Extreme performance of multi-layer laminated glass designs under blast loads
In this section, the numerical results will be presented and discussed. The discussion will encompass results such as numerical validation, failure modes, and the effects of different parameters. The dynamic performance, on the other hand, will be highlighted through the utilization of numerical modeling. To validate the numerical modeling, dynamic experimental data from the literature was employed.
Validation of finite element model
The validation of the numerical models was carried out using data from two publicly accessible field experiments. The initial FE validation relied on experimental findings reported by Osnes et al.10, while the subsequent validation employed data obtained from the experiments conducted by Kranzer et al.44.
Osnes validation
For validation purposes, an experimental study done by Osnes et al. was modeled10. It consists of an LG panel subjected to lateral blast pressure resulting in fracture, as seen in Fig. 7a, b. The glass specimen has dimensions of 400 mm × 400 mm, while the loaded area is 300 mm × 300 mm. The glass consists of two 4 mm annealed glass layers and one 3.8 mm PVB polymer interlayer. For more details on the experimental setup, we refer to Osnes et al.10. Neoprene rubber strips with a thickness of 4 mm are glued to the clamping plates and positioned on each side of the glass. The specimen is clamped between two 25 mm thick aluminum plates. All elements in the model were 3D hexahedral elements. The window panel is composed of three layers (two outer glass layers and one polymer interlayer), with each layer consisting of two elements through the thickness with a cross-section element size of 2.3 × 2.3 mm. For this work, a fixed interface between layers was used.
Examples of final explicit model color by total displacement.
Osnes et al. provided precise pressure–time history curves for the test10, which were then exported to ALE3D34 with a maximum pressure and impulse of 205.3 kPa and 1379.9 kPa-ms. Consequently, the ALE3D model utilized the actual load-time history for dynamic loading, deviating from the commonly assumed triangular loading often found in the literature. As shown in Fig. 8, the numerical and experimental results for maximum deflections of glass panels agreed satisfactorily. Table 5 shows the comparisons between the experimental data and ALE3D findings for the test done by Osnes et al.
Comparison between numerical and experimental results of Osnes et al. 10 (pressure = 205 kPa and impulse = 1379.9 kPa ms).
Furthermore, as shown in Fig. 8, the ALE3D FE predictions showed better conformity to the experiment results and matched the measured dynamic deflection during the early portion of the response until the peak deflection. In the current study, the difference between the peak deflection of experimental and numerical results is less than 1.2%.
Kranzer validation
The numerical models were validated using experimental data obtained from a shock tube test by Kranzer et al.44. The tested LG panel measured 1,100 mm in width and 900 mm in height, comprising two annealed glass panes, each 7.5 mm thick, bonded by a 1.5 mm PVB polymeric interlayer. To secure the LG panel within the frame, 50.8 mm wide rubber bites were employed. During the test, the LG panel was subjected to a dynamic pressure of 58 kPa and an impulse of 98.6 kPa-ms.
The experimental pressure–time history obtained from the shock tube test was imported into ALE3D34 to simulate the dynamic response of the LG specimen. Figure 9 illustrates the comparison between the ALE3D and experimental responses, highlighting close agreement, particularly during the initial phase of the dynamic response and up to the peak deflection and extending beyond the peak deflection. The midspan deflection observed experimentally was approximately 14.7 mm, while the FE model predicted a deflection of about 15.4 mm. This represents a difference of 4.7%, demonstrating a satisfactory correlation between the experimental and numerical results. The results indicate that the ALE3D predictions align well with the experimental data, particularly in capturing the early stages of the deflection response even after the peak deflection.
Comparison between numerical and experimental results of Kranzer 44.
Effect of interlayer type
The effects of interlayer types on the LG panels under a high and low blast load are investigated first. Figure 10a depicts the response of four different LG panels, each incorporating distinct interlayers (PVB, EVA, SG, TPU), subjected to a blast pressure of 150 kPa and an impulse of 1150.2 kPa-ms. Notably, the panel with an SG interlayer exhibited a maximum deflection of 10.3 mm at the center. Remarkably, this configuration displayed less damage in the interlayer compared to other samples, as depicted in Fig. 10a. In contrast, panels with PVB and TPU interlayers demonstrated higher deflections at the center, measuring 12.49 mm and 13.86 mm, respectively. Notably, the specimen with an EVA interlayer displayed the highest deflection at the center, measuring 19.34 mm.
Effect of Interlayer Type.
Moving on to Fig. 10b, which explores the response of the same LG panels under a higher blast pressure of 250 kPa and impulse of 1939.6 kPa-ms, the SG interlayer again showcased favorable characteristics. The panel with SG interlayer exhibited the lowest maximum deflection of 28.15 mm at the center, with less damage observed in the interlayer compared to other samples. Conversely, specimens with PVB and TPU interlayers displayed higher deflections at the center, measuring 38.24 mm and 97.71 mm, respectively. Notably, the specimen with an EVA interlayer suffered the most severe consequences, with a deflection measuring 150.68 mm, leading to complete panel failure and substantial damage in the interlayers.
Moving on to Fig. 10c, three different multilayer LG panels (three glass layers and two layers of polymeric interlayer) with PVB, EVA, and SG interlayers are studied under a blast pressure of 150 kPa. The panel with the SG interlayer again demonstrated superior performance, exhibiting the lowest maximum deflection of 3.98 mm at the center, with less damage observed in the interlayer. In contrast, panels with PVB and EVA interlayers displayed higher deflections at the center, measuring 5.7 mm and 14.45 mm, respectively. As before, the specimen with an EVA interlayer experienced panel failure, accompanied by significant damage in the interlayers.
Lastly, Fig. 10d investigates the performance of the same multilayer LG panels under a higher blast pressure of 250 kPa. The SG interlayer once again demonstrated favorable characteristics, displaying the lowest maximum deflection of 6.59 mm at the center, with less damage observed in the interlayer compared to other samples. Conversely, panels with PVB and EVA interlayers showed higher deflections at the center, measuring 9.27 mm and 23.65 mm, respectively. Again, the specimen with an EVA interlayer experienced the highest deflections, resulting in panel failure and substantial damage in the interlayers.
Overall, the effect highlights the significant impact of interlayer types on the blast response of LG panels. The SG interlayer consistently outperforms PVB, EVA, and TPU counterparts, exhibiting deflections consistently within a range of 15–40% lower than other interlayers across different blast pressures. Adding a third tempered glass layer significantly reduces peak deflection compared to the double-layer systems. These findings underscore the crucial role of glass configuration and interlayer material in enhancing blast resistance.
Additionally, the various interlayer and layup configurations create different fracture patterns in the glass layers. Figure 11 illustrates the various fracture patterns for the double-layer LG systems with different interlayers. LG with EVA and TPU interlayers both undergo catastrophic failure with the glass fracturing into four large sections. Interlayer tearing is also observed, particularly in the EVA system. SG and PVB interlayer systems have some observed cracking, but the fracture pattern is more diffuse compared to the EVA and TPU, which failed catastrophically. LG with SG interlayer only experiences the onset of fracture within the inner glass. The other LG configuration in this study failed with similar failure patterns. Most notably, LG systems that catastrophically failed all showed similar fracture patterns as the EVA and TPU systems.
Fracture patterns for LG systems consisting of PVB, EVA, SG, and TPU interlayers subjected to a 250 kPa max blast pressure. Grey represents the outer rubber strip clamping the LG, red represents the interlayer material, and the blue-green color represents the JH-2 damage parameter for the glass.
Effect of interlayer hybridization
In the investigation of the effects of interlayer hybridization on the LG panels under blast loads, Fig. 12 is dedicated to studying the response of two different LG panels, each incorporating distinct hybrid interlayer combinations (T_PVB_EVA_PVB_T and T_PVB_SG_PVB_T), subjected to a blast pressure of 150 and 250 kPa compared to panels with pure PVB interlayer. Hybrid interlayers underperformed the equivalent thickness PVB LG panel under both the low and high blast loads. Possibly due to unbalanced load sharing between a stiffer middle interlayer and the more compliant EVA outer membrane. A better setup would be as thick as possible mid-layer (SG) and as thin as possible outer EVA layers to aid in glass adhesion.
Effect of interlayer hybridization.
Effect of glass type
In the investigation of the effects of glass types on the blast resistance of LG panels, Fig. 13 examines the response of LG panels with three distinct glass types (annealed, heat strengthened, tempered) under a blast pressure of 150 kPa. Notably, the panel featuring tempered glass exhibited superior performance, displaying a maximum deflection of 12.5 mm at the center with less permanent deflection observed in the system compared to other samples, as illustrated in Fig. 13. Conversely, panels with heat-strengthened glass showcased higher deflections at the center, measuring 19 mm. Notably, the specimen incorporating annealed glass experienced the highest deflections at the center, measuring 100 mm, leading to panel failure and substantial permanent deflection, as depicted in Fig. 13. This marked difference in performance can be attributed to the inherent characteristics of tempered glass, which boasts a high tensile stress capacity, four times that of annealed glass and twice that of heat-strengthened glass.
In general, tempered glass demonstrates superior blast resistance with deflections consistently lower than other glasses, showing a notable percentage reduction of approximately 80% compared to annealed glass and 34% compared to heat-strengthened glass in the numerical modeling results. These findings underscore the substantial impact of glass type on enhancing structural integrity under blast loading conditions.
Effect of glass layer configuration
In this study, all LG panels consist of multiple layers, comprising three layers of tempered glass and two layers of EVA polymeric material. EVA was chosen as the interlayer as it adds the least resistance to the system, highlighting the specific performance of the glass configuration. The results presented in Fig. 14a highlight the significant impact of glass layer configuration on the response of multi-layer LG panels, particularly when replacing a 3/8″ panel with a 1/2″ thick panel. It is evident that an overall transition to 1/2″ thickness across all layers leads to a substantial reduction in maximum deflection, decreasing from 23.65 mm in the 3/8″ configuration to 13.71 mm, which corresponds to a remarkable 73% decrease. Moreover, when isolating the impact of layer thickness changes, focusing on the loaded (inner) layer proves more effective in minimizing deflection, with a thickness of 1/2″ resulting in a deflection of 19.34 mm compared to 22.56 mm for the non-loaded (outer) layer. Surprisingly, changing the mid-layer to 1/2″ thickness yields even better performance, with a deflection of 18.02 mm. Furthermore, exploring the effect of replacing two layers with 1/2″ thickness, it is observed that the 1/2″ Outer + 1/2″ Mid configuration exhibits a slight advantage, offering a 1–3% reduction in deflection compared to 1/2″ Mid + 1/2″ Inner and 1/2″ Outer + 1/2″ Inner configurations.
Effect of Glass Layer Configuration.
Moving on to Fig. 14b, which investigates the response of LG panels with a total thickness of 1 1/8″ under 250 kPa blast loads with different glass layer configurations and thicknesses, distinct trends emerge. The configuration of three layers with the same thickness (3/8″) results in the highest maximum deflection (23.65 mm) and more severe damage to the LG panel. However, configurations such as 1/4″-1/2″-3/8″ and 1/4″-5/8″-1/4″ demonstrate reduced deflections of 21.09 mm and 18.19 mm, respectively. Notably, the latter configuration with a thicker mid-layer exhibits the least deflection at the center of the specimens, surpassing the other configurations by 15–30%. This emphasizes the crucial role of layer thickness distribution in enhancing blast resistance.
Figure 14c extends the analysis to LG panels under 100 kPa blast loads, reinforcing the trends observed in Fig. 14b. The configuration of three layers with the same thickness (3/8″) yields the highest maximum deflection (10.64 mm). Contrarily, configurations like 1/4″-1/2″-3/8″ and 1/4″-5/8″-1/4″ showcase reduced deflections of 9.84 mm and 8.58 mm, respectively. Once again, the configuration with a thicker mid-layer proves to be the most effective in minimizing deflection, exhibiting a 15–24% advantage over other configurations. These findings underscore the critical influence of glass layer configuration on the blast response of multi-layer LG panels, providing valuable insights for optimizing their performance in real-world scenarios.
In summary, the study on multi-layer LG panels reveals a substantial influence of glass layer configuration on panel response. Transitioning to an all 1/2″ thickness configuration significantly reduces maximum deflection by 73%. Under 250 kPa blast loads, configurations with varied layer thicknesses demonstrate up to a 30% reduction in deflection compared to uniform thickness configurations. Similarly, under 100 kPa blast loads, varying thickness configurations lead to a 24% reduction in deflection, highlighting the importance of tailored layer configurations for optimizing panel performance.
Finding optimal layup
The exploration of optimal layups for multi-layer LG panels under blast loads, while maintaining a constant total glass thickness of 1 1/8″, involved the investigation of six different configurations through numerical modeling. In the first configuration, three constant glass layers with a thickness of 3/8″ each were analyzed as shown previously. The second configuration consisted of nine constant glass layers, each with a thickness of 1/8″. The third configuration introduced a variation with the middle layer at 6/8″ and the outer layers at 3/16″ each. The fourth configuration involved five alternating glass layers, starting with the inner layer at 1/8″ and sequentially increasing to 3/8″ in the middle layer and back to 1/8″ in the outer layer. The fifth configuration comprised four in-to-out gradient layers, starting with the inner layer at 1/8″ and gradually increasing to 3/8″ in the outer layer. Finally, the sixth configuration involved four out-to-in gradient layers, starting with the inner layer at 3/8″ and gradually decreasing to 1/8″ in the outer layer.
From Fig. 15, it is evident that configurations 1, 2, and 3 exhibit the maximum mid-span deflections, measuring 23.65 mm, 40.54 mm, and 12.28 mm, respectively. Notably, Configuration 2 displays severe damage in the panel under blast loads compared to the other configurations. On the other hand, Configurations 4, 5, and 6 showcase mid-span deflections of 26.41 mm, 30.25 mm, and 23.32 mm, respectively. Significantly, Configuration 6, characterized by an out-to-in gradient, demonstrates lower deflection and superior performance compared to Configuration 4 (alternating glass) and Configuration 5 (in-to-out gradient) by 13% and 30%, respectively.
Response of different configurations.
Figure 16 illustrates the crack patterns of the outer glass for various configurations. The severity of glass cracking follows closely with the relative max deflection performance of each configuration. Configurations 2, 4, and 5 perform the worst and display significant glass cracking, but no interlayer failure. Configurations 2 and 4 also display unique crack patterns due to the thin (1/8″) outer glass thickness. The thinner outer glass promotes higher levels of crack branching compared to other configurations, and Configuration 2 is very close to catastrophic failure as seen in Fig. 11. Configurations 1 and 6 exhibit some minor damage starting around the edges and at the center line of the glass. The top performer, Configuration 3, exhibits little damage and no residual deflection.
Outer glass crack patterns of the 6 layup configurations subjected to a 250 kPa max blast pressure. Grey represents the outer rubber strip clamping the LG, red represents the interlayer material, and the blue-green color represents the JH-2 damage parameter for the glass.
In conclusion, Configuration 3, featuring a thicker middle layer, stands out as the optimal layup, exhibiting the lowest deflection and the best overall performance compared to the other configurations by 230% to 90%. This underscores the critical role of layup design in enhancing the blast resistance of multi-layer LG panels.
Effect on energy absorption
Energy absorption is a key parameter in blast-resistant design, as it determines the panel’s ability to mitigate shock loads by dispersing impact energy45. The energy absorption behavior of six LG panel configurations, derived from finite element simulations, is summarized in Table 6 and illustrated in Fig. 17. Variations in interlayer and glass types significantly influence this performance metric. Systems with superior energy absorption reduce force transmission and structural deformation, offering enhanced protection against blast effects.
Force displacement dynamic response for different configurations including the energy absorption for each configuration.
Based on Fig. 17, Configuration 3, which utilizes SG as the interlayer material between tempered glass plies, exhibited the highest energy absorption capacity at 3994.0 J, representing a 25.8% increase compared to Configuration 1 with PVB. Also, this can be shown in the force displacement response as SG sustains higher force levels over extended displacements. This enhanced performance is attributed to the stiffness and strong bonding characteristics of the SG interlayer, which effectively distributes stress and enhances resistance to deformation. In contrast, Configuration 2 showed the lowest energy absorption value (2304.3 J), with a 27.4% reduction compared to Configuration 1. The lower stiffness of the EVA interlayer contributes to increased deformability and less efficient energy dissipation under such loads. The energy absorption for Configuration 4 was slightly lower (2960.0 J), 6.7% less than Configuration 1, reflecting TPU’s moderate stiffness and deformability under dynamic loading.
Configurations 5 and 6 introduced variations in the glass type while keeping the PVB interlayer constant. As shown in Fig. 17, Configuration 5, which utilized annealed glass, absorbed 3004.0 J, a 5.3% reduction, whereas Configuration 6, which incorporated heat-strengthened glass, achieved 3056.0 J, only 3.7% below Configuration1. In summary, interlayer material selection plays a critical role in defining the energy absorption characteristics of LG panels, with SG showing superior blast mitigation. Additionally, glass type influences performance, with heat-strengthened glass slightly outperforming annealed glass when paired with the same interlayer.
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