Effective Crack Length Research Articles

Effect of different loading rates on the fracture behavior of FRP‐reinforced concrete

AbstractIn order to study the effect of different loading rates on the fracture behavior of fiber‐reinforced polymer (FRP) reinforced concrete, the fracture experiments of FRP‐reinforced concrete beams under different loading rates were carried out. The calculation method of fracture toughness was given by analytic deduction, and the effects of different loading rates on the fracture parameters were analyzed. The experimental results show that there are three critical points in the fracture process of FRP‐reinforced concrete beam, which are the crack initiation load, crack resistance load, and ultimate load points. The effective crack length at the crack resistance load point increases with the increase of loading rate, and the effective crack length at the ultimate load point does not vary as the loading rate. With the increase of loading rate, the elastic modulus and fracture toughness increase gradually, and there is a logarithmic relationship with the loading rate, which has obvious rate correlation. The fracture process zone (FPZ) length of FRP‐reinforced concrete beams gradually decreases with the increase of loading rate.

Analysis of Crack Propagation Behaviors in RPV Dissimilar Metal Welded Joints Affected by Residual Stress.

In severe service environments, the presence of high local residual stress, significant organizational gradient, and nonlinear changes in material properties often leads to stress corrosion cracking (SCC) in dissimilar metal welded (DMW) joints. To accurately predict the crack growth rate, researching the initiation and propagation behavior of SCC cracks in DMW joints under residual stress (RS) is one of the most important methods to ensure the safe operation of nuclear power plants. Using the extended finite element method (XFEM), the crack propagation behaviors in DMW joints under different RS states are predicted and compared. The effects of RS, crack location, and initial crack length on crack propagation behavior are investigated. The crack in a DMW joint without RS deflects to the material of low yield strength. High residual stress urges the crack growing direction to deflect toward the material of high yield strength. Young's modulus has little impact on the crack deflection paths. The distance between the specimen symmetric line and the boundary line has little effect on the crack initiation and propagation within the RS field. A long initial crack is more likely to initiate and propagate than a short crack. To a long crack and the crack that is far from the interface of two materials, the impact of residual stress on the crack propagation path is significant when it is located in a material with high yield strength, while when the initial crack is located in the material with low yield strength, RS has a great influence on the deflection of a short crack growth direction on the condition that the crack is adjacent to the interface.

On the predictive capabilities of non‐local models for ductile crack propagation under different levels of stress triaxiality

AbstractDuctile materials are used in many applications such as hydrogen storage and transport, energy plants and additively manufactured components. High safety standards are vital for such applications, which underline the necessity of thoroughly investigating ductile failure to ensure safety and increase components efficiency. Ductile failure is mainly prompted by the evolution of the so‐called ductile damage, characterized by the nucleation, growth and coalescence of microvoids due to plastic deformation. Moreover, the plastic zones formed at the crack tip of ductile materials exhibit high sensitivity to the stress triaxiality level, which in turn distinctly depends on the geometry of the considered component. The quantification of the stress triaxiality at the crack tip is therefore essential to better understand and predict ductile crack propagation and failure. For that reason, a non‐local ductile damage model is employed in this work to simulate the ductile crack propagation under different stress triaxiality conditions. Different geometries are considered, such as constrained geometries of notched bending specimens and unconstrained geometries of center cracked tension specimens, which characterize the different triaxiality levels. To address the effects of thickness and initial crack length, three‐dimensional geometries are simulated, which account for the out‐of‐plane crack‐tip constraints. Finally, to evaluate the prediction quality of the simulations, corresponding experiments have been carried out and direct comparisons are conducted, with respect to the crack length, ductile crack propagation and resistance curves.

Application of the effective crack length method to model delamination of unidirectional composite laminates under Mode II shear loadings

Damage modelling of composite material delamination is an intense field of research to understand the complex composite failure behaviour and predict the residual strength of damaged structures. One of the widely employed methods to simulate delamination is the cohesive zone modelling (CZM) technique. To successfully utilize this approach, accurate characterisation of the interlaminar fracture toughness is crucial, while the composite delamination is dominated by Mode I and Mode II fracture in most cases. Numerous studies have been conducted on composite materials delamination under Mode I loadings using double cantilever beam (DCB) tests. Accordingly, the ASTM standard testing procedure and data reduction scheme to obtain Mode I fracture toughness (GIc) have been well established and widely accepted. However, it is still challenging to characterize the composite Mode II delamination resistance due to the susceptibility problems inherent to the existing testing methods and the lack of robust data reduction schemes to accurately identify the initial crack tip and monitor the crack growth. This study attempts to find a reliable solution to obtain the Mode II fracture toughness (GIIC) and an effective modelling strategy to simulate Mode II delamination in laminated composites. First, we reviewed the existing testing set-ups and surveyed the data reduction schemes conventionally used to obtain GIIC. The advantages and drawbacks of the three most used test methods, and particularly the standard end-notched flexure (ENF) test (ASTM D7905/D7905M) and the end-loaded split (ELS) test (ISO 15114:2014) were examined. Second, the advantages of the effective-crack-length-based data reduction schemes against the classical data reduction schemes were empirically studied with the ENF tests conducted on G40-800/5276-1 carbon-fibre reinforced composite laminate coupons. Although many studies have studied the accuracy of the effective-crack-length-based approaches from different aspects, there is a lack of direct comparison between the numerical results and experimental data. Our modelling study demonstrates that among the five data reduction schemes that are examined, the compliance calibration method (CCM) required by ASTM D7905 yields the most conservative GIIC values, which is suitable for establishing material property for a design purpose. The compliance-based beam method (CBBM) may generate the least conservative GIIC values, which are deemed to be the most accurate ones for modelling and simulation validation purposes. Finite element (FE) modelling of the ENF tests using the CZM technique was carried out and comprehensive parametric studies were conducted to achieve an efficient and robust strategy for delamination modelling of composite laminates under Mode II shear loadings.

Mode I fracture toughness determination and environmental durability evaluation of adhesive bonds by wedge test

This paper presents a study of a method for determining the fracture toughness of adhesive bonds under Mode I loading using the wedge test. The slope of adhesively bonded specimen arms at loading points was used to provide an effective crack length for the wedge test specimen. A simple expression was derived based on beam theory for the Mode I energy release rate. Finite element analyses were conducted on wedge specimens with a range of material and geometrical properties. Good agreement was found between the energy release rates from the beam theory-based expression and the virtual crack closure technique (VCCT). A comparison of various energy release rate expressions showed that the present expression was more accurate than the other expressions available in the literature. The results of this study suggest that the environmental durability of adhesive bonds with composite adherends as well as metallic adherends can be assessed in terms of their fracture toughness using the present method. Experiments under hot and humid conditions were performed on wedge specimens with adherends made of carbon fiber reinforced polymer (CFRP) composite laminate and titanium alloy, and the fracture toughness results were obtained.

Numerical Investigation on Crack Propagation of Three-Dimensional Pipeline Under Seismic Wave Loading

Cracks in transport pipelines significantly impact their structural safety, making pipeline fracture damage a major concern. While experimental tests can study crack growth, their setup and costs are substantial. To address this, our work involves parametric analyses to investigate the effects of initial crack length, load types and sizes, and pipe wall thickness on the crack tip stress field. The finite element model is established according to the actual operation, and the crack defects of the pipe are established by the extended finite element method (XFEM). The crack tip variation is studied by extracting the von Mises stress and strain at the crack tip. When the crack propagates, the stress field at the crack tip will fluctuate in a certain range. The relationship between stress field fluctuation and crack propagation was studied by changing the XFEM crack growth for comparative analysis. Utilizing 429 numerical results obtained from a parametric numerical model implemented with Python and Abaqus, we establish a back propagation (BP) neural network prediction model to forecast the stress field at the crack tip. The relative errors between the numerical results and the predictions by our model remain below 5%. In conclusion, our proposed approach for analyzing pipeline fracture under multiple loads proves valuable for pipeline safety assessment, and it offers useful insights for evaluating the suitability of transportation pipelines.

Monitoring for fatigue crack geometry in orthotropic steel bridge decks by application of reflected Lamb waves

Orthotropic steel bridge decks (OSDs) have been widely used as a crucial load-bearing structures in long-span bridges,. However, the weld connections in OSDs are susceptible to fatigue crack initiation due to the high stress cycle caused by vehicle loads. Reflected Lamb waves have potential in the monitoring of crack geometry, and different sensor arrangements are employed for different crack types in OSDs. Three full-scale specimens were fabricated and tested with the recommended sensor arrangements to continuously monitor two types of cracks in tests. Finite element models were also established and verified by the experimental results. Parametric studies were conducted to investigate the effects of sensor arrangements, crack lengths and angles on monitoring results. A wavelet transform algorithm was applied to analyze reflected waves and extract standardized wave features, based on which the crack geometry was evaluated. The experimental results reveal that the standardized wave features from the reflected Lamb waves change significantly with the increase of fatigue life, indicating that the features are sensitive to fatigue crack growth. The simulation results reveal that the standardized wave features effected by crack geometry are positively correlated with projected crack lengths perpendicular to the direction of wave propagation. The optimal arrangements of wave sensors for crack monitoring at deck-to-rib connections are to place excitation and reception sensors at 200 mm and 60 mm from the welds at crack initiation plates, respectively; while for cracks at rib-to-floorbeam connections, excitation and reception sensors are located at 200 mm and 50 mm distant from the horizontal welds at cut-out, respectively, and all sensors are 50 mm distant from vertical welds.

Fatigue life evaluation for ring-welded lap joints of stainless steel based on fracture mechanics approach

This study aims to evaluate the fatigue life of ring-welded lap joints of stainless steel with various geometries. It involves welding morphologies observations, static and fatigue tests under tensile-shear loading, and fatigue life evaluation based on fracture mechanics approach. Test results show that the interfacial failure occurs for each specimen under the static loading, and the static strength increases with an increase in weld area, as well as the degree of bending deformation during the test. In addition, three failure modes were identified under fatigue loadings, with crack propagation from the weld root to the weld metal surface accounting for over 90% of the fatigue life for most specimens. Taking into account the fatigue failure modes, a fracture mechanics-based method was used to unify the Fa-Nf curves of ring-welded lap joints with different geometries. This unified curve considers the effects of specimen geometries, crack length, loading ratio, and bending deformation. The analysis demonstrates that the fatigue life of ring-welded lap joints increases with an increase in the thickness of the sheet with a hole and the hole diameter, while decreases with the increasing loading ratio and bending deformation. By utilizing this method, the predicted fatigue life of various ring-welded lap joints can be controlled within a range that is four times of the measured values.

Hydraulic Fracturing Breakdown Pressure and Prediction of Maximum Horizontal In Situ Stress

Using the presented criteria for the breakdown pressure in which the breakdown pressure is related to the horizontal stress, the breakdown pressure in the hydraulic fracturing test is directly used in the estimation of the maximum horizontal in situ stress. However, the classical breakdown pressure criteria do not take into account the effects of near-wellbore stress field, so estimating the horizontal stress using them is accompanied by errors. A plane strain numerical model is presented to obtain the breakdown pressure, in which the effect of initial crack length are considered. In this model, it is assumed that the rock medium is impermeable and the breakdown occurs at the tip of two radially cracks. Thus, in this model, the effect of the initial crack length, which is not present in the classical models, is considered. The results obtained from the numerical model show the significant effect of the initial crack length on the breakdown pressure. Also, the comparison of the numerical model with the classical criteria shows that the condition of using the classical criteria to determine the breakdown pressure is that the ratio of the initial crack length to the borehole radius is very small. Using the numerical model, 1,456 datasets were prepared to train an artificial neural network to predict the maximum horizontal stress. Input parameters include breakdown pressure, minimum horizontal stress, initial crack length, and tensile strength. The evaluation of the results shows that the obtained neural network model has a good ability to predict the maximum horizontal stress.

Mode I and Mode II fracture behavior in pultruded glass fiber-polymer – Experimental and numerical investigation

Many recent works have shown that the capacity of pultruded glass fiber-polymer structural members is governed by interlaminar failure. However, there is still a lack of information regarding the fracture properties associated and the best techniques to be adopted. This paper aims to propose a testing methodology and to evaluate the interlaminar fracture of pultruded glass fiber-polymer specimens extracted from a composite bridge deck system. Both Modes I and II were investigated, through Double Cantilever Beam (DCB) and End-Loaded-Split (ELS) tests, respectively. The starter crack (or initial separation) was introduced via a water jet machine and the crack length was measured with the video extensometer technique. In all, nine different methods were applied to obtain the fracture toughness properties. The results are discussed and compared with 2D non-linear finite element models, where the cohesive zone model (CZM) approach was used. The Modified Beam Theory method (MBTASTM) presented the best results for crack propagation in Mode I, whereas differences lower than 1% from experiments were obtained when using the Corrected beam theory using effective crack length (CBTE) and the Experimental compliance method (EMC) methods for Mode II.

Influence of initial crack length on fracture properties of limestone using DIC technique

Due to limitations in equipment and testing methods, there is currently little literature studying the effect of initial crack length (a0) on fracture parameters. Considering that limestone is often associated with the construction of cultural heritage buildings, monuments, tunnels, subways and power stations, so limestone beams were used as the experimental objects, and were used to conduct three-point bending (3-p-b) tests based on digital image correlation (DIC) technique to study the influence of a0 on fracture parameters, including critical crack tip opening displacement (CTODc), nominal strength without considering the crack (σN), nominal strength considering the crack (σn), critical mid-span deflection (δc), critical crack mouth opening displacement (CMODc), unstable fracture toughness (KIcun), fracture energy (Gf) and fully developed fracture process zone length (lmFPZ). In addition, based on the boundary effect model (BEM), the relationships between the crack-to-depth ratio (α0 = a0/D) with KIcun and Gf were analyzed. The findings indicate that, as a0 increases, σN, KIcun, Gf, and lmFPZ decrease gradually, while CMODc, CTODc, and δc increase gradually; as two important parameters of the BEM, the boundary influence length (A1) and size-independent fracture energy (GF) are 27.08 mm and 74.67 N/m, respectively.

Effect of surface crack dimension on very low cycle fatigue crack growth behavior of circumferential cracked pipes

In this study, the effects of surface crack depth and length on the fracture behavior of circumferentially cracked pipes under very low cyclic loading were investigated via finite element (FE) damage analysis using an energy-based damage model. The FE analysis method was first validated by comparison with the SA508 Gr.1a surface-cracked pipe test results. Using FE damage analysis, a parametric study was conducted for a surface-cracked pipe with cracks of different depths and lengths, giving the same limit load. The variations in crack penetration and unstable fracture cycles depending on crack depth and length are discussed.

Numerical Investigation of Fatigue Crack Propagation Behaviour of 550E High-Performance Steel

The fatigue crack propagation behaviour of Q550E high-performance steel (HPS) is studied in this paper. Static tensile testing and fatigue crack propagation testing were carried out, and the results were compared with those of Q235. Finite element models were developed and verified against the experimental results. The impacts of the initial crack angle, crack depth ratio, stress ratio, thickness, and corrosion pitting on the fatigue crack propagation behaviour of the HPS were analysed. The results show that the fatigue life of Q550 was reduced by 18% due to the corrosion pitting, but it did not change the crack propagation path. When the stress intensity factor is higher than a certain value, the fatigue performance of Q235 is better than that of Q550E. The initial crack angle of 52.5° is the critical angle of the crack stress intensity factor. The steel tends to fracture as the crack depth ratio increases, and more attention should be paid to the effective crack length in engineering practice. An increasing stress ratio leads to a smaller stress intensity factor, and the thickness affects the stress intensity factor in the later stage. The crack stress intensity factor around the corrosion pits gradually decreases along the thickness direction, and the crack tips around the corrosion pits tend to reach the yield state initially, accelerating the fatigue fracture of the specimen and ultimately leading to a decrease in fatigue life.

Aeroelastic flutter of actively controlled nanocomposite beams with an open edge crack

Active control of aeroelastic flutter in composite structures is vital for improving the performance and safety of aerospace systems. Understanding the impact of cracks on flutter behavior of active controlled structures is of importance for early crack detection and accident prevention. The present work investigates the aeroelastic flutter of functionally graded (FG) graphene nanoplatelet (GNP)-reinforced nanocomposite (GNPRC) beams containing an edge crack under active control with an attached piezoelectric patch. The governing differential equations are derived using Hamilton's principle together with the Ritz method, based on the first order shear deformation theory (FSDT) and a rotational spring model. The flutter velocities of the system are determined by numerically solving the eigenvalue problem. Through a comprehensive parametric study, the effects of crack length and location, GNP parameters, and different control actions on the flutter velocities of the FG-GNPRC beams with different end supports are discussed. The results reveal that the presence of a crack reduces the flutter velocities of GNPRC beams, with the extent of reduction depending on the GNP distribution pattern, crack location and support ends. Additionally, the cracked GNPRC beams can be enhanced by attaching piezoelectric actuators with feedback gains at appropriate locations on the beam's surface.

A neutron radiography study on the drying of cement mortars: Effect of mixture composition and crack length

The drying process has a prominent impact on the volume changes, crack propagation and durability of concrete structures. This study is to quantify the moisture distribution in real-time drying cement mortars. Mortar prisms with different water-to-cement ratios (w/c) and superabsorbent polymers (SAP) amounts were cut into slices and prepared with distinct lengths of cut notches. They were subjected to accelerated drying during neutron radiography measurements. In mortars with higher w/c, the coarser pores accelerate water transport and lead to more rapid drying. The large voids and the SAP in the bulk of the specimens are emptied well before the exposed surface starts to dry out. The presence of notches enhances drying. However, the moisture loss through the notches is less efficient than through the external surfaces. The competition between evaporation from the surfaces and moisture transport within the material, in both liquid and gas forms, governs the moisture distribution evolution.

The effects of loading rates on the fracture characteristics at the bonding interface between steam concrete and self-compacting concrete using three-point bending test

The properties of bonding interface of Chinese Railway Track System III (CRTS III) slab ballastless track structure is important for the stability of operation, however, little is known about the interface fracture behaviors of CRTS III slab ballastless track structure. In this work, the three-point bending test under different loading rates was conducted on concrete specimens with a bonding interface between steam concrete (SC) and self-compacting concrete (SCC). The influences of loading rate on the fracture parameters and characteristics were investigated. The experimental results indicate that the failure patterns of concrete with bonding interface changed from debonding failure to spalling failure as the loading rate increased. The P-CMOD curve of concrete with a bonding interface demonstrated a similar pattern under different loading rates, which mainly included three stages: linear growth stage, crack development stage and failure destruction stage. The fracture parameters exhibited an obvious loading rate effect: the higher the loading rate, the higher the fracture energy, as well as the critical relative effective crack length, fracture toughness, and the deformation resistance of the bonding interface. It also revealed that more tortuous main crack and multiple crack paths could be observed with the increase in loading rate. A higher loading rate can promote the conversion of fracture process zone to macroscopic crack zone and also increase the fracture energy in the bonding interface.

An analytical method to calculate the time-varying mesh stiffness of spiral bevel gears with cracks

Time-varying mesh stiffness (TVMS) is one of the main dynamic excitation sources of gear transmission systems. The accurate calculation of TVMS is the foundation to comprehensively investigate the vibration of powertrain. Compared with the spur gear, the meshing process of spiral bevel gear is spatially time-varying, which makes the analytical calculation of TVMS more difficult. In this paper, the meshing relationship of spiral bevel gears is first established by extending the slice method of spur and helical gears to spiral bevel gear. Secondly, the analytical models of perfect and cracked spiral bevel gears are presented to evaluate TVMS. Meanwhile, the effects of crack length and depth on mesh stiffness are investigated. Thirdly, the influence of crack length and depth on the dynamic response are simulated based on the 8-DOF dynamic model of spiral bevel gear. Finally, the experiments are conducted to verify the effectiveness of the analytical model. Experimental results demonstrate that the existence of tooth crack fault makes the response characterized by periodic impact with the rotating frequency of cracked pinion.

Relation between electrically conductive properties and flexural behaviors of ultra‐high‐performance concrete

AbstractThe ability of the resistivity measurement to study the crack propagation behavior of the ultra‐high‐performance concrete (UHPC) under flexural loading was analyzed, and focused on investigating the effects of crack length and the fracture process zone (FPZ) on the change in electrical resistivity in the post‐cracking stage. The results indicated that the strain‐dependent resistivity characteristic was able to drawn by a linear‐fitting equation before the crack initiated (stage I). After the crack initiated, the change in electrical resistance of the UHPC can be good to reflect the crack development in the post‐cracking stages (II and III), then, the relationship between the crack propagation behavior and the fractional change in electrical resistance (FCR) can be quantitative analysis by using an exponential function. It was also found that the evolution of the crack length and FPZ also had an appreciable impact on the variation tendency of the FCR. The crack length increased dramatically at first and then increased smoothly with the increase of FRC, while the FPZ showed the reverse change trend.

XFEM for semipermeable crack in piezoelectric material with Maxwell stress

In this work, extended finite element method (XFEM) is implemented to model the semipermeable cracks in the piezoelectric material with Maxwell stresses. This Maxwell stress is induced due to the presence of an electric field at the crack faces and boundary of the piezoelectric material. To model the semipermeable crack with Maxwell stress, the crack tip is enriched with six-fold enrichment functions. The electro-mechanical interaction integral is modified and implemented for several crack configurations to compute the stress intensity factor (SIF). The accuracy of the XFEM-based semipermeable crack model in the presence of Maxwell stresses is demonstrated by validating with the analytical solution. The effects of crack length, far-field loading, Maxwell stress, and poling direction are investigated on the normalized SIF.

Fatigue life and fracture behaviors of aligned steel fiber reinforced cementitious composites (ASFRC)

Aligned and random steel fiber reinforced cementitious composites (ASFRC, SFRC) are prepared to study how fiber orientation and volume fraction affect the fatigue life and fracture behaviors of composites. The experimental results indicate the fatigue life of ASFRC exceeds that of SFRC by more than 8 times. Compared with SFRC, the critical effective crack length of ASFRC is improved by more than 17%, which can withstand greater deformation and crack propagation. And the improvement increases with enlarging fiber volume fraction (Vf). Furthermore, based on the experimental results, a two-parameters fracture model considering Vf is developed to predict the fatigue life.