Crack Model Research Articles

Fracture Analysis of Planar Cracks in 3D Thermal Piezoelectric Semiconductors

The study of piezoelectric semiconductor (PSC) materials and devices is experiencing rapid growth, giving rise to a burgeoning research domain known as piezotronics. Understanding the fracture behavior of PSC materials is essential for designing robust devices and ensuring their long-term functionality. A planar crack of arbitrary shape in the isotropic plane of a three-dimensional (3D) transversely isotropic thermal PSC body subjected to combined thermal-electrical-mechanical loadings is studied via the extended displacement discontinuity (EDD) boundary integral equation method. Under the framework of linearized basic equations and one-way thermal coupling, the hypersingular boundary integral equations with the volume integrals containing the temperature and carrier concentration are obtained and expressed by the EDDs which include displacement, electric potential, carrier concentration and temperature discontinuities across the crack surfaces and are the basic variables in analyzing crack problems. Based on the finite part of hypersingular integrals, the EDDs near the crack border are proved to have the classical behavior of O(r). Furthermore, the asymptotic solutions of extended stresses including the stress, electric displacement, current density and heat flux at the crack front are presented and display classical singular behavior of O(1/r). The extended stress intensity factors are defined and given in terms of EDDs. A 3D numerical model of a penny-shaped crack in the thermal PSC cylinder is established and used to verify the presented formulae.

Failure-mode scale transitions in RC and PC beams

Current design Standards for reinforced concrete beams prescribe to respect a minimum, ρmin, and a maximum, ρmax, reinforcement ratio in the design of structures. Below ρmin a brittle failure due to unstable crack propagation is expected. On the other hand, for ρ > ρmax a brittle failure due to concrete crushing is obtained. In this framework, a reinforced concrete element with ρmin < ρ < ρmax presents yielded steel at Ultimate Limite State (ULS) with a stable behaviour and no catastrophic loss of bearing capacity. Design Standards define ρmin and ρmax limits on the basis of the Bernoulli’s hypothesis of plane sections, and completely disregard size-scale effects. Within the present paper, Dimensional Analysis is used to determine the Brittleness Numbers that govern the behaviour of reinforced concrete (RC) as well as of prestressed reinforced concrete (PC) beams. Therefore, parametric analyses carried out by means of the Cohesive/Overlapping Crack Model (COCM) are used to study the ductile-to-brittle transitions in RC and PC beams, and to highlight the size-scale dependency of the two above-mentioned reinforcement limits.

Effect of interphase layer on matrix cracking in fiber reinforced ceramic matrix composites

The onset of matrix steady-state cracking stands as a pivotal mechanical characteristic in fiber reinforced ceramic matrix composites (FRCMCs), garnering substantial attention and investigations. Experimentally, it has been demonstrated that increasing interphase layer thickness may cause non-monotonic changes in matrix cracking stress. However, the existing models can hardly elucidate this phenomenon thoroughly due to the neglect of interphase thickness. This paper presents a comprehensive analytical model for the matrix cracking incorporating interphase, the Poisson effect, Coulomb friction, fiber asperities, residual thermal stress (RTS), and their coupling effects, along with a modified criterion for interfacial debonding that accounts for the presence of the axial RTS. Based on the proposed model, three distinct cracking domains, i.e., perfectly bonded, debonding with and without interfacial separation, have been identified with the critical conditions deduced analytically. Thereby the mechanism of the non-monotonic influence of interphase thickness is thoroughly revealed as the transition of cracking modes. Meanwhile, the role of interphase on the matrix cracking is systematically studied, and the results indicate that interphase has a notable effect through relieving axial RTS, adjusting interfacial friction, altering interfacial shear modulus, and influencing debonding toughness. The outcomes of this study offer valuable guidance for the interphase design of FRCMCs.

Shear strength of prestressed concrete beams with short shear span: Full‐scale experiments and evaluation of design methods

AbstractPrestressed concrete (PC) is increasingly used in civil engineering construction. Notably, research on shear resistance in PC beams with short shear span remains relatively limited, necessitating further comprehensive exploration. In the study, tests were conducted on bonded post‐tensioned PC T‐beams with short shear span (a/h = 1.0), subjecting them to monotonic loading destructive tests. These beams measured 24.9 m in length, 1.605 m in height, and had a top flange width of 2.0 m. They featured a uniform cross‐section with a 0.22 m web thickness. Given the size of the full‐scale test beams and space constraints for loading, an innovative loading scheme was devised to minimize the counterweight. Test results demonstrate the safety and feasibility of the loading scheme. The tests were conducted five times and the main test variables were the draped tendons and the quantity of horizontal web reinforcement. The tests revealed that horizontal web reinforcement significantly influenced crack propagation but had a minimal effect on shear strength. For the parameter values taken for the test beams, the prestressing level has less effect on the shear strength of the beam. Simultaneously, an investigation was conducted involving a total of 119 PC beams. This investigation aimed to evaluate the degree of conservatism and accuracy in shear design code provisions and shear strength equations derived from various standards, including the strut‐and‐tie model (STM) of ACI, AASHTO, and Tan, as well as the critical crack model of Yuan and the truss model of Laskar. Comparative analysis indicates that, the design method provided by Yuan exhibit relatively superior predictive capabilities.

NONLINEAR FINITE ELEMENT ANALYSIS OF COMPOSITE CONCRETE BEAMS

To study the nonlinear response of composite concrete beams, a finite element analysis is presented. Material nonlinearities as a result of nonlinear response of concrete in compression, crushing and cracking of concrete, strain softening and stiffening after cracking, yielding of reinforcement, bond- slip, shear-slip, and dowel action between the precast concrete beams and the cast-in-situ slabs are considered.A biaxial concrete model is adopted. Concrete is treated as an orthotropic material with smeared rotating crack model. The steel reinforcement is assumed to be in a uniaxial stress state and is modeled as a bilinear material. I A two-dimensional plane stress finite element type is used to model the concrete Reinforcement is represented by one-dimensional bar elements. Bond-slip and dowel action is modeled by using fictitious linkage elements with two springs at right angles. Shear-slip is modeled by using shear transfer in face elements with appropriate stiffness values Comparison between the results obtained by the finite element and available experimental results of composite concrete beams is made. The results compare satisfactorily with the experimental ones

Predictive models for flexible pavement fatigue cracking based on machine learning

Pavement performance prediction is crucial for ensuring the longevity and safety of road networks. In our extensive study, we employ a diverse array of techniques to enhance fatigue performance models in flexible pavements. The methodology begins with Random Forest feature selection, identifying the top 15 critical variables that significantly impact pavement performance. These variables form the basis for subsequent model development. Our investigation into model performance indicates the superiority of advanced machine learning methods such as Regression Trees (RT), Gaussian Process Regression (GPR), Support Vector Machines (SVM), Ensemble Trees (ET), and Artificial Neural Networks (ANN) over traditional linear regression methods. This consistent outperformance underscores their potential to reshape forecasting accuracy. Through extensive model optimization, we reveal robust performance across both complete and selected feature sets, emphasizing the importance of meticulous feature selection in enhancing forecast accuracy. The accuracy of our best optimized machine learning model is highlighted by its Performance Measurement metrics: RMSE of 22.416, MSE of 502.46, R-squared of 0.80848, and MAE of 8.9958. Additionally, comparative analysis with previous empirical models demonstrates that our best optimized machine learning model outperforms existing empirical models. This work underscores the significance of feature curation in pavement performance prediction, highlighting the potential of sophisticated modeling methodologies. Embracing cutting-edge technologies facilitates data-driven decisions, ultimately contributing to the development of more robust road networks, enhancing safety, and prolonging lifespan.

Mechanical properties of Ag-added DyBa2Cu3Oy superconducting melt-textured bulks prepared by the single-direction melt growth method

Ag-added DyBa2Cu3Oy superconducting melt-textured bulks were prepared using the newly developed single-direction melt growth (SDMG) method with different pre-heat-treatment conditions. Clearly distinct microstructures were observed depending on the pre-heat-treatment conditions and thickness of the bulks. Their mechanical properties were evaluated by use of Vickers microhardness measurements at varying applied forces. Vickers microhardness increases with an increase in the applied force for each sample, up to an importantly high value of ∼9 GPa at the saturated region, indicating all the prepared bulks demonstrate the untypical reverse indentation size effect (RISE) performance. In addition, the experimental results found from the saturation regions are examined by the mechanical methods such as Meyer's law, proportional sample resistance model, elastic/plastic deformation, Hays-Kendall (HK) approximation, and indentation-induced cracking (IIC) model. According to the mechanical modelling findings, the HK and IIC models are found as appropriate mechanical models describing the hardness values for all the studied bulks exhibiting RISE feature and the true values are suggested to lie between the estimated values of HK and IIC models.

3D modeling of cryogenic cracking by liquid nitrogen in coal under true triaxial stresses

Coalbed methane (CBM) plays an indispensable role in total natural gas production and consumption, and for the bottlenecks encountered in stimulating CBM reservoirs by conventional fracturing methods, studying more environment-friendly and efficient stimulation methods is imperative. Cryogenic fracturing using liquid nitrogen has been trialed for the development of coalbed methane, demonstrating great significance as more and more research corroborated. This study extended our previous coupled thermo-mechanical-damage (TMD) numerical procedure to investigate the cryogenic fracturing or damage process in 3D coal cubes. The cryogenic fractures on concrete cubes along with analytical solutions of temperature and first principle stress distributions for the borehole cooling process were first employed to verify the correctness and feasibility of this method, which incorporates the boundary conditions affected by the Leidenfrost effect at the initial stage. Then sensitivity analyses of cryogenic fracture generation including the maximum fracture cross-sectional area and the fractured volume were carried out. Results show that the coal rock with a high modulus of elasticity and coefficient of thermal expansion is more prone to be damaged in terms of the cross-sectional area and volume than other parameters within the parameter range analyzed. Damage cross-sectional area and damage volume expand with both the increasing coefficient of thermal expansion and the increasing modulus of elasticity, while they shrink with increasing heat capacity and coal density. Cryogenic fractures are relatively less sensitive to the thermal conductivity, density, and heat capacity of coal. This 3D modeling study provides a technical route and a panorama of the cryogenic fracturing process under varied conditions in opaque coal rocks.

Machine Learning Modeling of Wheel and Non-Wheel Path Longitudinal Cracking

Roads degrade over time due to various factors such as traffic loads, environmental conditions, and the quality of materials used. Significant investments have been poured into road construction globally, necessitating regular evaluations and the implementation of maintenance and rehabilitation (M&amp;R) strategies to keep the infrastructure performing at a satisfactory level. The development and refinement of performance prediction models are essential for forecasting the condition of pavements, especially to address longitudinal cracking distress, a major issue in thick asphalt pavements. This research leverages multiple machine learning methods to create models predicting non-wheel path (NWP) and wheel path (WP) longitudinal cracking using data from the Long-Term Pavement Performance (LTPP) program. This study highlights the marked differences in distress conditions between WP and NWP, underscoring the importance of precise models that cater to their unique features. Aging trends for both types of cracking were identified through correlation analysis, showing an increase in WP cracking with age and a higher initial International Roughness Index (IRI) linked to NWP cracking. Factors such as material characteristics, kinematic viscosity, pavement thickness, air voids, particle size distribution, temperature, KESAL, and asphalt properties were found to significantly influence both WP and NWP cracking. The Exponential Gaussian Process Regression (GPR) emerged as the best model for NWP cracking, showcasing exceptional accuracy with the lowest RMSE of 89.11, MSE of 7940.72, and an impressive R-Squared of 0.63. For WP cracking, the Squared Exponential GPR model was most effective, with the lowest RMSE of 12.00, MSE of 143.93, and a high R-Squared of 0.62. The GPR models, with specific kernels for each cracking type, proved their adaptability and efficiency in various pavement scenarios. A comparative analysis highlighted the superiority of our new machine learning model, which achieved an R2 of 0.767, outperforming previous empirical models, demonstrating the strength and precision of our machine learning approach in predicting longitudinal cracking.

Capacity assessment of uncorroded and corroded dapped‐end beams by NLFE and strut‐and‐tie based methods

AbstractThe verification of dapped‐end beams degraded by corrosion is a problem, especially for existing bridges in service. This paper proposes a nonlinear finite element (NLFE) modeling procedure and a simple strut‐and‐tie based procedure for predicting the response of dapped‐end beams subjected to chloride corrosion. Firstly, the finite element modeling strategy, based on the adoption of multilayer shell elements and the PARC_CL 2.1 crack model is described. Then, the degradation effects on concrete, rebars, and steel‐to‐concrete interaction are defined as a function of the propagation period of corrosion. In particular, the effects of corrosion on the reinforcement are modeled by applying a reduction of tensile strength that considers for both the reduction of cross‐section and the ultimate strain caused by pitting. Concrete splitting cracking due to volume expansion during rust formation is modeled by reducing the mechanical properties of concrete. Corrosion effects in steel‐to‐concrete interaction are modeled by applying a bond strength decay to the spring elements connecting corroded rebars—modeled with truss elements—and concrete multilayer shell elements. The proposed finite element procedure is used to study two scenarios based on different spatial distributions of corrosion‐prone areas. Subsequently, a simplified analytical approach based on the strut‐and‐corroded tie method—called S&amp;CT method—is proposed and compared with the finite element outcomes. Finally, the validations of the two proposed methods are presented with respect to a corroded dapped‐end beam, showing that corrosion of rebars affects the resistance mechanisms of the dapped‐end beam, by reducing both resistance and ductility. The proposed simplified analytical S&amp;CT method provides conservative and safe results compared to the numerical NLFE model and to experimental data.

A controllable generative model for generating pavement crack images in complex scenes

AbstractExisting crack recognition methods based on deep learning often face difficulties when detecting cracks in complex scenes such as brake marks, water marks, and shadows. The inadequate amount of available data can be primarily attributed to this factor. To address this issue, a controllable generative model of pavement cracks is proposed that can generate crack images in complex scenes by leveraging background images and crack mask images. The proposed model, the crack diffusion model (CDM), is based on the diffusion model network, which enables better control over the position and morphology of cracks by adjusting the conditional input of cracks. Experiments show that CDM has several advantages, including high definition, controllability, and sensitivity to narrow cracks. Utilizing CDM to create a synthetic crack data set in complex scenes resulted in substantial improvements of crack detection and segmentation. The method proposed in this study can effectively alleviate the effort required for data acquisition and labeling, especially in complex scenes.

Peridynamic simulation of fatigue crack growth in porous materials

Pores are a key type of concerns in additive manufacturing technology. They can significantly affect materials’ fatigue resistance and fatigue crack growth in the structures. In this paper, an intermediately-homogenized (IH) peridynamic (PD) fatigue crack model is introduced for simulating the fatigue crack growth in porous materials. The effect of micro-scale heterogeneity on fatigue failure is preserved in the IH-PD model, where stochastically-generated pre-damage matches materials’ porosity. The PD J-integral, a key parameter used to connect the fatigue simulation and the experimental measurements, is calculated under different porosities, and the independence of PD J-integral on its integration path is verified. Then, the PD fatigue crack model combined with the IH-PD material model is applied to study the dependence of the crack path and growth rate on porosity in compact tension alloy samples. The normalized fatigue life between experimental measurements and numerical results is compared. The normalized fatigue life-porosity relationship calculated from the IH-PD fatigue model matches the average trend of the experimental measurements.

Hydraulic fracturing simulation of concrete dam integrating intelligent crack detection and refined modeling methods

Concrete dams are prone to cracks during construction and operation process. Cracks on the upstream surface may induce the risk of hydraulic fracturing, thereby significantly reducing the safety of dam structure. Nevertheless, image processing technology, non-destructive testing technology and structural performance analysis technology with cracks are in a relatively independent state, leading to difficulties in analysis of actual cracks combined with numerical simulations. This paper proposes a novel approach for combination of intelligent identification technology and refined finite element method (FEM) for modeling and simulating the hydraulic fracturing resistance of the actual crack in concrete dams. With image processing technology and non-destructive testing technology, direction and depth of actual cracks are identified and extracted, then the 3D geometric model of actual cracks is generated. The refined model with the identified actual crack is constructed by the node projection strategy. This approach is used to assess the hydraulic fracturing resistance of the concrete dam with actual cracks in the alpine region. The results demonstrate that the critical crack depth of hydraulic fracturing is 12.93 m, and the opening width is 1.01 mm, which is 2.53 times the limit value for Class D cracks in the code (DL/T5251–2010). The refined modelling method based on actual crack detected on site can accurately evaluate the crack state compared to the conservative code.

Bond strength model between steel rebar and ultrahigh performance concrete containing coarse aggregates

To clarify the bond performance between steel rebar and ultrahigh performance concrete containing coarse aggregates (UHPC-CA), a total of 33 pull out specimens was cast. The effects of coarse aggregate particle size, coarse aggregate content, and steel fiber content on the failure modes and bond stress-slip curves of the specimens were studied. Based on the virtual crack model, considering the tensile contribution of steel fibers and the bridging effect of coarse aggregates, a model for the bond strength between UHPC-CA and steel rebar was established. The research findings indicated that there was a corresponding matching relationship between coarse aggregate particle size and the spacing of steel rebar ribs. In the 5–8 mm particle size group, the specimens showed 7.95% and 9.01% increases in bond strength compared to the 3–5 mm and 8–10 mm particle size groups, respectively. When the coarse aggregate content of UHPC-CA was 20%, the bond strength was the highest, increasing by 11.39% compared to specimens without coarse aggregates. The bond strength first increased and then decreased with increasing steel fiber content. Excessive steel fiber content could lead to the clustering of steel fibers, reducing the effective number of steel fibers contributing to toughening. The calculated results from the established bond strength model were compared with experimental and literature results, yielding an average ratio of 0.993 and a standard deviation of 0.166. This model effectively predicts the bond strength between UHPC-CA and steel rebar.

Analytic solution of pull-out failure on bond-slip relationship between deformed rebar and ultra-high-performance concrete

Numerous studies have explored the bond performance between deformed rebar and ultra-high-performance concrete (UHPC), yet an analytical solution to the bond-slip relationship remains elusive. This study presents an analytical solution of pull-out failure for the staged bond-slip constitutive relationship between rebar and UHPC, taking into account the meso-scale bond properties of fibers. The critical point coordinates for different stages are determined by the analytical solution. Utilizing the elastic mechanic solution of thick-walled cylinder under uniform internal pressure, the fictitious crack model, and the fiber-matrix discrete model, analytical solutions and simplified formulas for bond stress and slip at the critical points are provided respectively. The simplified formulas for predicting bond characteristics are proposed. The bond-slip test data are composed of 107 groups from 15 literatures, and the predictions of different formulas are compared. The average ratios of the theoretical ultimate bond stress and peak slip to the test results are 0.995 and 1.033, with a standard deviation of 0.179 and 0.231, and the error is generally within 20%. Compared with the bond-slip relationship, it is more reasonable that the ascending and descending sections are exponential. Moreover, the parameters in the bond-slip relationship can be calculated by the theoretical predictions of bond characteristics at each critical point.

Fractal theory based identification model for surface crack of building structures

The existing building structures are mainly composed of concrete and masonry structures. This paper proposes a Fractal Theory-based Method (FTM) designed to efficiently detect surface cracks in both concrete and masonry building structures, addressing limitations in existing crack recognition techniques, such as weak adaptability to complex building surfaces and requiring a large amount of computational and human resource. A novel Soft Box-Counting (SBC) algorithm is proposed to calculate texture roughness information from multi-channel and multi-scale crack images, effectively mitigating the influence of non-feature information on crack identification results. The SBC algorithm is integrated into neural networks through the fractal embedding mechanism, enhancing feature analysis through visualization experiments. The resulting FTM model integrates texture roughness information from crack images and employs fractal theory to accurately classify crack regions while minimizing the similarity between crack and non-crack regions. In comparison to existing models, FTM demonstrates superior identification performance at the same computational level on benchmark datasets for surface cracks in both concrete and masonry building structures. The FTM model exhibits enhanced identification universality and higher resource utilization efficiency.

Digital image correlation and cracked hinge model applied to notched beams reinforced with GFRP bars

In this study, three-point bending fracture tests of notched beams reinforced with a glass fiber-reinforced polymer bar are conducted. Plain concrete beams are also tested for comparison. Two different widths are considered for the beams. Digital image correlation (DIC) is used on the lateral surface of the beam to study the fracture process zone (FPZ) and neutral axis depths at different load stages. A non-linear analytical model named cracked hinge model and cross-sectional analysis are used to obtain the force in the bar and the interfacial slip between bar and concrete, which are compared to the results from pull-out tests.

Phase field modeling of mixed-mode crack in rocks incorporating heterogeneity and frictional damage

Heterogeneous rocks often exhibit a complex failure pattern of distributed tensile and shear cracks (mixed-mode cracks). In the present paper, we propose a modified phase field modeling (PFM) approach to simulate mixed-mode cracking in rocks, taking into account the effects of material heterogeneity and frictional damage. The proposed model combines the phase field method with a heterogeneous material representation and incorporates a frictional damage to capture the complex behavior of cracks in rocks. A variational formulation is derived based on the Mohr-Coulomb criterion to describe the evolution of the crack phase field. The proposed PFM-based mixed-mode crack growth model is validated against laboratory uniaxial compressive strength (UCS) tests on sandstone samples that contain a single macroscopic crack using digital image correlation (DIC). We performed a systematic characterization of the cracking and failure process as a function of macrocrack inclination angle, and found that the simulations well match the laboratory results. The results show that the length of wing cracks gradually decreases, and the nature of the damage gradually changes from tensile to shear as a function of macrocrack inclination angle. Based on this validation, we further developed a PFM model that considers multiple macrocracks. In these multi-crack simulations, we found that the crack initiation stress and peak stress decrease and then increase as the ligament angle increases. The proposed PFM-based mixed-mode crack growth model allows for the transition from single to multi-crack simulations and enables a more accurate assessment of the cracking evolution in rock.

Simulation of the surface and volume stress in the contact archwire/bracket for classical friction and critical contact angle

AbstractAimThe occlusion of the teeth is affected due to the appearance of micro-cracks resulting from maximum stresses in the contact zones between the wire and the bracket under normal and tangential loading. The objective of this study is to evaluate the surface and volume constraints in the presence of bonding and partial sliding zones on the contact surface between wires and supports. Knowledge of these stress fields will make it possible to better limit the surfaces where most of the micro-cracks occur. Indeed, the evaluation of the stress will facilitate the modelling or application of established micro crack models on this subject, because the initiation of micro-cracks often appears on the contact surface or just below it.Materials and methodsIn this study, the two most common situations of contact between the wire and the bracket were studied; the first corresponds to the situation where the wire is positioned in the center of the support (classic friction), and the second corresponds to the situation where the inclined wire touches the ends of the supports (critical contact angle).The MATHCAD software was used to simulate the damage zones for normal loading in the two cases studied (classic friction, critical contact angle). We proposed a Hertzian loading for the first case and a linear loading for the second case. Also, the effect of the additional load during wire tightening applied by the orthodontist was studied.ResultsThe charge concentration is located above the contact zone, of the order of 0.3P0 (pressure per unit of arbitrary normal length), according to Mathcad simulation results. The adhesion zone/micro-slip zone contact generates the largest tangential load, which is directed towards the side experiencing the most stress. We also observed that the stick area shifts towards the recessed side when the additional load is applied. Additionally, comparing the configurations, the critical contact angle resulted in a higher maximum shear stress.

Phase-field chemo-mechanical modelling of corrosion-induced cracking in reinforced concrete subjected to non-uniform chloride-induced corrosion

A model for corrosion-induced cracking of reinforced concrete subjected to non-uniform chloride-induced corrosion is presented. The gradual corrosion initiation of the steel surface is investigated by simulating chloride transport considering binding. The transport of iron from the steel surface, its subsequent precipitation into rust, and the associated precipitation-induced pressure are explicitly modelled. Model results, obtained through finite element simulations, agree very well with experimental data, showing significantly improved accuracy over uniform corrosion modelling. The results obtained from case studies reveal that crack-facilitated transport of chlorides cannot be neglected, that the size of the anodic region must be considered, and that precipitate accumulation in pores can take years.