laminated glass. Point C [Figure 4(b)] which situates at the bottom middle of the inside glass ply is selected for further analysis.

Figure 5 shows the vertical deformation curve of point C against time when *v* = 0.3 and 0.6 m/s. Same elastic impact problems are also solved by ABAQUS with the same mesh topology and CPS3 elements. It can be observed from Figure 5 that the deformation curves obtained from FDEM simulation agree closely well with those from ABAQUS. The projectiles bounce back completely at around t = 0.3 × 10^{−3} s for both 0.3 and 0.6 m/s impact. The oscillation trends are well represented by FDEM and validated with ABAQUS results.

#### 3.1.2 Comparison with hard impact.

A comparison study on the deformation curves of point C for both soft and hard impact at *v* = 0.6 m/s is performed. For hard body impact, Young’s modulus of projectile is set to be *E*_{projectile} = 200 GPa, while all other parameters are kept unaltered. Figure 6 plots the vertical deformation of point C under both soft and hard impact.

Referring to Figure 6, responses of soft and hard impact exhibit differently. Denote *d*_{hard} and *d*_{soft} the vertical deformation of point C for hard and soft impact, respectively. At the beginning, *d*_{hard} > *d*_{soft}, which is mainly because contact between the projectile and laminated glass is instantaneous and immediate in hard body impact. However, *d*_{soft} overtakes *d*_{hard} at around t = 0.2 × 10^{−3} s. The phenomenon that *d*_{hard} < *d*_{soft} at a later stage can be attributed to:

larger contact area between soft projectiles and laminated glass; and

smaller Young’s modulus of the projectile

*E*_{projectile}.

Once the soft projectile and the glass are fully in contact, further impact energy can be transferred to the laminated glass with a longer duration, leading to a larger *d*_{soft} at a later stage. For hard impact, contact area is restricted within a relatively small extent, and impact energy be transferred to the laminated glass is mainly at the initial stage.

Smaller *E*_{projectile} also enables the projectile more versatile in deforming and bouncing back, resulting in greater amount of impulse transferred to the laminated glass body. As is mentioned previously, the projectile fully bounces back at around t = 0.3 × 10^{−3}s for soft impact, while for hard impact, it is still in contact with the laminated glass body at this point of time. Impulse theorem can be used here to predict the impact force that the laminated glass subjects to, as:

*m*is the mass of the projectile, Δ

*t*is time step and Δ

*v*is the velocity difference between the two consecutive time steps. Assume the out-of-plane thickness is 1 × 10

^{−3}m, Figure 7 shows the impact forces that the laminated glass subjects to with both soft and hard projectile when

*v*= 0.6m/s. It can be clearly observed that peak force of hard impact is much higher and comes much earlier than that in soft impact. However, soft impact force owns a longer duration than that of hard impact. These characteristics also explain why

*d*

_{hard}>

*d*

_{soft}at the beginning, while

*d*

_{hard}<

*d*

_{soft}for later stage.

### 3.2 Fracture

Zhao *et al.* (2005) studied the crack initiation in automotive windshield subjected to head-form impact using the FEM. Energy release rate criterion is used to investigate the crack initiation location and time. The head-form impact is defined as the laminated glass subjects to the impact of a normal head. Albeit the shape of head is non-regular, a spherical projectile is normally used for simplicity. To model human head, a solid aluminium sphere is used to represent the skull, which is covered by a viscoelastic skin. The PVB interlayer could be treated as viscoelastic material should the loading duration is long enough. However, it is considered as linear elastic in this paper for simplicity because the impact duration is very short. Same assumption applies to the skin, as it behaves like a solid glassy material in short time (in the range of several microseconds). No debonding is assumed in Zhao *et al.* (2005) between glass plies and interlayer, implying the rupture of glass-interlayer interface is not considered and fractured glass fragments will adhere to the PVB interlayer during the impact simulation. This means that, as no debonding is occurring, less energy will be dissipated and less displacement will occur in the interface.

The specimen is 0.48-m long with *h*_{o} = *h*_{i} = 2 × 10^{−3}m and *h*_{inter} = 0.76 × 10^{−3}m. The radius of the projectile is *R* = 0.0723 m, and the mass is 4.5 kg. Thickness of the skin is 3 × 10^{−3}m and the initial impact velocity is 6.67 m/s. Material properties used in the FDEM analysis are tabulated in Table II from Zhao *et al.* (2005).

A close-up view for the mesh of the impact effective area and the projectile is given in Figure 8. Fine mesh with triangular elements of 0.2 × 10^{−3} m characteristic size is used in the middle of laminated glass, and the characteristic element size increases gradually from 0.2 × 10^{−3} m, 0.4 × 10^{−3} m, 1.0 × 10^{−3} m to 2.0 × 10^{−3} m at the utmost left. Same applies to the right. A total number of 14,706 elements are meshed within the laminated glass, and time step is 0.2 × 10^{−9} s.

#### 3.2.1 Damage initiation.

Referring to earlier investigation (Dharani and Yu, 2004; Dharani *et al.*, 2005) on fracture modes of laminated glass under soft body impact, three possible fracture regions (Figure 9) were defined as follows: Region A, which is located outside of the contact area; Region B, which is close to the centre of the interface between the impact side glass and the interlayer; and Region C, which is at the centre of the external surface of the non-impact side glass.

Selected simulation results at different time points from the FDEM are given in Figure 10. It can be observed from Figure 10 that first local damage occurs in region A; then flexural cracks are found in the outside glass ply in region B; and finally, the initiation of a dominant flexural crack can be observed in the inside glass ply in region C.

In this case, local damage in region A from the FDEM simulation is not available in Zhao *et al.* (2005) where the FEM was used, showing that the FDEM has advantages over the FEM in modelling glass fracture behaviour. Crack initiation time in region B is t = 4.2 × 10^{−6} s in FDEM simulation, and this value is 4.42 × 10^{−6} s in Zhao *et al.* (2005). The initiation time in region B from both the FDEM and the FEM agrees very well (Figure 11).

A further investigation on the variation of flexural crack initiation time in region B against outside and inside glass thickness shows that it increases with the increase of outside glass thickness, whereas it has little relevance to the increase of inside glass ply thickness.

#### 3.2.2 Comparison with monolithic glass.

Comparison study on the fracture of laminated and monolithic glass under the same head-form impact is performed. Same geometry and mesh topology are used for both the laminated and monolithic glass simulations. Figure 12 shows the fracture patterns of both the laminated and monolithic glass at t = 50 × 10^{−6} s.

It can be observed from Figure 12 that laminated glass behaves differently from monolithic glass under soft impact. In the monolithic glass, some through-thickness cracks have formed. It is believed that the projectile will penetrate the glass after some time. However, this is unlikely to occur in laminated glass as through-ply flexural cracks have been prevented by the interlayer and cannot develop further. Examination on the crack initiation in region C shows that for monolithic glass, the initiation time is t = 5.6 × 10^{−6} s, whereas it is 6 × 10^{−6} s for laminated glass, suggesting that laminated glass is more resistant to impact than its monolithic counterpart.

## 4. Further investigations

In this section, influence of impact velocity, Young’s modulus and shape of projectile on fracture responses of laminated glass under soft impact is investigated. The study is based on the laminated glass (baseline specimen) examined in Section 3.1.1. To enable the potential rupture of glass-interlayer interface, 200 J/m^{2} fracture energy is defined for the joint. Other material properties are kept unaltered if not stated explicitly.

### 4.1 Impact velocity

Impact velocity exerts a direct influence on the fracture responses of laminated glass. In this section, velocities vary from 5 to 15 m/s, and selected fracture images of laminated glass at t = 1 × 10^{−3} s are schematically shown in Figure 13.

Referring to Figure 13, when the impact velocity is low, e.g. *v* = 5 m/s, some local failure is found in the contact area, and a central flexural crack in the inside glass ply is also observed. Further increase of the impact velocity, e.g. *v* = 10 m/s, makes the beam exhibit crushing and bending. It is found that with the increase of *v*, glass failure near the interlayer gets serious and some small fragments are completely dissociated with the interlayer. Although the inside glass ply is protected by the interlayer from direct contact with the projectile, it experiences large deformation, and dominant flexural cracks are created. The damage at *v* = 15 m/s is quite severe, as crushing in the outside glass ply and flexural cracking in the inside glass ply lead to a larger failure region along the horizontal direction.

### 4.2 Young’s modulus of projectile

Young’s modulus of projectile (*E*_{projectile}) plays an important role in soft impact. The smaller the *E*_{projectile}, the softer the projectile is. In this section, different *E*_{projectile} ranges from 0.01 to 10 GPa is assigned to the projectile, covering material from very soft to hard.

Figure 14 schematically shows the transient failure responses of the laminated glass beam at *v* = 18 m/s impact with *E*_{projectile} = 0.01 GPa. It can be observed that for such small *E*_{projectile}, the fracture pattern is flexural dominant. Through-ply cracks are found in both outside and inside glass. Meanwhile, small fragments are captured around the contact surface.

Unlike hard body impact, deformation of projectile is quite obvious when *E*_{projectile} is small, and this is a well-known characteristic of soft body impact. Further investigation on normalised horizontal and vertical relative deformation curves *d*_{H}/*d* and *d*_{V}/*d* of the projectile are plotted in Figure 15, where positive indicates stretching while negative means compression. Herein, *d*_{H} and *d*_{V} are calculated from the absolute deformation of reference points defined in Figure 16, and *d* is the original diameter of the projectile. Figure 15 shows that with the increase of *E*_{projectile}, both *d*_{H}/*d* and *d*_{V}/*d* decay significantly. It is suggested that when *E*_{projectile} > 10GPa, projectile can be considered as hard body.

Referring to the crack patterns given in Figure 17, conclusions can be reached that for projectiles with a small *E*_{projectile}, e.g. 0.01 and 0.1 GPa, failure is flexural dominant. On the contrary, when *E*_{projectile} is getting larger, e.g. *E*_{projectile} = 1 and 10 GPa, failure is restricted within a relatively smaller area and inclined to be shear type. It is worth mentioning that failure mode is very close to that from hard body impact when *E*_{projectile} = 10 GPa, and thus 10 GPa can be deemed as the boundary between soft and hard impacts.

Normalised total kinetic energy curves with different Young’s modulus of projectile *E*_{projectile} are plotted in Figure 18. Referring to Figure 18, kinetic energy decays significantly with the increase of time. However, for smaller *E*_{projectile} (e.g. 0.01 and 0.1 GPa), curves exhibit notable wavy behaviour. The wavy finishes quickly for *E*_{projectile} = 0.1 GPa at around t = 0.4 × 10^{−3} s, while it is still going on up to the end of simulation for *E*_{projectile} = 0.01 GPa as the projectile is more deformable and capable of introducing energy onto the laminated glass. It can be concluded that the smaller the *E*_{projectile}, the more kinetic energy is expected to be absorbed by the laminated glass. In other words, higher energy absorption capacity has to be prepared for laminated glass should *E*_{projectile} is considerably small albeit less severe local damage is observed from Figure 17.

### 4.3 Projectile shape

The influence of projectile shape on fracture responses of laminated glass under soft impact is examined. Figure 19 shows three different projectiles, where (a) is the circular ball in Section 3.1.1 with *R = 0*.01 m; (b) is a 0.01 m × 0.02 m rectangle and (c) is a 0.02 × 0.02 m rectangle with two lower corners cut and its contact surface is 1.5 times of (b), i.e. 0.015 m. Both (b) and (c) are flat-nose projectiles. The three projectiles are set to be of the same mass, and the initial impact velocity is *v* = 10 m/s. All other material parameters are same as those in Section 3.1.1.

Figure 20 shows the crack patterns of laminated glass with different projectiles at t = 0.2 × 10^{−3} s. It is found that damage caused by flat-nose projectiles is more serious than that caused by the circular projectile. Comparing with flat-nose damage responses in Figure 20(b) and (c), it can be concluded that a smaller contact surface leads to a severer and more concentrated failure in the impact side glass; however, such failure is not that obvious as the impact force is distributed over a larger contact surface as is shown in Figure 20(c).

Further examination on the crack initiation time of the dominant flexural crack in non-impact side glass is plotted in Figure 21. It can be observed that crack initiation time decreases gradually with the increase of impact velocity for all three shape cases. Crack occurrence time in impact problems with flat-nose projectiles is much earlier than that with circular projectiles. For crack initiation, laminated glass is more sensitive to flat-nose projectiles with a larger contact surface, as curve (c) is always no higher than curve (b).

### 4.4 Discussions

Characteristics of soft impact damage of laminated glass are briefly addressed in this section through further simulations on impact velocity, Young’s modulus and shape of projectile.

For a particular soft projectile, the higher the impact velocity, the severer the damage of the laminated glass. However, soft impact failure patterns with different Young’s modulus of projectile *E*_{projectile} vary significantly. Under the same impact energy, small *E*_{projectile} tends to create flexural failure, whereas large *E*_{projectile} is inclined to produce shear type damage. It is suggested from the simulations that *E*_{projectile} = 10 GPa can be considered the boundary between hard and soft projectile. It is also suggested that for practical engineering applications, laminated glass should be prepared with enough energy absorption capacity, as small *E*_{projectile} introduces further impact energy that laminated glass shall undergo.

Regarding the shape of projectiles, laminated glass is more sensitive to soft projectiles with flat-nose than circular ones. It is also suggested that the larger the contact surface, the earlier the dominant flexural crack initiates in the non-impact side glass.

Generally, as an FEM-embedded and DEM-based computational method, the FDEM is capable of capturing elastic deformation before fracture, transitional process from continua to discontunua and post-damage fragmentation behaviour precisely. These merits are not available in FEM or rigid-sphere DEMs. In addition, very soft and very hard entities can be considered within one simulation, and their contact/impact is accurately evaluated by the well-established contact algorithm in FDEM. Reliable and reasonable results also prove that FDEM is a suitable tool for the simulation of soft impact damage on laminated glass.

## 5. Conclusions

The combined FDEM is successfully used in this paper for both elastic and damage analysis of laminated glass under soft body impact. A cohesive fracture model is used for predicting the failure of glass material and the glass-interlayer interface. The interlayer and projectile are assumed not to fracture in the simulation.

Simulations from the FDEM are compared with those from ABAQUS and known literature. Results have been validated, and a good agreement is achieved. Further investigations are performed on the impact velocity, Young’s modulus and shape of projectile. Concluding remarks are summarised as follows.

Elastic verification in Section 3.1 shows that simulation from the FDEM reaches good agreement with that from ABAQUS. Comparison with hard body impact suggests

*d*_{hard}>*d*_{soft}at the beginning of impact, however, this reverses at a later stage. It is also shown that the soft impact force the laminated glass subjects to has a longer duration and lower peak than that in hard impact.Crack initiation analysis in Section 3.2 shows that the initiation time and location of laminated glass under head-form impact agree well with results from the FEM. Cracks from the FDEM can be well mapped to the three-region framework proposed by previous researchers. The advantage of laminated glass over monolithic glass under soft impact is also demonstrated. It is shown that crack initiation time increases with the increase of the outside glass thickness, while it has little relevance to the thickness of inside glass ply.

Investigation on the influence of Young’s modulus of projectile (

*E*_{projectile}) suggests that for small*E*_{projectile}, fracture is flexural dominant. With the increase of*E*_{projectile}, failure is restricted within a relatively small area and inclined to shear type. It is shown that impact with*E*_{projectile}> 10 GPa can be considered as hard impact.Projectile shape plays a role in the soft impact damage responses of laminated glass. Comparing with circular impactors, flat-nose projectiles overwhelm the resistance of laminated glass more easily. Moreover, among different flat-nose projectiles, those with a smaller contact surface make the impact side glass experience severer failure, while those with a larger contact surface enable the dominant flexural crack in non-impact side glass initiate earlier.

Soft impact damage on laminated glass simulated by the FDEM is pilot and 2D-based in this paper. It is advised that high energy absorption capacity is necessary for laminated glass to resist potential impact energy that soft projectile may bring in. Future research work such as sophisticated modelling of orthotropic soft projectiles (wood) and different laminate strategies (combinations of glass plies and interlayers), and three-dimensional modelling can also be expected in the near future.

## Figures

Material properties used in the elastic impact analysis

Glass | PVB | Projectile | |
---|---|---|---|

Density (kg/m^{3}) |
2500.0 | 100.0 | 7800.0 |

Young’s modulus (GPa) | 70.0 | 0.1 | 1.0 |

Poisson’s ratio | 0.2 | 0.4 | 0.3 |

Tensile strength (MPa) | 30.0 | – | – |

Fracture energy (J/m^{2}) |
4.0 | – | – |

Material properties used in the head-form impact analysis

Glass | Interlayer | Skull | Skin | |
---|---|---|---|---|

Young’s modulus (GPa) | 72.0 | 0.33 | 70.0 | 1.7 |

Poisson’s ratio | 0.25 | 0.4 | 0.29 | 0.4 |

Density (kg/m^{3}) |
2500 | 1100 | 2700 | 1100 |

Tensile strength(MPa) | 30.0 | – | – | – |

Fracture energy(J/m^{2}) |
3.9 | – | – | – |

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## Acknowledgements

Financial supports from Jiangsu Shuang-Chuang Program and Suzhou University of Science and Technology Natural Research Fund are appreciated. Support on the FDEM from Professor Antonio Munjiza is gratefully acknowledged.