Anisotropic Crack Research Articles

Effect of anisotropy on 4H-SiC cracking behavior during diamond wire sawing

Cracking behavior caused by the anisotropy of single-crystal silicon carbide (SiC) brings challenges to the quality of the diamond wire sawing and grinding process. In this study, the effects of SiC anisotropy on machanical properties is analyzed based on Griffith’s theory. The results indicate that the fracture toughness and the fracture strength exhibit anisotropy. At the same time, an analytical model for the initiation and deflection of the surface radial crack is proposed based on the scratching stress field. On the basis of these results, the anisotropic machanism of the surface radial crack initiation, deflection, the surface radial crack initiation (SRCI) depth, and the residual scratching depth are investigated in combination with the single abrasive scratching experiment. The shear stress and the maximum principal stress are the primary driving forces for the initiation and deflection of surface radial crack, respectively. The direction of the minimum shear strength and the fracture strength determines the anisotropy of cracking behavior. Meanwhile, the anisotropy of the SRCI depth and the residual scratching depth is caused by the fracture strength anisotropy. This research offers fundamental insights into the anisotropic cracking behavior of SiC, thereby contributing to the precise control of crack damage and improve the quality of the SiC diamond wire sawing and the as-cut wafers grinding process.

Studying mechanism of anisotropic crack generation on C-, R-, A-, and M-planes of sapphire during ultra-precision orthogonal cutting using a visualized slip/fracture activation model

With the growing demand for the fabrication of microminiaturized components, a comprehensive understanding of material removal behavior during ultra-precision cutting has become increasingly significant. Single-crystal sapphire stands out as a promising material for microelectronic components, ultra-precision lenses, and semiconductor structures owing to its exceptional characteristics, such as high hardness, chemical stability, and optical properties. This paper focuses on understanding the mechanism responsible for generating anisotropic crack morphologies along various cutting orientations on four crystal planes (C-, R-, A-, and M-planes) of sapphire during ultra-precision orthogonal cutting. By employing a scanning electric microscope to examine the machined surfaces, the crack morphologies can be categorized into three distinct types on the basis of their distinctive features: layered, sculptured, and lateral. To understand the mechanism determining crack morphology, visualized parameters related to the plastic deformation and cleavage fracture parameters are utilized. These parameters provide insight into both the likelihood and direction of plastic deformation and fracture system activations. Analysis of the results shows that the formation of crack morphology is predominantly influenced by the directionality of crystallographic fracture system activation and by the interplay between fracture and plastic deformation system activations.

Effect of height-diameter ratio on the mechanical characteristics of shale with different bedding orientations

Geological exploration cores obtained from shale gas wells several kilometers deep often show different height-diameter ratios (H/D) because of complex geological conditions (core disking or developed fractures), which makes further standard specimen preparation for mechanical evaluation of reservoirs difficult. In multi-cluster hydraulic fracturing, shale reservoirs between planes of hydraulic fractures with different lengths could be simplified to have different H/D ratios. Discovering the effect of H/D on the mechanical characteristics of shale specimens with different bedding orientations will support mechanical evaluation tests of reservoirs based on disked geological cores and help to optimize multi-cluster fracturing programs. In this study, we performed uniaxial compression tests and acoustic emission (AE) monitoring on cylindrical Longmaxi shale specimens under five bedding orientations and four H/D ratios. The experimental results showed that both the H/D-dependent mechanical properties and AE parameters demonstrated significant anisotropy. Increasing H/D did not change the uniaxial compressive strength (UCS) evolution versus bedding orientation, demonstrating a V-shaped relationship, but enhanced the curve shape. The stress level of crack damage for the specimens significantly increased with increasing H/D, excluding the specimens with a bedding orientation of 0°. With increasing H/D, the cumulative AE counts of the specimens with each bedding orientation tended to exhibit a stepped jump against the loading time. The proportion of low-average-frequency AE signals (below 100 kHz) in specimens with bedding orientations of 45° and 60° increased to over 70% by increasing H/D, but it only increased to 40% in specimens with bedding orientations of 0°, 30°, and 90°. Finally, an empirical model that can reveal the effect of H/D on anisotropic UCS of shale reservoir was proposed, the anisotropic proportion of tensile and shear failure cracks in specimens under four H/D ratios was classified based on the AE data, and the effect of H/D on the anisotropic crack growth of specimens was discussed.

Phase-field modeling of anisotropic crack propagation based on higher-order nonlocal operator theory

This paper presents a novel higher-order nonlocal operator theory for the phase-field modeling of brittle fracture in anisotropic materials. Incorporating higher order nonlocal operators can enhance the accuracy of the phase-field model by effectively capturing long-range interactions that hold significance in numerous materials. The reproducing kernel particle method is employed to derive a nonlocal differential operator to enhance computational stability and accuracy. Moreover, the proposed method eliminates the need for direct computation of derivatives of the modified kernel function, which avoids the calculation of moment matrix derivatives and improves computational efficiency. The phase-field modeling of polycrystalline materials, considering the anisotropic fracture resistance of each grain, is implemented using this numerical framework. The present method is able to capture different scenarios intergranular and transgranular crack propagation patterns in polycrystalline materials. The proposed method involves a detailed representation of the complex process of crack initiation and propagation in 2D and 3D models of polycrystalline materials.

Phase field-based cohesive zone approach to model delamination in fiber-reinforced polymer composites

In the present work, a unified phase field-based cohesive zone model (PF-CZM) has been utilized to predict bulk fracture and most importantly interfacial delamination in carbon fiber-reinforced polymer composites (CFRP). The formulation is based on the classical phase-field approach of energy minimization, with a rational degradation function and a polynomial-type crack geometric function. Incorporation of those provides the PF theory to integrate various traction–separation behaviors by choosing optimal constitutive functions and makes the theory capable of predicting the quasi-brittle type of fracture. Since the interfacial delamination in composites occurs either due to adhesive failure or decohesion between stacked lamina, the PF-CZM model is used to predict such failure by exploiting the cohesive zone flavor of the model. Further, the model inherently incorporates the strength of the material without any additional calibration. Various standard simulations are performed considering CFRP geometry where delaminations due to adhesive failure or interface decohesion occur in a mode-I and mode-II fashion. The model is observed to predict mode-I and mode-II separation accurately. To test the accuracy of the model an experimental validation is also performed. In addition to the delamination, open hole tension (OHT) simulations of CFRP lamina for different fiber orientations are considered to validate the anisotropic crack growth predictions, and the results are compared with experiments.

The effect of microstructural barriers on transient crack growth in shape memory alloys

There are several issues to be solved in the fracture mechanics of shape memory alloys, one of them being the resistance to crack growth and therefore to fracture. This paper discusses the crack growth in a single crystal CoNiAl shape memory alloy under cyclic loading and the effect of micro-structural barriers. To observe the crack growth in detail, tests are conducted on edge-notched specimens. The displacement field is obtained using digital image correlation (DIC), and the fracture parameters are calculated by fitting anisotropic crack tip displacement equations to DIC data. Similar crack growth behaviors are observed in both superelastic and shape memory specimens, with a comparatively higher crack growth rate in the superelastic case: first a crack initiates at the notch and grows, then new cracks are observed to form near the tip of the main crack, or on the notch when the growth slows down. Then, further cyclic loading leads to the growth of the main crack and the new crack simultaneously with the two cracks merging at the end. Test specimens are examined post-failure with optical microscopy to better understand this complicated behavior. Results showed the presence of a non-transforming secondary (γ) phase around the regions where the propagating cracks slowed down, deviated, and/or stopped, improving the resistance of the shape memory alloy specimen to fracture.

In situ synchrotron radiation µCT indentation of cortical bone: Anisotropic crack propagation, local deformation, and fracture

The development of treatment strategies for skeletal diseases relies on the understanding of bone mechanical properties in relation to its structure at different length scales. At the microscale, indention techniques can be used to evaluate the elastic, plastic, and fracture behaviour of bone tissue. Here, we combined in situ high-resolution SRµCT indentation testing and digital volume correlation to elucidate the anisotropic crack propagation, deformation, and fracture of ovine cortical bone under Berkovich and spherical tips. Independently of the indenter type we observed significant dependence of the crack development due to the anisotropy ahead of the tip, with lower strains and smaller crack systems developing in samples indented in the transverse material direction, where the fibrillar bone ultrastructure is largely aligned perpendicular to the indentation direction. Such alignment allows to accommodate the strain energy, inhibiting crack propagation. Higher tensile hoop strains generally correlated with regions that display significant cracking radial to the indenter, indicating a predominant Mode I fracture. This was confirmed by the three-dimensional analysis of crack opening displacements and stress intensity factors along the crack front obtained for the first time from full displacement fields in bone tissue. The X-ray beam significantly influenced the relaxation behaviour independent of the tip. Raman analyses did not show significant changes in specimen composition after irradiation compared to non-irradiated tissue, suggesting an embrittlement process that may be linked to damage of the non-fibrillar organic matrix. This study highlights the importance of three-dimensional investigation of bone deformation and fracture behaviour to explore the mechanisms of bone failure in relation to structural changes due to ageing or disease. Statement of significanceCharacterising the three-dimensional deformation and fracture behaviour of bone remains essential to decipher the interplay between structure, function, and composition with the aim to improve fracture prevention strategies. The experimental methodology presented here, combining high-resolution imaging, indentation testing and digital volume correlation, allows us to quantify the local deformation, crack propagation, and fracture modes of cortical bone tissue. Our results highlight the anisotropic behaviour of osteonal bone and the complex crack propagation patterns and fracture modes initiating by the intricate stress states beneath the indenter tip. This is of wide interest not only for the understanding of bone fracture but also to understand other architectured (bio)structures providing an effective way to quantify their toughening mechanisms in relation to their main mechanical function.

Experimental study on the characteristics of anisotropic cracking behavior of shales under compression and tension

Experimental study on the characteristics of anisotropic cracking behavior of shales under compression and tension

Damage and failure mechanism of sapphire under ballistic loading based on a modified bond‐based peridynamic model

AbstractTo investigate the dynamic mechanical behaviors of c‐plane and a‐plane sapphire, a novel anisotropic constitutive model and fracture criterion are constructed on the basis of bond‐based peridynamics (BB‐PD) theory. And the concept of strain is introduced in the framework of BB‐PD. After that, the simulations of a‐ and c‐planes of sapphire under spherical and cylindrical impact are conducted. In addition to capturing the distribution of strain and damage, the histories of various fracture types such as the primary fracture front and cracks are monitored for quantitative analysis. The numerical predictions are shown to agree well with previous experimental results, and further reveal the damage and failure mechanisms of sapphire. The different forms of contact between the projectile and the target strongly influence the stress waves generated and energy transferred ultimately affecting the damage development process. The crystal orientation dominates the appearance of anisotropic crack modes. Crack bending and deflection, as well as spalling‐like fracture, are associated with wave reflection and intersection. Moreover, an in‐depth examination of the observed wave splitting phenomenon is performed.

Experimental investigation of the tensile behavior and acoustic emission characteristics of anisotropic shale under geothermal environment

Shale gas is becoming a top priority for future global energy consumption and climate change mitigation, and deep and ultradeep shale gas extraction cannot overlook the influence of the geothermal environment. This paper experimentally investigated the tensile behavior and acoustic emission (AE) characteristics of anisotropic shale under geothermal environment of 25–200 °C. The results indicate that the tensile strength and absorbed energy of all specimens decreased with increasing temperature, and minimum values occurred in specimens with a layer inclination of 90° at each temperature. The evolution of tensile strength and absorbed energy versus the layer inclination did not vary with increasing temperature, exhibiting an inverted-V shape. Anisotropic failure mode of specimens with layer inclinations of 30°, 45° and 60° was influenced by the increasing temperature, but central tensile fracturing in specimens with layer inclinations of 0° and 90° was temperature-independent. With increasing temperature, the cumulative AE hits of specimens showed a highly obvious step-up trend, and anisotropic crack initiation stress levels obtained via the AE definition significantly varied. Finally, microstructure response, fracture length and fracture location and proportion of fracture types were discussed, and potential applications and challenges of geothermal environment in hydraulic fracturing of deep shale reservoirs were proposed.

Experimental study on anisotropic fracture characteristics of coal using notched semi-circular bend specimen

To investigate the anisotropic fracture characteristics of coal, physical tests are carried out on semi-circular bend specimens with different pre-crack inclinations and bedding orientations. Regarding the coal as a transversely isotropic body, assigning its elastic properties to the finite element models, the crack geometry factors are calibrated, and stress distributions near the pre-crack tip are analyzed through numerical simulations. Then, the modes I and II critical stress intensity factors are determined based on fracture load. Experimental results show that bedding orientation and pre-crack inclination of coal specimens jointly affect their fracture mode and resistance, and mode I fracture dominates the fracture onset. For straight and inclined pre-cracks, the elliptic function and Fourier series can approximately describe the relationship between effective critical stress intensity factor and bedding angle, respectively. Besides, descriptions of typical propagation paths and their corresponding failure mechanisms are reported in detail. Further, the morphology of fracture surfaces is drawn based on scanning data; afterward, four equidistant cross-sectional profiles in different specimens are extracted and exhibited. Finally, an empirical equation is utilized to calculate the joint roughness coefficients of profiles. Comparing the differences among these coefficients is beneficial to quantitatively characterize anisotropic crack growth in coal.

Femtosecond Laser-Induced Anisotropic Structure and Nonlinear Optical Response of Yttria-Stabilized Zirconia Single Crystals with Different Planes.

Nonlinear optical properties have been extensively studied due to their promising nonlinear effects and various applications. With ultrashort duration and ultrahigh intensity, a femtosecond laser can fabricate various superior-quality micro-/nanostructures to improve the nonlinearity of materials, which are promising for stable and high-performance nonlinear devices. In this contribution, yttria-stabilized zirconia (YSZ) with fs laser-induced micro-/nanostructures is demonstrated to exhibit unique anisotropic light-material interaction and nonlinear optical response on [100], [110], and [111] planes. Time-resolved reflectivity of YSZ after fs laser excitation is investigated by a pump-probe experiment, which is consistent with simulations through the plasma model combined with a two-temperature model. These results indicate two early ablation mechanisms: Coulomb explosion and melting. Anisotropic crack structures are formed due to thermal stress, which is always ignored in fs laser fabrication and is verified by Raman mapping and analysis of slip systems on different crystal planes. Through the z-scan measurement, the nonlinear absorption (NLA) of crack structures is effectively improved, and a nearly 18 times enhancement of the NLA coefficient is acquired in [100] samples, while a 2 times enhancement in [110] and [111] samples. Such great enhancement of NLA is mainly due to the abundant presence of crack structures and the increase of fs laser-induced oxygen vacancies in [100] YSZ. These results provide a potential way of utilizing fs laser to improve the nonlinearity for the technological development in nonlinear devices.

FE-based damage modeling approach for short fiber reinforced thermoplastics under quasi-static load coupling anisotropic viscoplasticity and matrix degradation

It is challenging to predict the material degradation and crack initiation of short fiber reinforced thermoplastics (SFRT) components with high computation efficiency and low parameter identification effort. To achieve that, this work utilizes a hybrid method combining micro- and macro-mechanical approaches to describe the damage-coupled material behavior of SFRT. The Mori-Tanaka mean-field homogenization method is used to determine the effective linear elastic properties of SFRT, whereas the consideration of plasticity is based on a macro-mechanical anisotropic viscoplastic model. The effect of micro-damage in the matrix material on the macroscopic behaviors of SFRT is considered within the Continuum Damage Mechanics (CDM) framework. A nonlinear damage evolution law is implemented to account for the nonlinearity in the damage evolution. Targeting industrial applications, the proposed damage-coupled material model is implemented into the commercial FE software ANSYS with a novel stepwise damage updating process, requiring no user-defined subroutine. The model is calibrated with experimental data on flat specimens under monotonic and cyclic tensile loading. The FE simulation with the calibrated material model accurately describes the anisotropic deformation and crack initiation of the investigated SFRT material observed in experiments.

Multi phase-field modeling of anisotropic crack propagation in 3D fiber-reinforced composites based on an adaptive isogeometric meshfree collocation method

An anisotropic multi phase-field model is developed in this paper to investigate the interaction between the crack propagation and interfacial damage in a fiber-reinforced composite. The proposed modeling approach can capture the fracture patterns of composite microstructures through the introduction of the crack phase field and the interface phase field. By considering the free energy related to the interface and crack phase fields, the interfacial debonding, matrix cracking and the interaction of two fracture patterns can thus be simulated. The anisotropic phase-field approach is further adopted to describe the interface interaction associated with a crack. The phase-field equations are solved using the isogeometric-meshfree collocation approach to achieve high computational efficiency. An adaptive h-refinement scheme is incorporated into the phase-field formulations using phase-field variables and their gradients as the error indicators. The proposed method is shown to be effective and robust in both case studies of 2D and 3D fiber-reinforced composite microstructures. Moreover, fracture behaviors including the crack initiation, propagation, coalescence, interfacial debonding, and matrix cracking in composite microstructures are found to be precisely modeled by the proposed approach.

An anisotropic damage model combined with a tracking algorithm for modelling crack propagation

The development of a simple and efficient methodologies for numerically analyzing the material fracture process is very important in the field of computational mechanics. Damage mechanics approaches are still applied to fracture numerical analyses of many engineering practice problems. This paper focuses on the numerical prediction of crack propagation and fracture behavior by the combination of anisotropic damage model and tracking algorithm. In general, anisotropic damage models may be misunderstood to be used only in the simulations of anisotropic materials. However, it can be used for the anisotropic stiffness matrix induced by the crack plane in damaged isotropic materials. Although it is well known that the anisotropic damage model is superior to the isotropic damage model in fracture simulations, most of studies have combined the isotropic damage model and tracking algorithm, and few studies combine the anisotropic damage model and tracking algorithm. The issues of successfully combining the anisotropic damage model and crack tracking algorithm are addressed in this study. The anisotropic damage model is improved and a local tracking algorithm based on crack surface discretization is also modified. Various crack propagation problems are analyzed numerically to demonstrate the superior performance of the proposed approach.

Egg-speriments: Stretch, crack, and spin

Eggs are key ingredients in our kitchens because of their nutritional values and functional properties such as foaming, emulsifying, and gelling, offering a wide variety of culinary achievements. They also constitute ideal objects to illustrate a myriad of scientific concepts. In this article, we focus on several experiments (egg-speriments) that involve the singular properties of the liquids contained inside the eggshell, especially the egg white. We first characterize the rheology of an egg white in a rotational rheometer for constant and oscillatory shear stresses revealing its shear-thinning behavior and visco-elastic properties. Then, we measure the tendency of the fluid to generate very long filaments when stretched that we relate to the shear modulus of the material. Second, we explore the anisotropic crack pattern that forms on a thin film of egg white after it is spread on a surface and let dried. The anisotropy results from the long protein chains present in the egg white, which are straightened during film deposition. Finally, we consider the “spin test” that permits to distinguish between raw and hard-boiled eggs. To do so, we measure the residual rotation of a spinning raw egg after a short stop, which reflects the continuation of the internal flow. These observations are interpreted in terms of viscous damping of the internal flow consistently with the measurements deduced from rheology.

A new anisotropic poroelasticity model to describe damage accumulation during cyclic triaxial loading of rock

SUMMARY Crustal rocks undergo repeated cycles of stress over time. In complex tectonic environments where stresses may evolve both spatially and temporally, such as volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In this work, we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress–strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3-D Kaiser ‘damage memory’ effect.

Effect of interatomic potential on modelling fracture behavior in hcp titanium: a molecular dynamics study

Molecular dynamics (MD) simulations have unique advantages in capturing the details of the crack tip deformation at the atomic scale. As the accuracy of simulation results is heavily dependent on the selected interatomic potential, a comprehensive study of the anisotropic crack tip behavior of hcp titanium under plane strain mode-I loading with the commonly utilized potentials is presented in this paper. The typical crystallographic planes in hcp materials including {0001}, {101¯0}, {112¯0}, {101¯1} and {112¯2} are considered as the pre-existing crack planes. The intrinsic brittleness and ductility of different crack systems are discussed from the perspective of linear elastic fracture criteria. Depending on the selected potential, the dominant crack tip deformation mechanism may be basal a slip, prismatic a, pyramidal c+a slip or twinning modes in different crack systems. Finally, in comparison with experimental results, the different potentials are evaluated in the light of their capability to reproduce the experimentally observed crack tip deformation. Overall, the recent developed Mendelev-II potential is recommended for MD simulation of fracture behavior under mode-I loading, as this potential gives a more realistic crack tip response than other studied potentials.

Prediction of the anisotropic crack resistance of heterogeneous microstructures using a crack phase‐field model

AbstractIn this contribution, a variational crack phase‐field model for heterogeneous materials is used to study periodic microstructures. The discontinuity at material interfaces is taken into account by an additional static order parameter. A partial rank‐I relaxation ensures the pointwise fulfillment of the Hadamard jump condition and static equilibrium within the diffuse interface. Crack propagation is investigated for different orientations of hexagonal microstructures and various phenomena like toughening‐by‐weakening and an orientation‐dependent fracture toughness are observed.

Experimental Verification of the Isotropic Onset of Percolation in 3D Crack Networks in Polycrystalline Materials With Implications for the Applicability of Percolation Theory to Crustal Rocks

AbstractPercolation theory is often proposed as a framework for understanding flow and transport through fractured rock, yet the applicability of percolation theory to natural systems remains uncertain. Experimental verification of the predictions of percolation theory are challenging because of the difficulty in systematically creating 3D crack networks in crystalline materials. Using ice as a model for rock, we experimentally test the prediction of percolation theory that for a sufficiently large sample, the onset of percolation is isotropic even when the crack network is anisotropic. Consistent with theory, experimentally we find that in strongly anisotropic crack networks induced by uniaxial loading at a sufficiently high strain rate, the onset of percolation is nearly isotropic in samples where the dimension of the sample is about an order of magnitude greater than the length of the largest crack. The onset of percolation is isotropic even though nearly 90% of the induced cracks are oriented within about 10° of the direction of applied compression. A similitude analysis indicates that for typical geotherms and geologic strain rates, crack networks consistent with the predictions of percolation theory are only possible within the upper several tens of km of a nonsubducting granite slab and to depths of several hundreds of km in subducting slabs of gabbro.