Fracture Behavior Of Brittle Materials Research Articles

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.

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.

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.

Empirical Rule of Fruit Rind Fragmentation in Muskmelon Netting

The suberized netting tissue on the surface of muskmelons is a remnant of the rind fragmentation caused by the mechanical imbalance between the expanding flesh meat and the solidified epidermis during growth. The appearance of this netting pattern is an important indicator for assessing the quality of muskmelons; however, very few quantitative studies have been conducted on the geometry of the netting. This study statistically analyzed the areas of fine epidermis fragments surrounded by the net using image analysis and explored a common rule governing the probability distribution of the fragment area. We found that the fragment area distribution follows a universal law by the modified Bessel function, which is consistent with the theoretical argument for the fracture behavior of brittle materials.

Dynamic Crack Propagation and Its Interaction With Micro-Cracks in an Impact Problem

AbstractThe dynamic fracture behavior of brittle materials that contain micro-level cracks should be examined when material subjected to impact loading. We investigated the effect of micro-cracks on the propagation of macro-cracks that initiate from notch tips in the Kalthoff–Winkler experiment, a classical impact problem. To define predefined micro-cracks in three-dimensional space, we proposed a two-dimensional micro-crack plane definition in the bond-based peridynamics (PD) that is a non-local form of classical continuum theory. Randomly distributed micro-cracks with different number densities in a constant area and number in expending area models were examined to monitor the toughening of the material. The velocities of macro-crack propagation and the time required for completing fractures were considered in several predefined micro-cracks cases. It has been observed that toughening mechanism is only initiated by exceeding a certain number of micro-cracks; therefore, there is a positive correlation between the density of predefined micro-cracks and macro-crack propagation rate and, also, toughening mechanism.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

Tensile Piezoelectric Actuator: Fabrication, Characterization and Application

A multilayer piezoelectric actuator, with dimension of 10 mm×10 mm×60 mm, which can output a tensile displacement directly by exploring the d31 effect of piezoelectrics, was fabricated using soft Lead Zirconate Titanate (PZT) ceramics. The performance of the actuator was characterized by a special home-made experimental setup under electric fields varying from 200 to 1 000 V/mm with the preload varying from -150 to 100 N at room temperature. Results showed that it can output a maximum tensile displacement of 12 μm under unipolar electric field of 1 000 V/mm and preload was independent with generative displacement in the range of testing preload. Additionally, using the actuator, we built a micro loading apparatus, which can be used to test the fracture behavior of brittle materials.

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

AbstractA novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.

A Comprehensive Study on Crack Tip Parameters of Modified Ring Specimen for Mixed-Mode Fracture Toughness Tests on Brittle Materials

Abstract Modified ring (MR) specimen was suggested for investigating the mixed-mode (I/II) fracture behavior of brittle materials by rotating the crack orientation with respect to the loading direction. Crack tip fracture parameters (KI, KII, and T stress) of MR were calculated for different geometric dimensions. To verify the numerical modeling procedure, two sets of comparisons were drawn between the results of prior studies on MR Mode I fracture behavior and those of this study, showing good agreement between the results. Through some graphs, the effects of geometric parameters on YI, YII, and T* (dimensionless crack tip parameters) and also on βII (pure Mode II crack angle) were studied. In addition, the biaxiality ratio (B), as an influential factor in the generalized maximum tangential stress (GMTS) criterion, was calculated for the whole range of mode mixity in the MR specimens. Next, fracture behavior of the specimen was discussed by means of the GMTS criterion in terms of the results obtained for the biaxiality ratio (B). At the end, as an appendix, the entire results obtained for YI, YII, T*, and βII were presented.

Multi-scale modeling of microstructure dependent intergranular brittle fracture using a quantitative phase-field based method

The fracture behavior of brittle materials is strongly influenced by their underlying microstructure that needs explicit consideration for accurate prediction of fracture properties and the associated scatter. In this work, a hierarchical multi-scale approach is pursued to model microstructure sensitive brittle fracture. A quantitative phase-field based fracture model is utilized to capture the complex crack growth behavior in the microstructure and the related parameters are calibrated from lower length scale atomistic simulations instead of engineering scale experimental data. The workability of this approach is demonstrated by performing porosity dependent intergranular fracture simulations in UO2 and comparing the predictions with experiments.

Evaluation of subsurface crack depth during scratch test for optical glass BK7

To get insight into the deformation and fracture behavior of brittle materials during abrasive process, scratch tests with linearly increasing normal load and constant normal load were conducted on BK7 using Vickers indenters. The effect of the applied normal load on the characteristics of surface cracks as well as the square of the scratch depth was found insensitive to the two load conditions discussed here. By taking both scratch and residual depths into consideration, a model of scratch hardness for brittle material was developed. Based on this scratch hardness, the correlation between the depth of the subsurface cracks and the scratch depth was established and was found in general agreement with the experimental results.

Evaluation of surface cracking in micron and sub-micron scale scratch tests for optical glass BK7

In order to obtain the fundamental information on the deformation and fracture behavior of brittle materials during precision and ultra-precision grinding, micron and sub-micron scale scratch tests were conducted on optical glass BK7 using Vickers indenters. Three types of surface cracking were observed around the scratch grooves. They are lateral cracking, radial cracking and cracking in front of the moving indenter. It is found that lateral cracking is the main damage type due to its large damage size and low crack initiation load. The effect of surface cracking on the relationship between the normal load and the square of scratch depth was studied. The plastic zone size as well as the sliding blister field strength was expressed as a function of the contact zone size of the indenter. A prediction model for the size of damage zone induced by lateral cracking was established and was compared with experimental results.

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.

An Array of Parallel Edge Cracks with Alternating Lengths in a Strip Subjected to a Thermal Shock

Ceramics and other brittle materials suffer multiple surface cracking when subjected to quenching. These surface cracks greatly influence the thermal fracture behavior of brittle materials. This paper considers an array of parallel edge cracks with alternating lengths in an elastic plate subjected to a thermal shock. A Fourier transform/superposition method is used to derive the coupled integral equations that govern the displacement discontinuity gradients along the surfaces of the long and short cracks. Thermal stress intensity factors at the tips of the long and short cracks are calculated from the numerical solutions of the integral equations. The numerical results indicate that the crack length ratio and crack spacing have profound effects on the thermal stress intensity factors.

Theoretical analysis of Hertzian contact fracture: Ring crack

The axisymmetric fracture behavior of brittle materials under an applied indentation force is investigated by considering the pile-up of Somigliana ring dislocations. For such a mixed-mode crack problem, the stress intensity factors (SIFs) and strain energy release rate are obtained by solving a system of Cauchy singular integral equations. The Auerbach range is extensively studied during the formation of a shallow ring crack. The Auerbach constant is also determined from the exact solutions, enabling the prediction of surface energy from Hertzian indentation tests. The obtained results can be used to extract the fracture parameters of brittle materials by using the indentation technique.

Nanoindentation Size Effect of KDP Crystal by Instrumented Indentation Testing

Indentation tests and single-point scratch tests are probably the simplest methods of measuring the elastic, plastic and fracture behavior of brittle materials. In this paper, the nearsurface mechanical properties of KDP single crystal have been investigated including the elasticity like Young’s modulus E, and the plasticity like the hardness H. These material properties can be used to predict the material responses in optical manufacturing operations. Hardness and elastic modulus on different crystal plane of KDP single crystal have been examined under different loads by nanoindentation test, and the influence of the indentation load on hardness and elastic modulus have been also analyzed systematically. The results show the nanoindentation size effect, that is, the hardness and elastic modulus increase as the indentation load decreases. The hardness and elastic modulus have strong anisotropy in the different crystallographic orientation of the same crystal plane.

The Influence of Stress Ratio on the Fracture Behavior of Brittle Materials

The fracture behavior of brittle materials under different stress ratio has been investigated by means of numerical simulation method with software RFPA2D (Realistic Failure Process Analysis). The fracture dependence of brittle material on biaxial plane stress state was confirmed. The results show that the critical stress intensity factor under biaxial stress increases with the increase of biaxial stress ratio. The simulation tests reveal that the biaxial stresses have strong influence on the fracture properties of glass. The results confirmed that the strain criterion of fracture is feasible while brittle materials under complex stress state.

Numerical Approach to Fracture of Glass under Biaxial Stress

The fracture behavior of brittle materials under biaxial plane stress has been investigated by means of numerical simulation method with software MFPA2D (Material Failure Process Analysis). The aims of this study are to clarify the fracture dependence of brittle material on biaxial plane stress state. The observation of crack initiation and fracture behavior reveals that the biaxial stresses have strong influence on the fracture properties of glass. Thus, the fracture criterion by the stress intensity factor was questioned for the biaxial plane stress issues. It is confirmed that the tensile stress parallel to the crack plane is an important factor affecting crack arrest, while the compressive stress parallel to the crack plane contributes to crack opening.

OS08W0450 Numerical simulation of fracture behavior of brittle materials based on micro-crack formation

OS08W0450 Numerical simulation of fracture behavior of brittle materials based on micro-crack formation

OS8(2)-9(OS08W0450) Numerical Simulation of Fracture Behavior of Brittle Materials Based on Micro-Crack Formation

OS8(2)-9(OS08W0450) Numerical Simulation of Fracture Behavior of Brittle Materials Based on Micro-Crack Formation