Anisotropic Fracture Research Articles

Anisotropic fracture toughness of a selective laser melted martensitic stainless steel

Anisotropic fracture toughness of selective laser melted AISI 420 built in two build directions was investigated. Post-process heat treatments were performed at 200 °C and 400 °C to study the tempering effect. The parallel group exhibited better fracture toughness than the perpendicular group in both as-built and tempered states. KIC value of the 400 °C tempered state was superior to that of other states due to a coarser martensite phase. Elongated cellular structure was responsible for the anisotropic behavior because of a build direction effect, while the anisotropy was barely changed by the tempering treatments.

Nonlinear flow and permeability anisotropy characteristics in hydraulic fracturing-induced rock fractures subjected to various normal compressive stresses

Well productivity after hydraulic fracturing is strongly affected by the flow behaviors in created fracture complexity. In this study, gas flow tests were conducted in splitting fractures (induced by Brazilian splitting) and hydraulic fractures (created by hydraulic fracturing) to study the nonlinear fluid flow behaviors in rough fractures. 3D fracture surfaces were first digitally reproduced with a scanner and then the fracture geometry parameters (roughness profile index R_{p}, the root mean square of the fracture profile wall slope Z_{2}), aperture distributions were computed for both fractures. The influence of the fracture geometry characteristics on the nonlinear flow behaviors were systematically analyzed. The permeability anisotropy was numerically examined in detail. The results show that R_{p}, Z_{2} and mean aperture of hydraulic fractures are relatively smaller, indicating that the fracture surfaces are smoother. The transmissivity of splitting fracture is relatively higher than that of hydraulic ones, and the ratio of splitting to hydraulic one varies from 2.51 at sigma_{c} = 1 MPa to 60.95 at sigma_{c} = 40 MPa. By contrast, splitting fractures have larger critical Reynolds number and lower critical pressure gradient, implying that nonlinearity is easier to occur in splitting fractures. The average Forchheimer coefficient for splitting fractures is 0.00577, which is 1.5 times larger than that (0.0041) for hydraulic ones. In addition, the fractures exhibit strong permeability anisotropy and this anisotropic effect is significantly dependent on the loading stress. In general, the permeability anisotropy in hydraulic fracture is more significant, showing that their permeability anisotropy ratios K are larger and more sensitive to the loading. The obtained results confirm that there exist some discrepancies in flow behaviors between splitting and hydraulic fractures and for more accurate evaluation in engineering practice, hydraulic fractures should be fully considered.

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.

Cryogenic ductile and cleavage fracture of bcc metallic structures – Influence of anisotropy and stress states

The anisotropic cryogenic ductile and cleavage fracture properties of a body-centered cubic (bcc) steel at −196°C have been investigated under a broad spectrum of loading conditions, crossing stress triaxiality range from −1/3 to 1.5, and along three loading directions. Fracture is completely impeded in uniaxial compression tests. Conventional brittle behavior is only observed in high triaxiality conditions for the investigated bcc steel, and on the contrary ductile fracture with shear and void coalescence as underlying mechanisms takes place in low (simple shear) and moderate triaxiality (uniaxial tension) at −196°C. Cleavage fracture occurs after significant plasticity at −196°C under moderate triaxiality conditions during tensile tests using flat-notched specimens under plane-strain tension. For all the stress states, anisotropy has shown a profound influence in ductile fracture, brittle fracture, and, particularly in the transition region mixed with two failure types. It is concluded that the reason for the anisotropic transition of activated failure mechanisms crossing stress states at −196°C is because strain hardening capacity, Lankford coefficients, fracture initiation strain as well as cleavage fracture strength are all dependent on loading orientations. Based on the collected local critical stress and strain variables from finite element simulations using an evolving anisotropic plasticity model, an anisotropic unified fracture criterion revealing the underlying failure mechanisms is developed and demonstrates distinguished predictive capability in describing cryogenic ductile and cleavage fracture properties under different stress states and loading directions.

Characterization and Modeling of Anisotropic Fracture of Advanced High-Strength Steel Sheets

<div class="section abstract"><div class="htmlview paragraph">As an engineering approach of balanced complexity and accuracy, the Generalized Incremental Stress-State dependent damage Model (GISSMO) in LS-DYNA<sup>®</sup> has now been widely adopted by the automotive industry to predict metallic materials’ fracture occurrences in both forming and crashworthiness simulations. Calibration of the nominal GISSMO is typically based on material characterization data along a certain representative material orientation. Nevertheless, many rolled or extruded metallic materials, such as advanced high-strength steel (AHSS) sheets, exhibit accentuated anisotropic fracture behavior, even though, notably, some of these materials show comparatively weak anisotropic plasticity in the meantime. Accordingly, in this work, the deformation and fracture behavior of a selected AHSS grade, Q&P980 steel, was first characterized based on a series of mechanical experiments under simple shear, uniaxial tension, plane strain, and equi-biaxial tension conditions. Then, material models were calibrated based on the plasticity and fracture data. Two fracture models, either stress- or strain-based, were applied to fit the fracture loci of the target material, which then could be directly implemented into the material cards in LS-DYNA<sup>®</sup>. Particularly, to simulate the anisotropic fracture behavior of the target material, an extended GISSMO material card (eGISSMO) was introduced and highlighted in this work. Unlike the nominal GISSMO, the eGISSMO integrated the different anisotropic fracture loci and damage accumulation along three material orientations (longitudinal, diagonal, and transverse) into a single material card. In the subsequent validation based on a customized three-point-bending (3PB) testing setup on hat-section samples, only the finite element (FE) model using the calibrated eGISSMO successfully simulated the anisotropic fracture bifurcation observed in the actual experiments.</div></div>

Implications for identification of principal stress directions from acoustic emission characteristics of granite under biaxial compression experiments

The rock fracture characteristics and principal stress directions are crucial for prevention of geological disasters. In this study, we carried out biaxial compression tests on cubic granite samples of 100 mm in side length with different intermediate principal stress gradients in combination with acoustic emission (AE) technique. Results show that the fracture characteristics of granite samples change from ‘sudden and aggregated’ to ‘continuous and dispersed’ with the increase of the intermediate principal stress. The effect of increasing intermediate principal stress on AE amplitude is not significant, but it increases the proportions of high-frequency AE signals and shear cracks, which in turn increases the possibility of unstable rock failure. The difference of stress in different directions causes the anisotropy of rock fracture and thus leads to the obvious anisotropic characteristics of wave velocity variations. The anisotropy of wave velocity variations with stress difference is probable to identify the principal stress directions. The AE characteristics and the anisotropy of wave velocity variations of granite under two-dimensional stress are not only beneficial complements for rock fracture characteristic and principal stress direction identification, but also can provide a new analysis method for stability monitoring in practical rock engineering.

Deterministic and stochastic phase-field modeling of anisotropic brittle fracture

We investigate variational phase-field formulations of anisotropic brittle fracture to model zigzag crack patterns in cubic materials. Our objective is twofold: (i) to analytically derive and numerically test the fundamental behavioral aspects predicted by the two main available fourth-order models, and to guide the calibration of their unknown parameters; (ii) motivated by the pronounced non-uniqueness of the phase-field solution in the anisotropic case and uncertainties in the material model, to transition from a deterministic to a stochastic model by introducing a material-related random field in the anisotropic phase-field energy functional. We employ Monte Carlo, randomized quasi-Monte Carlo and stochastic spectral methods to estimate statistical moments of the phase-field variable. The two fourth-order phase-field models are shown to predict a very different response both in their deterministic and stochastic versions. For either modeling choice, we believe that the stochastic approach, which captures several possible zigzag crack paths, holds significant promise to enable meaningful predictions of anisotropic fracture with phase-field models.

Controlling and visualizing fracture of 2D crystals by wrinkling

Shaping two-dimensional (2D) crystals with well-defined edges along specific directions remains technically challenging due to the intrinsic lattice discreteness and anisotropy in their fracture toughness. The patterns of crystal cleavage are determined by the fracture resistance and loading conditions, and usually display kinking features. We show that the fracture of single-crystalline 2D films (MoS2, MoTe2, graphene) can be controlled by mechanically-induced wrinkles, and the distortion of their profiles can visualize the distorted local strain state near the crack tip. In thin samples with stretch-induced wrinkles, the elastic driving force with effective anisotropy steers crack propagation, resulting in straight edges following the corrugation profile. In contrast, thick samples remain flat under stretch for their elevated bending resistance, and the cracks advance with sawtooth patterns following the zigzag motif. The experimental findings are explained by wrinkling-induced elastic anisotropy, which dominates over fracture anisotropy. The control of fracture in 2D crystals can be applied to fabricate micro- and nanostructures for their applications in electromechanical and optoelectronic devices.

A study of severely deformed austenite and transformed martensite: Texture inheritance and high-temperature fracture anisotropy

A study of severely deformed austenite and transformed martensite: Texture inheritance and high-temperature fracture anisotropy

A crack-bridging model of brick and mortar architecture considering the anisotropic property

The attainment of both strength and toughness is a vital requirement for most engineering materials. Unfortunately these properties are generally mutually exclusive. Biological materials, which defeat the conflict of strength versus toughness, provide prototypes to design artificial composites. This paper presents a fracture model of brick and mortar architectures considering the anisotropy of natural materials, to reveal the toughening mechanism of crack-bridging and provide some guidelines for the design of high-performance bioinspired materials. Firstly, we establish an microstructure-based anisotropic fracture model. It is found that to accurately predict the fracture toughness, it is necessary to take into account material anisotropy. Then, the model is used to explore the toughening effect of geometric sizes and material parameters. The results demonstrate that the aspect ratio of brick and the stiffness ratio of brick and mortar are key parameters to influence fracture toughness. In addition, crack-bridging provides a dominant contribution to the crack resistance in the early stage of crack growth, and its contribution is gradually attenuated with crack growth.

Anisotropic Gurson–Tvergaard–Needleman model considering the anisotropic void behaviors

Anisotropic ductile fracture resulting from different microscopic void behaviors has a significant effect on material formability. To accurately predict the anisotropic ductile fracture, an anisotropic Gurson-Tvergarrd-Needleman (GTN) model considering the anisotropic void behaviors was proposed. The effect of high stress triaxiality on void nucleation was considered and remodeled through an additional stress dependent factor in the modeling formulation. Meanwhile, the anisotropic stress triaxiality was adopted. To describe the difference in damage accumulations along different material orientations, a new formulation related to anisotropic critical damage was proposed. Various uniaxial tensions including round bars and plate-shaped specimens were performed along 30° and 60° with respect to the rolling direction for 2024-T35 aluminum alloy. These experimental results, along with previously-published data, were used to validate the proposed model by comparing numerical predictions and experimental results in terms of the load responses and displacements at fracture (DAFs) along different loading directions. Remarkable improvement can be achieved when the contribution of high stress triaxiality, anisotropic void nucleation and critical damage are considered in the modeling of anisotropic ductile fracture. The proposed modeling formulations provide new ideas for the construction of anisotropic GTN series model.

Effect of Microstructural Anisotropy on Fracture Toughness of Selective‐Laser‐Melted 15‐5 PH Stainless Steel

Herein, the influence of microstructure anisotropy on fracture toughness of selective laser melting‐fabricated and directly aged 15‐5 PH stainless steel is investigated. A bimodal columnar (within the melt pool) and equiaxed (at the melt pool boundary) microstructure forms on the vertical plane, which results in a higher yield strength in the horizontal direction than the vertical direction. For fracture toughness, the value is 10% higher in the specimen with the crack propagation perpendicular to the build direction than parallel to the build direction. The main cause for such an anisotropic fracture toughness is related to the circuitous crack path along the melt pool boundary when the crack propagation is perpendicular to the build direction.

A gradient-enhanced damage model for anisotropic brittle fracture with interfacial damage in polycrystalline materials

This article presents a nonlocal gradient-enhanced damage model that uses direction-dependent damage evolution and interfacial damage to predict transgranular and intergranular cracks in polycrystalline materials at the microstructural level. The distinct grains within the polycrystalline morphology are modeled as anisotropic linear elastic domains with random spatial orientation and cubic symmetries. Transgranular micro-cracks are assumed to occur along specific preferential cleavage planes within each randomly oriented crystal and are described using a bulk damage variable. For intergranular fracture, a smeared description of interface decohesion is incorporated through an interface damage variable which depends on the modified interface kinematics based on a cohesive law that uses a smoothed displacement jump approximation. The coupled system of equations in the proposed computational framework is decoupled using an operator-split methodology to ensure a robust and straightforward computational implementation. Several numerical examples are presented, and simulations are performed on single crystal, bicrystals, and polycrystalline domains to demonstrate the capabilities and validation of the proposed model.

Fracture prediction based on attenuative anisotropy theory and its application to a shale gas reservoir

AbstractShale gas reservoirs require artificial hydraulic fracturing to achieve commercial gas production. Continental Jurassic shale reservoirs have several thin interlayers (e.g. sandstone and carbonate), which lead to pseudo-anisotropy of the seismic amplitude and velocity, and traditional technology for predicting anisotropic fractures has difficulty in identifying a true target. Based on the traditional theory of azimuthal anisotropy and the equivalent medium theory, in this paper, the approximate formula for the reflection coefficient of attenuating anisotropy and the equation for the azimuthal attenuating elastic impedance are derived. With the objective function established using Bayesian and group sparse inversion methods, parameters such as the fluid terms and fracture characteristics are obtained by solving the elastic matrix, and a highly accurate prediction of the 3D fracture density is obtained. The validity of this method is confirmed via a test on a single well and application to actual seismic data for a shale gas reservoir.

Graphyne-type nano-metamaterials: A comprehensive molecular dynamics simulation

With advances in nanotechnology, the search for novel and nontraditional materials beyond the already known nanostructures such as graphene and graphynes is rising. Recently, a graphyne-like nanostructure with the directional alignment of the acetylenic linkages, the so-called directional graphyne, as an interesting class of nano-metamaterials has been proposed which possesses fascinating physical properties. In this study, the mechanical behavior of the directional graphynes is investigated using molecular dynamics simulation. The effects of temperature, loading direction, and number of acetylenic bonds on the elastic and fracture properties are examined. Comparisons between the mechanical characteristics of the directional graphynes and those of the graphene and graphynes are also provided. The results reveal a high degree of anisotropy in Young's modulus and Poisson's ratio for the directional graphynes compared to the graphene and graphynes. However, the shear modulus is found to be insensitive to the loading direction for all three nanostructures. On the other hand, they all exhibit significant anisotropic fracture properties. An exception is observed for the fracture strain of the directional graphynes under shear loading. The failure mechanisms of the graphynes and directional graphynes are found to be different when the tensile loading is in the zigzag direction. Also, the results indicate that the directional graphynes exhibit interesting and different wrinkle behavior, and especially those with longer acetylenic linkages, are very flexible nanostructures under shear loadings.

The study of diffuse interface propagation of dynamic failure in advanced ceramics using the phase-field approach

Dynamic failure in advanced ceramic materials is a complex mechanical phenomenon, which is challenging to study in experimental and computational works. This work models and investigates the crack initiation, growth, propagation, and branching in two-dimensional single crystalline boron carbide at the nanometer length-scale and picosecond time-scale. A phase-field approach is used by carefully selecting the interfacial energy allowing a monolithic numerical solution method capturing strong coupling between mechanics and damage. Specifically, the transient Ginzburg–Landau equation is coupled with the balance of momentum including geometric nonlinearities and solved by using the open-source computing platform FEniCS. The monolithic computation ensures necessary accuracy for dynamic fracture under pure mode I loading, and also demonstrates the capability of crack branching depending on the loading rate. The effect of crack regularization length and kinetic coefficient on the crack interface profile and crack tip velocity is also studied. Altogether, the results are important for modeling anisotropic fracture in advanced ceramics and designing materials with desired dynamic failure characteristics.

Production performance simulation of a horizontal well in a shale gas reservoir considering the propagation of hydraulic fractures

In recent years, shale gas has become an important energy source due to its abundant reserves. Due to their extremely tight initial properties, shale gas reservoirs require the use of the multi-stage fractured horizontal well (MFHW) technique to break the shale rock, activate closed natural fractures, and form a complex fracture network. In this study, to solve the issue of how to describe the fracture network's geometry and to predict the production performance accurately, a model that couples the fracture propagation with the fracturing fluid and proppant flow in a horizontal wellbore and hydraulic fractures is established. The displacement discontinuity method (DDM) and finite volume method are used to iteratively obtain numerical simulations of the fracture propagation. The accuracy of the fracture propagation model is verified through comparison with analytical and numerical models. Then, the coupled continuous media and discrete fracture network model considering multiscale flow mechanisms in shale is developed, which is solved numerically using the control volume finite element method (CVFEM) and unstructured tri-prism grids. Finally, the numerical simulation models are successfully applied to synthetic and field cases, sensitivity analysis is conducted to evaluate the influences of the proppant injection, stress anisotropy and distribution of the natural fractures on the fracture propagation and production performance of the MFHW in a shale gas reservoir.

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.

Seismic inversion and fracture prediction in tilted transversely isotropic media

Abstract The conventional Amplitude variation with offset (AVO) inversion has been mainly developed for the isotropic media and therefore it is generally inapplicable to the anisotropic fractured formations. A set of tilted fractures in isotropic medium can be regarded as a transversely isotropic (TTI) medium. The reflection coefficient equation in TTI media contains many parameters such as anisotropic parameters, velocities, azimuth and dip angles. The selection of objective functions can significantly affect its performance in searching for the optimal solution. The seismic inversion of the TTI medium remains challenging because of its many parameters, and is very complicated after conversion into solving function problems. The genetic algorithm (GA) provides a universal framework to solve the optimization problem in complex systems, and it is independent of the types and disciplines of problems. In this study, the GA-based seismic prestack inversion of the TTI medium is implemented by constructing the objective functions of anisotropic parameters based on the TTI medium reflection coefficient approximation. The inversion performance is shown to be satisfactory on the one-dimensional well logging model, modified Hess model and the field datum. Furthermore, fracture filling materials are well predicted according to the theories of the equivalent medium for fractured materials and fracture weakness. The inversion results demonstrate the proposed method to be feasible and robust. The findings of this research are expected to provide theoretical guidance for the inversion of elastic parameters of anisotropic media and fracture type identification in hydrocarbon reservoirs.

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

This paper presents a unified framework for continuum-molecular modeling of anisotropic elasticity, fracture and diffusion-based problems within a generalized two-dimensional peridynamic theory. A variational procedure is proposed to derive the governing equations of the model, that postulates oriented material points interacting through pair potentials from which pairwise generalized actions are computed as energy conjugates to properly defined pairwise measures of primary field variables. While mass is considered as continuous function of volume, we define constitutive laws for long-range interactions such that the overall anisotropic behavior of the material is the result of the assigned elastic, conductive and failure micro-interaction properties. The non-central force assumption in elasticity, together with the definition of specific orientation-dependent micromoduli functions respecting material symmetries, allow to obtain a fully anisotropic non-local continuum using a purely pairwise description of deformation and constitutive properties. A general and consistent micro-macro moduli correspondence principle is also established, based on the formal analogy with the classic elastic and conductivity tensors. The main concepts presented in this work can be used for further developments of anisotropic continuum-molecular formulations to include other mechanical behaviors and coupled phenomena involving different physics.