Behavior Of Brittle Materials Research Articles

Cracking behavior of brittle materials under eccentric decoupled charge blasting

The decoupled charge structure is often used in controlled blasting. However, in actual engineering scenarios, boreholes are typically horizontal or inclined. The explosive is close to the borehole wall because of gravity action, resulting in an eccentric charge structure. In this study, concentric and eccentric decoupled charge blasting tests were conducted on 250 mm × 250 mm × 150 mm cuboid concrete specimens. The blast-induced fracture propagation behavior was evaluated using digital image correlation (DIC) technology, and surface fracture networks were extracted by image processing to investigate the fractal characteristics. A three-dimensional finite element model was established and verified using experimental data to reveal the influencing mechanism of the coupling medium and eccentricity coefficient on concrete fractures from the energy perspective. Finally, the borehole wall pressure (BWP) and displacement distribution with different charge structures and coupling media are analyzed theoretically, and the application of an eccentric charge structure in smooth blasting is discussed. The results reveal that nonequivalent BWP and displacement are produced in eccentric charge blasting, with a more evident crushed zone appearing on the coupled side owing to the higher energy utilization efficiency of the explosive. Sand had the largest fracture volume fraction ratio between the coupled and decoupled sides, effectively controlling the damage level on the decoupled side. The proposed eccentric decoupled charge-blasting scheme produced directional damage effects in the field test, maximizing the failure of the excavation rock while reducing the damage level to the reserved rock.

Special Issue “Dynamic Behavior of Brittle Materials”

Special Issue “Dynamic Behavior of Brittle Materials”

Three-dimensional modeling of impact fractures in brittle materials via peridynamics

Accurate prediction of the impact fracture behavior of brittle materials is crucial in various industries. The paper employs the peridynamic method to model the penetration and damage in brittle materials during impact. The proposed three-dimensional peridynamic impact fracture model (3D-PDIFM) overpasses other numerical models by adopting a new computational technique to couple the impact collisions of different types of projectiles with the peridynamic method. Moreover, the 3D-PDIFM is highly efficient in impact fracture simulations by focusing on the effects of the projectile without simulating its particles, thereby saving more computational efforts. Validation through comparison with experimental measurements and observations ensures that the 3D-PDIFM accurately represents the real-world impact fracture behavior of brittle materials. The paper also highlights the efficiency of the 3D-PDIFM in comparison to traditional mesh-based numerical simulations. Therefore, the 3D-PDIFM can be significant for practical engineering applications as efficient simulations can save time and computational resources. Using the validated model, the impact fracture behavior of PMMA under various conditions, such as changes in panel thickness, impact area, and projectile velocity, is investigated. This analysis gains more insights into how these factors affect the brittle material's response to impact. Moreover, the impact fracture behaviors of tempered glass and float glass panels are examined under different conditions of impact loadings. This study also explains the penetration and impact fracture phenomena in brittle materials. Overall, using the 3D-PDIFM as a modeling and simulation tool can help engineers and researchers analyze the behavior of glass panels under various impact scenarios, thus allowing for optimization of design parameters to improve impact resistance.

A Coupled Thermomechanical Crack Propagation Behavior of Brittle Materials by Peridynamic Differential Operator

A Coupled Thermomechanical Crack Propagation Behavior of Brittle Materials by Peridynamic Differential Operator

On the diversity of fracture behavior in a brittle solid with sets of preexisting small-scale cracks

Understanding the multiscale fracture behavior of brittle materials is of crucial importance not only in engineering applications but also in seismology where an earthquake source, usually assumed as one single, relatively large fracture region but in reality composed of relatively smaller multiple fractures, behaves mechanically in diverse ways, emit waves with different characters and may cause a single seismic event or even a cluster of earthquakes and earthquake swarms. For understanding the complex fracture processes, by employing the experimental technique of dynamic photoelasticity with high-speed video cameras, we have been simultaneously observing global, large-scale material behavior and local, smaller-scale evolution of waves and fractures in two-dimensional linear elastic brittle polycarbonate specimens. Each specimen has sets of preexisting small-scale parallel cracks prepared by a digital laser cutter and modeling large-scale geological fault planes, and it is subjected to external (quasi-)static and impact loads. Here we show some recent examples of the diverse fracture behavior observed in brittle birefringent solid specimens under tensile/compressive external loading. The fracture behavior is considerably dependent on the loading conditions, and developing fractures do not always break the specimen in an “unzipping” way, i.e. the specimen is not always divided along a perforation line consisting of small-scale cracks. Rather, the diverse fractures can easily jump to remote places, propagate back-and-forth or reversely move in the opposite direction compared with the initial one. Our findings may play a role in comprehending the generation mechanism of a cluster of fractures in brittle solids in general.

Research on damage failure mechanism and dynamic mechanical behavior of layered shale with different angles under confining pressure

AbstractThe hydrostatic or confining pressure of deep rocks has a significant impact on the mechanical behavior of brittle materials. Especially when confining pressure is applied, the mechanical properties of rock materials will undergo significant changes. Considering that the process of shale sample subjected to impact load is in a closed container in the dynamic triaxial SHPB test, the failure process of the sample cannot be observed. Meanwhile, the activation volume of the shale sample would be large and local failure would occur in the test under the high strain rate loading. Therefore, the finite element model of shale considering the bedding effect under confining pressure was established in this study. Taking shale materials with different bedding dip angles as simulation objects, the dynamic failure characteristics of shale were studied using the dynamic analysis software ANSYS/LS‐DYNA from three aspects: stress‐strain curve, failure growth process, and failure morphology. The research results obtained can serve as the key technical parameters for deep resource extraction.

Pressure-dependent deformation in brittle diamond

Distinguished from ductile metals, in brittle covalent materials like diamond, hydrostatic pressure is a prerequisite for triggering the plastic deformation. Consequently, the theoretical framework rooted in equilibrium lattice proves inadequate in describing the behavior of brittle covalent materials, making it essential to include extrinsic hydrostatic pressure effects. Here, we take diamond as a model and introduce hydrostatic pressure in the calculation of generalized stacking fault energies (GSFE). A deformation mechanism transition from perfect dislocation slipping on {200} plane to the partial dislocation slipping on {111} plane when the hydrostatic pressure exceeds 100 GPa is revealed by the pressure-coupled GSFE and further authenticated by nanocompression and diamond anvil cell experiments. Such pressure-dependent deformation mechanism is attributed to the different pressure sensitivities of lattice volume expansion during different slip systems operating. Our works provide insights into the activation of slip systems in diamond at the atomic scale and a route to study the plastic deformation behavior of brittle covalent materials.

A Numerical Study of the Dynamic Crack Behavior of Brittle Material Induced by Blast Waves.

Blast stress waves profoundly impact engineering structures, exciting and affecting the rupture process in brittle construction materials. A novel numerical model was introduced to investigate the initiation and propagation of cracks subjected to blast stress waves within the borehole-crack configuration. Twelve models were established with different crack lengths to simulate sandstone samples. The influence of crack length on crack initiation and propagation was investigated using those models. The linear equation of state was used to express the relationship between the pressure and density of the material. The major principal stress failure criterion was used to evaluate the failure of elements. A triangular pressure curve was adopted to produce the blast stress wave. The results indicated that the pre-crack length critically influenced the crack initiation and propagation mechanism by analyzing the stress history at the crack tip, crack propagation velocity, and distance. The inducement of a P-wave and S-wave is paramount in models with a short pre-crack. For long pre-crack models, Rayleigh waves significantly contribute to crack propagation.

Experimental and numerical simulation of three-point bending fracture of brittle materials with inverted T-shaped obstacle cracks

In rock materials, the interaction and coalescence of three-dimensional internal cracks play a fundamental role in material failure and instability. This study focused on the generation of three-dimensional internal cracks inside specimens using the three-dimensional internal laser-engraved crack (3D-ILC) method, without causing surface damage. Experimental and numerical investigations were conducted to examine the fracture behavior of brittle solid materials with and without obstacles during three-point bending tests. The experimental results revealed that obstacle cracks positioned horizontally in an inverted T configuration exhibited a shielding effect on the vertical cracks, resulting in reduced propagation velocity and decreased curvature at the lower tip of the vertical cracks. Crack initiation and propagation were promoted in the presence of obstacle cracks, forming distinct fracture patterns, such as pear-shaped and hook-shaped configurations. While the overall failure mode of the specimens was not significantly altered by the presence of obstacle cracks, dynamic fracture dual sources, and new Mode III cracks were observed on the fracture surfaces. The 3D-ILC method provided an effective means for studying the integration and penetration of pre-existing three-dimensional internal cracks. The findings of this study contribute to the theoretical understanding of fracture propagation through obstacles in brittle materials and provide a basis for further investigations using physical experiments.

The influence of defect shape on the cracking behavior of brittle materials

To understand the influence of defect shape on the cracking behaviors of brittle materials, three types of gypsum specimens containing different shape defects are designed, and three-point bending tests have been conducted. The results show that the shape of defects can affect the initiation and occurrence of tensile cracks, as the load continuous to increase, the tensile crack usually propagates along the direction of applied compression. The defect shape can also influence the strength of the specimen, and both tensile and shear cracks occur when the load is close to or greater than 50% of the peak strength. Defects with sharp corners are easy to induce the initiation and occurrence of tensile crack, whereas, for the defects with smooth edges, if the defect area is not large enough, it is difficult to breed tensile cracks. Additionally, defect shape has no effect on the fracture toughness, whereas the defect shape can influence the unstable toughness, and when the defect shape is triangular, the distribution of the unstable toughness value varies randomly, and when the defect shape is trapezoidal, the unstable toughness decreases with the increase of defect area. These results are expected to improve the understanding of brittle fracture and can be used to analyze the durability of concrete structures and the stability of rock slopes.

Innovative tensile test for brittle materials: Validation on graphite R4550

This paper proposes an innovative ultrasonic tensile test methodology for the assessment of quasi-static uniaxial mechanical properties and tensile strength of brittle materials. An ultrasonic testing machine, commonly employed for very high cycle fatigue tests, had its control and data acquisition systems adapted to induce specimen failure in about 100 cycles, avoiding cyclic load damage. The mechanical properties are thereafter estimated with a finite element model which simulates the experimental test. The proposed method has been validated by assessing the tensile strength of graphite R4550, characterized by brittle behaviour. The mechanical properties for graphite R4550 estimated with this experimental-numerical approach were found to be close to literature values obtained in different quasi-static testing configurations, confirming the effectiveness of the proposed method and the feasibility of employing the ultrasonic fatigue testing machine for studying the behaviour of brittle materials. Furthermore, the proposed methodology eliminated issues caused by mechanical fixtures and tensile testing machine alignment, while also allowing a considerable increase of the material loaded volume when compared to that of traditional test methods. The experimental and numerical approaches are successfully validated on graphite R4550, also highlighting its capability of characterizing the material nonlinear behaviour, including viscoelasticity and asymmetrical response in tension and compression.

Peridynamic simulation for the damage patterns of glass considering the influence of rate-dependence and pre-defects

This study presents a novel rate-dependent bond-based peridynamic model for predicting the mechanical behavior of brittle aluminosilicate glass under quasi-static and dynamic flexure loading. To achieve this, the damage criterion is modified with reference to the concept of strain rate in the classical continuum mechanics (CCM). Additionally, a peridynamic (PD) model with inhomogeneous critical stretch based on the Weibull distribution is proposed to account for the randomly distributed defects in glass and investigate their effect on crack initiation and propagation. The accuracy and rationality of the improved PD model are verified by comparing the calculated strength and fracture modes with the experimental results under quasi-static Ball-On-Ring (BOR) and dynamic low-velocity impact tests. The results show that the rate effect increases the damage threshold of glass, enhancing strength and damage ratio. Notably, flexural failures induced by tensile stress are observed under both static and dynamic loading. The rate-dependent inhomogeneous PD model indicates that glass inhomogeneity reduces strength while increasing crack propagation velocity (CPV). The introduction of pre-existing defects alters the symmetrical crack propagation pattern typically observed in homogeneous materials, resulting in a more randomized crack propagation path. Overall, the results can provide a promising approach for predicting the mechanical behavior of brittle materials.

Experimental and numerical studies on the mechanical behaviors of basic magnesium sulfate cement concrete under dynamic split-tension

Dynamic splitting-tensile tests were conducted on basic magnesium sulfate cement concrete (BMSCC) at three different water-cement ratios using a 75 mm diameter split Hopkinson pressure bar (SHPB). The failure process of BMSCC under dynamic splitting loading was simulated using the finite element software LS-DYNA and a random aggregate mesoscopic model. The results demonstrated the strain rate effect in BMSCC, where the dynamic splitting-tensile strength increased with higher strain rates. Furthermore, the strength grade of the material significantly influenced the growth rate of peak stress, with higher strength grades exhibiting faster rates. The dynamic increase factor (DIF), a parameter characterizing the dynamic behavior of brittle materials, exhibited a linear relationship with the logarithm of strain rate. The LS-DYNA software was employed to numerically simulate the dynamic splitting-tensile process at the meso-scale, yielding satisfactory results with relative errors of 12.7%, 6.3%, and 3.3% for the dynamic splitting-tensile strength at different water-cement ratios, respectively.

Simulation of machining behaviour of two-phase brittle materials during grinding by modelling single-grain scratching using a combination of FE and SPH methods

Two-phase, brittle-hard materials are widely used not only in the tool industry but also increasingly in the aerospace industry. Due to the two-phase nature, the materials have unique material properties adapted to the respective application. But the material properties also lead to challenging machinability. Therefore, two-phase, brittle-hard materials are mostly ground. The analogy process of single-grain scratching is used to analyse the material removal behaviour and design the grinding process. Since single-grain scratching is time-consuming and costly, it is desirable to substitute the analogy process with numerical simulation. This paper discusses the suitability of the Smooth Particle Hydrodynamic (SPH) simulation method in combination with the Finite Element Method (FEM) for single-grain scratching of two-phase, brittle-hard materials. The approach is validated using the examples of tungsten carbide-cobalt (WC-Co) cemented carbides and Silicon carbide fibre-reinforced silicon carbide (SiC/SiC) ceramics. For both applications, the material removal behaviour was optically analysed and in good agreement with the experimental results and theoretical assumptions. For SiC/SiC ceramics, several surface phenomena could be identified in the simulation as well as in the experimental results. The scratching forces were compared qualitatively and were in good agreement with the experimental results for both applications.

Simulation of Brittle Materials Based on Ordinary State-based Peridynamics

We present a coupled model for brittle materials based on the ordinary state-based peridynamics. The ordinary state-based peridynamics theory is suitable for describing the plastic incompressibility problem and has good application prospects in the fracture damage simulation of brittle materials. The brittle material is a material with a compressive load-bearing capacity greater than the tensile load-bearing capacity and has the characteristics of incompressibility, which is consistent with the application scope of ordinary state-based peridynamics. The mechanical behavior of brittle materials is simulated and analyzed using the ordinary state-based peridynamics theory coupled with brittle materials, and the validity of the model is verified using the finite element method. The results show that the model can effectively capture the displacement field distribution of the brittle material, and the comparison of the finite element results displacement field is consistent. Finally, crack extension analysis is performed on the brittle material plate with prefabricated defects, where the cracks extend along the defect location, bifurcate, and finally penetrate the upper and lower surfaces of the material. The results show that the model can effectively predict the crack expansion path of the material, which provides a new research idea for the simulation of crack expansion in brittle materials.

From macro fracture energy to micro bond breaking mechanisms – Shorter is tougher

We show a novel fracture behavior and properties of brittle materials not previously explored. These were made possible when merging macro to micro in fracture. Our findings are based on macro-scale fracture cleavage experiments of dynamic cracks propagating in brittle single-crystal silicon specimens, focusing on the crack’s energy-speed relationships, and the fine details of the crack front. From the micro-scale, we developed an atomistic model for bond-breaking mechanisms. These mechanisms are in the form of low-energy kink advance (migration) and high-energy kink formation (nucleation) along the crack front. The energy release rate (ERR) at crack initiation, G0, and its derivative, dG0/da≡Θ, in particular, play a major role in the novel behavior and properties. G0 and Θ are influenced by the precrack length, a0. The macro-scale experiments, the micro-scale atomistic model, and the gradient of the ERR, Θ, enabled the conclusions portrayed in this work.We identified that the cleavage energy is not a constant but bounded by the Griffith Barrier as the lower bound while the upper bound (apparently the lattice-trapping barrier) may reach 3 times the lower bound. We further suggest that a brittle material can be envisaged as comprising a pseudo-R-Curve behavior mechanism typical of metallic materials. A new and essential fracture mechanism was identified, which we term ‘quasi-propagation’, a transitional mechanism between initiation and propagation. During this mechanism, the sequence of the bond-breaking mechanisms is varying, causing an increase in the macroscale cleavage energy.The evaluated cleavage energy shows another novel behavior, that of ‘shorter is tougher’, namely, shorter cracks require higher energy to propagate, and, therefore, specimens with shorter cracks are stronger than that predicted by Griffith’s theory.

Thin‐walled concrete beams with stay‐in‐place flexible formworks and integrated textile shear reinforcement

AbstractThin‐walled textile‐reinforced concrete beams have recently emerged as a promising approach for material‐efficient design. However, the increased complexity of the formwork is a major challenge in implementing such elements for broader use in the construction industry. This study presents a novel type of stay‐in‐place flexible formworks with integrated textile reinforcement. The use of weft‐knitted textiles allows the integration of continuous high‐strength rovings as shear reinforcement and the introduction of spatial features within the fabric to guide bending‐active rods to shape the complex cross‐section geometry. The manufacturing procedure and the structural performance were investigated in an experimental campaign consisting of four concrete beams with I‐profile cross sections tested in three‐point bending, where aramid rovings were used for the shear and conventional deformed steel bars for the flexural reinforcement. The transverse reinforcement ratio proved to be essential in increasing the shear strength. Thereby, the use of digital image correlation measurements of the surface deformations allowed the direct assessment of the strains and, thus, the mechanical activation of the textile reinforcement. The full tensile capacity of all the aramid rovings crossing the governing crack could not be exploited due to the brittle material behavior, resulting in a progressive failure once the first roving reached its tensile strength. Compatibility‐based stress fields were used to predict the load‐deformation and failure behavior of the tested beams, which resulted in an excellent agreement of the ultimate loads and failure modes obtained from the model with the observations and results from the experiments.

A modified MERR model for predicting mode II fracture initiation angle considering boundary constraint effect

AbstractDuring the service process of brittle materials like marble, soda‐glass, and acrylic, mode II fracture is usually a typical failure mode. The fracture crack initiation, which is a critical factor affecting mode II fracture behavior, is an essential issue for understanding the fracture mechanism and determining fracture toughness. This paper proposed a modified maximum energy release rate model to predict the mode II fracture initiation angle through superimposing two idealized boundary conditions, remote loading, and crack‐face traction. The degree of the boundary constraint effect in finite‐size specimens was quantified by introducing the dimension‐ratio parameter. As experimentally validating through tension‐loading shear fracture tests of brittle poly(methyl methacrylate) (PMMA), the proposed model was demonstrated to be a good prediction of the mode II fracture initiation angle. The applicability of the proposed model was also verified with other brittle materials and fracture test techniques in references. The findings provide an insightful understanding of the mode II fracture behavior of brittle materials.

A length scale insensitive phase field model based on geometric function for brittle materials

The commonly used phase field model has a broad application in static and dynamic scenarios with brittle materials. Following the assumption of irreversibility of fracture, monotonically increasing phase and tensile strain energy are applied in the commonly used phase field model. By doing so, a clear stiffness reduction, however, is observed in stress–strain curve before reaching fracture strength, which conflicts with the linear elastic behavior of brittle materials. The limitation has also been mentioned in publications when length scale is the only parameter to adjust fracture strength. To solve these problems, a generalized quadratic geometric function is proposed to build a length scale insensitive phase field model. Governing equations and one-dimensional analytical solutions (homogeneous and nonhomogeneous solutions) of this length scale insensitive phase field model are presented. By adjusting the extra parameter in the generalized quadratic geometric function and zeroing negative phase, different phase profile (ranged from exponential profile to linear profile) and fracture strength can be obtained, which could be more suitable to cover different types of fractures. Meanwhile, a narrower crack band and linear elastic behavior can be guaranteed. LS-DYNA user-defined element and user-defined material subroutines are used to implement the proposed length scale insensitive phase field model. A tensile test successfully verifies the properties of a narrower crack band and linear elastic behavior. Three representative numerical examples show the feasibility of this model to simulate fracture propagation, including a Mode Ⅰ failure of wedge splitting test, a mixed-mode failure of l-shaped panel test and a mixed-mode failure of notched beam test. From the crack band and force–displacement curve, the proposed model can handle fracture propagation better for brittle materials.

Thermal effects on fracture and the brittle-to-ductile transition.

The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nanodevices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature-dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.