Quasi-static and low-velocity impact biaxial flexural fracture of aluminosilicate glass — An experimental and numerical study

Highlights

• Quasi-static Ball-On-Ring and Ring-On-Ring tests on aluminosilicate glass with 3D-DIC technique.

• Dynamic strengthening effect obtained from drop weight impact tests.

• The new FEM-SPH numerical method with JH-2 material model.

• Modified JH-2 parameters were used to better describe the dynamic tensile fracture.

Abstract

In this study, the quasi-static biaxial fracture behavior of aluminosilicate glass is investigated via Ball-On-Ring (BOR) and Ring-On-Ring (ROR) tests aided by a three-dimensional Digital Image Correlation (3D-DIC) technique. In-plane strain field and out of plane deformation distribution during the loading process can be obtained by this test system, overcoming the problem of inaccurate displacement data provided by the loading machine. During the loading process, a uniform strain distribution field is formed below the load ring of the ROR specimen while a gradient strain distribution is built for the BOR specimens. For dynamic loading conditions, low-velocity impact BOR tests are conducted at velocities of 2 m/s and 4 m/s showing a dynamic strengthening effect and high-speed cameras provide detailed fracture and failure sequences of the glass plates. Finite Element Method (FEM) simulations with the JH-2 material model are carried out showing good consistency with experimental results for the quasi-static loading conditions. FEM coupled to Smooth Particle Hydrodynamics (FEM-SPH) technique is utilized for dynamic simulations to solve the element distortion and non-physical problems. The influence of the tensile strain rate effect on low-velocity impact behavior of aluminosilicate glass is analyzed in detail. The original JH-2 model does not provide a reasonable prediction of the dynamic tensile response of brittle materials and the model requires further modifications to describe the dynamic tensile fracture behavior. By introducing rate-dependence maximum hydrostatic tensile strength ${\sigma }_{t,max}$ to the updated model, better predictions for the contact force and projectile residual velocity histories of low-velocity impact tests can be provided.

Introduction

Glass structures are increasingly used in transportation, defense and architecture areas due to the unique transparency property and good mechanical characteristics (such as high compression strength, hardness and stiffness) of silicate glass. Glass usually possesses high compression strength but relatively low tensile strength [1] and tensile fracture is a main threat to glass structures in service. Glass tensile fracture starts from randomly distributed surface flaws, followed by suddenly brittle failure of structures, which may cause economic loss and even human injuries [2]. Thus, reliable evaluation methods are required to assess the mechanical strength of glass structures. For brittle materials with low failure strain, direct tensile tests are usually difficult to conduct. Flexural tests are commonly used for strength assessment of brittle materials including glass, ceramics and concrete [3], [4], [5].

Three-point-bending and four-point-bending tests are the simplest traditional flexural tests methods. However, edge defects introduced during the specimens’ manufacturing process may affect the testing results for bar-shaped specimens [6]. Biaxial flexural tests have been developed to overcome this problem. The Ball-On-Ring (BOR) and Ring-On-Ring (ROR) tests are experimental methods used to characterize biaxial flexural strength of brittle materials. In these tests, an equibiaxial tensile stress state is formed in the center of the specimen, while the outer edge bears a much lower stress [7]. These biaxial flexural methods have been applied to glass [8], ceramics [9], concrete [10] and recently even woven composite plates [11]. During the loading process, the displacement of specimens is usually provided by the loading machine. Strain gauges can be used to measure the strain of specimens upon fracture. However, displacement provided by a loading machine may be higher than the real value due to the compliance and free play related to the machine structures. Strain gauges can provide only strain information for one single point and a large number of gauges are needed to obtain a full picture of strain distribution on the plate specimen. 3D-DIC technique can be utilized to overcome these drawbacks of traditional measurement methods [12]. 3D-DIC is a non-contact and full-field deformation measurement method successfully used to characterize surface deformation, out of plane displacement and even crack tracking [13], [14], [15]. However, 3D-DIC technique is rarely applied to biaxial flexural tests because the specimens usually cannot be photographed directly considering the existence of the loading fixtures.

Besides quasi-static loading conditions, glass components are also threatened by extreme loads such as impact and, hence, recently more attention has been paid to the dynamic behavior and impact response of glass specimens or structures. Split Hopkinson Pressure Bar (SHPB) tests were conducted on glass specimens showing that both compression and tensile strengths are rate sensitive [16], [17], [18], [19]. Dynamic 3PB and 4PB tests also confirmed this positive strain rate effect [3], [20], [21]. For biaxial flexural tests, X. Nie et al. [22] developed a dynamic equibiaxial ring-on-ring flexural testing technique based on a modified SHPB system. It was found that the flexural strength of borosilicate glass increased with increasing loading rates for all the different surface conditions studied. MJ Meyland et al. [23] investigated the loading rate effects of the biaxial flexural strength of soda–lime–silica glass by a large number of ROR tests in a specially designed servo-hydraulic high-speed test rig and an 85% increase in strength with loading rate was observed. Pauw [24] conducted a drop-weight test with circular monolithic glass specimens and observed multiple cracks and debris from the failed glass plates, apparently different from quasi-static loading. It can be seen that the materials tested in these studies are usually soda-lime glass or borosilicate glass. The impact response of the specific aluminosilicate glass is still limited and will be introduced in this work.

In order to analyze the fracture and failure behavior of aluminosilicate glass, a large number of numerical simulation studies have been conducted. Some advanced numerical methods have shown potential and good consistence with experimental observations in some particular loading conditions, such as Peridynamics (PD) [25], Discrete Element Method (DEM) [26] and Phase-field (PF) method [27]. These methods are usually able to simulate the brittle fracture behavior in some specific loading conditions with one set of parameters but sometimes cannot provide reasonable results for complex loading conditions [28]. FEM is still the most commonly used method in engineering applications [29], [30], [31]. In order to overcome the element distortion problems for continuum damage mechanics (CDM) simulation and non-physical mass loss problems in element erosion process, Finite Element Method coupled to Smooth Particle Hydrodynamics (FEM-SPH) technique has been successfully applied in brittle fracture simulation under impact loadings [28], [32], [33]. In this new approach, the failed finite elements will be converted into SPH particles. The newly generated SPH particles inherit all the mechanical properties of the eroded solid elements including the mass, kinematic and constitutive properties, thus fulfilling the principle of mass and energy conservation [34]. This recently proposed method is applied to the low-velocity impact simulation of aluminosilicate glass in this study.

The focus of this paper is on the quasi-static and low-velocity impact biaxial flexural behavior of aluminosilicate glass, including both experiments (BOR, ROR) and simulations. In quasi-static tests, 3D-DIC technique is applied to biaxial flexural tests with a specifically designed loading fixture with the purpose of obtaining the full-field deformation of plate specimens. For dynamic loading, the new FEM-SPH numerical method with updated JH-2 model is utilized to obtain reasonable dynamic fracture response of glass specimens. The paper is organized as following. Section 2 provides a description of the investigated glass material as well as the testing methods combining mechanical tests with 3D-DIC and high-speed photography techniques. In Section 3, the JH-2 constitutive material model is described, followed by the numerical model definition for quasi-static and dynamic loadings. The experimental results, numerical analysis and discussions for the quasi-static and low-velocity impact responses are shown in detail in Section 4 and Section 5 respectively. In the final Section 6, some conclusions are drawn from these results.