Mixed-mode Fracture Research Articles

Research on the mixed-mode fracture damage characteristics of shale soaked in different drilling fluids

Drilling fluid is a vital component in drilling engineering and can be considered as the lifeblood of the drilling. It serves multiple functions such as cooling the drill bit, cleaning the wellbore, and maintaining wellbore stability. However, when the drilling fluid penetrate into the formation, it significantly reduces the mechanical properties of the rocks thus making the wellbore prone to instability. This paper focuses on the studying the fracture characteristics of shale samples with different pre-crack angles (15°, 30°, 45°) when immersion in different types of drilling fluids (water-based drilling fluid, alcohol-based drilling fluid, oil-based drilling fluid) using the SCB (Semi-circular bending) test. During the experiment, digital image correlation and acoustic emission techniques were employed to monitor and analyze the fracture characteristics of shale. The research findings showed that as the pre-crack angle increases, the fracture toughness and effective fracture toughness of Mode I fractures decrease continuously, while the fracture toughness of Mode II fractures gradually increases. The impact of drilling fluids on the fracture toughness of shale samples is in the following order: water-based drilling fluid > alcohol-based drilling fluid > oil-based drilling fluid. The length of the fracture process zone (FPZ) decreased with the increase of the pre-crack angle, and the FPZ length under different drilling fluid immersion shows varying degrees of enlargement, with the following effect: water-based drilling fluid > alcohol-based drilling fluid > oil-based drilling fluid. The horizontal strain and horizontal displacement generated before the rock sample fractures increase with the increasing angle of the pre-crack. After immersion in drilling fluid, the layering of horizontal displacement field becomes more evident, with the degree of straightness of horizontal displacement affecting it in the following order: oil-based drilling fluid > alcohol-based drilling fluid > water-based drilling fluid. As the pre-crack angle of the SCB sample gradually increases, the relative decrease in acoustic emission energy becomes more pronounced, and the decrease in b-value becomes more significant. After immersion in drilling fluid, the acoustic emission becomes more pronounced, and the b-value becomes more disorderly and decreases further. Finally, by analyzing the fracture patterns of SCB samples immersed in different drilling fluids, relevant fracture mode diagrams were established. The findings could be useful in developing strategies for optimizing drilling fluid selection and fracture stimulation design in shale formations.

Stress intensity factor analysis for mixed-mode fracture behavior of inclined semi-elliptical surface crack in stiffened plate under tension load

This study aims to investigate the mixed-mode fracture behavior of stiffened plates with inclined semi-elliptical surface cracks (ISSCs). For this purpose, a new numerical model is developed for the fracture analysis using FRANC 3D in combination with ABAQUS. Normalized stress intensity factors (SIFs) are used to analyze the fracture behavior at the surface and deepest points of the surface crack. Additionally, an arrest parameter ψ is proposed to quantify the level of crack arrest under mixed-mode conditions. Then, a thorough investigation is conducted to examine the fracture behavior of stiffened plates with ISSCs, focusing on the effects of aspect ratio, relative depth, spacing ratio, stiffness coefficient, crack angle, and loading mode. The findings indicate that the restraint effect of stiffeners on the fracture of large surface cracks is significantly stronger compared to small surface cracks. It is also identified that the restraint effect is more pronounced at the surface point than at the deepest point. Finally, a set of novel formulas is derived to evaluate the mixed-mode SIFs in stiffened plates through statistical analysis of the results.

Experimental analysis on the mixed-mode fracture behavior of structural adhesives

The wide use of adhesive joints supposes that accurate strength predictions methods exist for design. Cohesive zone models (CZM) consist of the most accepted method, although the fracture toughness (GC) of the adhesive in the different loading modes should be firstly characterized, and the mixed-mode behavior or fracture envelope known. This work experimentally evaluates the cracked-lap shear (CLS) test for mixed-mode GC assessment of two epoxy adhesives. Different theoretical reduction methods were evaluated. The work consisted of testing CLS specimens with the different adhesives, and carrying out the respective data processing. Results showed that the model of Brussat et al. led to offset results compared to the other methods.

I-II mixed fracture characterization of hot mix asphalt under tensile test using notched semi-circular specimens

I-II mixed mode fracture is a common fracture pattern of asphalt pavement under the coupled tension and shearing loads. To address the roles of reclaimed asphalt pavement (RAP) and loading effect, this study proposed a novel test method to characterize the I-II mixed fracture toughness of two types of asphalt mixture. Within the novel tensile test, direct tension load could be applied on the bottom of the notched semi-circular specimens at −10 °C. I-II mixed fracture could be generated by varying the notch angle. Fracture parameters, including the stress intensity factors of mode I and mode II fracture (KIC and KIIC) and the T stress were obtained for specimens with five notch angles, including 0∘, 15∘, 30∘, 45∘ and 60∘, respectively. Results indicated that from 0∘ to 30∘, pure mode I to pure mode II fracture could be generated. Under the same loading rate, compared to mixture A, mixture B presented superior fracture toughness in terms of mode I and mode II stress intensity factors (KI and KII), which was attributed to the fact that the inclusion of RAP in mixture A deteriorated the fracture resistance. Loading rate played positive effect on the fracture toughness. From 1 mm/min to 5 mm/min, the improvements of KIC were 52% and 33% for mixture A and B, respectively. For KIIC, the increase of loading rate enhanced the pure mode II fracture resistance by 30% and 20% for mixture A and B, respectively. Several fracture criteria were adopted for the fracture prediction. Comparison was performed between the test data and the predictions. It was found that compared to MTS criterion, the inclusion of T stress in GMTS criterion made the prediction closer to the test data. Compared to GMTS and GEMTS criteria, GEMTS criterion could provide better estimates for I-II mixed mode, indicating considering the effect of fracture mode on the critical distance (rc) could make the prediction with a higher reliability.

A node-splitting lattice spring model coupled with a J-integral formulation as a fracture criterion

A global energy minimization criterion based on Griffith’s theory is introduced for the node-splitting lattice spring model. The fracture criterion is computed by both direct numerical simulations of energy release rate G and through a J-integral formulation for comparison and validation. For mode I fractures, the standard implementation of J-integral formulation yields very good estimations of the energy release rate, but for mixed mode fracture the estimations deviates from the direct calculated energy release rate. The reasons for this discrepancy are elucidated and an approach to best approximate the J value is given. This method is compared with the more standard maximum tip stress threshold crack criterion, and shows a much better prediction of the energy release rate and is more robust under grid refinement.

Using cohesive zone models with digital image correlation to obtain a mixed mode I/II fracture envelope of a tough epoxy

This work describes a method in which the digital image correlation (DIC) method and finite element analysis (FEA) were used to create a quasi-static mixed-mode fracture envelope for bonded joints consisting of 2024-T3 Al adherends and a tough structural epoxy adhesive. Symmetric and asymmetric versions of double cantilever beam, single-leg bend, and end-notched flexure tests are used to populate the mixed-mode fracture envelope with results at several mode mixities. Experiments are conducted in a universal testing machine while recording images for subsequent DIC analysis. Finite element analysis is used to implement cohesive zone models (CZMs) of the adhesive fracture and to account for plastic deformation of adherends. Mode I and mode II traction separation laws (TSLs) are determined from a property identification method with a Benzeggagh–Kenane mixed-mode coupling law used to model mixed-mode behavior. FEA results are shown to provide a good agreement to both the crosshead displacement and DIC data. The methods in this paper serve as a potential framework for future calibration of mixed-mode fracture envelopes for joints bonded with very tough adhesives that complicate assessment with traditional data analysis methods.

Application of modified fracture criteria incorporating T-stress for various cracked specimens under mixed mode I-II loading

Accurate assessment of fracture behavior and life prediction of cracked materials based on the mixed mode fracture criteria is of utmost importance in fracture mechanics. In this study, the modified fracture criteria incorporating T-stress for mixed mode I-II cracks were comprehensively reviewed. Additionally, a comparative analysis was conducted between the experimental results obtained from five different cracked configurations and the theoretical predictions according to these modified criteria. Moreover, a brief discussion was held regarding the effect of T-stress on both crack initiation angle and fracture toughness, accompanied by providing some suggestions. The results revealed that the predictive accuracy of modified criteria exhibited noticeable variations across different cracked configurations due to the significant disparities in both the sign and magnitude of T-stress around the crack tip. However, it was observed that the predicted curves based on the modified fracture criteria for the semi-circular bend and edge-crack triangular specimens had remarkable similarities owing to their similar biaxial stress ratio B. When the mode II loading dominated, the generalized maximum tangential stress, generalized minimum strain energy density and generalized averaged strain energy density criteria were suitable for the semi-circular bend, edge-crack triangular, central crack rectangular and short bend beam specimens with positive T-stresses, whereas the maximum tangential strain, generalized maximum tangential stress and generalized maximum tangential strain energy density criteria could provide better theoretical predictions for central cracked Brazilian disk specimens having a negative T-stress.

A dynamic description of the smoothing gradient damage model for quasi-brittle failure

Quasi-static simulations are of limited interest because cracks, if they are not severely constrained, propagate dynamically. When natural disasters such as earthquakes or explosions happen, structures made of quasi-brittle or brittle materials can suffer from failures activated by, for instance, loading at a high rate. Dynamic fractures, especially dynamic crack branching, are often observed during those events. We present in this paper, for the first time, a dynamic description of the smoothing gradient-enhanced damage model towards the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching. The study is carried out using low-order finite elements, and the merits of the developed approach are examined through our numerical experiments, including mixed-mode fracture and dynamic crack branching simulations.

Designing a simple and suitable laboratory test specimen for investigating the general mixed mode I/II/III fracture problem

A novel test specimen was designed for experimental investigations of pure and mixed mode fracture. This novel test configuration is called “modified edge notched disc bend” (M-ENDB) specimen. The M-ENDB specimen has a circular disc shape with an edge crack along its diameter that is loaded using asymmetric three-point bending. Different fracture parameters including: stress intensity factors (SIFs), geometry factors, T-stress, biaxiality ratio (BR), and out-of-plane constraint factor (Tz) were determined for the suggested disc bend specimen using the extensive finite element (FE) analyses. According to the obtained results, the proposed specimen can present all combinations of mode mixities, including pure modes I, II, and III as well as mixed-mode I/II, I/III, and I/II/III deformations. Afterwards, a large number of pure and mixed-mode fracture toughness experiments were carried out on polyurethane (PUR) foam to examine the capabilities of the suggested M-ENDB specimen. Fracture path, fracture surface, fracture toughness, work of fracture, and critical T-stress of broken foams under general mixed mode conditions were investigated. Mixed mode I/II/III fracture toughness value was smaller than the pure mode I fracture toughness (KIc) value showing the weakness of brittle materials against multi-axial fracture compared to pure tensile type fracture.

Study of mixed-mode fracture in functionally graded material using an adaptive phase-field fracture model

This work systematically investigates the mixed-mode fracture propagation in functionally graded materials. The crack trajectory and load–displacement responses were effectively simulated using the mixed-mode phase field approach in combination with an adaptive mesh refinement technique. The mesh refinement is carried out using quadtree decompositions, and the elements with hanging nodes are handled as n−sided polygons. The adaptive implementation is validated by solving benchmark problems from the literature. The adaptive technique demonstrates greater computational efficiency by significantly reducing the number of elements without compromising the accuracy of the solution. This study provides insight into how fracture propagation behavior is influenced by gradient profile, material gradation, crack location, energy release rate, and displacement configuration in uni-directional and bi-directional functionally graded material. Remarkably, it is found that the peak load on the load–displacement graph changes noticeably, and the fracture path remains constant despite variations in the critical energy release rate. Notably, the results show that materials with lower fracture toughness have an early failure when studying a center fractured plate. This thorough examination deepens our understanding of the propagation of mixed-mode cracks and provides insight into improving the analysis and design methodologies for functionally graded materials.

Peridynamic modeling of step-path failure in rock slopes

This work is devoted to investigating the step-path failure of rock slopes using peridynamic theory. To this end, an extended bond-based peridynamic model that can explicitly distinguish between tensile and shear cracks from mixed-mode fracture phenomena, previously proposed by the authors, is first introduced. Then, the fracture processes of gypsum specimens with various triple-flaw distributions under uniaxial compression are simulated at a laboratory scale. Tensile, shear, and mixed tensile-shear failure modes are reproduced, and the feasibility of the numerical tool is verified via comparison with experimental observations. Finally, the progressive failure of rock slopes at the field scale is analyzed, in which crack initiation, propagation, coalescence, and eventual structural damage are well captured. The types of crack propagation and coalescence predicted in this study contribute to understanding step-path failure mechanisms in experimental research and nature.

J integral strain-curvature approach for multilayer fracture specimens with unknown thickness and stiffness of layers

In the coming years, many wind turbines will reach their planned design life, and it is of great interest to investigate if their service life can be extended so that the turbines can produce a larger amount of electricity before decommissioning. Such an assessment can include the measurement of the fracture mechanics properties of materials interfaces, e.g., for trailing edge bondlines, web foot bondlines and interfaces between layers in the load-carrying main spars. It would then be preferable to conduct the fracture mechanics testing and data analysis by approaches that give accurate results with the smallest amount of testing. In the present work we propose an approach for measurement of mixed mode fracture resistance (and mixed cohesive laws) that does not require knowledge of the stiffness properties and the elastic centre of the laminates of the test specimens. This is advantageous since the layer stiffness, layer thickness and the lay-up of a laminate cut from an old blade may not be known. Furthermore, the elastic properties of polymer resins of bondlines and matrix materials in fibre composites can have changed (aging) due to the blades long-time environmental exposure.

Interfacial debonding mechanism of magnesium phosphate cement onto old concrete substrates under freeze-thaw conditions

The interface created by the repair of damaged ordinary Portland concrete (OPC) structures using magnesium phosphate cement (MPC) is prone to cracking and debonding under freeze-thaw (F-T) conditions and may even cause engineering disasters. In this study, the entire debonding process, moisture migration and debonding mechanism of the MPC-OPC composite interface under F-T actions were investigated and a novel mixed mode fracture criterion was established. The primary findings are drawn as follows: (i) The interfacial crack initiates and propagates along the interface or kinks into the MPC side during F-T actions, depending on the position and thickness of the localized interface F-T damage zone (IFDZ) close to the interface on the MPC side; (ii) The net suction force causes capillary and film water in the mesopores and micropores to migrate to the freezing macropores inside the interface layer, whereas the increase in the liquid pressure caused by the water-ice phase transition causes crack initiation in the macropores and even the interface layer damage; (iii) The stiffness difference between MPC and OPC increases as the molar ratio of magnesia and phosphate (M/P) or the mass ratio of water to cement (W/B) of MPC increases, and the interface debonding mode shifts from propagating along the interface to kinking into the MPC side.

Quasi-static tensile failure mechanism analysis of CFRP/Al countersunk electromagnetic riveted joints with different rivet-hole clearances

CFRP/Al countersunk riveting can meet the requirements of aircraft aerodynamic shape and lightweight joining. This paper reports an experimental study on the forming mechanism and quasi-static tensile failure of single-lap electromagnetic riveted joints with varying rivet-hole clearances. The aim is to quantitatively evaluate their deformation characteristics and mechanical properties. The failure process and fracture mechanism are revealed through the use of digital image correlation (DIC) and scanning electron microscope (SEM). The results demonstrate that the rivet-hole clearance has a significant impact on the initial damage and mechanical properties of riveted joints. The interference is not uniformly distributed in the Al sheet and the CFRP sheet. Increasing the clearance can delay the occurrence of damage of the laminate under external load. As the clearance increases, the riveted joint failure mode changes from rivet sheared off to manufactured head fracture and rivet pull-off, and the rivet fracture shows a brittle- ductile mixed fracture mode. Additionally, the initial riveting damage of the joint does not determine the final extent of damage to the laminate after failure, and the bearing damage of CFRP laminates increases with the increase in the load-carrying capacity of the joint.

Experimental analysis and modeling of subsurface cracks with random propagation for ceramic material on rolling contact fatigue

During the degradation of critical rotating components using ceramic materials, due to the uncertainty of the failure generation mechanism, the high nonlinearity of failure evolution and the diversity of failure modes, the unpredictability of sudden failure triggered by random propagation of subsurface cracks poses a great challenge to the operation and maintenance. Based on the finite element model reconstructed from fatigue tests, an early failure evolution model for ceramic bearings considering random propagation of subsurface cracks is constructed in this paper. Throughout the work, the position coordinates of critical nodes characterizing the degree of crack propagation (α, β, γ) are introduced to visualize the influence of propagation on the finite element of crack front during the whole rolling contact process, whose errors (ɛ) are stabilized at 10%. Then Monte Carlo Simulation is used to generate the randomness events of crack propagation, which satisfies the uncertainty characteristics of early failure initiation and propagation under actual working conditions. The results show that the first deflection shows strong randomness. Afterwards, the main cracks move away from the surface in mixed fracture mode, and finally form abrupt spall after several deflections. The proposed model not only reveals the sudden failure mechanism of ceramic bearing under uncertain crack propagation, but also effectively evaluates performance degradation of critical rotating components using ceramic materials.

Effect of linear heat input on the interface and mechanical properties of steel/CFRP laser welding joint

An investigation on laser joining of PA66 carbon fiber reinforced plastic (CFRP) to DP780 dual-phase steel was presented. Effect of linear heat input on the interface and mechanical properties of steel/CFRP joint was performed. When linear heat input increases, the softening phenomenon is not observed in heat-affected region of dual-phase steel. Meanwhile, the melting point and decomposition temperature of resin are less impacted. The maximum tensile-shear force of steel/CFRP joint reaches 1959.4 N. The interface temperature is contained between melting and decomposition temperature of resin, the spreading of resin on steel surface is promoted, and a favorable steel/CFRP bonding interface is obtained. In addition, the new chemical bonds such as M−C and M−O are formed, which is conducive to the chemical connection of steel/CFRP interface. However, as excessive linear heat input is applied, the interface temperature will exceed the decomposition temperature of resin, resulting the generation of decomposing pores. Moreover, due to excessive heat on resin, its crystallinity decreases, the interface between resin and fiber is weakened, so that the fracture behaves as a mixed fracture mode of interface and cohesion fractures, which deteriorates steel/CFRP joint properties.

Pure (I and II) and mixed-mode (I+II) fracture characterisation of unidirectional AS4/Low-melt-PolyaryletherketoneTM polymer composites

This paper reports an experimental and numerical study on the mixed-mode I+II fracture characterisation of unidirectional AS4/low-melt-Polyaryletherketone (AS4/LMPAEKTM) composites. To address the fracture law characterising the material mixed-mode fracture behaviour, a suitable approach is used, simply applying two different loading conditions regarding five mechanical tests and specimen configurations. Scoping to characterise fracture under pure mode I loading and under mixed-mode I+II loading with mode I predominance, the peel test loading condition is used, respectively, for symmetric and asymmetric double-cantilever beam tests (DCB and ADCB). The three-point bending loading condition is used in order to characterise fracture under pure mode II loading by end-notch flexure test (ENF) and mixed-mode I+II with moderate and predominant mode II, respecting symmetric and asymmetric single-leg bending tests (SLB and ASLB). To diminish the influence of crack monitoring ambiguity on the crack length analysis during experiments, data reduction schemes based on the compliance-based beam method (CBBM) were used. Additionally, numerical finite element analyses were conducted in order to validate the data reduction method and the mode partition strategy based on cohesive zone modelling (CZM). Overall, a good agreement between numerical and experimental results was obtained, providing an adequate identification of the energy fracture criterion.

A Quasi-2D Exploration of Mixed-Mode Fracture Propagation in Concrete Semi-Circular Chevron-Notched Disks

Most semi-circular bend (SCB) tests on concrete have been conducted with a pre-crack with a straight-through tip, thereby undermining the determination of the tensile fracture toughness (KIc). Therefore, the present study involved mixed-mode (tensile–shearing) fracture propagation in concrete semi-circular chevron-notched disks (i.e., with a sharp notch tip) using SCB tests and the FRANC2D numerical simulation software. The inclined notch angle (β) was varied from 0° to 70° while the other settings remained fixed, and the crack mouth opening displacement (CMOD) of the notch was measured constantly. The stress distribution was analyzed using finite-element simulations, and the experimental results showed that this testing method was robust. The maximum failure load and the fracture propagation angle increased with β, and wing fracture was observed. With FRANC2D simulating these SCB tests successfully, it was found that the tensile stress concentration around the notch tip moved toward the upper face of the notch, and the compressive stress concentration formed on the notch tip. The tensile mode was generated as the CMOD kept increasing for β = 0–30°, whereas the mixed mode became more evident as the CMOD kept decreasing for β = 45–70°. The fracture process zone was found for β = 0–30° but not for β = 45–70°. This mixed-mode fracture is predicted better by the criterion of extended maximum tangential strain than by other criteria, and there is a linear relationship between CMOD and KIc, as examined previously for pavement and concrete materials.

Numerical simulation of the effect of interface morphology on the fracture behavior of bi-material Brazilian disks

As the most fragile component in a bi-material structures, the performance of rock-concrete interface will greatly affect the stability and durability of the whole structure. To investigate the influence of interface morphology on the interface bearing capacity and fracture characteristics of bi-material Brazilian disks, the sandstone-concrete bi-material Brazilian disk is taken as the research object, a series of sandstone-concrete bi-material Brazilian disks with interfaces of different groove widths, depths and spacings are simulated based on the cohesive zone model (CZM) method in this paper, and the effects of loading angle and location of groove interfaces on the fracture behavior are also investigated, the loading rate of all models is 0.1 mm/min. The loading angle is the main factor affecting the fracture patterns of the bi-material Brazilian disks. The loading angle increases from 0° to 90°, and the failure patterns can be divided into sawtooth fracture along the groove, mixed mode of sawtooth fracture along the groove and tensile fracture of the matrix, and tensile fracture of the matrix. The interface is the main bearing part at small loading angles, and when the loading angle exceeds 30°, the matrix is the main bearing part, and at this time, the morphology of the interface has little influence on the failure patterns and bearing performances of the specimens. The groove interface significantly improves the bearing capacity of the interface, in which the groove width has the greatest influence on the bearing capacity of the interface, and the groove spacing affects the location of crack propagation along the sawtooth (rock sawtooth or concrete sawtooth). The location of the groove interface affects the crack propagation mode at the interface, and this study mainly presents three cracking modes: failure along the rock sawtooth, failure along the concrete sawtooth and the combined failure of the rock sawtooth and the concrete sawtooth.

The microstructure and mechanical properties of aluminum/steel welded joint with Ni foil interlayers by FSLW

Friction stir lap welding experiments between 6061 aluminum alloy plate and DP590 dual-phase steel plate were carried out. The effects of welding parameters and addition of Ni foil interlayers with different thickness on the microstructures and mechanical properties of the lap joints were investigated. The shear strength of the joint reached the maximum value of 6597 N and showed a mixed ductile-brittle fracture mode when the welding speed, the rotating speed and the thickness of the Ni foil intermediate layer were set to 100 mm/min, 900 rpm and 0.3 mm, respectively. A certain amount of beneficial plastic AlNi and FeNi3 intermetallic compounds are formed through the reaction of Al, Fe and Ni at the aluminum alloy/steel interface.