Fracture Toughness Anisotropy Research Articles

Phase-field fracture modelling of piezoelectric quasicrystals

In this paper, an electro-elastic phase field model is developed for brittle fracture in piezoelectric quasicrystals. The elastic field of quasicrystals is composite of a phonon field and a phason field. The phonon field, phason field and electric field are coupled with each other, and the phonon and electric loadings trigger the variation of both the phonon and phason elastic energies, which then together contribute to crack evolution. The cracks initiation and propagation in piezoelectric quasicrystals under quasi-static mechanical loading and electric loading can be well predicted. Several numerical examples are performed to evaluate the effects of electric field and anisotropic fracture toughness. Simulation results show that the electric field influences the initial force, peak force, fracture displacement and crack path. For the single-edge notched tensile test, the effects of electric field force on the initial force, peak force and fracture displacement are obvious. For the single-edge notched shear test, the electric field force has no effect on the initial force, but it affects the peak force, fracture displacement and crack path. For the porous plate tensile test, a high-intensity electric field can deflect crack substantially resulting in passing through different holes. Further simulation indicates that the anisotropic fracture toughness has a significant effect on peak force, fracture displacement, and crack path. The present model can be used to simulate various fracture problems of piezoelectric quasicrystals.

Anisotropic Fracture of Two-Dimensional Ta2NiSe5.

Anisotropic two-dimensional materials present a diverse range of physical characteristics, making them well-suited for applications in photonics and optoelectronics. While mechanical properties play a crucial role in determining the reliability and efficacy of 2D material-based devices, the fracture behavior of anisotropic 2D crystals remains relatively unexplored. Toward this end, we herein present the first measurement of the anisotropic fracture toughness of 2D Ta2NiSe5 by microelectromechanical system-based tensile tests. Our findings reveal a significant in-plane anisotropic ratio (∼3.0), accounting for crystal orientation-dependent crack paths. As the thickness increases, we observe an intriguing intraplanar-to-interplanar transition of fracture along the a-axis, manifesting as stepwise crack features attributed to interlayer slippage. In contrast, ruptures along the c-axis surprisingly exhibit persistent straightness and smoothness regardless of thickness, owing to the robust interlayer shear resistance. Our work affords a promising avenue for the construction of future electronics based on nanoribbons with atomically sharp edges.

Numerical investigation of mode I fracture toughness anisotropy of deeply textured shale

The fracturing behavior of shale is controlled by the complex interaction between texture plane and rock matrix. This study develops a numerical model of semicircular bending of textured shale, integrating considerations of texture inclination and strength using the finite discrete element method, to examine the impact of shale anisotropy on damage patterns and fracture toughness. The results disclose the following insights: (1) Mode I fracture toughness anisotropy is significant, with fracture toughness showing a negative correlation with texture inclination and a positive correlation with texture strength. (2) Typical failure modes of SCB specimens encompass tensile failure across textured planes, tensile-shear mixed failure, tensile failure along texture planes, and tensile failure along the matrix. (3) For inclination angles ranging from 0° to 90°, cracks tend to deflect along the texture, leading to a fracture surface with high roughness. The fracture surface roughness was higher along the direction of maximum principal stress for the 0° and 90° specimens compared to the Divider specimens, while it was lower along the thickness direction compared to the Divider specimens. (4) The toughening mechanism of textured shales is categorized into three classes: separation along the texture, fracture path deflection, and texture cracking. Texture strength mainly influences texture cracking, while texture inclination primarily affects the deflection of crack paths and separation along the texture. (5) The criterion for predicting modified fracture toughness accurately predicts the anisotropic fracture toughness of shale compared to the conventional criterion for predicting fracture toughness.

Anisotropic Mechanical Behaviors of Shale Rock and Their Relation to Hydraulic Fracturing in a Shale Reservoir: A Review

Shale gas is an important supplement to the supply of natural gas resources and plays an important role on the world’s energy stage. The efficient implementation of hydraulic fracturing is the key issue in the exploration and exploitation of shale gas. The existence of bedding structure results in a distinct anisotropy of shale rock formation. The anisotropic behaviors of shale rock have important impacts on wellbore stability, hydraulic fracture propagation, and the formation of complex fracture networks. This paper briefly reviews previous work on the anisotropic mechanical properties of shale rock and their relation to hydraulic fracturing in shale reservoirs. In this paper, the research status of work addressing the lithological characteristics of shale rock is summarized first, particularly work considering the mineral constituent, which determines its physical and mechanical behavior in essence. Then the anisotropic physical and mechanical properties of shale specimens, including ultrasonic anisotropy, mechanical behavior under uniaxial and triaxial compression tests, and tensile property under the Brazilian test, are summarized, and the state of the literature on fracture toughness anisotropy is discussed. The concerns of anisotropic mechanical behavior under laboratory tests are emphasized in this paper, particularly the evaluation of shale brittleness based on mechanical characteristics, which is discussed in detail. Finally, further concerns such as the effects of bedding plane on hydraulic fracturing failure strength, crack propagation, and failure pattern are also drawn out. This review study will provide a better understanding of current research findings on the anisotropic mechanical properties of shale rock, which can provide insight into the shale anisotropy related to the fracture propagation of hydraulic fracturing in shale reservoirs.

Rock Anisotropy Promotes Hydraulic Fracture Containment at Depth

AbstractWe report laboratory experiments and numerical simulations demonstrating that the anisotropic characteristics of rocks play a major role in the elongation of hydraulic fractures (HFs) propagating in a plane perpendicular to the rocks' inherent layering (the bedding planes in sedimentary rocks and foliation planes in metamorphic rocks). Transverse anisotropy leads to larger HF extension in the parallel‐to‐layers/divider direction compared to the perpendicular‐to‐layers/arrester direction. This directly promotes vertical containment of HFs in most sedimentary basins worldwide even in the absence of any favorable in‐situ stress contrasts or other material heterogeneities. More importantly, the ratio of the energy dissipated in fluid viscous flow in the fracture to the energy dissipated in the creation of new surfaces is found to play a critical role on fracture elongation, with fracture‐energy dominated HFs being the most elongated while the viscous dominated ones remain more circular. These results open the door to a better engineering and control of HFs containment at depth in view of the competition between material anisotropy (both elastic stiffnesses and fracture toughness anisotropy) and injection parameters (fluid viscosity and rate of injection).

Multiple kinking of a tensile crack in the brittle multilayered media abundant with closely-parallel weak interfaces

Crack kinking is a basic way to form a complex crack trajectory in a multilayered solid abundant with weak interfaces. However, it remains unclear that under which condition a multi-kinked crack emerges with the influence of closely-parallel weak interfaces. According to a basic crack kink criterion, here we consider a brittle multilayered plate with a tensile edge crack to seek the occurrence condition of the multi-kinking behavior. The strain energy release rate ratio of the crack during its propagation is examined based on finite element simulations. We find a value domain of intersection angle and fracture toughness ratio, where the fracture toughness anisotropy competes with the load anisotropy to orient the crack propagation direction. We obtain the continual kinking condition of the tensile edge crack, including the intersection angle range about 0∼38° and the closed form upper and lower bounds of the fracture toughness ratio range. Our multi-kinking results for the tensile crack are helpful to understand the formation of complex crack patterns in the multilayered materials under complicated loads.

Role of precipitate-induced [formula omitted] twins on anisotropic fracture behavior in Mg-3Al-0.5Ce alloys

Anisotropic fracture toughness (FT) in a hot-rolled Mg-3Al-0.5Ce magnesium alloy has been investigated using fatigue pre-cracked compact tension (CT) specimens with the notch (an)‖ to the rolling direction (RD) and transverse direction (TD). During testing, notable non-linear load–displacement behavior before peak load indicated significant crack tip plasticity. Thus, elastic–plastic FT (JIC) was evaluated and found to be 20.7N/mm and 15.8N/mm for an‖ to RD and TD, respectively. Long-aligned Al11Ce3 precipitates were present in this alloy within the elongated grain boundaries along RD. During FT testing, profuse 101¯2〈101¯1〉 extension twins (ET) with c-axis almost ‖ and lamellae morphology almost ⊥ to RD formed between these elongated precipitates, irrespective of the notch, an‖ to RD or TD. The ET lamellae ⊥ and ∥ to crack path lead to trans and inter lamellar crack for an‖ to RD and TD, respectively. Translamellar crack in an‖ to RD leads to comparatively high strain hardening, dislocation density, geometrically necessary boundaries, and grain refinement, indicating larger plastic energy dissipation and thereby has higher JIC than in an‖ to TD with interlamellar crack.

Effect of size and anisotropy on mode I fracture toughness of coal

Obtaining the accurate fracture toughness of coal considering bedding angle and independent of size is of great significance to the evaluation of the initiation pressure in the hydraulic fracturing of coal seam. In this study, the newly proposed modified semi-circular bending test was used to conduct mode I fracture testing of coal samples with different sizes and bedding angles. A four-dimensional lattice spring model (4D-LSM) was established based on the cohesive zone model considering bedding planes to study the effects of specimen size and bedding angle the fracture toughness and fracture pattern of coal. The size effect and anisotropy characteristics of fracture toughness of coal were analyzed by using linear elastic fracture mechanics and Bazant size effect law (SEL) theory. The results show that the fracture toughness of coal has obvious size effect and anisotropy. In quasi-brittle materials, the fracture toughness increases with the increase of specimen size due to the fracture process zone (FPZ). However, the fracture toughness of coal affected by microcracks generally decreases with the increase of specimen size. The size effect of fracture toughness of coal is jointly determined by the FPZ with increasing effect and the microcrack with reducing effect. The fracture toughness of coal increases with the increase of bedding angle. The bedding angle has no influence on the fracture toughness size effect of coal, but the microcracks associated with the bedding plane have a greater influence on the fracture toughness size effect. The specimen size only affects the fracture toughness value, but has no obvious effect on the fracture toughness anisotropy. Based on Bazant SEL theory, a fracture toughness size effect model considering microcracks and bedding angles was established. The research results have reference significance for crack initiation and propagation in hydraulic fracturing of coal seam.

Mechanical properties anisotropy of Ti−6Al−4V alloy fabricated by β forging

The anisotropy of tensile properties and fracture toughness of Ti−6Al−4V (Ti64) alloy fabricated by β forging was investigated. In order to evaluate anisotropic mechanical properties, the microstructure and crystallographic texture of billets with different orientations were characterized, and the influence of sampling direction on tensile properties and fracture toughness was studied. The results reveal that the prior β grains of Ti64 billet display pan-cake-type characteristics. At room temperature, the alloy is mainly composed of α phase, and several α phase variants produced by β→α phase transformation decrease the α texture intensity. The anisotropy of mechanical properties is affected by prior β grain morphology and the slip activation related to α texture. The initiation toughness was obtained by the J-integral resistance curve method. The initiation toughness was divided into intrinsic and extrinsic toughness by calculation. The anisotropy of intrinsic toughness is mainly attributed to the size of crack tip plastic zone, which is affected by prior β grain morphology. In contrast, the extrinsic toughness is affected by zigzag degree of crack, which is mainly influenced by α lamellae and colonies.

The anisotropy of fracture toughness of an α+β titanium alloy by β forging

This study aims to investigate the anisotropic fracture toughness of an α+β titanium alloy processed by β forging. A typical basket-weave microstructure is observed, including the primary α (αp) phase, micron-scaled secondary α (αs) phase and residual β phase. The tensile test results show that the anisotropic strength results from the fine grain strengthening as well as the texture strengthening, and the plasticity difference is determined by the normal stress acting on the main crack in the fracture process. The orientation of the specimen also has a significant impact on fracture toughness. The corresponding toughening models of underlying damage mechanism with different orientations are proposed and discussed. It is found that the internal toughening mechanism is dominant, and external toughening mechanism also plays an important role in fracture toughness, including delamination and crack deflection caused by elongated β grains arrangement. Finally, the differences of J-integral resistance curves with different orientations are investigated in detail. The strength and fracture toughness values, KJIC (crack-initiation toughness) and KSS (growth toughness), are both highest when loading along radial direction (RD), and the positive effects of β grain morphology and two-phase texture on anisotropy of KJIC are summarized.

Fracture toughness of AlSi10Mg alloy produced by direct energy deposition with different crack plane orientations

The fracture and tensile behaviors of the AlSi10Mg alloy processed by Direct Energy Deposition were investigated. Three-point bending fracture toughness and tensile specimens were tested at room temperature along different crack plane orientations and loading directions. Before being machined and tested, the printed samples were subjected to heat treatment at 300 °C for 2 h to relieve the residual stresses. Microstructural and fractographic analyses were performed to investigate the fracture mechanisms and the crack propagation paths for each crack orientation. Significant differences in the fracture toughness were observed among the crack plane orientations. Specimens with cracks oriented in the X-Y direction featured the highest fracture toughness values (JIc = 11.96 kJ/m2), whereas the Z-Y crack orientation (perpendicular to the printing direction) performed the lowest fracture toughness values (JIc = 8.91 kJ/m2). The anisotropy in fracture toughness is mainly related to a preferential crack propagation path along the melt pool boundaries. At melt pool boundaries, pores are preferentially placed, coarsening of the microstructure occurs and there is higher Si content, leading to that area being less ductile and less resistant to crack propagation.

Anisotropic and elastoplastic mode‐I fracture toughnesses of three additively manufactured polymers fabricated via material extrusion and powder bed fusion

AbstractTwo types of additive manufacturing (AM) techniques, fused filament fabrication (FFF) and selective laser sintering (SLS), were employed to fabricate specimens from three widely used AM polymers: polylactic acid (PLA), acrylonitrile butadiene styrene (ABS), and polyamide (PA): the first two using FFF and PA using SLS. The single‐edge notch bending (SENB) test was employed to measure the mode‐I fracture toughnesses of bulk and AM specimens in three directions relative to the printing direction. Unlike their bulk counterparts, AM polymers exhibited anisotropic fracture toughness. The degree of anisotropy in FFF‐PLA was much larger than FFF‐ABS and SLS‐PA. The smallest fracture toughness value for each AM polymer was achieved along the transverse printing direction. Different AM techniques affect fracture toughness differently. For instance, FFF is shown to increase PLA's plastic deformation, while SLS reduces PA's ductility. The decrease in fracture toughness is consistently observed when transitioning from bulk polymers to AM ones, reaching as much as 75%. This study provides insights into the fracture toughness of AM parts made via popular plastics, which are crucial for designing structural parts using FFF and SLS processes.

Experimental and numerical investigation on the fracture behavior of deep anisotropic shale reservoir under in-situ temperature

Deep resource extraction is of great importance in advancing shale gas development. To obtain the fracture behavior of deep anisotropic shale reservoirs under in-situ temperatures, a series of fracture experiment on the Longmaxi shale specimens with 5 bedding orientations after constructing in-situ temperatures of 25–200 °C was conducted, as well as corresponding extended finite element method (XFEM) simulation by ABAQUS. The results reveal that increasing in-situ temperature decreases the fracture toughness but increases the fracture toughness anisotropy. Bounded by 100 °C, the fracture toughness varying versus bedding orientation shows two categories. With increasing in-situ temperature, the acoustic emission (AE) activity of specimens with bedding orientations of 45° and 60° develops at lower load levels, showing rapid AE hit development starting at the 20% and 60% peak load at 200 °C. Fracture path in specimens with bedding orientations of 0°, 30° and 90° is roughly not impacted by increasing in-situ temperature, but that in specimens with bedding orientations of 45° and 60° is impacted obviously. XFEM models match well with the experimental observations and give deeper analyses on the interaction between the fracture propagation and bedding plane. Finally, potential applications of elevated in-situ temperatures on deep shale gas extraction were proposed.

Fracture toughness anisotropy of Ti17 disk fabricated by through-transus-processed forging and the role of toughening mechanisms

The fracture toughness anisotropy of the Ti17 disk fabricated by through-transus-processed forging was discussed. For the specimens in different directions, the fracture initiation toughness Ki was calculated through the crack tip opening displacement, and the contribution of the crack tip blunting and dimple formation to the fracture initiation toughness was distinguished. Furthermore, the origin resulting in the fracture toughness anisotropy was analyzed according to the energy criterion for fracture. The results reveal that the specimen directions have a significant influence on the global fracture toughness and the crack propagation path. Meanwhile, the fracture initiation toughness occupies a significant portion of the global fracture toughness, and it reflects the ability of the crack tip plasticity. In addition, a schematic illustration is applied to demonstrate the toughening mechanism. This reveals that the different specimen directions result in the crack deflection or shearing off the ligament, leading to increased fracture toughness compared with the weak specimen direction.

Cracking direction in graphene under mixed mode loading

Crack branching in graphene under complex stresses is investigated by molecular dynamics simulations and boundary-layer models. Using the maximum energy release rate (MERR) criterion, an analogy of Wulff curve is plotted considering the anisotropic fracture toughness of hexagonal graphene, which shows the direction of crack kinking (local bump on the curve) is consistent with that of the weak fracture toughness (along zigzag edge). The angle of crack kinking prefers 0°/30°/60°, rather than the angle predicted by maximum circumferential stress criterion. The T-stress along crack front, obtained by the over-deterministic method, can indicate the possibility of kink by its transformation between positive and negative, especially for zigzag cracks. This study incorporates Wulff-like curve and MERR criterion to provide an accurate prediction of nanocrack paths in graphene.

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.

Could effective fracture toughness of polycrystalline aggregates exceed inner grain fracture toughness by adjusting toughness of grain boundary?

Obtaining intergranular and transgranular fractures through grain boundary engineering has been considered an efficient technique that improves the effective fracture toughness of polycrystalline aggregates. In this paper, the idealized hexagonal microstructure, random microstructures, and microstructures of grains with large aspect ratios are analyzed through a semi-analytical approach and the cohesive finite element method. The results indicate that when the aspect ratio of grains is not too large, the crack paths consisting of intergranular and transgranular fractures are approximately Mode I fracture morphologies among these microstructures. As the ratio of toughness between grain boundaries and grains varies, the effective fracture toughness of the microstructure can be increased more than the grain boundary fracture toughness but cannot exceed the inner grain fracture toughness.In contrast, the microstructure of grains with a large aspect ratio leads to deflected crack paths that are unexpectedly obtained, which implies that the approximate Mode-I intergranular fracture along transverse direction is almost impossible. The results demonstrate that the projected energy dissipation rate along the direction perpendicular to the loading axis can be significantly improved beyond the inner grain fracture toughness by enlarging the aspect ratio of the grains. Nevertheless, the mixed-mode effective fracture toughness is still limited to the grain fracture toughness. Corresponding experiments are also carried out to qualitatively verify the numerical results. The underlying mechanism for this deflection of fracture path is due to the strong anisotropy of fracture toughness. The higher the grain aspect ratio, the greater the anisotropy of the macroscopic effective fracture toughness. The energy favored fracture path is determined by the largest ratio between the driving force and the toughness of fracture over all directions. Therefore, cracks cannot propagate in the direction of the maximum fracture toughness when the aspect ratio of the grain is sufficiently large. The fracture diagrams that vary with the aspect ratio of grain and the ratio of fracture toughness between the grain and grain boundary are provided. The results can provide valuable guidance for designing microstructures and improving fracture toughness in materials.

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.

Effect of wet‐jet milling on the c‐axis orientation of hydroxyapatite ceramics fabricated using a strong magnetic field

AbstractControlling the crystal orientation of hydroxyapatite, an inorganic material that is a major component of human hard tissues is important to fabricate better artificial bones and artificial tooth roots. To obtain highly oriented hydroxyapatite ceramics under a strong magnetic field, a good dispersion of the raw materials in the slurry must be obtained. This study investigates the effect of wet‐jet milling of a slurry on the orientation of hydroxyapatite ceramics fabricated using a strong magnetic field. Although the prolonged ball milling with ZrO2 balls of the raw powder fractures the primary particles of hydroxyapatite, wet‐jet milling is used to successfully pulverize agglomerated hydroxyapatite raw powder without changing the morphology of the primary particles. Evidently, ceramics with a highly oriented c‐axis of hydroxyapatite are obtained by molding the wet‐jet milled slurry in a strong rotating magnetic field. They exhibit anisotropy in fracture toughness, and the fracture toughness calculated from the crack length perpendicular to the rotating axis is higher than that calculated from the crack length parallel to it. Furthermore, these values are higher than those of randomly oriented hydroxyapatite ceramics, which may be owing to the crystal orientation dependence of the fracture toughness of the hydroxyapatite grains and grain boundaries.

Fracture behavior of Hastelloy X elaborated by laser powder bed fusion: Influence of microstructure and building direction

Laser Power Bed Fusion (LPBF) results in complex meso and microstructures, which significantly change the fracture mechanisms of Hastelloy X superalloys. This article aims to investigate the role played by original crack orientation (perpendicular or co-linear to sample lasing planes) on the fracture toughness values of LPBF HX. Single notched three-point bending samples were manufactured vertically (V) or horizontally (H) to estimate the fracture toughness for these two original crack directions. The highest value (about 1360 kJ/m²) is computed in V specimens with an original crack parallel to the lasing plane whereas a value of 1042 kJ/m² is estimated in H specimens with the second crack orientation. Compared to the values obtained in cast specimens, the fracture toughness of LPBF specimens is virtually 5–6 times higher. A non-self-similar cracking is specific to V specimens revealing a more tortuous crack path than in H specimens with self-similar cracking. In both cases, ductile failure is driven by both transgranular and intergranular modes. Nevertheless, the strong morphological texture contributes to promote intragranular fracture mode in V specimens which requires more energy than the one dissipated by an intergranular failure associated to H samples. Consequently, the fracture toughness is significantly higher in V specimens. • Fracture tests were conducted on Hastelloy X specimens elaborated by Laser Power Bed Fusion with two build directions. • In H specimens, intergranular fracture is dominant due to the grain boundaries aligned with the initial notch. • In V specimens, transgranular fracture occurs along with grain boundaries perpendicular to the initial notch. • The morphological texture is responsible for the fracture toughness anisotropy.