Crack Initiation Angle Research Articles

Experimental study on the quasi-static loading rate dependency of mixed-mode I/II fractures for marble rocks

To explore the quasi-static loading rate effect on the mixed-mode I/II fractures of rock materials, the centrally cracked Brazilian disc (CCBD) specimens prepared from a marble rock were tested under different mixed-mode loading conditions (Me = 0, 1/3, 2/3, and 1) and quasi-static loading rates (0.05 mm·min−1, 0.1 mm·min−1, 0.5 mm·min−1, and 5 mm·min−1), and the generalized maximum tangential strain energy density (GMTSED) criterion was also derived to discuss the development of mixed-mode fracture toughness and crack initiation angle. Based on the experimental and analytical results, several conclusions were obtained. (1) The mixed-mode fracture toughness gradually increases with increasing the quasi-static loading rate, while the crack initiation angle and fracture geometry of the tested specimens change barely; the specimen might have a higher rate dependency of the fracture toughness under mode I dominant loading. (2) The modified criteria (GMTSED, EMTSN, and GMTS) match well with the experimental results; the theoretical predictions based on GMTSED criterion is between the predictions of the EMTSN and GMTS criteria. (3) The critical distance of the tested rock is not sensitive to the quasi-static loading rate, which means that the fracture behavior, i.e. crack initiation angle and mixed-mode fracture resistance, under quasi-static high loading rate can be well predicted by only taking into account the critical distance obtained at quasi-static low loading rate.

Theoretical Analysis of Stress Intensity Factor for Two Asymmetric Cracks Emanating from Water Conveyance Tunnel

The water conveyance tunnel has been widely applied in tunnel engineering, which may be subjected to compressive stress and shear stress from rock and faults, respectively. The internal pressure caused by water in the tunnel will make the appearance of cracks and propagation, resulting in disasters. In order to study the effects of the cracks and compressive stress on the cracked tunnel model, a plane model containing a circular hole with two unequal cracks under the compression loads, shear stress and internal pressure was established in this study. Complex variable function and conformal mapping function were implemented to theoretically derive the stress intensity factors (SIFs) at the crack tip in the rock mass, the numerical simulation was conducted to validate the theoretical solutions. The results indicate that the numerical results using the ABAQUS code were in good agreement with the theoretical solutions. The effects of compressive stress, shear stress, internal pressure, crack length and crack inclination angle on model II SIFs were discussed, the initiation angle and initiation pressure of different rock materials were also studied. When the crack inclination angle changes from [Formula: see text] to [Formula: see text], the tunnel is easily destroyed. With the increase of the right crack length, the increasing rate of the SIFs increases quickly first and then linearly, however, the left crack length has a slight effect on SIFs. When the crack inclination angle is [Formula: see text], the crack initiation angle reaches the maximum value.

Mixed-mode fracture (K<sub>I</sub> and K<sub>II</sub>) evaluation in epoxy resin using ASENB configuration

Asymmetric Single Edge Notched Bend (ASENB) specimen which is exposed to asymmetric 3-point bending is used to estimate the mixed-mode fracture (I/II) in epoxy. The mode I and mode II combination stress intensity factors (SIF) were calculated for various locations of loading points and different crack lengths using the finite element analysis tool ANSYS. By selecting suitable points for the support positions with the loading point mode I to mode II mixities can be achieved. Then, several fracture tests on epoxy resin were conducted using the suggested ASENB specimen. The crack path follows a straight line for mode I fracture and a curved path from the crack initiation angle for mode II fracture and mode II dominant loading. The broken specimen surfaces under various conditions of loading were observed using scanning electron microscopy (SEM). Fractured specimen surfaces of the tested specimens showed reasonably smooth patterns indicating cleavage fracture.

Fatigue damage and fracture evolution characteristics of sandstone under multistage intermittent cyclic loading

To explore the damage evolution and fracture law of rock under intermittent fatigue disturbance, multistage intermittent cyclic loading experiments were performed on red sandstone with prefabricated cracks at different angles. The fatigue damage and fracture evolution characteristics of rock samples were analyzed by combining acoustic emission (AE) technology and digital image correlation (DIC) method. The results showed that deformation parameters increased first and then stabilized gradually at the initial stage of loading. When rock samples were close to failure, the plastic strain accumulated rapidly, and the elastic modulus and deformation modulus decreased rapidly. The fatigue damage was characterized by first deceleration accumulation, then steady increase and finally accelerated development. A fatigue damage evolution model considering the initial damage was established based on the axial strain. The AE evolution could be divided into four stages: initial (SI), quiet (SII), stable increase (SIII) and rapid increase (SIV). Only after the Kaiser effect disappeared, the samples had significant AE in the load holding stage. The macroscopic crack initiation stress and angle of samples were proportional to prefabricated crack angle. The crack propagation was dominated by tensile cracks during loading, and crack propagation scale in the load holding stage was smaller than that in the cyclic loading stage. The effect of prefabricated crack angle on fracture characteristics was the difference in the proportion of shear fractures.

Theoretical and Experimental Study considering the Influence of T-Stress on the Fracture Behavior of Compression-Shear Crack

The influence of the nonsingular stress term (T-stress), existing in the Williams expansion of the crack tip stress field, on the fracture behavior of the compressive-shear crack is comprehensively considered in this paper. According to the stress boundary conditions on the crack surfaces, the theoretical solution of the stress field around the closed crack tip is established using the complex potential theory, which includes not only the singular term containing the stress intensity factor KII but also three nonsingular terms (T-stress: Tx, Ty, and Txy) without KII. Then, the differences between tangential stresses and shear stresses at the crack tip obtained in the cases with and without T-stress are compared, respectively. Outcome indicates that there are tangential tensile stress and compressive stress zones at the crack tip when considering T-stress, while only the former exists when ignoring T-stress. In the case of considering T-stress, an improved crack initiation criterion is proposed, where the maximum tangential tensile stress and maximum shear stress are utilized simultaneously to predict the crack initiation and failure mode under the multiaxial compression stress state. Besides, the triaxial compression tests were carried out on the prismatic rock-like material samples with a central crack, and the effectiveness and validity of the proposed criterion are verified by comparing the experimental results and theoretical predictions. It reveals that the proposed criterion can reliably predict the crack initiation angles and failure modes with higher accuracy than traditional fracture criterion.

Advanced numerical simulations considering crack orientation for fatigue damage quantification using nonlinear guided waves

A numerical study including a fatigue crack trajectory simulation was undertaken by means of separating morphing and adaptive remeshing technology (SMART) Crack Growth in ANSYS, on the basis of which the simulations of nonlinear ultrasonic waves for fatigue damage detection using the precise fatigue crack trajectory was achieved. The simulated crack trajectory was first validated by experimental results in terms of crack initiation angle and number of fatigue cycles and was subsequently utilised for crack quantification based on second harmonic method. The results revealed that the nonlinearity in terms of the trend and magnitude with respect to crack length in the advanced simulation is closer to that in the experimental results than the common simulation approach where damage was modelled as a straight line crack. Given that the influence of crack orientation on contact acoustic nonlinearity (CAN) was taken into consideration, the developed advanced simulation could further enhance the capability of numerical modelling for simulating the interaction between nonlinear guided waves and fatigue crack, facilitating the fundamental investigation of CAN mechanism.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

Mixed modes crack paths in SCB specimens obtained via SLS

The paper presents experimental results of the crack path in Semi-Circular Bend (SCB) specimens obtained through additive manufacturing using Selective Laser Sintering (SLS) process. Determination of fracture parameters for components obtained via Additive manufacturing is a challenging topic, due to the influence of manufacturing parameters on the mechanical properties. Several researches provided the fracture toughness of SLS components, however there are not yet available results regarding the crack paths in such materials. The SCB specimens were designed with different crack orientations (0°, 15°, 30°, 45°, and 54°) and manufactured using EOS Formiga – SLS equipment (energy density 0.066 J/mm2, chamber temperature 169.5 °C, layer thickness 0.1 mm) using PA2200 material. The specimens were tested in symmetric three point bending configuration, creating 6 mode mixity from mode I (0° – crack orientation) to pure mode II (54° – crack orientation). Tests were performed at room temperature using 2 mm/min loading speed in a Zwick ProLine Z005 testing machine. For each crack orientation five specimens were tested. Crack initiation angle and crack propagation were measured by image digitization after the mechanical testing and presented in accordance to the initial orientation of the crack. Also, numerical simulation of crack path was conducted in the same way like the experiment and results were compared to the measured one.

Numerical analysis of crack initiation angles and propagation paths in adhesively bonded joints under mixed mode I/II loading using a novel test specimen

In the present work, first, the effect of adherent type on the fracture parameters of a novel mixed mode I/II fracture specimen called bi-material inclined notch short bend beam (BI-SBB) is investigated by using the J-integral method. Then, the crack propagation path is obtained incrementally based on the maximum tangential stress (MTS) fracture criterion. In the next step, the crack propagation path is examined once again using the hybrid XFEM-CZM approach. To do that, in the adhesive region, the elements are enriched and in the adherent and adhesive interface, cohesive surface is used. The results showed that for the mode I loading, based on both methods, the crack propagation path is along the initial crack and inside the adhesive. But under mode II and mixed mode I/II loading, the crack kinks towards the adherent-adhesive interface. However, kinking slop obtain from the hybrid approach is steeper than the path obtained from the MTS criterion. According to the hybrid approach, once the crack reaches the adherent-adhesive interface, crack growth in the XFEM domain ceases and the damage appears on the cohesive surface. Then delamination propagates at the interfaces between the adhesive and adherents as the loading increases.

Three-Dimensional analysis of mixed mode Compact-Tension-Shear (CTS) Specimens: Stress intensity Factors, T-stresses and crack initiation angles

In order to characterize the crack tip stress field in three-dimensional fatigue and fracture problems, stress intensity factor and T-stress solutions are usually necessary. In this paper, extensive three-dimensional (3D) finite element models are constructed for Compact-Tension-Shear (CTS) specimen, which is one of the most widely used specimens for fatigue and fracture tests under mixed-mode I&II loading. In-plane and out-of-plane geometric dimensions including varying crack depths ratios (a/W = 0.3, 0.5 and 0.7) and thicknesses ratios (B/W = 0.1, 0.3 and 0.5) are considered under different loading angles (β = 0°, 15°, 30°, 45°, 60°, 75° and 90°). The results of stress intensity factors (KI,KII and KIII) and T-stresses (T11 and T33) along the crack front are computed and analyzed. The combined effects of geometric dimensions and loading angles on these fracture parameters have been illustrated. The solutions of the parameters are then described using empirical formulae by fitting numerical results with the least-squares method. Solutions obtained have been used to predict the crack initiation angles for CTS specimens based on mixed-mode fracture criteria including the maximum tangential stress (MTS) criterion, the generalized MTS (GMTS) criterion, the strain energy density (SED) criterion and the generalized SED (GSED) criterion. Solutions are useful for fracture and fatigue problems of mixed-mode I&II, such as analysis of the constraint effects on fracture toughness and propagation path of fatigue crack.

Disturbance effect of weak Mode-II loading on the fracture of Mode-I crack

For pure Mode-I deformation, there are four energy-based driving forces acting respectively on the corresponding four local boundaries around the crack tip, which determines the basic and underlying fracture configurations. However, these fracture patterns should be broken once weak Mode-II loading arises. The present analysis indicates that for a cracked solid under Mode-I loading with disturbance of weak Mode-II loading, the whole boundary around a crack tip should be divided into six subintervals, on which there are six corresponding energy-based driving forces acting respectively. In this case, the underlying fracture configurations in form of the crack branching are much more likely to be triggered. Meanwhile a small parameter ε has been introduced to quantify the impact of weak Mode-II loading on the energy-based configuration driving forces, critical crack initiation angles and K-based fracture toughness. The typical crack branching behaviours, such as the crack initiation angles and corresponding K-based fracture toughness predicted in present article, agree well with the experimental results and observations. Present theory of crack branching applies to dynamic fracture analysis, and the underlying branching fracture trends predicted by present article can be triggered by impact or even impulse loading. Present investigation would help to refresh the traditional understanding on Mode-I crack branching.

Phase‐field fracture simulations of a four‐point bending test

AbstractPhase‐field fracture simulations have been established to simulate crack propagation in solid structures. The method employs a variational framework which has been proven to converge to Griffith' classical model for brittle fracture. Here we investigate the predictiveness of phase‐field fracture through a four‐point bending test in a mixed mode condition, and we discuss the possibilities to perform such simulation with the finite element software ABAQUS. The comparison with the experiments allows estimating the quality of the method with respect to failure loads, crack initiation angles, propagation path, and fracture surface.

Effect of notch depth ratio on mode I and mixed mode I-II fracture properties of engineered cementitious composites (ECC)

The effect of initial notch depth ratios (a/h) on the mode I and mixed mode I-II fracture properties of ECC was studied by using three-point bending test and four-point shear test, respectively. For mode I fracture, the initial fracture toughness KICini and unstable fracture toughness KICun- and KICun+ instead of KICun based on double-K fracture criterion are calculated. The mode I fracture energy GI is calculated by load-crack mouth opening displacement curve (P-CMOD). For mixed mode I-II fracture, the initial effective stress intensity factor (Keffini) are calculated by using nonlinear finite element software and the mixed mode fracture energy GI–II is analyzed. Also, crack propagation mechanism of ECC under mixed mode I-II fracture is analyzed from P-CMOD curve and load-crack mouth sliding displacement (P-CMSD) curve, and mixed mode I-II crack propagation of ECC is divided into six stage. It is found that when 0.3 ≤ a/h ≤ 0.8, the KICini does not change. While, KICun increases when a/h increases from 0.1 to 0.3, decreases when a/h increases from 0.3 to 0.7 and GI decreases with the a/h increasing from 0.3 to 0.8. GI–II is much larger than GI due to an obvious inclined fracture process zone with many micro-cracks dissipating energy in the mixed mode I-II fracture. The GI–II increases with the a/h increasing from 0.1 to 0.6 and decreases with the increase of the a/h from 0.6 to 0.8. While, the crack initiation angle increases with the increase of a/h in the mode I-II fracture.

Prediction of crack initiation angle in brittle structures containing inclined cracks

Prediction of crack initiation angle in brittle structures containing inclined cracks

Crack evolution law and failure mode of red sandstone under fatigue–creep interaction

AbstractTo explore the fracture characteristics of rock under the interaction of fatigue load and creep load, fatigue–creep interactive loading experiments were performed on red sandstone with prefabricated cracks. The crack evolution process and failure mode were analyzed using acoustic emission technology and digital image correlation. The results showed that crack growth mainly occurred in the fatigue loading stage; the crack evolution of the sample could be divided into three stages: nucleation and initiation ( ), stable expansion ( ), and unstable fracture ( ). There were distinct differences in the crack propagation modes of the rock samples with different prefabricated crack angles. The relationship between the crack initiation angle and prefabricated crack angle was analyzed based on the maximum circumferential stress theory. Moreover, with an increase in the prefabricated crack angle, the rock sample gradually changed from compression–shear failure to tension–shear failure.

Crack Evolution and Failure Modes of Shale Containing a Pre-Existing Fissure under Compression.

To investigate the crack evolution of Longmaxi shales with a single prefabricated fissure, a CCD (charge coupled device) camera and AE (acoustic emission) monitoring equipment were employed. On the basis of real-time CCD photographs and AE events, a real-time crack evolution process in fissured shale specimens under uniaxial compression was investigated. The crack initiation angle and extension angle were calculated, the relationship between the crack initiation stress, strength, and crack angle was compared, and the proportion of tensile and shear cracks at different stages of the whole compression process was briefly analyzed. The results demonstrate that, with the increase in fissure angle (α), the weakening ability of the prefabricated fissure to uniaxial compressive strength and crack initiation stress was reduced. The initial cracks and secondary cracks always appeared at the tip of the pre-existing fissure in the form of tensile cracks for α = 30–90°. The crack initiation angle and expansion angle increased first and then decreased rapidly with α increasing. Furthermore, the ultimate failure modes were mixed tensile and shear failure when α = 0–90°. The crack evolution of the fissured shale was progressive, but the final failure of the fissured specimen occurred rapidly. Furthermore, the appearance of the cracks, stress drops, and AE counts had good consistency in time.

Geometry Effects on Mode I Brittle Fracture in VO-Notched PMMA Specimens.

This paper gathers experimental and theoretical investigations about both the geometry-dependent fracture initiation angle and the fracture strength in VO-notched polymethyl methacrylate (PMMA) specimens under mode I loading conditions. The numerical analyses revealed that despite the application of pure mode I loading on the geometrically symmetric VO-notched samples, the maximum tangential stress occurs at two points symmetrically placed on either side of the notch bisector line. The experimental tests performed on some specimens showed that a crack does not necessarily propagate along the notch bisector line. Stress-based theoretical studies were then carried out to justify the experimental findings. The conventional maximum tangential stress (MTS) criterion gave weak predictions of the fracture. Therefore, the predictions were checked with the generalized MTS (GMTS) criterion by taking into consideration the higher-order stress terms. It was demonstrated that the GMTS criterion predictions have satisfactory consistency with the experimental results of the crack initiation angle and the fracture strength.

Thermo-hydro-mechanical-chemical (THMC) coupling fracture criterion of brittle rock

Based on analysis of thermo-hydro-mechanical-chemical (THMC) coupling mechanism for brittle rock, THMC coupling indicator in terms of rock porosity was introduced to represent the influencing degree of THMC coupling field on stress field in order to establish THMC coupling fracture criterion. A novel real-time measurement method of permeability (related to porosity) was proposed to determine the THMC coupling indicator, and self-designed THMC coupling tests and scanning electron microscope tests were conducted on pre-cracked red sandstone specimens to study the macroscopic and microscopic fracture mechanism. Research results show that the higher the hydraulic pressure is, the smaller the crack initiation load is and the easier the Mode I fracture occurs. Test results are in good agreement with prediction results (crack initiation load and angle, and fracture mode), which can verify the effectiveness of the newly established THMC coupling fracture criterion. This new fracture criterion can be also further extended to predict THMC coupling fracture of multi-crack problem.

Experimental study on mechanical properties and failure modes of pre-existing cracks in sandstone during uniaxial tension/compression testing

Cylindrical sandstone specimens with same crack lengths and different crack inclinations (β) were subjected to direct tensile testing (DTT) and uniaxial compression testing (UCT) in a laboratory. Meanwhile, the acoustic emission signals, mechanical and acoustic characteristics, numerical simulation results and the failure modes of the specimens were analyzed. The test results showed that the existence of cracks had a weak effect on the strength of the specimens during DTT/UCT, while the strengths of the specimens increased gradually with β. Further, the elastic modulus of rock gradually increased with an increase in β during UCT, while it was almost unchanged during DTT. The ultimate strain of all the specimens gradually increased with β. For all specimens, mode-Ⅰ cracking was initiated at the tip of the pre-existing crack during DTT; finally, tensile failure was observed. There is a certain difference between the initiation angle obtained in the test results and the theoretical value derived using the maximum hoop stress theory. The specimen theoretically exhibited mode-Ⅰ crack initiation when β ∈ [60°~90°] during UCT, while demonstrating mode-Ⅱ crack initiation at other β values; however, the experimental crack initiation angle was different from the theoretical value that fulfills the plane fracture criterion. The acoustic emission (AE) event only occurred when the specimen was critically damaged during DTT; the entire process from the initiation of the crack to the instability failure of the specimen occurs within a short time. Meanwhile, the AE signal accompanied the entire loading process during UCT, which can clearly distinguish the crack initiation stress of the specimens. In addition, the simulation results of the fracture characteristics of the specimens and the experimental results are in general agreement.

Analysis of multi-crack propagation by using the extended boundary element method

A new way is proposed to simulate the crack propagation paths of the multi-cracked structure. Firstly, the complete displacement and stress fields of the multi-cracked structure are calculated by the extended boundary element method (XBEM) coupled with characteristic analysis of the crack tip. Secondly, based on the maximum circumferential stress criterion by considering the contribution of the non-singular stress terms, the crack initiation angles are obtained. Thirdly, the cracks propagate forward along the crack initiation angles to form a new multi-cracked structure. During this process, boundary element adaptive mesh technique is established and the XBEM is used to analyze the newly formed multi-cracked structure repeatedly. Finally, the crack propagation paths of the multi-cracked structure are obtained. Numerical examples show that the results obtained by the XBEM are in good agreement with the experimental results.