Search

A novel modified dog-bone shape direct tensile test is proposed and compared with the wedge splitting test as well as Brazilian test. The acoustic emission and digital image correlation techniques are adopted for monitoring the entire fracture process. The tensile strength determined by Brazilian test and wedge splitting test are higher than that evaluated by the direct tensile test. For direct tensile test, the specimens lost their integrity immediately after reaching the tensile strength and its predominant fracture mode is tensile nature cracking. The wedge splitting test enables the stable crack propagation because of the development of remarkable fracture process zone, which contributes to the presence of intensive shear cracking. The fracture behaviour of Brazilian test has the material brittleness dependence. For brittleness reduced refractories, the quasi-stable failure process is noticed. The deviations of the tensile strength, fracture process and failure mode for the three Mode I tensile tests are attributed to the different mechanical principles, the geometry/size effect and heterogeneity effect.

This work investigates the possibility of replication of natural rock specimens, which can be used to analyze rock mechanical behavior by subjecting a number of identical specimens to tensile tests and a variety of analysis methods. We compare the properties of fractures generated in artificial sandstone specimens to those generated in natural sandstone specimens. Artificial sandstone specimens, created using 3D additive manufacturing printing processes, were subject to tensile failure using the Brazilian test method and the results from these tests were compared to results from Brazilian tests conducted on natural sandstones. The specimens included two distinct types of synthetic rock, unaltered from the manufacturers typical process, and three natural sandstones. For each test, the loading history to failure of the specimens was recorded and the failure mode was confirmed using digital imaging techniques. In addition, three-dimensional images were taken of the fracture surfaces, which were then used to compare the geometric characteristics of all materials tested. The indirect tensile strength of the artificial sandstone specimens ranged between 1.0 and 2.8 MPa. Natural sandstone specimens with a wide range of indirect tensile strengths were tested for comparison. These included a strong sandstone, an intermediate sandstone, and a weak sandstone; which were found to have indirect tensile strength ranges of 10.5–25.5 MPa, 4.4–6.4 MPa, and 0.9–1.1 MPa, respectively. Digital image correlation confirmed that the artificial specimens generally failed in a tensile (mode I) fracture, similar to the natural specimens. Likewise, fracture surface roughness measures showed no clear distinction between weak natural and artificial sandstones. This indicates that there are distinct similarities between the fractures generated in the natural and artificial sandstones of comparable indirect tensile strengths. The three-dimensionally printed sandstone specimens are shown to exhibit indirect tensile strength, surface roughness and crack propagation behavior which resembles a weak natural sandstone.

First, the Equivalent Material Concept (EMC), originally proposed by the author in 2012, is newly formulated in a way the effects of the plastic region ahead of the notch tip prior to the formation of crack at the notch tip on tensile strength of the equivalent material are taken into consideration. The new EMC is linked to the mean stress (MS) brittle fracture criterion to predict the load-carrying capacity (LCC) of some V-notched specimens reported in the literature, made of very ductile steel and subjected to pure mode I loading. It is revealed that the experimentally obtained LCCs could be well predicted by means of the new EMC-MS criterion, without needing elastic-plastic analyses or the failure criteria in the context of the elastic-plastic fracture mechanics.

From a macroscopic point of view, the dynamic tensile response of concrete is mainly due to the viscous behavior of the bulk material and inertia effects at multi-scale levels. It has been suggested that almost all of these mechanisms have to be considered as intrinsic material properties and explicitly included in the constitutive relations of the continuum model. It is discussed and demonstrated that the use of semi-empirical dynamic strength increase factor (DIF) functions to numerically describe rate effects do not characterize true constitutive relations of the material. A strain-rate dependent formulation is used to describe the strength and fracture energy increase of concrete under dynamic tensile loading conditions. However, instead of the commonly used e (instantaneous strain-rate) to update the constitutive law, an effective rate (R) is considered. With this new concept a time scale is introduced in the constitutive law which restrains the ‘evolution of rate’, to represent the inherent dynamic properties of concrete. This has a weak regularization effect and acts as a localization limiter. Mesh objectivity is recovered with the addition of a material length scale to the constitutive relations, here accomplished by an explicit stress-based nonlocal regularization scheme. Two sets of modified split Hopkinson bar tests are simulated for validation, using respectively notched and un-notched specimens. The results are objective and in good agreement with the experiments.

The influence of defect band on the tensile failure in high pressure die casting of AM60B magnesium alloy was studied by in situ scanning electron microscope. Results showed that the size and distribution of the externally solidified crystals (ESCs) had a significant influence on the tensile behavior induced by defect band in the specimen. In the specimen with few ESCs, the crack would initiate at the gas-shrinkage pore in the center of the specimen. Further crack propagation at the defect band was hindered by the surrounding dense microstructure, and the effect of defect band on the tensile failure was just reducing the efficient force bearing area. In the specimen with large and complex ESCs, the microstructure around the defect band would become coarse and comprised of large porosities with complex morphology. The defect band would act as crack initiation site and facilitate the crack propagation to both center and surface of the specimen, leading to the final fracture.

This study presents the use of the dynamic particle difference method (PDM) to analyze tensile failure in concrete subjected to high loading rates. In general, strong form-based meshfree methods suffer from limitations pertaining to the material modeling of concrete because concrete exhibits both softening and damage behaviors that initiate crack growth under an impact load. These methods are generally based on the direct discretization of the governing equations, such as Navier's equation, which involves second-order differentiation. However, conventional material models are based on the first-order derivatives of displacement. The newly developed dynamic PDM can effectively address the limitations of material modeling using a combination of first-order derivative approximations. This circumvents the requirement for high-order derivative approximations, which are essential in strong formulations, such as the finite difference method and point collocation method. The strain rate effect caused by an extremely high loading speed was successfully modeled by accurately reflecting the energy dissipations that result from the cohesive property of the concrete and brittle cracking. Although the developed method incorporates the elastic constitutive relation, it enables the effective modeling of these nonlinear effects. In addition, it can reduce the computational effort. The proportional damping algorithm simulates the effect of velocity in the equation of motion and the cohesion effect in the concrete material. The damage model and the visibility criterion adequately handle crack initiation and propagation in the concrete member. Furthermore, it is noteworthy that the final discrete forms of the dynamic PDM are similar to the integrands of the weak form in the conventional finite element formulation. We ascertained that the stiffness and mass proportional damping effects are related to the inertia and strain of the material, respectively. It was confirmed that the location and direction of crack propagation in concrete varied with the strain rate. Hence, the accuracy and robustness of the proposed method were successfully verified by simulation, and the strain-rate dependency of concrete fracture was efficiently simulated using the proposed method.

The focus of this paper is to understand the effect of voids on the damage mechanism of the composite under out-of-plane tensile load with different lay-up temperature conditions. A micro-scale model for ply-by-ply structure is established containing intralaminar and interlaminar domain in which voids are generated by a random irregular voids generation algorithm to explore the role of voids (intra-ply voids and inter-ply voids) on the transverse damage behavior of the composite. Then, a macro-scale model containing elements with and without void is established to capture crack propagation behavior in the specimen. Analysis of voids in variation layup temperatures are conducted experimentally and numerically. The results show that with the increasing lay-up temperature, the porosity increases from 1% to 4.5%, and the void distribution changes from the intra-ply voids dominant to the inter-ply voids dominant, while the out-of-plane tensile strength decreases by about 30%.

Powder metallurgical open-cell steel foams made of hollow struts are of great interest for impact resistance. Here we report experimental results of high-resolution characterisation of single struts, extracted from a commercially available steel foam. Synchrotron radiation X-ray microtomography reveals that the hollow struts are made of triplets of lens shaped rods, connected to each other along the long axis, appearing triangular in cross-sections. The struts have a non-uniform geometry and they include macro and micropores as well as high-density inclusion powder particles, poorly fused with the matrix. Micro-tensile testing showed that tensile failure is accompanied by longitudinal unzipping due to shear along the thinner material found near the hollow corners. Included, higher-density powder particles deflect crack propagation along the interface with the matrix, where much porosity is observed. Results of finite element simulations well match our mechanical tests, revealing plastic deformation due to bending and significant shear stresses arising between neighbouring rods within the same strut. The failure behaviour and the mechanical response of sintered struts in steel foams produced using non-uniformly coated polyurethane templates is the result of an interplay between the triplet geometry, sub-micron pores, precipitates and high-density inclusions. Keywords: Synchrotron radiation μCT, Metal foam, Micro-tensile testing, Finite-element simulation, Crack propagation, Microporosity

The material properties and failure modes of concrete depend on loading rate. For realistic simulation of concrete behavior under dynamic loading, it is essential that this rate dependency be considered. This paper proposes a three-dimensional lattice model—formed from rigid-body-spring elements—that incorporates the rate dependency of concrete strength, elastic modulus, and fracture energy. This is achieved by introducing a visco-elasto-plastic damage unit (formed from a combination of dashpots and Coulomb friction devices) into the rigid-body-spring elements. The results of simulations of elastic wave propagation and comparisons with experimental results reported in the literature validate the model for basic load patterns. Further, changes in the dynamic failure mode with differing loading rates, studied through simulation of the Split Hopkinson Pressure Bar test, are shown to be in agreement with experimental results obtained with respect to strength and fracture locations.

In this paper, a theoretical model is proposed to predict the initial failure location and the failure progression of the lattice structures made from the elastic-brittle bulk materials. The effects of size and topology on the tensile failure behavior of multiple representative lattice structures (2D auxetic, 2D diamond, 2D triangular1 and 2D triangular2), under various geometry design conditions (including cell topology, cell size and number of unit cells), are systematically investigated through the proposed analytical model. From the results, it was shown that the 2D bending-dominated structures with lower nodal connectivity (number of struts that meet in joints) (2D auxetic and 2D diamond) exhibited a relatively progressive crack propagation pattern, while the 2D stretching-dominated structures with higher nodal connectivity (2D triangular1 and 2D triangular2) appear to exhibit rather catastrophic brittle fracture failure. During the failure fracture propagation, the energy absorption of the 2D stretching-dominated structures were significantly higher than that of the 2D bending-dominated structures. Moreover, for all lattice designs, the tensile failure behaviors tend to converge to more consistent patterns when the unit cell numbers increase beyond certain limitations.

Tensile failure behavior of concrete invariably dominates the behavior of concrete specimens as well as structural elements and it is strongly affected by loading rate. The present study focuses on the effects of loading rate and heterogeneity of meso-/micro-structure on the failure pattern and the macroscopic mechanical properties of concrete. For simplicity, concrete is regarded as a two-phase composite composed of aggregate and mortar matrix at meso-scale. The damaged plasticity theory combined with strain-rate effect is employed to describe the dynamic mechanical behavior of mortar matrix, and the aggregate phase is assumed to be elastic. The dynamic tensile failure modes of a single-edge notched concrete specimen and the L specimen under different loading rates are numerically investigated. The simulation results indicate that dynamic failure pattern and the direction of crack propagation of concrete have pronounced loading rate sensitivity. With the increase of loading rate, the failure mode of concrete changes from mode-I to mixed mode. The more complex the meso-structure is, the higher the interaction intensity between the meso components has and the more complicated the crack paths are, resulting in a more obvious crack branching behavior. Furthermore, as loading rate increases much more branching cracks generate within concrete and the width of the damaged region increases, implying that the fracture process at relatively high strain rates requires more energy demand to reach failure. And this should be the main reason for the improvement of the dynamic tensile strength of concrete.

This study numerically simulates strain-rate dependent transverse tensile failure of unidirectional composites. The authors’ previous study reported that the failure mode depends on the strain rate, with an interface-failure-dominant mode at a relatively high strain rate and a matrix-failure-dominant mode at relatively low strain rate. The present study aims to demonstrate this failure-mode transition by a periodic unit-cell simulation containing 20 fibers located randomly in the matrix. An elasto-viscoplastic constitutive equation that involves continuum damage mechanics regarding yielding and cavitation-induced brittle failure is used for the matrix. A cohesive zone model is employed for the fiber–matrix interface, considering mixed-mode interfacial failure. For the results, the relationship between failure modes and the strain rate is consistent with the authors’ previous studies.

For the potential use of ultrafine grained materials for high performance kinetic energy penetrators of caliber projectile, the shear failure of 4130 steel having two different ultrafine grained (UFG) structures was examined under the tensile mode. 4130 steel with a lamellar UFG structure and with an equiaxed UFG structure was fabricated by equal channel angular pressing with routes A and Bc, respectively. Yield strength of UFG steel was enhanced almost twice compared to that of coarse grained counterpart while the former exhibited drastic ductility loss due to a lack of strain hardenability. Tensile failure of the steel having a lamellar UFG structure is manifested in sequence by formation of few sharp shear bands inclined by 45° to the stress axis, propagation of only one shear band of them, broad conjugate shear band formation and propagation, and failure in the shear mode along the first-formed shear band. In addition, large cracks parallel to the tensile stress were simultaneously developed due to its lamellar nature. The steel with an equiaxed UFG structure undergoing tensile rupture is characterized by a series of sequential processes of formation of one broad shear band inclined by 45° to the stress axis, its propagation, another broad conjugate shear band formation and propagation, and failure in the opening mode with the zigzag pattern. These characteristics were discussed with the aid of the models suggested for enhanced shear formability of nanocrystalline and/or UFG materials.

Bonded scarf repairs are used in composite structures when high strength recovery is desired or when there is a requirement for a smooth surface to satisfy aerodynamic requirements. Experimental and finite element study is carried out to understand the damage propagation and ultimate strength of scarf patch repaired CFRP laminates under uni-axial tensile load here. The ultimate strength and damage propagation in scarf repaired laminates has been investigated with respect to change in scarf angle and patch diameter. It is revealed from the results that damage is initiated in adhesive film at the bonded interface of 0° plies of parent laminate and patch in and then propagates in circumferential direction around scarf patch. It is found that some damage occurs in the parent laminate before the damage initiation in the adhesive film. After the adhesive film failure, the damage in parent laminate quickly propagates transversely to the free edge sides of the laminate and failure occurs. The results of this investigation provide further insight into the damage mechanisms in scarf repairs of composite structures under tensile load. This study may be helpful in improving the design and analysis techniques for scarf patch repair of composite structures.

The influence of internal stress anisotropy resulting from anisotropic loading in a roll-to-roll (R2R) process, and polymer substrate anisotropy on the crack onset strain (COS) of thin oxide coatings was analyzed. Experimental data obtained for R2R processed films were compared with data obtained using an isotropic sheet-to-sheet (S2S) process with the same anisotropic substrate. In the R2R case the COS was found to increase by 20% between the transverse direction and the machine direction. In the S2S case the COS was found to be independent of orientation, except at a 45° in-plane orientation with respect to the machine direction, where it was 15% higher. The internal stress in the machine direction could not be determined, presumably due to deposition-induced curvature changes of the polymer substrate, and was therefore fitted to the COS data. Fracture mechanics analysis and finite element modeling of the experimental data showed that the influence of substrate anisotropy was marginal, and that it was the process-induced internal strain in the coating which controlled the COS. © 2010 Elsevier B.V.

A Monte Carlo simulation is established to predict the failure strain of unidirectional fibre composites. The effect of matrix shear yielding of a high performance epoxy resin is introduced into the model through load sharing factors between the fibres adjacent to fibre-break(s). Strain concentration factors (SCF) of fibres are obtained using Finite Element Methods (FEM) in a three dimensional multi-fibre unit cell containing one, two and three adjoining fibre-break(s). The tensile strains of the surviving adjacent fibres are intensified as a function of their distances from the fracture. A statistical simulation is carried out to predict the failure strain of a single layer of unidirectional (UD) fibre composites with the thickness of the fibre ineffective length. Using the weakest link theory, the ultimate failure strain of a real size UD composite is predicted.

Carbon nanotubes (CNT) possess remarkable mechanical, thermal and electrical properties, which combined with their low density and high aspect ratio, make them a very attractive candidate as reinforcing materials for the development of an entirely new class of composites. However, to determine CNTs mechanical properties in a direct experimental way is a challenging and not economical task, because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. Moreover, there is still a lack of the fundamental knowledge regarding the strength and failure behaviour of carbon nanotubes. Due to nanoscale, most of the continuum based classical fracture mechanics are not really suitable to describe the failure evolution. Failure of nanotubes has been mainly investigated using molecular dynamics theory. In this paper, we present an innovative method for modelling the failure of carbon nanotubes under uniaxial tensile loading. CNT can be thought as structural systems, where the primary bond between two nearest-neighbouring atoms forms the axially loaded-bearing components member and the individual atom acts as joints of the related load-bearing members. A Finite Element Model, based on the molecular mechanics theory, is proposed in this paper in order to investigate the fracture progress in Zig-Zag and Armchair carbon nanotube with defects under uniaxial tensile stress. The novelty of the proposed approach lies in the use of nonlinear axial and torsional springs to model the local interaction and breakage of bonds of CNT atoms under axial loads. The complete load–displacement relationship of Force/Displacement curve for a (5, 5) and a (9, 0) nanotube up to the complete fracture was obtained. Further, with a continuum assumption, it was possible to define a Stress/Strain curve with ultimate strength and strain. The results show that the effect of chirality on the mechanical properties and failure mode of CNTs was quite significant and cannot be neglected. Moreover, the results are in good agreement with experimental data and classical molecular dynamics simulation validating, therefore, the proposed modelling approach.

A description is given of the mechanisms causing tensile failure in 2-D carbon-carbon composites containing plain-weave fabric reinforcements. The carbon fibers in the composites were made from a rayon precursor and had both a low modulus (6–8 Msi) and a low strength (60 ksi). Two types of carbon-carbon material were studied, with the same fiber content but differing in matrix structure. The first material contained a carbon matrix deposited entirely by chemical vapor deposition (CVD). The second material contained a carbon matrix formed by two steps: initial pyrolysis of a phenolic resin to 4500°F, and then a subsequent CVD deposition. Specimens from both materials were loaded to failure in tension and afterwards microstructural observations were made of crack development. Based upon these observations it was concluded that the mode of failure of the fiber bundles within the composites depended upon the curvature of the bundles. Fiber bundles with small curvatures failed due to tensile stress, or due to a combination of tensile and bending stresses. Fiber bundles with large curvatures failed due to shear stresses, at the point where the local fiber direction was most inclined to the applied load. The shape of the theoretical envelope predicting this shear failure shows good agreement with published data on the ultimate strength of carbon-carbon laminates.

Pre-cracked double torsion specimens of Arkansas Novaculite were deformed (1) in the load relaxation mode, and (2) at a fast cross-head speed using an Instron deformation machine to obtain stress intensity factor ( K I )-crack velocity ( v ) data for stress corrosion in liquid water. The fracture toughness ( K Ic ) was found to be 1.335 ± 0.075 MN m −3/2 . At temperatures from 20°C to 80°C the stress corrosion index, n ( v ∞ K n I was 25.1 ± 1.5 and the activation enthalpy for crack propagation was 69.5 ± 1.7 kJ mole −1 . The K I -v data at 20°C were used to generate a diagram predicting the influence of strain rate on tensile fracture stress. These predictions were in good agreement with the fracture stress determined by bend experiments in liquid water at 20°C. Both the predictions and the experimental results are consistent with a monotonie reduction in tensile fracture stress from approximately 72 MN m −2 to 39 MN m −2 as strain rate is reduced from 6 · 10 −5 s −1 down to 10 −10 s −1 . At strain rates faster than approximately 6 · 10 −5 s −1 stress corrosion does not influence the tensile fracture stress. It is unlikely that Novaculite will exhibit a fundamental fracture stress during deformation at even the slowest geological strain rates.

In this work, the tensile failure of magnesia, rebound magnesia-chrome and chrome-containing magnesia-spinel refractories under the Brazilian test were investigated. The digital image correlation and acoustic emission were applied simultaneously for ensuring the validity of Brazilian test and studying the fracture process. The brittle refractories fail abruptly while reaching their load peaks because of the unstable crack propagation. However, the chrome-containing magnesia-spinel refractory shows a reduced brittleness due to the pre-existing microcracks, which promotes quasi-stable crack propagation evidenced by the nonlinearity in the pre-peak region and the softening in the post-peak region. Besides, the thickness-to-diameter ratio has a great influence on the fracture behaviour, which also shows brittleness dependence. The fracture behaviour of rebound magnesia-chrome refractory varies from brittle to less brittle while the thickness increasing from 10 mm to 50 mm. The quasi-stable crack propagation favors the central crack initiation and ensures the tensile failure under the Brazilian test.

Coal joints and cleats are geological discontinuities that are the most important factors that affect the mechanical responses of a coal mass under stress. The joint and coal mass interaction and the mode of failure dominate the mechanical behaviour of jointed coal masses, and therefore the stability of coal excavations. The shear or mixed shear/tensile failure changes to tensile failure by increasing the confining pressure, discontinuity length and angle. This paper extends a thermodynamic approach to constitutive modelling of the coal mass by developing local and non-local damage models based on the joint and cleat density and the dip angle. A consistent and rigorous statistical framework is constructed, which incorporates both local and non-local features into the constitutive modelling. This is an important consideration in developing damage constitutive models based on the trajectory of the failure surfaces in a coal mass. An equation is derived to calculate the fracture energy which is a function of the joint density either in a single direction or crossed conditions. Keywords: Joint density, Dissipated energy, Coal mass, Damage model

This paper investigates different tensile fracture initiation criteria on the plane-strain configuration of a defect-free openhole wellbore. It aims to model the effect of the internal pressurization of a wellbore drilled in the direction of one of the principal stresses. We compare a brittle initiation model that accounts for both the necessary stress and energy conditions (mixed criteria) for the development of a fracture with a bilinear cohesive zone model which can degenerate either to the Dugdale rectangular softening model or the linear softening model. Moreover, we propose an approximation of the mixed criteria which amounts to solving a single scalar nonlinear equation. The effect of the wellbore size on the load at fracture initiation observed experimentally is well reproduced by these different models which all provide a similar response. The size effect on tensile failure is governed by the ratio I between a material lengthscale l m over a structural lengthscale l s : I = l m / l s . The material lengthscale is defined as the square of the ratio between the material fracture toughness over its tensile strength l m = K Ic 2 / σ T 2 , while the structural lengthscale is here simply the wellbore radius l s = a . For small values of I (i.e., I 0.1 ), tensile crack initiation is dominated by strength with vanishingly small size effects, while for large value of I ( I > 10 ), crack initiation is dominated by energy requirements and the initiation pressure increases with I . The far-field stresses modify the transition between a strength-dominated to an energy-dominated tensile failure as a function of I . A higher mean compressive far-field stress tends to make the failure more strength-driven, while higher differential far-field compressive stress promotes an energy-driven tensile failure.

Based on the work for a combined damage/plasticity model of geologic materials and the bifurcation analysis of material failure, an analytical framework is established to study the rate-dependent transition from continuum damage to discrete fracture in dynamic brittle failure. Because of the simple formulation, a vectorized constitutive model solver can be designed for large-scale computer simulation. A continuum tangent stiffness tensor is invoked for the tensile damage evolution such that the bifurcation analysis can be performed to identify the initiation and orientation of tensile failure. It is shown that the orientation of tensile failure is rate-independent although the limit state is rate-dependent for the rate-dependent tensile damage model. Sample problems are considered to demonstrate the features of the proposed approach.

This paper presents an analysis of Weibull statistics applied to tensile failure of soil grains compressed between flat platens. The aim is to validate the use of Weibull applied to single soil grains, since such a statistical approach can then be used to analyse particle survival in aggregates comprising many soil particles. Particles of Quiou sand have been compressed diametrically between flat platens. A characteristic stress at failure can be defined as the diametral force divided by the square of the particle diameter at failure. Approximately 30 grains were tested for each of the following nominal particle sizes: 1 mm, 2 mm, 4 mm, 8 mm and 16 mm diameter. It was found that the data could be well described by the Weibull statistics of brittle ceramics, which requires an assumption of geometric similarity to be made, and the Weibull modulus could be taken to be about 1.5. This is shown to be in agreement with the observation that the average crushing force is not a strong function of particle size. The force required to break a small particle asperity is also shown not to be a strong function of the asperity size, consistent with the observed Weibull modulus. The paper provides evidence that Weibull can reasonably be applied to the tensile failure of soil grains, thus validating the use of Weibull as a tool in the analysis of particle crushing.

This paper presents an experimental investigation of the mechanical behavior and failure mechanism of three-dimensional (3D) orthogonal woven CFRP composite panels. The 3D composite panels are preformed using Torayca T-300 (3K) carbon fiber, and then infused with the Epicote 828 epoxy resin. The nominal proportions of the stuffer yarn, the filler yarn and the warp weaver (or z yarn) are 1:1.2:0.2, respectively, and the overall fiber volume fraction is 43%. The 3D fiber architectures are measured and visualized in a micrograph form. Quasi-static tensile coupon tests are carried out to measure the in-plane Young's modulus, Poisson's ratio, tensile failure strengths and failure strains in both stuffer and filler yarn directions. Test results reveal that the average Young's modulus in the filler yarn direction is higher than that in the stuffer yarn direction, and the average failure strain in the filler yarn direction is lower than that in the stuffer yarn direction. The average failure strength in the filler yarn direction is slightly higher than that in the stuffer yarn direction. The fracture surfaces are studied using the scanning electron microscope (SEM) and the failure mechanism are then discussed. It is noted by studying the fracture surface that the fracture surface is always perpendicular to the loading direction. The crack causes the z yarn/matrix interface to debond. Also, the fracture of specimen cut along the x- (or stuffer yarn) direction causes filler yarn/matrix interface to debond and stuffer yarn to break, and the fracture of specimen cut along the y- (or filler yarn) direction causes stuffer yarn/matrix interface to debond and filler yarn to break. The testing results are then used to validate the developed models in Parts II and III of these series papers. In Part II, simplified analytical and finite element models are proposed to predict the mechanical property and failure strengths for the 3D orthogonal woven CFRP composites. In Part III, a curved beam model resting on an elastic foundation is presented to predict the tensile strength in the filler direction, and then to investigate the effect of some geometrical parameters on the tensile failure strength in the filler yarn direction.

In this paper, we performed uniaxial compression tests on fine sandstone–coal, coarse sandstone–coal, and oil shale–coal bi-material samples to investigate the lithology effects on their strength, macro-failure initiation (MFI), energy evolution, and failure characteristics, respectively. Uniaxial stress–strain characteristics of the samples primarily depended on the coal and were affected by coal–rock interactions. These interactions involved the following aspects: (1) The differences in the mechanical properties of rock and coal affected their stress states near the interface. They were in triaxial compression state with strength increasing or in triaxial compression-tension state with strength decreasing. (2) During the pre-peak stage, the rock deformation affected the values of input energy, elastic energy, and dissipated energy. Damage and energy accumulation in coal were also limited by rock deformation, resulting in higher strengths for the bi-material samples compared to pure coal samples. (3) During the post-peak stage, the rebound deformation of rock was accompanied by the elastic energy release, which promoted the failure of coal. MFI of the samples occurred within the coal. MFI models mainly included the tensile fracture of coal near the interface, the initiation and propagation of macro-cracks, and the development and evolution of micro-defects, accompanied by varying degrees of surface spalling or ejection failure. The coal showed the splitting ejection failure. The oil shale and coarse sandstone exhibited tensile failure or tensile–shear composite failure due to crack propagation in coal. Failure was not evident in the fine sandstone. The coal in the oil shale-coal bi-material samples became more broken due to the most serious rebound deformation of oil shale.

The long-term durability of the interface between FRP (fiber reinforced polymer) and concrete is crucial to the safety of FRP strengthened concrete structures. Some experimental works have been carried out to investigate the effect of environmental factors on model II fracture behavior of the FRP-to-concrete interface. However, fewer efforts have been made to estimate interfacial durability under mode I loading. This study evaluates the mode I fracture energy release rate of CFRP (carbon fiber reinforced polymer)-to-concrete interface subjected to freeze-thaw cycling, acid attack, and alkali attack. Significant decrease of fracture energy release rate is observed after environmental conditioning. With the increase of freeze-thaw cycles and soaking time, the failure mode of the specimen changes from tensile failure of concrete to adhesive failure along the interface. Test results also confirm that the durability of the CFRP-to-concrete interface can be improved by application of silane coupling agent under freeze-thaw cycling and alkaline condition.

SiCf/PyC/SiC and SiCf/BN/SiC mini-composites comprising single tow SiC fibre-reinforced SiC with chemical vapor deposited PyC or BN interface layers are fabricated. The microstructure evolutions of the mini-composite samples as the oxidation temperature increases (oxidation at 1000, 1200, 1400, and 1600 °C in air for 2 h) are observed by scanning electron microscopy, energy dispersive spectrometry, and X-ray diffraction characterization methods. The damage evolution for each component of the as-fabricated SiCf/SiC composites (SiC fibre, PyC/BN interface, SiC matrix, and mesophase) is mapped as a three-dimensional (3D) image and quantified with X-ray computed tomography. The mechanical performance of the composites is investigated via tensile tests. The results reveal that tensile failure occurs after the delamination and fibre pull-out in the SiCf/PyC/SiC composites due to the volatilization of the PyC interface at high temperatures in the air environment. Meanwhile, the gaps between the fibres and matrix lead to rapid oxidation and crack propagation from the SiC matrix to SiC fibre, resulting in the failure of the SiCf/PyC/SiC composites as the oxidation temperature increases to 1600 °C. On the other hand, the oxidation products of B2O3 molten compounds (reacted from the BN interface) fill up the fracture, cracks, and voids in the SiC matrix, providing excellent strength retention at elevated oxidation temperatures. Moreover, under the protection of B2O3, the SiCf/BN/SiC mini-composites show a nearly intact microstructure of the SiC fibre, a low void growth rate from the matrix to fibre, and inhibition of new void formation and the SiO2 grain growth from room to high temperatures. This work provides guidance for predicting the service life of SiCf/PyC/SiC and SiCf/BN/SiC composite materials, and is fundamental for establishing multiscale damage models on a local scale.

Externally bonding using epoxy is one of major applying method for FRP strengthening technology. The long-term performance of the epoxy/concrete interface has been proven to be a key for practical application of FRP strengthening, especially when the strengthened structures are exposed to severe environmental conditions. In this study, an experimental program has been carried out to examine the effect of freeze–thaw cycles (soaked in tap water and 5% sodium sulfate solution) on the deterioration of the epoxy/concrete interface through a novel wedge splitting test, which can directly measure the traction-separation law of the interface under mode I loading. The effect of silane treatment on the freeze–thaw resistance of the interface was also examined. A simplified tri-linear constitutive model of the epoxy/concrete interface was obtained according to the test results. Results showed that both the ultimate bond strength and the fracture energy decrease exponentially with the number of freeze–thaw cycles. Under mode I loading, the failure mode of the reference specimen is the tensile failure of the concrete. With the increase of freeze–thaw cycles, the failure mode gradually turns into adhesive failure along the epoxy/concrete interface. Testing results also confirm that the freeze–thaw resistance of the epoxy/concrete interface can be improved by application of silane coupling agent.

Gradient nanograined Ti (GNG Ti) samples were produced by a surface rolling treatment. The mechanical properties were evaluated by microhardness and tensile tests. The results indicated that GNG Ti achieved an optimized combination of strength and ductility relative to the free-standing nano/ultrafine-grained Ti. The deformation and fracture mechanisms were studied using transmission electron microscope (TEM) and scanning electron microscope (SEM). As the grain size reduced from the coarse-grained (CG) matrix to the nano/ultrafine-grained (NG/UFG) layer, the transition from conventional plastic deformation mechanisms, such as dislocation activity and twinning deformation, to grain boundary-mediated deformation mechanisms, such as stress-inducing grain growth, was identified. At the early stage of tensile deformation, the microcracks were first initiated in the CG and deformed grain (DG) regions rather than in the NG/UFG region and the CG/DG interface had a deflection effect on crack propagation. After tensile failure, the fracture morphology showed a mixture of ductile dimples and shear band-like regions.

Ductile stainless steel fibres were used as interlayers to enhance the interlaminar fracture toughness of carbon fibre reinforced plastics (CFRPs). The stainless steel fibres were placed at the mid-plane of CFRPs either longitudinally or transversely to the crack growth direction . Mechanical properties and fracture toughness of the CFRPs were studied using uniaxial tensile test and double cantilever beam test , respectively. The Young’s modulus and tensile strength of CFRPs remained essentially the same due to the incorporation of steel fibres longitudinally to the loading direction, and decreased slightly for adding steel fibres transversely to the loading direction. Significant improvements in the fracture energy of CFRPs were achieved for adding stainless steel fibres, i.e. the mean fracture propagation energy increased from 482 J/m 2 for the control to 2295 J/m2 for CFRPs with transverse steel fibres at a density of 320 filaments/mm. The main toughening mechanisms of the steel fibres were investigated to be extensive steel fibre bridging and tensile failure. A more pronounced toughness increment was observed for adding steel fibres transversely to the crack growth direction due to the additional mechanisms of carbon fibre delamination and breakage.

Complex geological factures are often encountered in the tunneling boring machine (TBM) excavation leading to many serious problems, especially the mixed ground conditions involving in the different geological properties should be paid more attention. To better investigate the effects of the mixed ground characteristics on rock fragmentation process by double TBM cutters, the model embedded crack propagation algorithm combined with M-C failure criterion has been calibrated for the mixed ground by double disc cutters. And then, the cutting simulations are conducted by 3DEC considering joint spacing, joint orientation and confining stress. The results under different conditions indicate that smaller joint spacing implying weaker properties favorably cause more cracks initiation and propagation by double cutters, and the cracks are tending to propagate along the joint plane and facilitate the rock chips beneath the cutters. And it is found that the joints are inclined to the soft rocks, more shear failure induces more cracks propagating inside the soft rocks, indicating that these rocks can be fragmented more completely. Meanwhile, with the increase of confining stress, rock fragmentation is more difficult resulting in the decrease of the cutting efficiency, especially the cracks induced by shear failure in soft rocks propagating along the free surface and interface cannot link the minor cracks by tensile failure in hard rocks to form rock chips. Furthermore, as noted from the variation of fragmentation load and specific energy under different conditions, smaller joints spacing causes smaller fragmentation load and specific energy to improve the cutting efficiency, however, greater confining stress gives more restrain for the cracks propagation, and the rock chips cannot effectively form between two types of rocks, resulting in lower fragmentation efficiency. And in addition, the optimal cutter spacing has also been analyzed under above conditions, which helps to provide appropriate measures for improvement of rock fragmentation efficiency and TBM performance during the TBM excavation process.

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces slide over each other subject to friction, is a non-trivial extension of this approach. A major difference is that part of the material stiffness in the damaged region must be retained to avoid interpenetration of the crack faces. This problem is resolved here by employing an anisotropic modification to the elastic stiffness tensor in the damaged region. This has the benefit of driving frictional cracks into the correct orientation, according to the Mohr–Coulomb failure criteria, but three issues remain. The first is that the shear discontinuity introduces some spurious stress perturbations around crack regions that are narrow (less than 3-4 elements wide). This is ameliorated by Helmholtz smoothing to allow efficient simulation on a coarse mesh. The second is that the complementarity of shear stress means that the shear stiffness is removed normal to the crack interface as well as parallel to it, and the third is that there are two potentially active failure planes at each point. Both these latter two issues are resolved by the introduction of a novel failure plane selection variable, which regulates either single plane or dual plane failure, and prevents the growth of erroneous cracks normal to the crack face. Both local and non-local models are investigated for linear and exponential strain softening responses. Unlike the non-local model, the local model demonstrates some mesh-size dependence, but it still retains some properties of interest, in that it supports narrower cracks and more rapidly forms a preference for the growth of a single crack when there are a number of competing cracks. The model is implemented in commercial finite element package COMSOL Multiphysics v5.5 and validated against two benchmark simulations: biaxial compression and the failure of a 45° slope. The correct crack angles, stipulated by the Mohr–Coulomb friction angle , are correctly reproduced, as is the post-failure residual frictional force in biaxial compression. The effect of the shear fracture energy on the force–displacement response is investigated, demonstrating successful simulation of the range of material behaviour expected in geological samples, from broad ranged gradual collapse to sharp, almost instantaneous failure.

The mechanical properties and fracture mechanism of shale are vital to the design of hydraulic fracturing schemes. To better understand the formation and evolution of hierarchical crack networks in shales, a scanning electron microscope (SEM) with a loading device was applied to carry out three-point bending experiment on Longmaxi shale with different crack-depth ratios (CDR). The micro-damage and fracture processes of shale were observed in situ. Based on the double-K fracture criterion, the subcritical crack length, and the initial and unstable fracture toughness were calculated theoretically. The results demonstrated that the crack initial load, peak load, and subcritical crack length decreased significantly with the increase of the CDR. Both the initial and unstable fracture toughness were relatively stable when the CDR was between 0.3 and 0.5, and they can be regarded as constants. The meso-failure mechanism of shale was tensile and shear failure, and fracture patterns were inter-granular, trans-granular and coupled fracture. Generally, tensile failure typically results in irregular rough sections, whereas shear failure results in smooth sections with parallel slip lines. The micropores inside and between the crystals can induce the connection and penetration of cracks. The initiation of microcracks is the result of the continuous accumulation and nucleation of multiple micro/nanoscale damage, and the tortuous crack path is caused by the variation in the local stress field at the crack tip. In addition, clump and smooth joint model (SJM) were introduced to simulate the effect of the sedimentary particle and bedding plane on crack propagation based on particle flow code in two dimensions (PFC2D). The simulation results were in good agreement with the experimental observations.

When subjected to long-term static loading, with the accumulation of damage and fracture, brittle rock would fails when the static loading is lower than the compressive strength of the rock, and the increasing of the static loading can generally shorten the time required for the brittle rock failure. To explore the relationship between the durability of the brittle rock and the applied static loading, in this paper, the propagation modes of the microcracks in brittle rock under the static loading in the subcritical crack growth stage are uniformly attributed to the tensile mode, and the total time required for microcrack propagation in the subcritical crack growth stage is chosen as the criterion for judging the durability index of brittle rock. Based on the Maxwell model, the local effective tensile stress that drives crack propagation is derived. The phenomenon of brittle rock exhibiting tensile failure under the compressive stress is preliminarily explained, and the corresponding requirements for this phenomenon to occur are also presented. A new expression of rock durability prediction with a clear physical meaning is established. The key parameter, i.e., the durability index “ n ” in the newly derived expression is obtained through fitting, and the relationship between the durability index and the rock type is preliminarily analysed. This study may provide an approach for preliminarily estimating the durability of brittle rock.

In-situ stress has complex impacts on the blasting excavation of rock mass, but the effect of confining pressure on the crack propagation under repeated blast loading is still unclear. This study investigated the effect of confining pressure on blasting damage through theoretical, experimental and numerical analyses. First, the stress distribution around blasthole under static loading was theoretically analyzed. Then, the parameters of Riedel-Hiermaier-Thoma (RHT) model were determined and validated by repeated blast tests. The effect of confining pressure on the failure mode of granite sample was included. Finally, pre-split blasting of rock slope was numerically simulated to explore the failure behaviors of rock mass under in-situ stress conditions. The numerical results indicate that the RHT model can well reproduce the tensile failure behavior and dynamic crack propagation of granite sample. Confining pressure significantly changes the failure mode of granite sample and the blast-induced cracks mainly propagate along the direction of maximum principal stress. Repeated blast loading has little contribution to rock breakage in the direction of minimum principal stress. The pre-split blasting technology can considerably improve the stability of remaining rock mass in the blasting excavation of rock slope. A plum-blossom-shape arrangement of blastholes and delayed initiation of production holes can promote the quality of blasting operations under pre-stress conditions.

Bedding planes are common in coal seams, and have a significant influence on the crack expansion of coal masses. In this paper, the fracture patterns of coal masses during the blasting process are explored. Firstly, the damage zone at the tip of beddings is calculated based on the Kachanov equation, and crack connections among bedding planes are also discussed. Secondly, a constitutive model considering dynamic compressive and tensile failure is applied to analyze blasting-induced fracture propagation in coal masses using LS-DYNA software. The bedding plane, which is 0.2 m, 0.4 m and 0.6 m from the borehole respectively, is inserted into coal masses to explore its effects on the reflection and transmission of blasting stress waves. Parallel bedding planes and cross-joint planes are simulated to study fracture patterns during the blasting process. The results indicate that the transmission coefficient (Tcoe) of stress waves at a bedding plane constantly decreases with increasing distance from the bedding to the borehole, and an increased number of beddings can result in decreased transmission at beddings. The effects of double-borehole blasting are also studied at 0 ms, 1 ms, 2 ms and 3 ms of delay time, respectively. The results indicate that crack initiation and propagation between two adjacent boreholes are closely related to detonation delay time, and fracture networks between two boreholes form when the delay time of adjacent boreholes is more than 3 ms.

Hydraulic fracturing could be a useful method for controlling the propagation path of cracks near an injection borehole by means of the perforating technique, pre-manufactured cracks, or the natural defects of the rock mass. The crack propagation path is not commonly along a fixed direction. Rather, it is likely to deflect gradually toward the direction of maximum horizontal stress. In order to study the behaviours of crack deflection in the hydraulic fracturing process, granite specimens having a through hole with pre-manufactured cracks on both sides, with a size of 1000 × 1000 × 1000 mm, were used in fracturing tests. The acoustic emission events during the whole fracturing process were recorded by an acoustic emission measurement system. The value of the horizontal stress difference during the tests clearly impacted the crack propagation path during the fracturing process. (1) New cracks were initiated from the tip of the pre-manufactured crack under the different loading conditions used in the tests, and the pre-manufactured crack was able to supply an initiation point for crack propagation. When the horizontal stress difference approached the average tensile strength value of the specimens, the crack propagation path on the surface of the specimen became irregular. (2) The work done during the hydraulic fracturing process was used mostly to overcome the restriction of the horizontal stress. A greater value of horizontal stress difference resulted in greater curvature of the crack propagation path. Additionally, the value of the horizontal stress difference was in proportion with the value of the energy for crack initiation. (3) The main failure model of the cracks generated during the fracturing process was tensile failure. Shear failure, with the high energy release, occurred mostly at the moment of crack initiation, when crack deflection activities were observed. The cracks generated by shear failure during the fracturing process were usually irregular.

This paper detailed the development of a numerical model for simulating the nonlinear behaviour of the concrete masonry infilled RC frames subjected to in-plane lateral loading. The ABAQUS finite element software was used in the modeling. Nonlinear behaviour as well as cracking and crushing of concrete and masonry blocks were simulated using the Concrete Damaged Plasticity (CDP) model. The cohesive element method combined with hyperbolic Drucker-Prager and shear and tensile failure criteria were used to capture the possible failure mechanisms in mortar joints. Concurrent with the finite element modeling, an experimental study was also conducted and results of masonry infilled RC frame specimens incorporating infill openings and interfacial gaps were used to validate the model. The validation showed that the model can accurately simulate the behaviour and predict the strength of masonry infilled RC frames. A sensitivity study was subsequently conducted where the influence of mortar joint failure surface parameters, mortar dilatancy, and fracture energy on the lateral behaviour of infilled RC frames was investigated. Results showed that the in-plane behaviour of infilled RC frames was significantly affected by the input parameters of mortar failure surface and dilatancy and less affected by those of mortar fracture energy.

Different fracture patterns can be observed because of different material properties, even the geometry and loading are the same. However, most of the known phase-field fracture models have only considered the tensile failure and may not be directly applicable to the shear fracture. In this paper, a phase-field model for mixed-mode fracture is proposed based on a unified tensile fracture criterion. The proposed model is developed from the unified phase-field theory and the original unified phase-field model can be recovered as a particular case. General softening laws for cohesive zone models can also be considered. The unified tensile fracture criterion is embedded in the proposed mixed-mode phase-field model and different fracture patterns can be obtained in the simulation according to the material properties, including failures based on both maximum normal stress and maximum shear stress criteria. The crack propagation direction can be easily determined by the unified tensile fracture criterion. Compared with the classical phase-field model, two additional material parameters are needed, i.e., the failure tension strength and the ratio of the critical shear failure stress to the critical normal fracture stress. Numerical examples have shown that the proposed model has the ability to model mixed-mode fractures, and can also be applied to rock-like brittle materials under compression.

In rock engineering, the failure mechanism of a fractured rock mass under compression-shear stress has been focused on, but the effect of filler in fracture-filled rock masses has not received widespread attention. In this research, compression-shear tests are performed on rock-like specimens with three fissures under four filling conditions, unfilled, gypsum filled, cement filled and resin filled, to obtain the effect of three fillers on the mechanical characteristics and failure mode of fractured specimens. The discrete element method (DEM) is used to analyse the crack propagation and coalescence of the specimens. The results show that the peak load and displacement of specimens primarily depend on the strength of the fillers and inclination angle of the central fissure. For gypsum and cement filled specimens, when the fissure inclination angle is small, the influence of fillers on the peak load and displacement is obvious, but the effect can be neglected when the fissure inclination angle is large. The resin has a remarkable influence on the peak load and displacement of all specimens. Three failure modes were found in this study. Failure mode I primarily occurs when the fissure inclination angle is 0°. Failure mode II appears in specimens with a fissure inclination angle equal to 30° or 45°. The failure mode of specimens with a fissure inclination angle equal to 60°, 75° or 90° is defined as mode III. For the failure mode, the action mechanism of filler is to weaken stress borne by rock-like material. The larger the weakening degree of the shear stress is, the easier tensile failure occurs in filled specimens. However, when the stress is substantially weakened, the failure mode of filled specimens is similar to that of specimens containing no fissures.

Extended finite element method (XFEM) is introduced in this study, and the normal direction of fracture surface under different failure modes is determined, which provides a new and efficient technology for failure prediction of composite laminates. According to the failure criterion, a user-defined FORTRAN subroutine (UDMGINI) has been written for Abaqus/Standard solver to model the damage initiation and crack propagation of G23 out-of-plane shear test. By comparing the load–displacement curve, strain field and failure mode of experiment, FEM and XFEM, XFEM can effectively predict the crack initiation and propagation. Meanwhile, the crack path of matrix failure simulated by XFEM is smooth without bifurcation, which is more consistent with experimental result. Moreover, by comparing damage factors of specimen before damage initiation in G23 test, it is found that the matrix tensile failure occurs more easily than matrix compressive failure at the root of V-notch, where cracks are the first to initiate.

Acoustic emissions (AE) and stress–strain curve analysis are accepted methods of analyzing crack propagation and monitoring various failure stages, including crack closure and the crack initiation level, during rock failure under brittle rock loading. This study designed a series of three-point bending tests and shear fracture tests to investigate the features of AE signals for different modes. The Extended Finite Element Method (XFEM) is also adopted to simulate these experiments processes. The obtained results indicate that the maximum load for the shear fracture mode is approximately three times larger than that for the tensile fracture mode and that the displacement in the shear fracture mode is also larger than that in the tensile fracture mode. AE signals had higher AF (average frequency) and lower Rise Angle (RA) (ratio of the rise time to the peak amplitude) values when tensile failure occurred, while they exhibited lower AF and higher RA values when shear failure occurred. Accumulative AE energy for the shear mode is significantly larger than that for type I tensile fracture. The influence of inhomogeneity is also evident, as signals acquired at different distances exhibit distinct characteristics. The results show that AE leads to the characterization of the dominant fracture mode using only two AE descriptors. Note that we also should reasonably arrange AE sensors to monitor large-scale projects in the field.

In this paper, the fracture toughness associated with longitudinal tensile failure and the fracture energy associated with transverse compression failure of T700/CP-02A/B carbon-epoxy unidirectional composites are measured from different tests. For this type of composite, the critical energy release rate based on linear elastic fracture mechanics (LEFM) and the fracture energy based on digital image correlation (DIC) techniques were calculated to investigate the validity of the concept of fracture energy. The results of the transverse compression test showed that damage appeared in the composites when the loading work reached the fracture energy value of 9.63 kJ/m2. Based on the results of the fracture toughness test, carbon fiber reinforced polymer (CFRP) tendons with the same material and craftsmanship were used to investigate the fracture behavior after damage appeared due to the anchorage pressure. The experimental results showed that longitudinal cracking would occur in the damaged CFRP tendons under longitudinal tension and ultimately lead to splitting failure. The applied prestress for CFRP tendons is sufficient to cause splitting failure of damaged CFRP tendons in a prestressed structure.

This study investigates the influence of microstructure on the strength properties of individual cell walls of closed-cell stabilized aluminium foams (SAFs). Optical microscopy (OM), micro-computed X-ray tomography (µ-CT), electron backscattering diffraction (EBSD), and energy dispersive X-ray spectroscopy (EDS) analyses were conducted to examine the microstructural properties of SAF cell walls. Novel micro-tensile tests were performed to investigate the strength properties of individual cell walls. Microstructural analysis of the SAF cell walls revealed that the material consists of eutectic Al-Si and dendritic a-Al with an inhomogeneous distribution of intermetallic particles and micro-pores (void defects). These microstructural features affected the micro-mechanism fracture behaviour and tensile strength of the specimens. Laser-based extensometer and digital image correlation (DIC) analyses were employed to observe the strain fields of individual tensile specimens. The tensile failure mode of these materials has been evaluated using microstructural analysis of post-mortem specimens, revealing a brittle cleavage fracture of the cell wall materials. The micro-porosities and intermetallic particles reduced the strength under tensile loading, limiting the elongation to fracture on average to ~3.2% and an average ultimate tensile strength to ~192 MPa. Finally, interactions between crack propagation and obstructing intermetallic compounds during the tensile deformation have been elucidated.

The dynamic mechanical properties and fracture process of rock materials with pre-existing flaws are crucial for explaining the failure mechanisms of deeply buried constructions. To investigate the mechanical properties and fracture behavior of flawed granite subjected to dynamic loading, dynamic experiments were conducted on granite specimens by using a split-Hopkinson pressure bar test system. The effects of strain rate and flaw inclination angle on granite strength and deformation properties were investigated. The white patch initiation, micro-crack propagation, and failure mode were analyzed using a high-speed camera and digital image correlation technology. The fracture mechanism was revealed by quantitatively analyzing the localized strain field and fractal features. The results demonstrated that the dynamic strength and deformation of the flawed specimen compared to an intact specimen had more obvious strain rate effects. The development of white patches determined the direction and path of crack propagation. The fracture process and shear-tensile failure mode were closely correlated with the evolution of the strain field. Furthermore, the fractal characteristics indicated that a larger fractal dimension resulted in a more complex fracture distribution and mixed failure modes. These results provide a reference for the construction design and safety control of deep rock engineering.

The radial (minimum) stress of the near-boundary rockmass in deep excavations plays a key role in inducing rock failures such as spalling and strainbursts. In this study, a strainburst is treated as a structural failure of the near-boundary rockmass. The influence of the radial stress acting asymmetrically on one boundary surface of the burst volume on strainbursts is numerically investigated using a 3D bonded block distinct element method (DEM). The 3D DEM model for simulating the overall process of strainbursts is introduced and its effectiveness is verified by comparing with the analogous true triaxial experiments. Then based on the simulation results, the influence of radial stress on strainbursts is studied from the perspectives of deformation and strength characteristics, fracturing process, crack development, failure mode and energy balance. In addition, discussions of the mechanisms of the influence of radial stress on strainbursts are presented from the perspectives of fracture mechanics and a graphical explanation. Results show that, as the radial stress increases, the strength of the strainburst sample exhibits a quadratic law that increases first and then decreases, the number of shear cracks increases remarkably, the degree of accumulated rock damage precedes burst is getting higher and higher, the failure mode of strainbursts transforms gradually from a tensile-type to a shear-type, and the kinetic energy is getting higher and higher. The fundamental influence of radial stress on strainbursts is concluded as its suppression effect on the tensile failure mechanism of brittle rocks.

A detailed understanding of the failure characteristics of infilled jointed rock is a key concern in underground engineering and is critical to the design, construction and maintenance of relevant projects. In this paper, uniaxial compression tests were performed to investigate the effect of the joint arrangement (different rock bridge angles) on the strength and crack propagation of red sandstone containing a set of preexisting infilled flaws of the same sizes and angles, while the crack fracturing process was observed by AE and strain monitoring. When the angle between the rock bridge and loading stress was less than 24°, the rock mass failure form was tensile failure with some localized shear failure occurring in the rock bridge damaged by crack penetration, leading to an overall decrease in the carrying capacity. The turning points of the strain and AE signal were clearly observed to be caused by the initiation and propagation of cracks, and the energy consumed by the initiation of shear cracks was greater than that of tensile cracks. The study was further conducted using the fracture mechanics numerical code FRACOD to investigate the crack propagation law and failure mechanism under different loading stress conditions. Simulation results from three 2D similar models showed that the percentage of open fractures decreased, but slipping increased; in addition, the total length of the fractures was greatly reduced with increasing confining stress. These results are important and valuable for understanding the crack mechanism of rock engineering in deep underground mining excavations.

In this study, the dynamic fracture coalescence of Fangshan granite specimens was studied using the Split Hopkinson Pressure Bar system. Two prefabricated surface cracks with varying inclination angles and inner tip distances were applied to the granite specimens. Two high-speed cameras were set up on two sides of the specimens, one for the side with speckles and the other for crack propagation. According to the crack coalescence mode, the experimental outcome was classified into three types, namely Tensile crack coalescence, Tensile crack and second tension crack coalescence and Tensile crack and second shear crack coalescence. The coalescence mode is mainly a tensile failure, and the change in the inner tip distance of the prefabricated cracks had little effect on the coalescence mode. Digital Image Correlation (DIC) measurement results showed that there were obvious strain concentration areas instead of strain concentration bands in the crack coalescence area. This phenomenon is considerably different from the Brazilian disc tests. The alteration of the inclination angle was expected to have an impact on the coalescence area, thereby leading the coalescence area to change continuously. There was an elliptical enveloping area for crack coalescence. After dynamic equilibrium, the specimen was in a compressed state. The size of the enveloping area was significantly affected by the inclination of the prefabricated cracks.

We have investigated the damage evolution and crack propagation of tuff rocks under axially cyclic tension–compression (T–C) loading with different amplitudes. The field of axial strains in the rock surface was obtained by three-dimensional digital image correlation (3D-DIC) method. The apparent strains were used to analyze the damage evolution along with the nucleation and propagation of microcracks until rock failure. The experimental results demonstrated that a local damage zone (LDZ) was formed when the loading amplitude exceeded a certain value, and the rock sample was prone to tensile failure under T–C cyclic loading. Based on arrangement of the virtual extensometers on the field of axial strains, the axial stress–strain curves, maximum axial strain, secant moduli, and dissipated energy evolution were obtained as a function of cycle number. It was observed that the variations in these mechanical parameters and dissipated energy significantly increased in the T–C cycle test with the increase in the loading amplitude. Particularly, due to obvious accumulation of residual compressive strain during the first cycle, the maximum tension stress increased, secant modulus decreased, and the dissipated energy evidently increased under tension during the second cycle. Furthermore, the mechanical parameters and dissipated energy evolution as a function of cycle number inside and outside the LDZ under 80% amplitude confirmed that the deformation mainly occurred inside the LDZ and the energy mainly dissipated for the nucleation and propagation of tensile microcracks vertical to the loading direction inside the LDZ during rock failure process.