Crack Propagation In Brittle Solids Research Articles

3D internal crack propagation in brittle solids under non-uniform temperature field: Experimental and numerical simulation

In the field of engineering, elevated temperatures often induce thermal stress. Especially in brittle materials, the propagation of internal cracks under such thermal stress is frequently the primary cause of failure. We utilize the 3D internal laser-engraved crack technology to create internal cracks at various locations inside the half-Brazilian disk specimens. By precisely controlling the power of the heating device, we achieved temperature non-uniformity of the external heat source, resulting in uneven heating of the material’s surface. Simultaneously, by adjusting the geometry of the material and using semi-Brazilian disk specimens, we generated uneven temperature gradients and thermal capacities along different heat conduction paths. The internal cracks at different locations also affect the distribution of thermal stress in the material, further influencing the formation of the non-uniform temperature fields (NUTF). Through the above methods, we successfully conducted physical experiments on the 3D propagation of internal cracks in brittle materials under NUTF. Additionally, we utilized J-integral and the finite element method for thermal analysis to conduct thermo-mechanical coupled 3D numerical simulations. Furthermore, we employed a polarising microscope to analyze the microscopic morphology of 3D internal cracks. Finally, we revealed the mechanism of 3D internal crack propagation under NUTF. The results show that prefabricated internal cracks in group A produce “n-shaped” crack at a height of 15 mm and “u-shaped” cracks at heights of 25 mm and 35 mm. Meanwhile, in group B, the eccentric prefabricated internal cracks ultimately produce “s-shaped” cracks. Through analysis, it was determined that the differential formation occurred due to relative sliding between the upper and lower surfaces of the crack under longitudinal shear stress induced by NUTF. Group A cracks have smooth surfaces, which are mode I-II cracks. group B generated “lance-like” fractures with obvious “anti-binary tree”, which are mixed mode I-II-III cracks. These findings provide an experimental and theoretical basis for the study of 3D internal crack propagation modes under NUTF and deepen the understanding of fracture mechanics in brittle materials.

Meso-scale size effects of material heterogeneities on crack propagation in brittle solids: Perspectives from phase-field simulations

Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the fracture process zone but small compared to that of the application. The specific configuration (both geometrical and mechanical) of this mesoscale heterogeneity is generally recognized as important in controlling crack propagation behavior and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic brittle fracture navigates through a linear array of mesoscale inclusions. Using a variational phase-field (PF) approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation (and the resulting toughening) under Mode-I loading for various configurations of inclusions. We identify an interplay between the size of inclusion and that of the K-dominant zone in the presence of elastic heterogeneity: matching these two sizes gives rise to the best toughening outcome for a given area fraction of inclusions. We discuss mechanisms that rationalize this observation and the importance of the length scale parameter used in PF models in interpreting simulation results. Our work sheds physical insight into the interaction between size effects and material properties, thereby opening a venue for the rational design of functional (architected) composites for dynamic fracture applications.

Characteristics of crack growth in brittle solids with the effects of material heterogeneity and multi-crack interaction

AbstractDespite the extensive research on crack propagation in brittle solids, numerous unexplored problems still necessitate in-depth study. In this work, we focus on numerical modeling of multi-crack growth, aiming to explore the effect of material heterogeneity and multi-crack interaction on this process. To do this, an improved singular-finite element method (singular-FEM) is proposed with incorporation of heterogeneity and crack interaction. An efficient algorithm is proposed for simulating multi-crack propagation and interaction. Stress singularity near crack tip is reproduced by the singular elements. The singular-FEM is convenient and cost-effective, as the zone far away from crack tips is directly discretized using linear elements, in contrast to the quadratic or transition elements utilized in traditional FEM. Next, the proposed method is validated through benchmark study. Numerical results demonstrate that the superiority of the singular-FEM, which combines the merits of low cost and high accuracy. Then, the mechanics of crack growth are explored in more complex scenarios, accounting for the effects of crack interaction, loading condition and heterogeneity on crack trajectory, stress field and energy release rate. The findings reveal that the combined effect of heterogeneity and crack interaction plays a critical role in the phenomenon of crack growth, and the proposed method is capable of effectively modeling the process.

Modeling of coupled thermo-mechanical crack propagation in brittle solids using adaptive phase field method with scaled boundary finite element method

Complex crack patterns caused by thermally induced stresses commonly occur during thermal shrinkage in brittle materials, such as ceramic. Modeling the propagation of complex cracks can be tedious, computationally intensive and time consuming when multiple cracks initiate simultaneously. In this paper, the coupled thermo-mechanical Phase Field Model (PFM) is adopted, which facilitates the treatment of crack initiation, growth, bifurcation and coalescence in a unified framework. However, to represent the crack, the PFM requires a very fine mesh which increases the computational burden especially when the crack locations are not known as a priori. Aiming to efficiently reveal the crack morphogenesis and evolution in brittle material subjected to thermal shock, a space adaptive PFM is developed by refining the elements in the vicinity of crack propagating path on the fly, which reduces the number of elements and reduces the computational cost eventually. The Scaled Boundary Finite Element Method is applied with the quadtree mesh in this work to achieve the adaptive approach in the PFM as it is highly complementary. The presented numerical examples are showing good agreement with experiments and other results available in the literature, further, higher computational efficiency is achieved by employing the adaptive approach.

A peridynamic differential operator-based scheme for the extended bond-based peridynamics and its application to fracture problems of brittle solids

In order to describe the mechanical behavior of solids with arbitrary Poisson’s ratio values, an extended bond-based peridynamic (XBB-PD) model was developed in the authors’ previous work by taking both the bond longitudinal and tangential deformations into account. In the current work, a peridynamic differential operator based implementation scheme is presented for the XBB-PD model. An energy-based failure criterion is introduced to describe the failure and crack propagation in brittle solids. First, two elastic examples are solved to validate the proposed approach. The m- and δ- convergence studies are carried out. Subsequentially, several numerical examples of crack propagation problems are simulated. All simulations show good agreement with the results reported in the references, demonstrating the flexibility and capabilities of the developed approach in the simulation of crack propagation in brittle solids.

A coarse-grained concurrent multiscale method for simulating brittle fracture

This paper proposed a concurrent multiscale method for modeling crack propagation in brittle solids. The method couples the continuum finite element domain with a recently-developed coarse-grained atomistic potential, which has been developed to simulate crack nucleation and propagation within the molecular dynamics domain. The main advantage of this potential is to suppress dislocation nucleation from the crack tip which significantly eases the coupling procedure. In this multiscale framework, complexities like large deformation, crack nucleation and propagation are simulated in the atomistic domain while the rest such as elastic wave propagation and boundary conditions are modeled in the continuum domain. As a result, the atomistic area will be limited around the cracking zone which increases the computational efficiency. Two examples of edge crack propagation and sliding surfaces in contact are presented and compared with the fully atomistic models to verify and check the efficiency of the proposed multiscale method. The comparison shows that the proposed method can accurately capture the crack formation while the computation cost reduces significantly.

Influence of fracture incubation time on dynamic crack propagation in brittle solids

The paper is devoted to theoretical study of the longitudinal shear (mode II) crack unstable growth dynamics in brittle materials. We considered two main regimes of the dynamic propagation of the crack (sub-Rayleigh and supershear) and their implementation conditions. The research was carried out by computer simulation with the Movable Cellular Automaton method, using the generalized kinetic fracture model, which takes into account the finite duration of local fracture (fracture incubation time). It is shown that the fracture incubation time is a key parameter, which determines the transition conditions of the shear crack growth process from the sub-Rayleigh regime to supershear.

Fracture of brittle materials under uniaxial compression

Fracture under compressive loading is distinctly different compared to fracture under tensile loading. One contributing factor is that interatomic bonds have to be stretched to be broken: compressing the interatomic spacing cannot break an interatomic bond. This is demonstrated by the fact that no fracture occurs in materials loaded in hydrostatic compression, even at extreme magnitudes. It is believed that fracture in compressive stress fields starts due to local tensile stresses which develop around a discontinuity (e.g. an air bubble). A 2D numerical study is conducted to study the effect of the shape and size of such a discontinuity on crack propagation in a macroscopic uniaxial compressive stress field. The results of this study highlight the major differences between tensile crack propagation and compressive crack propagation in brittle solids.

On crack propagation in brittle material using the distinct lattice spring model

With the rapid development of high-performance computing, Lattice Spring Models (LSMs) using a simple fracturing law demonstrate many prospects for simulating crack propagation in brittle solids. In this paper, a comprehensive study on crack propagation in brittle material is conducted using the distinct lattice spring model (DLSM) with high-performance computing and physical tests on crack propagation in brittle material from this work and the literature. The relationship between the simple fracturing law and the fracture criterion based on linear elastic fracture mechanics is investigated for the first time. The work involved includes the correlation between the Stress Intensity Factor (SIF) and spring deformation, the influence of the particle size on fracture toughness, and the relationship between the micro-spring failure and the critical stress intensity factors. Our results indicate that the simple fracturing law based on spring deformation may be easier and more fundamental for understanding crack propagation in brittle materials than fracture-toughness-based criteria. The applicability of the simple fracturing law is further confirmed from numerical modelling of crack propagation and coalescence problems with complex pre-existing cracks. Our results show that models with an appropriate resolution can simulate the crack path reasonably. Finally, the advantages of using the simple fracturing law are highlighted through multiple dynamic crack propagation and three-dimensional fracturing.

Numerical solution for mixed mode crack propagation in brittle solids combined with finite element method and failure criteria

This paper presents a numerical method for mixed mode crack propagation in brittle solids combined with finite element method and failure criteria. For a crack in the brittle solids under external loading condition, there is a plastic core region existed at the crack tip, the crack propagation will happened when the solid element is plastic yield, and the crack will propagate under biaxial loading conditions forming wing cracks. The stress intensity factors of an element are related to its stress state. Combined with the finite element method, the D-P failure criterion is used to determine the crack propagation path. Computed results show that the crack initiation angle is influenced by the crack inclination, loading pattern, loading ratio and the friction effect of crack surface. The crack is more easily propagated under tensile stress condition than compressive stress condition, and the mean stress, deviatoric stress, maximum shear strain and yielded elements are increased with increased external loading.

Novel approaches to multiscale modelling in materials science

Computational modelling techniques are now widely employed in materials science, due to recent advances in computing power and simulation methodologies, since they can enable rapid testing of theoretical predictions or understanding of complex experimental data at relatively low cost. However, many problems at the leading edge of materials science involve collective phenomena that occur over a range of time and length scales which are intrinsically difficult to capture in a single simulation. This review summarises some of the latest developments in multiscale modelling techniques over the past decade, as applied to selected problems in materials science and engineering, thereby motivating the reader to explore how such techniques might be applied in their own area of specialty. Methods for accelerating molecular dynamics by enhancement of kinetic barrier crossing, such as hyperdynamics and metadynamics, are discussed alongside mesoscale simulation techniques, such as dissipative particle dynamics or adaptive coarse graining, for enabling larger and longer simulations. The applications are mainly focused on simulations of microstructure and mechanical properties, and examples of surface diffusion in metals, radiation damage in ceramics, strengthening of nanocrystalline metals and alloys, crack propagation in brittle solids, polymer chain relaxation in nanocomposites and the control of nucleation in biomimetic materials are discussed.

The simulation of dynamic crack propagation using the cohesive segments method

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.

A technique for the in-situ observation of stable crack propagation in brittle solids

A technique for the in-situ observation of stable crack propagation in brittle solids

Atomically sharp cracks in brittle solids: an electron microscopy study

The issue of bond rupture versus microplasticity as an essential mechanism of crack propagation in brittle solids is addressed. A detailed survey of existing theoretical and experimental evidence relating to this issue highlights the need for direct observations of events within the crack-tip “process zone”, at a level approaching 10 nm. Transmission electron microscopy is accordingly used to study arrested cracks about sharp-contact (Vickers indentation and particle impact) sites in Si, Ge, SiC and Al2O3. The nature of the deformation which accommodates the irreversible contact impression is first investigated, in the light of Marsh's proposal of an “equivalence” between indentation and crack-tip zone processes. Interfacial and tip regions of the surrounding cracks are then examined for any trace of a plasticity-controlled fracture process. Dislocation-like images are indeed evident at the crack planes, but these are shown to be totally inconsistent with any conventional slip mechanism. The close connection between the dislocation patterns and moire fringe systems along the cracks points to “lattice mismatch” contrast in association with a partial closure and healing operation at the interface. Analysis of all other details in the crack patterns, e.g. the presence of a crack-front contrast band indicative of a residual strain field and the disposition of interfacial fracture steps relative to the dislocation/moire system, reinforces this interpretation. It is concluded that the concept of an atomically sharp crack provides a sound basis for the theory of fracture of brittle solids.

Determining the kinetics of crack propagation in brittle solids during fracture in a surface-active medium

Determining the kinetics of crack propagation in brittle solids during fracture in a surface-active medium

Crack propagation under constant deformation and thermal stress fracture

An analogy is drawn for crack propagation in brittle solids under constant deformation (strain) and under thermal shock. Following the original approach by Berry it is shown theoretically that under constant deformation an initially short crack, unstable at a critical strain, propagates to a new length which requires a finite increase in strain before it will become unstable again. Similar behavior is expected under conditions of thermal shock where an initially short crack, unstable at a critical temperature difference, propagates to a new length such that a finite increase in temperature difference is required before the crack will again continue to propagate. Relative changes in strength as a result of this type of crack behavior are predicted and verified by experimental results for two industrial polycrystalline aluminum oxides subjected to thermal shock by means of a water quench.