Pre-crack Length Research Articles

Mode II fracture properties of parallel neosinocalamus affinis bamboo strand lumber

This study investigates the Mode II fracture properties in the RL and TL planes of parallel neosinocalamus affinis bamboo strand lumber. Eighty End-Notched Flexure (ENF) specimens were designed, varying pre-crack lengths and specimen widths. Digital Image Correlation (DIC) was employed to analyze strain variations during the development of the fracture process zone (FPZ) and crack propagation stages. The Compliance Based Beam Method (CBBM) and equivalent crack length calculations were used to determine the strain energy release rate (GIIC) of PNABSL. R curves and crack growth rate curves revealed that crack propagation in the RL and TL planes. The results indicated that Mode II fracture propagation in both the RL and TL planes of PNABSL predominantly exhibited self-similar cracking, though the fracture surfaces were rough and uneven, with noticeable fiber bridging. The study found that Mode II fracture propagation was less stable in the RL plane compared to the TL plane, which is attributed to the easier fracturing of thick-walled fiber cells in the RL plane. The critical strain energy release rate for PNABSL was determined, offering valuable insights into its fracture behavior.

Small data reliability analysis in concrete three-point bending tests: A Weibull mixture model approach based on Weibull fracture theory

Due to the high costs and time-consuming nature of experiments, data from concrete three-point bending tests are usually limited. Additionally, the performance of concrete is influenced by various factors such as mix composition and sample preparation methods, leading to significant variability in test results. This poses a major challenge for the reliability analysis of small data from repeated tests. In reliability analysis, statistical models are particularly important as they allow for the prediction of performance and failure probabilities based on existing data. However, traditional statistical methods require a large number of similar samples for data processing and may need specific adjustments due to the diversity of practical applications. To address these issues, this study proposes a mixture model that combines domain knowledge of concrete with Weibull fracture theory and uses the Clustering-Circular Block Bootstrap method for sample augmentation. By analyzing real data obtained from concrete three-point bending tests, we accurately estimated the failure probability of concrete. Additionally, the study uses Gaussian process regression with a spectral mixture kernel function to fit the threshold fracture strength of concrete and estimate failure probabilities. The results show that the proposed method can accurately fit small datasets, with a RMSE of 0.320 and a MAPE of 0.100. The nominal bending strength range at a 5% failure probability is 2.0 MPa to 6.5 MPa, depending on the sample height and pre-crack length. Statistical learning demonstrates that the proposed method excels in fitting small datasets, providing a solid framework for predicting concrete strength and reliability.

A micro-macro mechanism of hydraulic fracturing with initial stress state effect of brittle rock

The external initial stress state seriously affects the hydraulic fracturing process of rocks. However, the external initial stress effect on the mechanical relationship between the hydraulic pressure and the internal microcrack extension in brittle rocks is rarely studied. This paper proposes a micro-macro mechanical model for predicting the hydraulic fracturing process of brittle rock under compressive stress. Based on the correlation of the stress intensity factor at the tip of the extended micro-cracks, the hydraulic pressure, and the force characteristics of the cracks inside the brittle rock, the evolution law of the hydraulic pressure with the wing crack length is determined. The effects of confining pressure, axial pressure, stress difference, initial crack angle, initial crack length, initial crack density and rock fracture toughness on the hydraulic initiation stress and peak stress are discussed. The rationality of hydraulic fracturing models is verified by experimental comparison. With the increase of axial pressure, stress difference, fracture toughness, initial crack length and initial crack density, the hydraulic initiation and peak stress of rock decrease, and with the increase of confining pressure and fracture toughness, the hydraulic initiation stress and peak stress of rock increase. The study results optimize the parameters such as pre-crack angle, pre-crack length, and external loading conditions based on rock characteristics. It helps to grasp the progress of hydraulic fracturing according to the nature of rock and the degree of hydraulic pressure change, improve the efficiency of hydraulic fracturing, and enhance economic benefits.

An experimental and analytical study of mode I fracture and crack kinking in thick adhesive joints

This study investigates the fracture behavior of thick adhesive joints manufactured with composite adherends and bonded with an epoxy-based structural adhesive common to the wind turbine industry. For that purpose, double cantilever beam specimens with an adhesive thickness of approximately 10 mm and different pre-crack lengths are manufactured and tested under mode I loading. Analytical approaches are compared to assess the energy release rate, including the simple beam theory, modified beam theory, compliance calibration method, and beam on an elastic and elastic-plastic foundation. In order to evaluate the applicability of the analytical approaches, an in-situ measurement method based on Digital Image Correlation is also employed to determine the energy release rate of the thick adhesive joints. The crack propagation angle is determined theoretically using the second-order crack kinking theory. A good correlation is observed between the theoretical predictions and experimental results. Furthermore, it is demonstrated that due to the T-stress, the crack tends to deviate from the middle of the joint and propagate towards the interface. By comparing different data reduction methods to evaluate the energy release rate of thick adhesive joints, recommendations for their fracture analysis are made, pinpointing the beam on an elastic and elastic-plastic foundation as the most suitable model.

Mixed mode fracture properties of interface for composite MPC and cement concrete specimen with asymmetric semicircular bending beam

This paper investigates the interface fracture behavior of composite magnesium phosphate cement (MPC) and concrete asymmetric semicircular bending beam (ASCB) specimens under various loading conditions including pure mode I, mixed mode I&II, and pure mode II. Initially, finite element simulations are employed to compute and analyze the basic geometric characteristics of the ASCB specimens.. Subsequently, experimental tests are performed to determine the flexural strengths for different pre-crack lengths, and the critical stress intensity factors of ASCB specimens are obtained through testing. Then, parameters for the interface cohesive model are derived. Finally, the interface cohesive model for the composite MPC and concrete ASCB specimen is validated through numerical simulation. The present work show that a pure mode I opening crack represents the weakest form of the structure, and the flexural strength decreases with an increase in precrack length. The crack resistance at the repair interface is approximately 60% lower than the bearing capacity of pure mode II fractures. Intensity factor envelope analysis reveals that mixed mode I&II fractures should be avoided in composite structures experiencing complex stress states. The cohesive model effectively captures the interfacial bonding performance. When combined with the extended finite element method (XFEM), the cohesive model facilitates accurate simulation of the specimen’s interface fracture, demonstrating consistency with experimental results.

A peridynamic-informed deep learning model for brittle damage prediction

Physics-informed Neural Network (PINN) has been introduced recently to predict and understand complex physical phenomena by directly incorporating feedback from governing equations. While PINNs offer remarkable capabilities, challenges arise when addressing discontinuities and heterogeneity, potentially compromising accuracy and reliability in prediction outcomes. In this study, a novel approach that combines the principles of peridynamic (PD) theory with PINN is presented to predict quasi-static damage and crack propagation in brittle materials. To achieve high prediction accuracy and convergence rate, the linearized PD governing equation is enforced in the PINN’s residual-based loss function. The proposed PD-INN is able to learn and capture complicated displacement patterns associated with different geometrical parameters, such as pre-crack position and length. The computational method presented in this study can be implemented to any PD constitutive model like Bond-Based PD or State-Based PD as well as any horizon factor. Several enhancements like cyclical annealing schedule and deformation gradient aware optimization technique are proposed to ensure the model would not get stuck in its trivial solution. The model’s performance assessment is conducted by monitoring the behavior of loss function throughout the training process. The results obtained through PD-INN demonstrate a satisfactory level of agreement in 2D and 3D when compared with the ground truth deformation from high-fidelity techniques like PD direct numerical method and Extended finite element method (X-FEM). Our results show the ability of the nonlocal PD-INN to predict damage and crack propagation accurately and efficiently.

Pre-notch and pre-crack size effects on T-peel fracture behaviors of SAC305 solder joints

T-peel test of ductile adhesive is always an interesting and important topic in peeling mechanics and fracture mechanics. In this paper, the pre-notch and pre-crack effect on the T-peel test with a ductile adhesive layer is studied. Based on the experimental test of SAC 305 adhesive and copper adherent T-peel tests, it is found that the peak loads, fracture toughness, resistance curve, and adhesive toughness are sensitive to pre-crack or pre-notch lengths. Short pre-notch or pre-crack trigger unsteady state debonding frequently, and deep pre-notch or pre-crack conditions achieve steady state debonding more easily. Different data reduction schemes such as simple beam theory (SBT), corrected beam theory (CBT), and compliance-based beam method (CBBM) will lead to variations of fracture toughness extractions for T-peel tests. Trapezoidal shape cohesive zone model (CZM) is found to be easier matching T-peel tests conducted in this paper. However, T-peel samples with shorter pre-notch or pre-crack lengths are hard to simulate with the CZM method due to the unstable crack propagation. The reasons, which may lead to the discrepancy between pre-notch and pre-crack T-peel samples, are also presented and discussed. The selection of different pre-notch or pre-crack lengths is a very important factor that needs to be considered in the T-peel test.

Peridynamics for the fracture study on multi-layer graphene sheets

Understanding the fracture properties of graphene sheets is a crucial step towards their practical applications. However, due to the limitations of experimental operations and all-atom (AA) methods, investigating the fracture of large-sized nano graphene sheets remains a formidable challenge. Especially, study on the layer-by-layer fracture of multi-layer graphene sheets (MLGS) is nearly impossible. To overcome this challenge, a peridynamic (PD) model is proposed in this study, which comprises the intra-layer part and the inter-layer part. The proposed PD model is validated by comparing the fracture toughness and the fracture forms of MLGS with existing experiments. It is found that the uniaxial tensile stress-strain curve of pre-cracked MLGS is closely related to the number of graphene layers in MLGS. The fracture property of MLGS can be enhanced by increasing the number of graphene layers, reducing the pre-crack length and blunting the pre-crack tip. Notably, asynchronous crack propagation with independent path observed in MLGS is a unique mechanism for strengthening the fracture property, which is distinct from monolayer graphene sheet. In this work, the PD theory is extended for the first time to investigate the in-plane fracture of large-sized nano MLGS.

Performance of digital image correction technique for mild steel with different strain hardening effects

This paper investigates the performance of Digital Image Correction (DIC) technique in determining the initial fracture toughness of mild steel with different strain hardening effects. To achieve this goal, the results of DIC technique-based method are compared with those of the commonly used unloading compliance (UC) method. The comparison results reveal that the DIC technique-based method exhibit a good agreement with the UC method in determining initial fracture toughness, with a deviation of less than 3.0 %. Additionally, the DIC technique-based method demonstrates the consistency in determining the initial fracture toughness, independent of the ratio of initial pre-crack length to width. Furthermore, the importance of strain hardening effects on initial fracture toughness follows the order of strain hardening capacity, effective yield stress, and yield offset. The significance of this paper is that it provides a deep understanding of the performance of the DIC technique in determining the initial fracture toughness of mild steel.

Prediction of graphene's mechanical and fracture properties via peridynamics

Although graphene is believed to be the strongest material, many properties of this material are still worth exploring and discovering, especially the influence of inevitable defects in its preparation on the mechanical and fracture properties which are of high significance. This work provides a new feasible way to study the mechanical and fracture properties of graphene. The novelties of this study are threefold: (1) A novel peridynamic (PD) model is proposed for polycrystalline graphene in which grains of large size exist; (2) The coupling effect of the pre-crack length and the grain size on the inverse pseudo Hall-Petch relation is revealed; (3) The results confirm the applicability of classical Griffith theory in brittle fracture analysis of graphene. Based on the proposed PD model, dependence of the mechanical and fracture properties on the grain size which changes from a few to hundreds of nanometers is investigated in this study. The fracture forms of graphene are consistent with the experimental observations. Based on the Griffith theory, the obtained fracture toughness such as Kc (i.e. 3.8MPam - 6.3MPam) or Gc (i.e. 14.0 J/m2 – 40.9 J/m2) is comparable with previously reported theoretical and experimental values, which proves the validity of the proposed PD model. Besides, the fracture toughness can be greatly enhanced by the blunt pre-crack tip. This work presents insights into mechanical failure of graphene and guidance on fragmentation of graphene for its practical use.

A Numerical Study of the Dynamic Crack Behavior of Brittle Material Induced by Blast Waves.

Blast stress waves profoundly impact engineering structures, exciting and affecting the rupture process in brittle construction materials. A novel numerical model was introduced to investigate the initiation and propagation of cracks subjected to blast stress waves within the borehole-crack configuration. Twelve models were established with different crack lengths to simulate sandstone samples. The influence of crack length on crack initiation and propagation was investigated using those models. The linear equation of state was used to express the relationship between the pressure and density of the material. The major principal stress failure criterion was used to evaluate the failure of elements. A triangular pressure curve was adopted to produce the blast stress wave. The results indicated that the pre-crack length critically influenced the crack initiation and propagation mechanism by analyzing the stress history at the crack tip, crack propagation velocity, and distance. The inducement of a P-wave and S-wave is paramount in models with a short pre-crack. For long pre-crack models, Rayleigh waves significantly contribute to crack propagation.

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

Fracture behavior and energy efficiency of silica under a tensile load using molecular dynamics

Existing theories on the energy consumption of comminution are mainly applicable at the macroscopic and mesoscopic scales, and there is a lack of studies on the fracture behavior and energy efficiency at the microscopic scale. To reveal the energy evolution of the comminution process at the atomic scale, silica was subjected to a tensile load test using a molecular dynamics simulation. The crack propagation behavior, mechanical properties, major energy changes, and energy efficiency were analyzed for the comminution process of silica. The results showed that the mineral morphology and load direction affected the number and propagation path of cracks and that the crack propagation direction was generally perpendicular to the load direction. With an increase in the pre-crack length, the breaking strength, Young's modulus, elastic energy, input energy, and new surface energy of the specimens decreased to varying degrees. The energy efficiency can be significantly improved by creating pre-cracks, changing the morphology of silica to an amorphous state, and applying a load perpendicular to the crack direction. The maximum energy efficiency was 6.69 times the minimum value. This study explains the influence of pre-cracking, mineral morphology, and load direction on energy efficiency at the atomic scale and reveals the fracture mechanism and energy evolution of silica during comminution. This is of positive significance for reducing energy consumption by improving the energy efficiency of comminution processes.

From macro fracture energy to micro bond breaking mechanisms – Shorter is tougher

We show a novel fracture behavior and properties of brittle materials not previously explored. These were made possible when merging macro to micro in fracture. Our findings are based on macro-scale fracture cleavage experiments of dynamic cracks propagating in brittle single-crystal silicon specimens, focusing on the crack’s energy-speed relationships, and the fine details of the crack front. From the micro-scale, we developed an atomistic model for bond-breaking mechanisms. These mechanisms are in the form of low-energy kink advance (migration) and high-energy kink formation (nucleation) along the crack front. The energy release rate (ERR) at crack initiation, G0, and its derivative, dG0/da≡Θ, in particular, play a major role in the novel behavior and properties. G0 and Θ are influenced by the precrack length, a0. The macro-scale experiments, the micro-scale atomistic model, and the gradient of the ERR, Θ, enabled the conclusions portrayed in this work.We identified that the cleavage energy is not a constant but bounded by the Griffith Barrier as the lower bound while the upper bound (apparently the lattice-trapping barrier) may reach 3 times the lower bound. We further suggest that a brittle material can be envisaged as comprising a pseudo-R-Curve behavior mechanism typical of metallic materials. A new and essential fracture mechanism was identified, which we term ‘quasi-propagation’, a transitional mechanism between initiation and propagation. During this mechanism, the sequence of the bond-breaking mechanisms is varying, causing an increase in the macroscale cleavage energy.The evaluated cleavage energy shows another novel behavior, that of ‘shorter is tougher’, namely, shorter cracks require higher energy to propagate, and, therefore, specimens with shorter cracks are stronger than that predicted by Griffith’s theory.

Fracture of V-notched natural rubber composites used in heavy-duty tire tread

Natural rubber-based composites have proven efficacy as candidate materials for heavy-duty tire tread. The mechanical properties of these composites depend on the type of filler and their loading; thus, a comparative investigation of material properties was carried out in this study for carbon black and silica-filled natural rubber composites. The mechanical properties of silica-filled rubber composites with silane loading of 16 wt% of silica were found to have optimum mechanical and fracture properties, but carbon black had better reinforcing efficacy after 300% elongation. The experimental investigations and finite element analysis show that the J-integral decreases with increasing crack opening angle. A decrement of 22% is observed in J-integral when crack opening angle varies from 300 to 600 for rubber composites with a pre-crack length of 5 mm. The geometry factor depended on the type of filler when the crack opening angle is increased for the composites having a large pre-crack length. We envisage that this study will be helpful for rectifying design faults of different rubber composites used in industrial applications, especially for passenger and heavy-duty tires.

The cyclic R-curve method for predicting fatigue crack growth threshold based on modified strip-yield model of plasticity-induced crack closure under fully reversed loading

A strip-yield model modified to leave plastically deformed stretch in the wake of the advancing crack tip is applied to simulate the buildup of plasticity-induced crack closure with crack extension from precracks with various lengths under fully reversed loading. Two types of precracks are examined: open precracks which remain open even under cyclic compression, and closed precracks which may close under compression. The effects of precrack type and length on fatigue thresholds were systematically examined. Because of a sharp increase of crack opening stress with crack extension, the effective stress intensity range ΔKeff drops initially and then turns to increase. Assuming a constant threshold value of ΔKeff for steels, new master curve equations are proposed for the cyclic R-curve. The effect of the precrack type on fatigue thresholds is successfully derived for different precrack lengths.

Controlling roof with potential rock burst risk through different pre-crack length: Mechanism and effect research

Controlling roof with potential rock burst risk through different pre-crack length: Mechanism and effect research

Fatigue thresholds of precracked specimens predicted by modified strip-yield model for plasticity-induced crack closure

A strip-yield model modified to leave plastically deformed stretch in the wake of the advancing crack tip is applied to simulate the development of plasticity-induced crack closure with crack extension from precracks with various lengths under the stress ratio R = 0. The effects of precrack length and yield stress on fatigue thresholds were systematically examined. Because of a sharp increase of crack opening stress with crack extension, the effective stress intensity range ΔKeff drops initially and then turns to increase. Assuming the threshold value of ΔKeff for steels, a master curve equation is proposed for the cyclic R-curve. The effects of precrcrack length and material yield stress on fatigue thresholds are successfully derived.

Numerical simulation of pre-cracked thin aluminum alloy skin repaired with a FRP patch: Pre-crack length studies

The fatigue life of a thin pre-cracked aluminium-alloy panel, repaired with Carbon Fiber Reinforced Plastics (CFRP) patch on one side, is investigated using a numerical model. CFRP plies of different lengths are used to form patch which in turn repair pre-cracked aluminium skin. Numerical studies are performed to determine variation in stress intensity factor (SIF) range and bulging out deflection of specimen subjected to minimum and maximum fatigue load. Patch width to pre-crack and length to pre-crack ratio are kept constant for different pre-crack studies. Numerical simulations are carried out for three different pre-crack length. Three different patch configurations are studied for each pre-crack length. Maximum stress considered is at 50 % yield strength of aluminium skin. The numerical model is simulated by using ANSYS 15.0, a Finite Element Analysis package. The interface behaviour between the skin and the patch is simulated by using cohesive zone material model (CZM). Stress intensity factor (SIF) is determined from J-integral results. Relation between SIF range and crack length can be used to determine fatigue crack propagation by invoking the Paris law. It is found that with increasing the patch length, ΔKI decreased significantly which may result into the increase of the fatigue life.

Investigating the performance of high-strength steel shear wall with opening and pre-crack Community Verified icon

The use of steel shear wall in engineering construction, including high-rise building projects that bear several sides, is very interesting and practical. Since the steel shear wall with opening may be damaged by pre-cracks and cause damage to the shear wall, in this study, the effect of pre-crack and opening in the three-span and one-span frame with steel shear wall has been evaluated. In this study, 48 samples have been studied using finite element method and Abaqus software. Separate and lateral loading has been applied to the samples and pre-crack positions, pre-crack length and shear steel sheet material have been investigated The results of this study showed that the numerical model made for the shear wall provides reliable answers compared to the laboratory model. In the studied shear walls, the parameter of crack length and crack position has a great effect on the ductility capacity, while it has little effect on the hardness and strength index. The most critical pre-crack modes in the horizontal position, located at the top or bottom corner of the frame, have had a great impact on the lateral behavior and reduced ductility by 60% and wall strength by 32%. On the other hand, by changing the materials of the shear wall steel sheet from LYP steel to St37 and St52, the ultimate strength and hardness have increased by 3.63 and 1.45 times, respectively, and the ductility has decreased by 30% .