Strain Crack Research Articles

A Correlation Analysis-Based Structural Load Estimation Method for RC Beams Using Machine Vision and Numerical Simulation

The correlation analysis between current surface cracks of structures and external loads can provide important insights into determining the structural residual bearing capacity. The classical regression assessment method based on experimental data not only relies on costly structure experiments; it also lacks interpretability. Therefore, a novel load estimation method for RC beams, based on correlation analysis between detected crack images and strain contour plots calculated by FEM, is proposed. The distinct discrepancies between crack images and strain contour figures, coupled with the stochastic nature of actual crack distributions, pose considerable challenges for load estimation tasks. Therefore, a new correlation index model is initially introduced to quantify the correlation between the two types of images in the proposed method. Subsequently, a deep neural network (DNN) is trained as a FEM surrogate model to quickly predict the structural strain response by considering material uncertainties. Ultimately, the range of the optimal load level and its confidence interval are determined via statistical analysis of the load estimations under different random fields. The validation results of RC beams under four-point bending loads show that the proposed algorithm can quickly estimate load levels based on numerical simulation results, and the mean absolute percentage error (MAPE) for load estimation based solely on a single measured structural crack image is 20.68%.

Structural health detection sensor based on RFID technology

In order to achieve structural health monitoring, a frequency-domain-based chipless radio-frequency identification sensor has been studied. The sensor is composed of an octagonal patch antenna and a Taconic CER-10 substrate, with overall dimensions of 24 × 24 × 1.27 mm3. Crack detection and strain detection simulations were conducted in the 3–6 and 6–12 GHz dual-frequency bands using HFSS. The results show that the sensor's resonant frequency decreases under tensile strain and increases under compressive strain. As the width, depth, and length of structural cracks increase, the sensor's resonant frequency shifts to lower frequencies. The designed structural health monitoring sensor can detect structural strain and damage with millimeter-level resolution through resonant frequency shifts. The sensor's maximum strain capacities under three different mechanical strains are −40% to 90%, −70% to 120%, and −40% to 90%, respectively. The sensor can detect changes in crack width, depth, and length without deformation, demonstrating a linear relationship between crack expansion and resonant frequency.

A mathematical model for predicting the electro-mechanical behavior of biomimetic crack sensors: Effect of crack depth and gap

Various biomimetic microstructures, such as porous, cracks, wrinkles, micro-pyramids, and micro-domes, are applied to improve the sensing performance of mechanical sensors. Among them, the crack-based strain sensors are widely investigated due to high sensitivity and fast response time. To clearly describe the relationship between crack morphology and sensor sensitivity, a mathematical model is developed for investigating the performance of a poly(3,4-ethylenedioxythiophene)-silicon oxide/polydimethylsiloxane (SiOx/PDMS) based crack strain sensor. First, the displacement field of a crack tip is calculated based on the theory of fracture mechanics, and the mathematical relationship between the crack depth, crack gap, and strain is obtained. The predicted crack depth of the SiOx thin film's thicknesses in 7.91 μm (SiOx/PDMS-7.91) is 2.82 μm, with the error of 3.75% compared to the experimental result. Correspondingly, the deviation of SiOx/PDMS-7.91 is 5.74% between the predicted crack gap and the experimental data. Second, above the aforementioned crack tip characteristics, the mathematical model based on crack edges contacts probability (CECP) is used to construct the relationship between the crack tip characteristics, applied stress, and device sensitivity. The maximum predicted sensitivity can reach 3562.68 compared with the experimental data of 3800.44, and the deviation is about 6.26%. Moreover, the CECP model has good universality with the other reported crack-based strain sensors. It can be concluded that crack morphology affects the distribution and quantity of conductive paths. When the strain sensor is subjected to external forces, brittle thin films generate a certain number of bumped-like elements for microcracks. The wider and deeper crack will increase the relative resistance change and the decrease of conductive paths, resulting in a rapid increase in the sensitivity of the strain sensor.

Damage accumulation in carbon steel under low-cycle loading at the crack initiation stage and strain ageing temperature

Based on the strain criterion for fatigue fracture and experimental studies, the damage accumulation kinetics from recoverable plastic strain (plastic strain in the tensile half-cycle), from the unilateral accumulation and elastic strain with the increasing number of loading cycles was studied. The influence of stress ageing on the redistribution of the levels of these components of damage, depending on the number of cycles before destruction, was studied. Depending on the load level, the limit states (formation of a surface macro-crack or buckling failure of strain stability due to the formation of an internal crack in the quasi-static fracture range) were established. Strain ageing reduces the range of quasi-static fracture. It is shown that the critical values of strains and stresses correspond to the limit states. The parameters determining the capacity of structural materials under static and cyclic loading under conditions of stress ageing are confirmed.

A Study on the Damage Evolution Law of Layered Rocks Based on Ultrasonic Waves Considering Initial Damage

The damage evolution process of layered rock is influenced by its fine structure, lamination direction, and confining pressure, exhibiting significant anisotropic characteristics. This study focuses on shale as the research object, employing indoor tests and theoretical analysis to define damage variables and initial damage based on ultrasonic wave velocity. This research investigates the damage evolution law of layered rock under varying confining pressures and dip angles. The findings reveal that damage variables defined using transverse wave velocity effectively reflect the damage evolution process. Additionally, confining pressure significantly affects damage evolution, with increasing pressure causing a rightward shift in the damage variable–strain curve and an increase in initial damage. The slab inclination angle also influences damage evolution; samples with 45° and 60° inclinations are more susceptible to damage, with initial damage showing a trend of increasing and then decreasing. To accurately describe the relationship between damage variables and strain during the loading process, this paper establishes a segmented damage evolution equation characterized by wave velocity. Initially, an inverse proportional function is employed to characterize the strain before crack closure. Subsequently, a logistic function represents the curve from crack strain to peak strain. This combined approach provides a comprehensive depiction of the damage evolution. This study underscores the importance of considering confining pressure and laminar inclination in the analysis of rock stability and integrity. These results provide critical insights into the damage evolution characteristics of layered rocks, offering valuable references for engineering safety assessments.

Investigation of static mechanical characteristics and numerical simulation of fractal gangue cemented backfill materials

This study investigated the static mechanical responses of gangue cemented backfill materials (GCBM) with aggregate particle size distribution (APSD) satisfied fractal grading theory. The recycling of gangue in GCBM alleviates gangue accumulation pollution and improves mining production efficiency. Macroscopically, uniaxial compression experiments regarding various loading strain rates (ε̇) on gangue cemented backfill specimens (GCBS) were conducted. Acoustic emission monitoring and digital image correlation technique were employed to reveal crack activities and strain field evolution in real time. Microscopically, scanning electron microscopy and numerical specimens considering APSD were utilized to analyze the microstructure and damage process. The deterioration mechanisms and quantified number of cracks were explored at the micro level. The conclusions are as follows: (1) The axial stress (σ) of GCBM increased with fractal dimension (D) of APSD and ε̇. For the same σ, cumulative AE counts decreased with increasing ε̇ and D. (2) The main failure mode of the GCBS under static loading was tensile failure, exhibiting tensile cracks initiating at the bonding–aggregate interface. (3) The increase in the proportion of fine aggregate contributed to the optimization of the microstructures of the GCBS (4) An increased proportion of fine aggregate in the GCBS improved the synergistic load-bearing capacity between the cementing and aggregate mediums, leading to an enhancement in the σ.

The study on fracture response of cracked pipeline considering the Lüders effect

Since pipeline steel typically exhibits yield discontinuities, some pipelines may experience high local strains during service that exceed the strain limits required by existing fracture assessment methods, thereby posing a significant threat to pipeline integrity. By establishing a finite element fracture model of a cracked pipeline with the Lüders effect and incorporating a developed constitutive model with a trilinear stress-strain relationship, the mechanical and fracture responses of the cracked pipeline with the Lüders effect under uniaxial tensile loading are analyzed in this study. The effects of crack configurations and material parameters on the crack driving force are discussed in detail. The results indicate that an increase in crack length and strain hardening exponent lowers the crack driving force plateau and shortens its length. Conversely, increases in crack depth, softening modulus, and Lüders strain raise the crack driving force plateau. Specifically, as crack depth increases, the plateau length of the crack driving force shortens, while an increase in the softening modulus and Lüders strain extends the plateau length. These conclusions provide guidance for the fracture analysis and assessment of pipelines with cracks affected by the Lüders effect.

Numerical study on flexural behaviour of sulphate corroded RC beams strengthened with ultra-high-performance concrete

Ultra-high-performance concrete (UHPC) has found extensive application in the strengthening of existing reinforced concrete (RC) structures; however, limited knowledge exists regarding its use in RC structures exposed to sulphate attacks. This study developed a non-linear finite element analysis (FEA) model to predict the flexural behaviour of sulphate corroded RC beams strengthened with UHPC jackets. The FEA model, validated with experimental results, was extended to examine UHPC configurations and thicknesses. Evaluation included ultimate load capacity, serviceability state, and stiffness. Crack patterns, load-deflection behaviour, and strain distribution were analysed for strengthened beams at their respective ultimate loads along the mid-span cross-section height. FEA results showed diverse configurations significantly enhanced the load-carrying capacity of sulphate corroded RC beams by 54.5-88.6%. Strengthened beams exhibited a 64% increase in flexural moment capacity, with notable improvements in cracking and post-cracking stiffness. Strain distribution analysis revealed UHPC strengthening increased strain values, emphasising UHPC jackets’ substantial role in resisting stresses and enhancing flexural behaviour. As expected, the three-sided UHPC configuration outperformed two-sided and bottom-side ones. Increasing UHPC thickness proved most effective in bottom-side strengthening, followed by three-sided, with a lesser effect in two-sided strengthening. Theoretical predictions from the suggested flexural moment capacity calculation aligned well with FEA results.

3D mesoscale discrete element modeling of hybrid fiber-reinforced concrete

To investigate the relationship of hybrid fiber volume friction on the mechanical properties and failure mechanisms of steel-polypropylene hybrid fiber reinforced concrete (HFRC), the study constructs a three-dimensional, five-phase mesoscale model using the Discrete Element Method (DEM), which consists of mortar, coarse aggregate, polypropylene fibers (PPF), steel fibers (SF), and the interfacial transition zone (ITZ). The axial compression test results of twelve cubic specimens with four different hybrid fiber combinations (0.5 % SF + 0.05 % PPF, 0.5 % SF + 0.1 % PPF, 1.0 % SF + 0.05 % PPF, 1.0 % SF + 0.1 % PPF) were used to validate the model’s accuracy, examining the influence of fiber content on the mechanical performance and cracking features of HFRC. Directed by experimental mix proportions, the model employed cluster particle modules with realistic aggregate geometries and randomly distributed SFs to simulate concrete microstructure. Utilizing the Flat-Joint Model (FJM) in DEM software (PFC3D), two contact models are developed: one FJM with bi-nonlinear softening segments to describe the ITZ between steel fibers and PPF-reinforced mortar (PFRM); another FJM considering the volume fraction effect of SF to describe the ITZ between coarse aggregate and FRM. Both models were experimentally validated, proving their accuracy. The results indicate that the established DEM model can accurately simulate the stress-strain relationship and failure modes of HFRC under compression. The hybrid fibers increased the compressive strength by 2.13–17.33 % and reduced the cracking strain by 5.25–9.33 %. Furthermore, the computational findings reveal that PPF primarily affects the crack initiation phase, while SF plays a significant role in the overall crack propagation stage. This discovery holds significant importance for understanding and optimizing the structural performance of HFRC.

An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

AbstractMicrocrack growth during progressive compressive failure in brittle rocks strongly influences the safety of deep underground engineering. The external shear stress τxy on brittle rocks greatly affects microcrack growth and progressive failure. However, the theoretical mechanism of the growth direction evolution of the newly generated wing crack during progressive failure has rarely been studied. A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. This model consists of the wing crack growth model under the principal compressive stresses, the direction correlation of the general stress, the principal stress and the initial microcrack inclination, and the relationship between the wing crack length and strain. The shear stress effect on the relationship between y‐direction stress and wing crack growth and the relationship between y‐direction stress and y‐direction strain are analyzed. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y‐direction peak stress and the wing crack growth direction during the progressive compressive failure considering shear stress is also discussed. A crucial conclusion is that the direction of wing crack growth has a U‐shaped variation with the growth of the wing crack. The rationality of the analytical results is verified by an experiment and from numerical results. The study results provide theoretical support for the evaluation of the safety and stability of surrounding rocks in deep underground engineering.

A sawtooth constitutive model describing strain hardening and multiple cracking of ECC under uniaxial tension

Abstract By collecting engineered cementitious composite (ECC) uniaxial tensile experimental research data, aiming at the multiple cracking characteristics of the strain hardening stage of the ECC stress–strain curve, a theoretical model describing the constitutive relationship of the ECC uniaxial tensile stress–strain – the multiple cracking sawtooth model – is proposed. Several model parameters were obtained with the fitting analysis of many ECC uniaxial tensile stress–strain curves. The application conditions and influencing factors of the three-order multi-crack “sawtooth” model of polyvinyl alcohol (PVA)-ECC and polyethylene (PE)-ECC and the four-order multi-crack “sawtooth” model of PVA-ECC are studied. The result shows that the higher the fiber reinforcement index, the better the tensile properties of ECC. The fiber reinforcement index is linearly correlated with the initial crack stress and ultimate tensile stress of PVA-ECC and with the ultimate tensile stress and ultimate tensile strain of PE-ECC. The characteristic points of PVA-ECC in the multi-crack cracking stage are as follows: the greater the initial cracking strain, the smaller the ultimate tensile strain, showing an exponential correlation; The greater the initial cracking stress is, the greater the ultimate tensile stress is, and the two are linearly correlated.

Linear fractal evolution characteristics of rock crack distributions during loading process

To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.

CDPM2F: A damage-plasticity approach for modelling the failure of strain hardening cementitious composites

For the use of micro-mechanics based constitutive models for fibre reinforced strain hardening cementitious composites in finite element simulations of structural components, it is required to link the crack opening at the scale of fibres to the cracking strain at the scale of structural components. We aim to establish this link by incorporating a micro-mechanics based fibre bridging stress crack opening law into a macroscopic damage-plasticity approach, which we call CDPM2F. The model is implemented in the open-source finite element program OOFEM. The model produces mesh-insensitive results and its response agrees well with experimental results for failure in tension, shear and compression reported in the literature.

Finite element modeling of active cracking in actively reinforced concrete pavement slab exposed to fluctuating temperature

The continuously reinforced concrete pavement (CRCP) system grapples with challenges such as non-uniform transverse crack patterns and the need for substantial reinforcement. Field research on the Belgian CRCP sections along motorway E313 indicates that active cracking induced by partial surface saw-cuts consistently leads to transverse crack patterns. This study introduces an innovative modification to the CRCP: the actively reinforced concrete pavement design (ARCP). The ARCP leverages partial surface saw-cuts to reduce reinforcement needs by replacing continuous-length steel bars with partial-length counterparts. The main objective of the present study is to develop a 3D finite element (FE) model capturing the active cracking behavior of ARCP under realistic external temperature variations. Comparative analysis with CRCP considers early-age crack patterns, crack strain development, and the distribution of maximum steel stress for different steel ratios (0.67%, 0.75%, and 0.85%). FE simulation results align with field data, indicating that ARCP exhibits similar early-age cracking behavior to CRCP but with a significant 24 to 42% reduction in total reinforcement. This innovation presents a promising avenue for addressing CRCP challenges while optimizing material usage in pavement construction.

The tensile properties of adhesively bonded single lap joints with short kevlar fiber

In this paper, short Kevlar fiber was added to epoxy resin adhesive to form a short fiber toughened adhesive, and its effect on the static strength and elongation at break of Carbon fiber laminate adhesively bonded single lap joints was investigated. 1 wt%, 2 wt%, 3 wt% and 4 wt% short Kevlar fibers were added to make short fiber toughened adhesive joints to investigate the effects of different contents of short Kevlar fibers on the connecting properties of the test pieces of Carbon fiber laminate single lap adhesively bonded joints; In addition, microscopic toughening mechanism of short Kevlar fiber in adhesives revealed by combining DIC technique and SEM technique. The test results showed that the addition of appropriate amount of short Kevlar fiber could slow down the crack extension compared with the without toughening specimens, but the toughening effect was weakened by excessive content. 2 wt% short Kevlar fiber toughened specimens achieved the best toughening effect, with 30.52 % increase in peak load and 25.78 % increase in elongation in tensile test. The combination of DIC and SEM further showed that short Kevlar fiber toughened joints absorb crack strain energy through fiber-bridging thus increasing adhesive properties.

Effect of multiscale fibers and cenospheres on the uniaxial tensile behavior of ultra-high performance concrete subjected to high temperatures

Exposure to high temperatures causes a significant deterioration in the mechanical properties of ultra-high-performance concrete. Considering the characteristics of multiscale defects, it is expected to improve the residual tensile performance of ultra-high-performance concrete by incorporating multiscale fibers (including polyethylene fibers, steel fibers, calcium sulfate whiskers, carbon fibers, and carbon nanotubes). An investigation is conducted to examine the impact of multiscale fibers, CE, and temperature ranging from 25 to 800 °C on several aspects of multiscale fibers ultra-high-performance concrete (MSFUHPC), including first cracking strength and strain, ultimate strength and strain, failure mode, as well as the tensile stress-strain relationship. The results show that above 400 °C, multiscale fibers can enhance the first cracking strength, and the effects of calcium sulfate whiskers and CE on the first cracking strain depend on the temperature and their content. It is found that Steel fibers and CE can enhance the strain-hardening ability, and multiscale fibers and CE can increase the residual tensile strength and peak strain at high temperatures. At room temperature, multi-scale fibers and CE increase the maximum tensile strength and ultimate strain of MSFUHPC by 1.28 and 45.92 times, respectively. Moreover, multiscale fibers can refine the pore structure and reduce the porosity at 800 °C. While CE can decrease the increasing rate of porosity with temperature. Furthermore, the uniaxial tensile stress-strain relationship of MSFUHPC after being subjected to high temperatures is suggested based on experimental results, taking into account the influence of multiscale fibers, CE, and temperature.

Crack-based hydrogel strain sensors with high sensitivity and wide linear range

Recently, owing to their high sensitivity, spider-inspired crack strain sensors have received considerable attention. However, their short linear range leads to severe limitations in their application in sports health monitoring. Herein, we fabricated a cracked hydrogel strain sensor with a wide linear range using κ-carrageenan and polyacrylamide. This crack hydrogel strain sensor has a wide linear range (ε = 250 %) and excellent linearity (R2 ≈ 0.999) while ensuring high sensitivity (gauge factor GF = 2.2). Moreover, this sensor is sensitive to small vibration signals. We compared it with a traditional hydrogel strain sensor and analyzed how crack appeared. Finally, we presented the application of this sensor in human health monitoring and detection of multiaxial strains.

Parametric study of side collision-induced denting failures on the ultimate strength of a handy-size containership under vertical bending

This study focuses on analysing the collision behaviour and residual ultimate bending strength of a container ship following a collision. Initially, computational models employing nonlinear finite element analysis (NFEA) were used to consider dynamic material parameters like strain rate and crack strain. The accuracy of this numerical approach was verified by comparison with test results. Subsequently, various collision scenarios were analyzed using ABAQUS software, encompassing diverse impact velocities, indenter shapes, and boundary conditions. The aim was to evaluate the reduction in the residual ultimate bending strength of a container ship hull resulting from collisions at both sagging and hogging moments. Finally, empirical equations were formulated to forecast the residual ultimate bending strength based on numerical findings. These equations exhibited excellent accuracy when validated against numerical and experimental data. This methodology and its equations provide valuable tools for assessing the post-collision strength of container ships and enhancing maritime transportation safety.

A case study on early-age cracking of high-strength concrete construction by coupled thermal-mechanical analysis and field monitoring

The use of high-strength concrete (HSC) in constructing high-rise reinforced concrete buildings and their deep foundations is becoming more popular because of the significant reduction in member size and, thus, self-weight in structural members. However, the higher cement content in HSC may result in increased heat of hydration and autogenous shrinkage, growing concerns about forming early-age cracks in HSC structural members. This case study assessed the early-age cracking of HSC in bored pile construction of high-rise buildings. A nonlinear transient coupled thermal-mechanical response analysis was performed to evaluate the potential of early-age cracking caused by the heat of hydration generated in the HSC using ABAQUS and two subprograms, USDFLD and UEXPAN. A 3-D finite element model was developed considering thermal effects, time-dependent evolution of early-age strength and stiffness of HSC, crack strain development, autogenous shrinkage, and stress-relaxation in the analysis. Field measurements were carried out on a 3-m diameter bored pile constructed using Grade C50/60 HSC (fck,cube = 60 MPa) for a high-rise building project in Hong Kong to evaluate the validity of the numerical model. Optical fiber sensors were used to monitor the temperature changes of the pile for approximately 380 hours after casting. The temporal and spatial temperature distributions measured in the field measurements agree well with the simulations. Large thermal gradients and high tensile stress zones were observed across the horizontal cross-sections of the pile, resulting in the formation of vertical annular cracks. Based on the results of the analysis, the maximum crack widths were predicted and compared with the durability crack width limits.

Flexural behaviour of damaged concrete T-beams reinforced with ultra-high performance concrete filling

To improve the flexural performance of damaged reinforced concrete T-beams, a method of filling ultra-high performance concrete (UHPC) in the damaged area was adopted. Experimental studies were conducted on two UHPC-reinforced concrete T-beams with different lengths of damaged areas and one undamaged concrete T-beam as a reference. Crack distribution, failure modes, cracking loads, flexural capacities, and strain variation of the specimens were analyzed. Subsequently, a nonlinear finite element (FE) model of the UHPC-reinforced T-beam was developed using ABAQUS, and the FE model results were compared with the experimental results to validate the accuracy of the FE simulation method. The results indicated that the two UHPC-reinforced T-beams exhibited a similar flexural failure process to the undamaged T-beam. The longitudinal tensile strain distribution at the mid-span section showed that the composite section formed by the filling of UHPC in the damaged region still adhered the assumption of the planar section. Owing to the excellent bond performance between UHPC and the existing concrete, the main cracks of the UHPC-reinforced T-beams appeared in the chiseled area, and the crack widths of the UHPC-reinforced T-beams under the same load were smaller than those of the reference T-beam. Overall, the reinforcing method of filling UHPC in the damaged region can restore or even enhance the flexural performance of the damaged reinforced concrete T-beams.