Cracked Components Research Articles

A study on load sharing characteristics of the planetary gear train system with cracked gears

Load sharing characteristic is very important for the reliability of the planetary gear train. Cracked gears can make the load sharing performance become worse. Nevertheless, previous studies have not paid enough attention to the influence of cracked gears on the load sharing behavior, when compared with the impact of multiple factors under healthy condition. An 18 degrees of freedom dynamic model for the spur planetary gear train is established based on the centralized parameters theory in this paper. The influences of cracked gears on the load sharing behavior are investigated, which include the cracked sun gear, the planet gear containing cracked side meshing with the sun gear, the planet gear having cracked side meshing with the ring gear and the cracked ring gear. Additionally, the sensitivity analysis of the external and internal load sharing behavior to different cracked components is conducted. The results indicate that the load distribution becomes more uneven with the propagation of crack in the sun gear and ring gear, while the change regulation is different for each cracked planet gear. Moreover, the load sharing characteristic of the external meshing is more sensitive to the cracked sun gear and the planet gear 1, which has the crack side meshing with the ring gear. While the load sharing characteristic of the internal meshing is more sensitive to the cracked ring gear and the planet gear 3, which owns the crack side meshing with the ring gear than others. The output of this paper will be useful for the crack fault diagnose and fault source identification of the planetary gear train system.

Phase-field approach for fracture prediction of brittle cracked components

The versatility of the phase-field method (PFM) in predicting elusive fracture trajectories has attracted researchers in recent years; however, limited focus has been directed toward fracture load prediction for brittle materials. This study presents a computationally low-cost and straightforward framework based on phase-field modeling to predict the fracture loads and fracture initiantion angles of brittle cracked components under in-plane loading conditions. The framework was assessed through a comprehensive comparison between numerical and experimental data for various specimens and test configurations. Despite using 1D analytical formulations for calculating phase-field parameters, great accordance between empirical data and simulation results demonstrated the effectiveness of the proposed model. A technique that restricts the computation of the phase-field variable merely around the crack tip was applied to significantly reduce the computational costs of PFM simulations. Furthermore, we examined different numerical aspects and confirmed the robustness of the proposed procedure.

The analysis of scaled cracked components

A recent arrival in the open literature is the scaling theory finite similitude bringing into existence a countably infinite number of new similitude rules. The application of the theory to fracture mechanics has revealed that the first-order similitude rule is applicable in the sense that information gleaned from two fractured scaled components can be combined to capture the response of a third. This paper examines an unexplored aspect of the finite similitude theory, in that, it is shown how it can be re-configured for the purposes of scaling analysis. This is achieved by retaining the first derivative (with respect to scale) in the first-order rule and on involving an additional transport equation. The approach assumes the first-order rule to be exact, which is confirmed here, but in addition, has the advantage of automatically accounting for any defect-size related size effects that are present. It is a top-down scheme with analysis performed under the constraint of an imposed rule. To instigate the methodology, fracture mechanics for the first time is defined on a new scaling space, where all physical quantities are deemed dependent on a single dimensional scaling parameter β. This approach is demonstrated to facilitate the imposition of similitude rules and has led to the discovery of new relationships that connect fatigue responses at two sizes. Although analysis here is limited to linear elastic fracture mechanics (LEFM), it is demonstrated through proof, analytical, and experimentally validated numerical models, that the approach provides an exact scaling theory for fatigue.

Fatigue cracking prediction of RIOHTrack full-scale test track based on variable-order fractional Burgers model

We propose a modified thermal cracking (MTC) model in this paper, which utilizes the evolution of crack propagation to predict the number and density of cracks that will form on the RIOHTrack full-scale test track. We incorporate the variable-order fractional Burgers model as an important component of the thermal cracking (TC) model, for calculating the creep compliance. Furthermore, we apply the Levenberg–Marquardt (LM) algorithm as a data-driven approach, for parameter fitting. The MTC model is constructed technically through creep compliance approximation compute and parameter fitting as follows. First, we employ the variable-order fractional Burgers model to calculate the asymptotic creep compliance of each pavement segment within the RIOHTrack full-scale test track. More precisely, we derive the explicit asymptotic expansion of creep compliance based on the variable-order fractional Burgers model. Such an asymptotic expansion represented by the Gamma function is a simplified representation of the creep compliance, and it ensures that the fitting accuracy R2 is greater than 0.87. Parameter fitting of the creep compliance is based on the RIOHTrack full-scale pavement test data, using the LM algorithm. Then, the creep compliance in the original TC model is mathematically upgraded to the above variable-order fractional approximation form, and parameters in the MTC model are numerically estimated using the LM algorithm based on prior knowledge from the RIOHTrack test data. Our prediction analyses based on the RIOHTrack data demonstrate the superior performance of the proposed MTC model.

Optimizing light and heavy aromatic ratios in fluid catalytic cracking slurry oil for mesophase pitch with wide-area optically anisotropic texture

Aromatics are the preponderant component of fluid catalytic cracking (FCC) slurry oil, with notable differences in molecular structure between the light and heavy aromatics. The effect of these differences on the formation and optically anisotropic texture of mesophase remains elusive, impeding the preparation of high-quality mesophase pitch. This paper aims to regulate the ratio of light to heavy aromatics in the FCC slurry oil for optimizing the optically anisotropic texture of mesophase pitch. The results show that the heavy aromatics possess higher aromaticity, longer alkane side chains, larger molecular size and more reactive structures (methylene bridges, n-alkane structures) compared with the light aromatics. As an “accelerator”, heavy aromatics can form mesophase quickly. Light aromatics not only served as a “diluent,” but also assumed the function of a “lubricant”, which facilitated the orderly arrangement of aromatic molecular lamellar. The system exhibits moderate reactivity that inhibits excessive condensation and modifies the structural orientation of pyrolysis products with the 2/5 ratio of light to heavy aromatics. Under these conditions, a high-quality mesophase pitch (d002 = 3.485 Å, Lc = 19.832 Å) with wide-area optically anisotropic texture, suitable softening point (262 °C) and short polymerization time (t = 5.5 h) was obtained. This work provides theoretical support for the preparation of high-quality mesophase pitch by regulating the components of slurry oil.

Source types of induced earthquakes in underground mines: Revealed by regional moment tensor inversion

Mining-induced earthquakes have been very frequent in recent years due to increasing mechanized mining. Compared with natural earthquakes, even a small one may cause significant damage to the mine area and its surroundings. Source type identification is important for better understanding the physical processes and is a crucial and fundamental issue for hazard assessment and emergency rescue in the mining environment. The moment tensor (MT) theory plays a pivotal role in distinguishing different source types. In this study, we concentrated on two strong reported “mine collapse earthquakes” in Qufu (ML 3.2, July 13, 2020) and Zoucheng (ML2.9, June 09, 2020), Shandong Province, China. Seismograms from regional seismic stations were utilized to calculate the full moment tensors through low-frequency full-waveform inversion. Our results show that the two studied events exhibit notably different source types. The DC (Double-Couple) component of both events are 5% (Qufu) and 60% (Zoucheng), respectively. The Qufu event which contains approximately 75% closing crack component, is more consistent with the theoretical models of collapse seismic source. However, the Zoucheng event, which exhibits a significant proportion of DC components, demonstrates characteristics typical of shear failure. Focusing on the Zoucheng event, which occurred at the Dongtan Coal Mine, further research was conducted on a local mining scale. Analyzed in conjunction with microseismic sensor data, geologic setting, and mining progress, we illustrated that the source type of Zoucheng event is not a collapse one. The fracture slip of a thick-hard roof due to an overlying load, characterized by a large DC component, is a plausible geomechanical interpretation.

Experimental and numerical analysis of the behavior of rehabilitated aluminum structures using chopped strand mat GFRP composite patches

PurposeThis paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.Design/methodology/approachSingle-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.FindingsThe width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.Originality/valueThis study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.Graphical abstract

Fatigue crack growth simulation by extended finite element method: A review of case studies

AbstractNumerical simulation of fatigue crack growth (FCG) is presented, based on the application of the extended finite element method (XFEM). Couple of case studies are presented, as a review of recent experience of the Belgrade school of XFEM simulations, established at the Faculty of Mechanical Engineering. Case studies comprised Charpy specimen with initial crack at the notch tip, oil rig pipe with an axial surface crack, pressure vessels with a crack at the welded joint with connecting pipe, turbine shaft with a crack at the transition radius, optimization of a wing spar in respect to FCG, the effect of mesh size on fatigue life estimation of a stringer panel, fatigue life estimation of wing‐to‐fuselage connecting lug, geometry effect on fatigue life of orthopedic plates and fatigue life of hip implant. Based on these case studies, XFEM is discussed in respect to its accuracy and efficiency. It is concluded that XFEM is a versatile tool for simulation of FCG, providing an excellent option for precise and reliable fatigue life of a cracked component.

Validated assessment of power plant components with flaws and defects operating under long-term creep and isothermal creep-fatigue loading

An extensive database of frequently used heat-resistant steels 1 %Cr, 9–10 %Cr and 12 %Cr steels at application-typical temperatures was evaluated using the Nikbin-Smith-Webster model. Influencing factors, such as the initial plasticization and the specimen thickness, were investigated in the evaluation of the fracture mechanics material characteristic values. A thickness influencing factor fB for crack initiation is proposed, which improves the crack initiation estimation using the NSW model and reduces its over-conservatism notably. It could be shown that the crack initiation and especially the crack growth under creep loading can be described with sufficient accuracy by the modification of the NSW model. The limitation in the application of the C*-parameter could also be shown and explained by the Two-Criteria-Diagram (2CD). It should be applied to crack geometries with predominant crack tip damage. The 2CD is shown as preferred method for a more precise, material-related understanding and assessment of the crack initiation process.Based on the recalculation of fracture mechanics tests on CT und DENT specimens, the analytical approaches for the description of crack initiation and growth under creep and isothermal creep-fatigue loading could be validated in the long-term range by comparison with the experimental results up to 100,000 h.Finally, the transferability of these approaches from CT und DENT specimens to large components was investigated by calculating cracked components under practical creep and isothermal creep fatigue loading using these methods. It has been shown that the load level and the duration of holding time are decisive for the crack initiation and the crack growth under isothermal creep-fatigue loading. In the case of high stress and shorter holding times, the damage is predominantly influenced by fatigue. With lower stress and longer holding times, creep plays a more important role.

Stresses in repair welding of high-strength steels—part 2: heat control and stress optimization

In welding of high-strength steels, e.g. for foundations and erection structures of wind energy plants, unacceptable defects can occasionally be found in the weld area, which should be removed by thermal gouging and subsequent re-welding. High shrinkage restraint of repair welds may lead to crack formation and component failure, predominantly in interaction with degraded microstructures and mechanical properties due to repair cycles. This study aims for elaboration of recommendations for repair concepts appropriate to the stresses and materials involved to avoid cold cracking, damage and expensive reworking. In part 1 [1] of this study, systematic investigations of influences of shrinkage restraint on residual stresses and cold cracking risk during repair welding of two high-strength steels S500MLO for offshore application and S960QL for mobile crane structures were focussed. In this part 2, the microstructure, particularly hardness, and residual stresses due to gouging and influences of heat control parameters in repair welding are analysed. A clear reduction in residual stress after gouging can be observed, especially for the specimens with restrained transverse shrinkage. Gouging to a depth of approx. 2/3 of the seam height does not lead to a complete relaxation of the observed reaction forces. Particularly for the higher strength steel S960QL, there are pronounced areas influenced by the gouging process in which a degradation of the microstructure and properties should be assumed. Overall, the repair welds show a significant increase in the width of the weld and HAZ compared to the original weld, especially in the case of S960QL/G89. The repair welds show higher welding-induced stresses than the original welds, especially in the areas of the HAZ and the base metal close to the weld seam. This behaviour can be attributed overall to increased restraint conditions due to the remaining root weld or shorter gouge grooves. In good agreement with earlier investigations, the residual stresses transverse to the weld can be significantly reduced by upwardly limited working or interpass temperatures, and the reaction stresses resulting from high restraint conditions can be effectively counteracted. The influence of the heat input on the stress formation is low compared to the interpass temperature for both test materials.

Online identification methods for low-order wheel polygons coupled with axle cracks

Wheel polygons pose a threat to the safety of train operations due to wheel fatigue, necessitating online identification. The online identification of wheel polygons predominantly relies on the axle box vertical nx (n-multiple integer of axle rotation frequency) signals generated by wheel polygons. The low-order vertical nx signals are easy coupling to other faults like axle cracks, leading to errors in wheel polygon identification. A signal decoupling method is crucial for removing the crack components from the vertical nx signal to obtain more accurate identification results for low-order wheel polygons. Employing principles of signal superposition for different faults, this article proposes a method to decouple the wheel polygon nx signal from the vertical nx signal by subtracting the crack-related portion. This method has been validated through an ABAQUS + SIMPACK online rigid-flexible coupling model, indicating that it significantly improves the accuracy of wheel polygon identification. The 1x amplitude of the decoupled signal decreased by 60.78%, and the 2x amplitude decreased by 55.79%.

Stresses in repair welding of high-strength steels—part 1: restraint and cold cracking risk

The sustainable and resource-efficient production of wind energy plants requires the use of modern high-strength fine-grain structural steels. This applies to both foundation and erection structures, like mobile or ship cranes. During the assembly of steel structures, unacceptable defects can occasionally be found in the weld area. In most cases, the economical solution would be local thermal gouging of the affected areas and re-welding. Due to the high shrinkage restraint of the joint groove in the overall structure, the superposition of global and local welding-induced stresses may lead to crack formation and component failure, particularly in interaction with the degradation of the microstructure and mechanical properties of high-strength steels during the repair process. However, manufacturers hardly have any information about these issues and there is a lack of recommendations and guidelines to take these safety-relevant aspects into account in adequate repair concepts. The aim of this research is to derive recommendations for repair concepts appropriate to the stresses and materials involved providing a basis for standards and guidelines to avoid cold cracking, damage and expensive reworking especially for high-strength steels. Part 1 of this study involves systematic investigations of influences of shrinkage restraint during repair welding of two high-strength steels S500MLO for offshore application and S960QL for mobile crane structures. The quantification of the shrinkage restraint of repair weld joints was achieved by means of experimental and numerical restraint intensity analysis. In welding experiments with self-restrained slot specimens, restraint intensity and introduction of hydrogen via the welding arc using anti spatter spray were varied systematically to analyse the effect on welding result, residual stresses and cold cracking. It could be shown that increasing restraint intensities result in significantly higher transverse residual stress levels. In the case of hydrogen introduction S500MLO showed no cold cracking independent of the restraint conditions. However, S960QL was found to be considerably cold cracking sensitive if hydrogen is introduced. With increasing restraint intensity length and number of cold cracks increases significantly. Part 2 [1] of this study is focussed on microstructure and residual stresses due to gouging and stress optimization via adequate heat control parameters in repair welding.

Fatigue crack driving force of railway bogie frames using rigid-flexible coupled dynamics: A case for beam model

The stress intensity factor is essential to determine the residual fatigue lifetime of cracked components. However, the traditional method used to determine the stress intensity factor is very difficult to characterize the dynamic behaviors of structure arising from the fatigue crack. This paper proposed a methodology to determine the dynamic stress intensity factor (DSIF) of a crack incorporating with the rigid-flexible coupled dynamics. Firstly, a rigid-flexible coupled dynamic model of cantilever beam representing the typical structure of bogie frame with a straight crack was developed based on SIMPACK platform. In the model, the equivalent spring - contact element was employed to model the contact behaviors of crack interface. Subsequently, the DSIF considering the crack closure effect was calculated by the node displacement extrapolation. The validity of proposed method was demonstrated through comparing the DSIF with those obtained by other analytical methods. The results suggest that the proposed methodology can characterize the closure effect of crack, and yield more accurate estimation for the DSIF. This method establishes a link between the multibody system dynamics and the fracture mechanics, which enable us to calculate the DSIF of crack under the operating condition using a rigid-flexible coupled dynamic model.

TheGeneral Crack Component Modelfor reversed cyclic shear

AbstractA growing body of research has shown that reversed cyclic shear loading of reinforced concrete (RC) causes effects that are not accounted for in monotonic behavioral models. Notable among these effects are a reduction in shear strength and significant plastic offsets. This paper presents the General Crack Component Model, a rational, mechanics‐based model that explicitly considers the constitutive behavior of cracks in RC. Cracked RC is treated as a series–parallel system of bonded and unbonded regions, where the crack interfaces have both crack closing hysteresis and a kinematic contact constraint. Validation was performed using data from monotonic and reversed cyclic experiments on panel elements, and has shown that this analytical model is able to accurately capture the salient features of reversed cyclic shear behavior.

Mixed mode brittle fracture prediction in cracks under frictional condition

Neglecting frictional forces between crack surfaces in the brittle fracture of bodies subjected to compressive-shear loading conditions can result in significant fracture load underestimations when using the fracture criteria. The present research suggests a new trial-and-error procedure for predicting the fracture load of cracked components in the presence of frictional forces, which depends on the imposed compressive stress. For validating the proposed model, the results derived from the numerical method are compared with the empirical fracture loads over a wide range of loading and geometry configurations. The experiments are carried out for two different specimens, namely the center cracked Brazilian disk (CCBD) and a redesigned test specimen called angled-edge asymmetric semi-circular bending (AASCB), both made of Polymethyl-methacrylate (PMMA). The accordance between the numerical outcomes and the experimental data from the compression-shear tests demonstrates the effectiveness of the method.

Discontinuous quarter-point boundary elements revisited: Computation of T-stress in two-dimensional cracked components

This paper analyzes the use of discontinuous quarter-point quadratic elements in a dual or hypersingular boundary element context to compute the T-stress for cracked 2-D isotropic components. The performance of this approach has been demonstrated in the past for stress intensity factors (SIFs) computation and, herein, it is revisited to assess its adequacy for T-stress evaluation. To this end, novel direct extrapolation formulas that determine the T-stress from the computed nodal displacements at the collocation nodes of the discontinuous quarter-point element are proposed, and their accuracy and effectiveness is satisfactorily tested by several numerical examples involving 2-D cracked Carbon NanoTube (CNT) reinforced composites. SIFs extrapolated from the computed nodal crack opening displacements and T-stress evaluated from the computed stresses at internal points (close to the crack-tip) are also presented for completeness. The proposed techniques are a valid and easy-to-implement alternative to the interaction integral approaches when determining SIFs and T-stress.

Metal 3D‐Printing for Repair of Steel Structures

AbstractThis work employs an innovative technique, wire arc additive manufacturing (WAAM) which is a type of directed energy deposition, for fatigue strengthening of cracked steel components. Different steel plates with a central crack were tested under high‐cycle fatigue loading regime, including a reference plate, a plate repaired by WAAM with as‐deposited profile, and a plate repaired by WAAM and subsequently machined to reduce stress concentration factors. Corresponding finite element simulation was conducted to provide a better understanding on the mechanism of WAAM‐repair. The existing central crack in the reference plate propagated and led to a rupture after 0.94 million cycles, while those in the two WAAM‐repaired plates did not propagate, due to the increased net cross‐section and the compressive stresses induced by the depositing process. However, in the second plate, a new crack initiated at the root of WAAM profile as a result of local stress concentration, and the fatigue life reached 2.2 million cycles (2.3 times as the reference plate). The third plate, on the other hand, survived more than 9 million fatigue cycles with no visible degradation, thanks to its smooth machined profile. The findings of this work indicate that WAAM repair shows great potential as a technique to address fatigue‐related damages in steel structures.

Fracture Behaviour of Carbon Steel Straight Pipe with Through-Wall Crack under Cyclic Loading

Carbon steel straight pipes form part of the primary heat transport system of nuclear power plants. They may be subjected to dynamic-cyclic loads during earthquake event. This dynamic cyclic loading significantly affects the fracture resistance and the load carrying capacity of cracked components. Further, for the application of leak-before-break concepts, experimental investigations are essential. Therefore, the aim of the present study is to investigate the effect of cyclic loading on fracture resistance of through-wall cracked straight pipes. The paper presents details of the cyclic fracture test on a straight pipe and the results thereof. The behaviour of the pipe was compared with the fracture behaviour under monotonic loading. The study has shown that the load capacity of the pipe is reduced under cyclic loading and the failure is by cyclic tearing followed by sudden collapse.

Numerical prediction of warm pre-stressing effects for a steam turbine steel

In warm pre-stressing (WPS), the fracture resistance of cracked steel components is raised when subjected to certain temperature-load histories. WPS’s beneficial effects enhance safety margins and potentially prolong fatigue life. However, understanding and predicting the WPS effects is crucial for employing such benefits. This study utilised pre-cracked compact tension specimens made from steam turbine steel for WPS and baseline fracture toughness testing. Two typical WPS cycles were investigated (L-C-F and L-U-C-F), and an increase in fracture resistance was observed for both cycles. The WPS tests were simulated using finite element analysis to understand its effects and predict the increase in fracture resistance. A local approach was followed based on accumulative plastic strain magnitude ahead of the crack tip. Since cleavage fracture is triggered by active plasticity, the WPS fracture is assumed when accumulated plasticity exceeds the residual plastic zone formed at the crack tip due to the initial pre-load.

Crack analysis and modeling in concrete beams reinforced with FRP composite sheets

In this article using the principles and relationships governing fracture mechanics and finite elements cracking in the first mode for reinforced concrete beams reinforced with FRP sheets are analyzed and modeled. In this method to simulate the crack in reinforced beams, the relations for determining the stress intensity coefficients with the presence of rebars and reinforcement sheets are developed. Here, it is assumed that a composite sheet is completely bound to the bottom surface of the beam under pure bending moment. In the proposed method beam components are divided into two categories, including components without cracks and components with cracks. In components without cracks, relations, equations, and the conventional stiffness matrix governing the beam are used, taking into account the changes in the moment of inertia caused by the presence of reinforcements and FRP sheets. In the finite component with a crack, the crack profile is simulated by creating a geometric defect in the beam section. So that the reduction in the hardness of the component with a crack is equivalent to the change in the dimensions of the discontinuity. Here, the changes in the hardness of the cracked component are calculated and presented as a function of the modified stress intensity coefficients. To ensure the correctness and accuracy of the presented method, all the analyzes are implemented in Abaqus software. The comparison of the obtained results shows that the presented method is a suitable method for the analysis of reinforced concrete structures resistant to cracking. So that it can be extended and developed for other models with proper accuracy.