Tension Fracture Research Articles

Experimental Evaluation of Conjugate Flaws on Rock Dynamic Fracturing

The fracture behaviors of rocks under dynamic loading are significantly affected by flaws. Understanding regarding this fundamental mechanism of flaw-induced dynamic fracturing could aid in reducing dynamic geohazards in deep rock engineering. In this study, a series of dynamic loading experiments are conducted on conjugate flawed white sandstone specimens to study the effect of the geometric configuration of flaws on dynamic fracturing. The results show that the geometry configuration of flaws and the loading conditions both strongly affect cracking and failure behaviors. Two types of shear cracks and three types of tensile cracks are observed, four coalescence patterns are identified, and the global failure modes of rock are usually coupled with two or more coalescence patterns. The inhibiting and enhancing mechanism of flaws in regards to potential shear fracture are obtained. These two failure mechanisms depend on the angular relationship between the flaws and the potential shear strain field. The “guiding effect” of the flaws results in the deviation and deformation of shear cracks. Moreover, it is found that the loading condition dominates the fracture tendency of rock macroscopically, while the geometric setting of flaws significantly affects the fracture behavior and failure mode locally.

Comparative study on the low-velocity impact properties of unidirectional flax and carbon fiber reinforced epoxy plates

Flax and carbon fibers reinforced polymer composites have high potentials to be used as sustainable building materials. To understand the impact resistance of these fiber composites, the present article studied the impact resistance of unidirectional flax fiber and carbon fiber reinforced polymer (FFRP and CFRP) composite plates. The impact response, damage resistance, and impact tolerance were investigated using drop hammer impact and compression after impact (CAI) tests. The internal damage of FFRP and CFRP due to impact loads was studied using acoustic emission technology. In addition, the development process of impact damage was analyzed. CFRP plates show a higher specific energy absorption rate than that of FFRP, because of the more serious internal damage and brittle fracture tendencies. Matrix cracking was the primary damage in FFRP and CFRP under impact load. Compared with CFRP, FFRP possesses a higher CAI due to less damage. Further expansion of the matrix crack caused by the original impact occurs in the impacted fiber-reinforced polymer composites (FRP) under a compressive load.

Structure- and lithofacies-controlled natural fracture developments in shale: Implications for shale gas accumulation in the Wufeng-Longmaxi Formations, Fuling Field, Sichuan Basin, China

Descriptions, field emission-scanning electron microscopy and geochemical analyses on shale core samples taken from the fractured intervals of the Wufeng-Longmaxi Formations in three wells from the Fuling Field were used to understand the developmental properties of natural fractures and elucidate their controlling factors. Furthermore, the effects of geological fractures on shale gas accumulation were systematically analyzed. The macro-fractures observed in the shale cores are mainly non-tectonic bedding fractures; to a lesser extent, tectonic fractures, including oblique shear, vertical tension and tension-shear fractures, as well as bed-parallel slip fractures are visible. In contrast, micro-fractures are mainly interparticulate, intraparticulate, and grain marginal in nature. The extent of natural fracture development is controlled by external structural and internal lithofacies factors. For shales with similar lithofacies, the development degree of tectonic fractures increases with decreasing distance from the tectonically deformed and faulted zones. Within the same structural zone, the fractures are well developed in shales of organic matter-rich S-3 (i.e., argillaceous-rich siliceous) lithofacies. The study of fracture properties and their controlling factors has resulted in a model for the development of natural fractures in Wufeng-Longmaxi Shales generated by both structural and lithofacies effects. Overall, shale reservoirs in a “fractured but not broken” state are the most favorable ones for gas accumulation.

Failure process and stability analysis of landslides in Southwest China while considering rainfall and supporting conditions

Landslides frequently occur in several mountainous areas because of their unique engineering–geological conditions and other external factors (earthquakes, rainfall, etc.). In this paper, the landslide in Southwest China is used as the research objective to examine the landslide’s stability under different working conditions. The influencing factors and the formation mechanism of the landslide are analyzed based on the geological environment and essential characteristics of the landslide. In addition, the transfer coefficient method and the GeoStudio software were used to assess the landslide stability. The analysis results demonstrate that the joint action of landforms, geological structures, rainfall, and other factors caused the landslide. Furthermore, the slipped tension fracture induced the failure mode. The transfer coefficient method results showed that the landslide was stable under natural conditions and unstable under rainstorm conditions, which is consistent with the numerical simulation result. The shear strength sensitivity analysis results depicted an apparent linear relationship among cohesion c, internal friction angle φ, and stability coefficient. Moreover, the stability of the unstable slope is more sensitive to φ than to c.

Direct shield cutting of large-diameter reinforced concrete group piles: Case study on Shenyang Metro construction

Increasing demand for subways or metros has resulted in the need to build new tunnels in close proximity of pile foundations of existing underground structures. This study presents the details of cutting of existing large diameters reinforced concrete group piles which lie in the excavation path of the new tunnel directly by shield. Investigation is made based on the on-site case study of the construction of the right tunnel of Shenyang Metro Line 4, which crosses the Shenyang North Station of Metro Line 2. During the process, 17 reinforced concrete piles with diameters ranging from 800 to 1000 mm were cut. The details of the ground improvement, the replacement of the cutter, the cutting of the reinforced concrete piles, and the wear of the cutter are presented in this paper. From the monitoring data, it is found that the advancing speed is lower during the cutting of reinforced concrete piles, and the values of thrust and torque fluctuate. The field measurements show that the settlements and horizontal displacements in the existing tunnel and metro station are within the allowable limits when the reinforced concrete piles are cut directly with the shield. During the cutting of the reinforced concrete piles, the steel rebars usually break under tensile stress, and the tension fracture accounts for 66.2 % of the total fracture of steel rebars. The cutters installed at different heights have a cumulative effect on the cutting of piles, and the cutters installed at higher positions have a protective effect on the cutters installed at lower heights. The average wear amount of rippers at 165, 175, and 210 heights are 6 mm, 15.2 mm, and 24.8 mm respectively. The construction method used in this project can serve as a reference and experience for similar future projects.

Effect of high pressure salt water absorption on the mechanical characteristics of additively manufactured polymers

An experimental study has been performed to investigate the coupled effects of hydrostatic deep depth pressure and sustained salt-water immersion on the mechanical properties and material structure of additively manufactured (AM) polymer based materials. The materials that were evaluated in the study were produced by both the material extrusion and vat photopolymerization printing methods. The material extrusion materials consisted of Stratasys ULTEM 9085 and Markforged Onyx and the vat photopolymerization material was Accura ClearVue resin. Water immersion was conducted with 3.5% NaCl solution at room temperature under a pressure of 34.5 MPa in a novel test facility for long duration, high pressure water saturation. The respective materials were characterized in three conditions: (1) baseline with no water saturation, (2) 30 day water immersion, and (3) 60 day water immersion. The change in mechanical properties as a function of aging time was quantified through controlled laboratory testing, namely tension, compression, flexure, and in-plane fracture toughness. Additionally, a microscopic evaluation was performed to evaluate the physical material degradation between layer bonding due to the saline water absorption. The significant findings of the study highlight that salt water immersion has differing effects on additively manufactured materials based on the material composition of the base material and thus significant consideration must be given to material selection in marine environments.

Features of lumbar spine texture extracted from routine MRI correlate with bone mineral density and can potentially differentiate patients with and without fragility fractures in the spine

The use of routine magnetic resonance imaging (MRI) to potentially assess skeletal fragility has been widely studied in osteoporosis. The aim of this study was to evaluate bone texture attributes (TA) from routine lumbar spine (LS) MRI and their correlation with vertebral fragility fractures (VFF) and bone mineral density (BMD). Sixty-four post-menopausal women were submitted to LS densitometry, total spine radiographs, and routine T2-weighted LS MRI. Twenty-two TA were extracted with the platform IBEX from L3 vertebra. The statistical difference was evaluated using ANOVA and Duncan's post-test. Correlation analyses were performed using Spearman's coefficient. Statistical significance was considered when P<0.05. The results did not show a significant difference in BMD between the women with and without fractures. Two bone TA (cluster tendency and variance) were significantly lower in the fracture group. Cluster tendency with VFF in osteopenia was 1.54±1.37 and in osteoporosis was 1.11±58. Cluster tendency without VFF in osteopenia was 2.23±1.38 and in osteoporosis was 1.88±1.14). Variance with VFF in osteopenia was 1.44±1.37 and in osteoporosis was 1.13±59. Variance without VFF in osteopenia was 2.34±1.38 and in osteoporosis was 1.89±1.14. There was a significant correlation between BMD and cluster prominence (r=0.409), cluster tendency (r=0.345), correlation (r=0.570), entropy (r=0.364), information measure corr1 (r=0.378), inverse variance (r=0.449), sum entropy (r=0.320), variance (r=0.338), sum average (r=-0.274), and sum variance (r=-0.266). Our results demonstrated the potential use of TA extracted from routine MRI as a biomarker to assess osteoporosis and identify the tendency of skeletal fragility vertebral fractures.

Modeling of both tensional-shear and compressive-shear fractures by a unified phase-field model

Many phase-field models have been developed in recent years to captue different fracture modes from tensional to shear, tensional-shear, and compressive-shear fractures. However, there seems no phase-field model that can simulate the tensional, shear, tensional-shear, and compressive-shear fractures at the same time under complex stress states. In this paper, a unified phase-field model is proposed in the framework of the original phase-field theory. A universal fracture criterion, that can predict both tensional-shear and compressive-shear fractures under complex stress states is embedded in the proposed phase-field, and the failure compression strength is introduced to consider the fracture under a compressive stress state. Therefore, the crack direction can be directly determined from the universal fracture criterion. The strain energy of undamaged configuration is decomposed into three parts, the tensional/compressive part, the shear part, and the rest part. The tensional/compressive and shear parts can be degraded by different degradation functions or the same degradation function. Cohesive fracture models with general softening laws and the classical brittle fracture model can be used in the proposed model, and the length scale has much less influence on the global response if cohesive fracture models with general softening laws are applied. Numerical examples show that the proposed model has the ability to simulate both the tensional-shear and compressive-shear fractures in rock-like materials and the results are in good agreement with the experiments.

A structure metric for quantitative assessment of fracture surfaces in 3D conceived based on confocal laser scanning microscopy data

Assessment of fracture surfaces typically involves the identification of qualitative features such as dimples, grain facets, and river patterns to determine type of fracture. The present study formulates a measure termed Real-to-Projected Area (RPA) ratio/metric to quantitatively assess fracture surfaces. Fractures surfaces of several metallic alloys tested monotonically and in fatigue to fracture including three Mg alloys, a Ti alloy in two conditions, and a Ni-based superalloy were observed using confocal laser scanning microscopy in 3D and quantitatively assessed using the metric. The metric successfully separated fracture surfaces obtained after fatigue testing from those obtained after monotonic tension testing. Specifically, the values of the metric were found to be in the range of 40–80 pct for fatigue fracture, while 90–140 pct for monotonic tension fracture. As a result, the metric can be used to distinguish between fracture in fatigue and fracture in monotonic tension when fracture types / loading modes are unknown. Moreover, the metric is sensitive to ductility of tested alloys as well as any presence of critical defects in the microstructure responsible for rapid fracture such as intermetallic inclusions. An added utility of the metric is also to identify outliers in the data such as invalid mechanical tests. • Real-to-Projected Area (RPA) ratio/metric is defined to quantitatively assess fracture surfaces. • Fracture surfaces of several alloys are observed using confocal laser scanning microscopy and quantified using the metric. • The metric can successfully separate fatigue fracture surfaces from monotonic tension fracture surfaces. • The metric is sensitive to ductility of tested alloys and defects in the microstructure such as intermetallic inclusions. • The metric can identify outliers in testing to fracture data such as invalid mechanical tests.

Numerical Modeling of Steel Fiber Reinforced Concrete Beam with Notched under Three-point Bending Test

This paper presents numerical modeling using the 3D nonlinear finite element method, which utilizes the multi-surface plasticity model. Steel-fiber reinforced concrete's strength, ductility enhancement, and mechanical behavior under tension are implemented inside the tension fracture model. The proposed model differentiated the contribution from concrete and steel fiber that resist the tensile force and later combined as one response of steel fiber reinforced concrete under tension using the superposition method. The contribution of the steel fiber that resists tension in the proposed model can have residual stresses, which correspond to the slip of the fiber embedded inside the concrete while maintaining its load-carrying capacity via the bond-slip friction between the concrete and the steel fiber. The proposed model is implemented inside an in-house 3D-NLFEA package. The model was verified with the available test result in the literature for SFRC with hooked-end and plain straight fiber. A comparison with another numerical result from the literature using ATENA is also presented to demonstrate the numerical model further. Differences in the SFRC mechanical behavior modeling between the 3D-NLFEA and ATENA are discussed thoroughly. From the comparisons, the 3D-NLFEA package with the proposed tension fracture model can reasonably predict the response of SFRC. For modeling the SFRC with plain straight fiber, only an adjustment on the tensile fracture energy for plain concrete is adopted.

Injury-mechanism directness as a key factor for fracture laterality in pediatric extremity fractures

BackgroundAssociations between certain extremity fracture sites and laterality in pediatric trauma are well known, whereas the rationale for such laterality tendencies are unclear. We hypothesized that the laterality tendency of a specific fracture would be affected by directness of injury mechanism and not by the fracture site itself. MethodsWe retrospectively enrolled 1382 children (aged 2–16 years) who were diagnosed with extremity fractures sustained during loss-of-balance situations and investigated the laterality tendencies (dominant vs. non-dominant extremity) of specific fracture sites. Multivariate analyses were sequentially performed to adjust for potential confounding variables-with and without injury-mechanism directness as a covariate. ResultsIn the upper extremities, the non-dominant side was more prone to fractures (p < 0.001), especially of the distal supracondylar humerus, radial and/or ulnar shaft, and distal radius. In the lower extremities, the dominant side was more frequently fractured (p < 0.001), especially at the tibial shaft and distal tibia. However, the predisposing effects of specific fracture sites on fracture laterality were not statistically significant when in analysis adjusted for injury-mechanism directness as a covariate. Fracture laterality was affected by whether the injury mechanism was direct or indirect. Indirect injury to the upper extremity was strongly associated with non-dominant arm injury (odds ratio 0.686 [95% CI 0.517–0.991]; p = 0.009), whereas indirect injury to the lower extremity was strongly associated with dominant leg injury (odds ratio 2.138 [95% CI 1.444–3.165]; p < 0.001). ConclusionsInjury-mechanism directness, rather than fracture site itself, is a key factor that affects fracture laterality in pediatric extremity fractures. These findings are helpful for improving our understanding of which factors may affect fracture laterality among children.

Deformation mechanisms and fracture in tension under cyclic bending plus compression, single point and double-sided incremental sheet forming processes

This study investigates the deformation and fracture mechanisms of two testing methods, tension under cyclic bending (TCB) and tension under cyclic bending plus compression (TCBC) and their relationship to single point (SPIF) and double-sided (DSIF) incremental sheet forming processes. Experimental tests were carried out by using a bespoke TCBC test rig and a DSIF machine with grade 1 pure Ti samples. The results show the elongation-to-fracture has a high relevance to the bending depth and compression, which leads to detailed investigation to the stress and strain evolutions in the local bending region using finite element (FE) method. A new Gurson-Tvergaard-Needleman (GTN) model is proposed with a modified shear damage mechanism utilising experimental fracture strain loci to calibrate the Lode angle effect under low stress triaxiality. It is found the bending and reverse-bending stages correspond to different stress states and significantly affect the fracture occurrence in TCB, TCBC and SPIF, DSIF processes. For the first time, the stress paths in the plane of stress triaxiality and Lode parameter are used to reveal the transition of deformation modes from equi-biaxial to plane strain tension in SPIF and DSIF, as compared to the plane stress tension in TCB and TCBC. Using the new GTN model, the simulation gives accurate predictions to the elongation-to-fracture in TCB and TCBC, and the fracture depth in SPIF and DSIF with an error of less than 8% in comparison to the experimental results. Although there is a distinction between the equi-biaxial and uniaxial tension deformations, the study concludes that the TCB and TCBC tests provide an insight into the formability improvement and represent intrinsic deformation mechanisms of SPIF and DSIF processes, an ongoing research question, which has drawn considerable attention in recent years.

A numerical study on the correlation of ductile crack extension in Ni-based clad pipe girth welds with circumferential surface cracks and clamped SE(T) specimens

This work describes a numerical investigation on the relationships between ductile crack extension in Ni-based clad pipe girth welds and an API X80 pipeline steel with circumferential surface cracks and SE(T) specimens under fixed grip conditions. A primary objective is to gain further insight and understanding of the effects of constraint on ductile tearing behavior in piping components with dissimilar girth welds and how well crack growth resistance curves measured using single edge notched tension fracture specimens correlate with ductile fracture behavior in circumferentially surface cracked pipes. The numerical description of CTOD−R curves employs a computational cell approach incorporating the Gurson–Tvergaard (GT) constitutive model to simulate ductile crack extension in the crack configurations analyzed. The numerical analyses consider predictions of ductile crack growth in 3-D models of circumferentially cracked pipes with varying crack depth over pipe thickness ratio, a/t, from measured J-resistance curves derived from fracture resistance testing of clamped SE(T) specimens. The analyses also focus on comparing predictions of ductile crack extension using two different definitions for the CTOD.

A Phase Field Model for the Damage and Fracture of Multiple Network Elastomers

Abstract This work develops a continuum phase field model for predicting the damage initiation and crack propagation in multiple network elastomers. Previous researches have revealed that failure of multiple network elastomers involves microscopic damage initiation by the chain scission of filler network and macroscopic fracture by penetrating crack of matrix network. However, most existing models for multiple network elastomers only deal with its finite deformation and strain softening process, which are unable to capture the initiation and propagation of cracks. In this work, to bridge the microscopic damage and the macroscopic fracture of multiple network elastomers in the finite deformation model, we incorporate the phase field variable of crack surface density to model the crack propagation and the internal damage variable to model the chain scission. By forming a multi-field variational framework, the developed model can be used to simulate the macroscopic deformation and fracture of multiple network elastomers. Through a finite element implementation of the phase field model, previous experiment results obtained from uniaxial tension and unilateral fracture can be well predicted. Moreover, experimentally observed damage zone formed by sacrificing filler network to achieve toughening effect is also numerically illustrated in simulation, giving much clearer pictures for the contributions of different energy dissipation mechanisms.

Effect of the notch depth on fracture behavior of TC4 titanium alloy sheets

To evaluate the low-stress brittle fracture of TC4 titanium alloy sheet structures, the effect of notch depth (d) on the fracture behavior of the 1.8 mm thick TC4 titanium alloy sheets was investigated combied with tensile tests and digital image correlation method. The results show that the ductile–brittle transition (DBT) occurs with increasing notch depths. Ductile fracture occurs for the notched samples with d = 0.5–1.5 mm, and a uniform plastic deformation stage is observed in the load–displacement (P-L) curves, and there are stretch zone and the stable crack propagation zone in the fracture surfaces. Brittle fracture occurs for the notched samples with d = 3.0–5.0 mm, and there is only the linear elastic stage in the P-L curves, and no stretch zone in the fracture surfaces. The samples at the middle notch depths (d = 2.0–2.5 mm) are in the transition from ductile to brittle fracture, and there exists the elastoplastic deformation stage in the P-L curves, and the stretch zone and stable crack propagation zone are both decreased. The analysis of notch fracture parameters shows that fracture of notched samples is controlled by the stress concentration and the stress field intensity of an imaginary crack with the same notch depth. The effect of crack gradually increases with increasing d, which results in increased brittle fracture tendency. Moreover, the fracture energy γf can characterize the DBT of notched TC4 titanium alloy sheets, and the γf is proportional tothe ratio of critical plastic zone size to d (rpc/d). Finally, the rpc/d is proposed to characterize the DBT of the notched TC4 titanium alloy sheets, and the criterion of the DBT for the notched TC4 titanium alloy sheets is obtained.

Modeling Deformation and Fracture of Boron-Based Ceramics with Nonuniform Grain and Phase Boundaries and Thermal-Residual Stress

A phase field framework of elasticity, inelasticity, and fracture mechanics is invoked to study the behavior of ceramic materials. Mechanisms addressed by phase field theory include deformation twinning, dislocation slip, amorphization, and anisotropic cleavage fracture. Failure along grain and phase boundaries is resolved explicitly, whereWeibull statistics are used to characterize the surface energies of such boundaries. Residual stress incurred by mismatching coefficients of thermal expansion among phases is included. Polycrystalline materials of interest are the ultra-hard ceramics boron carbide (B4C) and boron carbide-titanium diboride (B4C-TiB2), the latter a dual-phase composite. Recent advancements in processing technology enable the production of these materials via spark-plasma sintering (SPS) at nearly full theoretical density. Numerical simulations invoking biaxial loading (e.g., pure shear) demonstrate how properties and mechanisms at the scale of the microstructure influence overall strength and ductility. In agreement with experimental inferences, simulations show that plasticity is more prevalent in the TiB2 phase of the composite and reduces the tendency for transgranular fracture. The composite demonstrates greater overall strength and ductility than monolithic B4C in both simulations and experiments. Toughening of the more brittle B4C phase from residual stress, in addition to crack mitigation from the stronger and more ductile TiB2 phase are deemed advantageous attributes of the composite.

Pure and mixed-mode (I/III) fracture toughness of preplaced aggregate fibrous concrete and slurry infiltrated fibre concrete and hybrid combination comprising nano carbon tubes

Concrete is the most widely used and inexpensive material in the construction sector. However, due to its weakness in tension, the cracking and brittle fracturing of concrete is considered a major deficiency. Advancements in fibrous concretes have recently been emerged to mitigate this issue. Preplaced Aggregate Fibrous Concrete (PAFC) and Slurry Infiltrated Fibrous Concrete (SIFCON) are unique cement composites made of fibres with surpassing mechanical properties and exceptional toughness values. The production of PAFC and SIFCON involves packing of aggregates and fibres in the mould and filling the gaps between the aggregates with the high flowability injected cement grout. Nevertheless, the mono and hybrid layered effect of PAFC and SIFCON on fracture toughness is still unexplored and needs special attention to bridge this research gap. This research examined the pure (I and III) and mixed (I/III) modes of fracture toughness of PAFC, SIFCON and hybrid two-layered PAFC-SIFCON samples. For this purpose, many notched specimens of circular disc shapes were prepared using single and double-layer concepts. To investigate the effect of fibres, three different fibre types were used; hooked-end steel fibre, macro polypropylene fibre and hybrid shape of crimped-hooked end steel fibre with dosages of 2.4% and 8% by volume to produce PAFC and SIFCON, respectively. Additionally, multi-walled nano-carbon tubes (MWCNT) were added to the composites with a dosage of 0.1% by cement weight. The compressive strength, stress intensity factors, effective stress intensity factors, mixity parameter, failure pattern, range of fracture toughness and scanning electron microscope were examined, discussed, and compared. Results indicated that pure mode III has a greater cracking risk than both mode I and mixed-mode I/III. The mixed-mode fracture toughness of PAFC specimens improved by 33.07 to 67.94%. Similarly, this improvement ranged from 59.77 to 210.70% for SIFCON and from 51.0 to 131.55% for PAFC-SIFCON. In addition, the fracture toughness of SIFCON is considerably higher than the PAFC and hybrid combination. In all three composite types, the hybrid shape steel fibre outperformed the hooked-end steel and polypropylene fibre under all three modes.

3D morphology and formation mechanism of fractures developed by true triaxial stress

As main part of underground rock mass, the three-dimensional (3D) morphology of natural fractures plays an important role in rock mass stability. Based on previous studies on 3D morphology, this study probes into the law and mechanism regarding the influence of the confining pressure constraints on 3D morphological features of natural fractures. First, fracture surfaces were obtained by true triaxial compression test and 3D laser scanning. Then 3D morphological parameters of fractures were calculated by using Grasselli’s model. The results show that the failure mode of granites developed by true triaxial stress can be categorized into tension failure and shear failure. Based on the spatial position of fractures, they can be divided into tension fracture surface, S-1 shear fracture surface, and S-2 shear fracture surface. Micro-failure of the tension fracture surface is dominated by mainly intergranular fracture; the maximum height of asperities on the fracture surface and the 3D roughness of fracture surfaces are influenced by σ 3 only and they are greater than those of shear fracture surfaces, a lower overall uniformity than tension fracture surface. S-1 shear fracture surface and S-2 shear fracture surface are dominated by intragranular and intergranular coupling fracture. The maximum height of asperities on the fracture surface and 3D roughness of fracture surface are affected by σ 1 , σ 2 , and σ 3 . With the increase of σ 2 or σ 3 , the cutting off of asperities on the fracture surface becomes more common, the maximum height of asperities and 3D roughness of fracture surface further decrease, and the overall uniformity gets further improved. The experimental results are favorable for selecting technical parameters of enhanced geothermal development and the safety of underground mine engineering.

Multi-phase field approach to tensile fracture and compressive crushing in grained heterogeneous materials

The variational approach to brittle fracture is herein extended to deal with the simultaneous interplay of two failure mechanisms affecting grained heterogeneous materials in compression, namely fracture in tension and crushing in compression. The problem is addressed within the context of a multi-phase field variational approach, with two independent damage variables associated to each failure mechanism. The proposed computational method implemented in the open source FEniCS finite element software is applied to 2D mesoscale models of concrete specimens in compression. The predicted trends for specimens with different aspect ratios and different degree of lateral confinement are consistent with experimental results on apparent compressive strength and with typically observed failure patterns.

Discrete Element Simulation of Fracture Evolution around a Borehole for Gas Extraction in Coal Seams.

The stability analysis of underground caverns, tunnels, and boreholes is of great significance to underground engineering. In order to study the stress change of the coal around a hole and the evolution law of fractures during the coal seam drilling process, the discrete element simulation of the coal seam drilling process was carried out by using the particle flow code (PFC2D). The results show that during the drilling process, under the influence of confining pressure and drilling disturbance, the coal stress field around the hole and the development of fractures around the hole have the characteristics of zoning and dynamic evolution. In the axial direction of the borehole, it is divided into front and rear areas, and in the vertical axial direction, it is divided into the drilling disturbance zone and the confining pressure main control zone. During the drilling process, the direction of the maximum principal stress in the front zone gradually changes from the vertical hole axis to the direction parallel to the hole axis, and tension fractures are mainly developed along the drilling direction. In the rear zone, the principal stress direction tends to be stable and the principal stress value undergoes dynamic changes, and a large number of vertical hole axis tension fractures are developed. The drilling disturbance zone appears near the hole wall and has an important influence on the stability of the hole wall, while the confining pressure main control zone determines the antireflection effect around the hole and the influence radius of the hole. This work helps the understanding of the damage range and failure characteristics of the surrounding rock during the drilling process and has great significance for the guidance of drilling design.