Crack Curving Research Articles

An alternative and robust formulation of the fatigue crack growth rate curve for long cracks

Crack growth simulations are an important method for estimating the remaining service life of components and structures with cracks under cyclic loading. In particular, the evaluation of cracks emanating from clinched joints is a major challenge because the fracture mechanical properties of the sheet materials can change locally due to the joining process. Special specimens are used to determine the relevant crack growth rate curves. For the application of these curves within simulation programs, they are described using crack propagation equations. This requires an accurate formulaic description of the entire crack curve with clearly identifiable parameters that unambiguously describe certain characteristics of the crack growth rate curve. Known approaches either describe only parts of the crack growth rate curve or the single parameters affect different characteristics of the curve and thus influence each other. Therefore, a new alternative and robust mathematical fit of the crack growth rate curve is developed and validated with experimental results.

An Evaluation of Asphalt Mixture Crack Resistance and Identification of Influential Factors

The crack resistance of asphalt pavement mixtures directly impact pavement service condition and pavement distress. And characterizing the crack resistance of a pavement mixture can reflect the crack resistance potential of asphalt pavement. This study analyzes several representative highway sections based on time, material, and service conditions to identify the mixture type of three layers. Semi-circular bending tests are conducted at 15 °C, and load–displacement curves are recorded. Factor independence analysis is performed, and combinations showcasing the cracking performance of the surface layer, middle layer, and bottom layer are selected. Analysis of variance (ANOVA) evaluating the indices versus selected factors for the three layers identifies significant influencing factors, and the crack resistance is analyzed based on these significant factors. The crack resistance of the middle layer with the highest truck loads is significantly lower than the two other lanes and the shoulder. Transverse crack spacing (TCS) can be used to directly evaluate the crack resistance of the mixture. The Factor dots upper rate (FUDR) and absolute Factor dots upper rate (absFUDR) indices are introduced to quantify the percentage deviation of a factor specimen from the average crack resistance index–fracture energy ratio, indicating whether the crack curve becomes sharper or flatter. The factor dots upper rate index is then applied to characterize the factors, and the results are reasonable. It is found only on the surface and middle layers that the service age has significant impacts on crack resistance, the Transverse crack spacing has significant impacts on crack resistance index, and the Factor dots upper rate can identify the brittleness of mixtures with different factors.

Tailored microwave thermal crack heating model and its application in cutting ceramics

A tailored microwave thermal crack heating model to elaborate the process of curve trajectory cutting and the mechanism of action between microwave and materials is innovatively presented. The model of microwave thermal crack cutting Al2O3 ceramics is established, and the cutting process of microwave thermal crack curve trajectory is simulated. In the research of thermal crack cutting, the distribution of the temperature field and stress field are obtained by simulation calculation. The section quality, crack trajectory offset, and surface crack trajectory consistency of the machining results are characterized. As for the surface prefabricated trajectory, the crack propagation law of surface prefabricated trajectory different from that of section prefabricated crack is revealed by simulation analysis. The mechanism and effect of crack propagation control are simulated and experimentally studied by surface prefabricated trajectory and local cooling methods. The experimental results indicate that the local cooling method can improve the consistency of the upper and lower surface trajectories during crack growth. In summary, it is expected that this study could provide a theoretical reference regarding microwave cutting ceramics based on the thermal crack method and pave the way for microwave manufacturing in various industrial applications.

Reconstruct lower‐dimensional crack paths from phase‐field point cloud

AbstractBecause of the smeared representation of phase‐field fracture, reconstructing lower‐dimensional crack paths is challenging, which may impede the further applications of the phase‐field method in the modeling of fault friction and fluid flow in fracture. In the present work, we propose to capture the crack curves or surfaces from two‐dimensional or three‐dimensional phase‐field point cloud using an optimized ridge regression algorithm, and k‐nearest neighbor and principal component analysis are used to estimate the normal direction of each segment on the identified discrete crack path. The sensitivity and computational efficiency of the proposed method are investigated thoroughly. Subsequently, this method is extended to reconstruct the complex discrete fracture networks. Finally, several benchmarks for fracture, fault friction and fluid flow problems are presented to demonstrate the strength of the proposed approach.

Flexural Performance of Steel Bar Reinforced Sea Sand Concrete Beams Exposed to Tidal Environment

The advancement of marine engineering has brought close attention to the durability of concrete structures. In order to investigate the time-varying performance of reinforced concrete beams in a marine environment and to better apply sea sand directly in marine engineering, this paper describes tests and analysis on the flexural performance of reinforced sea sand concrete beams after being exposed to a tidal environment. Eight beams were tested using four-point static loading equipment. The variation parameters included the type of mixing water, longitudinal reinforcement rate, sea sand replacement rate and duration of service. The force damage process and damage pattern were observed. The load–maximum width crack curve and load–deflection curve were obtained. The effects of each variation parameter on the mechanical properties such as ultimate bearing capacity, initial rigidity, energy dissipation coefficient and ductility coefficient were analyzed. The test results show that compared with the specimens exposed to the tidal environment for 90 days, the peak load of the specimens decreased by 5.6%, the initial rigidity decreased by 60.9% and the ductility coefficient decreased by 41% after 270 days of exposure, while the peak deflection and energy dissipation indexes first increased and then decreased. The seawater mixing can enhance the peak load and cracking load of the specimens, but the initial rigidity, peak deflection, energy dissipation coefficient and ductility coefficient of the specimens are reduced to some extent. The initial rigidity of the specimens tended to increase with the increase in the sea sand replacement, but the peak load decreased. Under the same reinforcement rate, reducing the diameter of the reinforcement is beneficial to improve the initial rigidity of the specimen, while using the reinforcement with higher elongation can effectively enhance the peak deflection of the specimen. Based on the Chinese code, the calculation method of flexural bearing capacity with modified concrete strength is proposed, and the calculation results are in good agreement with the test results.

Experimental Study on Shear Transfer Performance of Uncracked Monolithic Steel Fiber Concrete

Shear transfer performance at interface of steel fiber reinforced concrete (SFRC) is of great importance that many factors influence the shear transfer performance of SFRC such as concrete strength and aggregate interlock, reinforcement dowel action and steel fiber. Many studies have focused on part of the factors. The shear transfer performance of uncracked monolithic SFRC is studied in this paper by considering the combined effects of cohesion, clamping stress, confined stress, reinforcement, and steel fiber. Thus, this study presents a series of direct shear tests by Z-type push-off specimens. The direct shear strength, failure mode and failure process of plain SFRC and reinforced SFRC are studied, and their shear stress-slip and shear stress-crack width responses of the tested specimens are obtained. Test results showed that reinforcement and steel fibers can improve the ductile behavior and shear strength of the shear interface simultaneously. And shear stress-slip and —crack curves of the test specimens with those combined effects are strongly nonlinear. Finally, based on the existing shear strength calculation model and the test results of this paper, a shear transfer calculation formula of SFRC interface is proposed and verified according to the Mohr Coulomb failure criteria.

Variation of Fracture Toughness with Biaxial Load and T-Stress under Mode I Condition

The effect of a biaxial load on brittle fractures of solids under predominantly elastic deformation and mode I loading conditions is studied in this article. A cross-shaped specimen is used in this work, and the variation of T-stress is achieved by changing the load applied to the arm parallel to the crack. In the tests, under a series of different loads parallel to the crack, a series of load values perpendicular to the crack are obtained, and the stress intensity factor is calculated by FEM (Finite Element Analysis). The test data demonstrate that the apparent fracture toughness of the material varies with the load parallel to the crack and the T-stress, since the T-stress is directly related to the load parallel to the crack. If only the first term of the Williams series solution is used to describe the stress field near the crack tip, the variation of KC is unexplained; therefore, more than one term in the Williams series solutions is used to develop the theory of biaxial effect on solid fracture behavior. The fracture criterion based on this consideration is also used to predict crack instability or crack curving under mode I load conditions. Experimental data are presented and compared with the theory.

Flexural behavior of GFRP bars reinforced seawater sea sand concrete beams exposed to marine environment: Experimental and numerical study

Experimental and numerical investigations were conducted on the flexural behavior of GFRP bars reinforced seawater sea sand concrete (GFRP-reinforced SWSSC) beams after exposed to marine environment. A total of eight beams were tested by using a four-point static loading facility. Variables included the exposure environment, the exposure duration, the water for mixing and curing, and the sea sand replacement ratio. The failure process and failure modes of the specimens were observed, the load versus deflection curves and the deflection versus maximum width crack curves were obtained. The effects of various parameters on the ultimate bearing capacity, initial stiffness, and ductility coefficient were analyzed. In addition, the finite element analysis (FEA) method was used to simulate the flexural behavior of GFRP-reinforced SWSSC beams, and the parametric analysis was then conducted to investigate the effect of reinforcement ratio and shear-to-span ratio on the flexural behavior of the beam. The test results show that, after 270 days of exposure, compared with the general atmospheric environment, the ultimate bearing capacity of the specimen is increased by 28.0 % after being exposed to salt-spray environment while decreased by 13.0 % after being exposed to tidal environment. During a 270-day exposure duration to tidal environment, with the increase of the exposure duration, the ultimate bearing capacity increases first and then decreases, while both the initial stiffness and ductility coefficient of specimens decrease. The use of seawater for mixing and curing is detrimental to the initial stiffness and ductility coefficient of the specimens. The increase in sea sand replacement ratio is detrimental to specimens' ultimate bearing capacity and initial stiffness. Besides, FEA results indicate that increasing the longitudinal reinforcement ratio can obviously improve the ultimate bearing capacity and the post-cracking stiffness of the specimen. Based on the current China, America, and Canada codes, the calculation method of the flexural capacity of GFRP-reinforced SWSSC beams exposed to marine environment is discussed and the prediction value of long-term ultimate bearing capacity is given.

Texture Feature Extraction and Morphological Analysis of Landslide Based on Image Edge Detection

Landslides in nature are harmful to economic development and people’s lives and cause irreparable losses to the environment. With the application of image detection technology and intelligent algorithm, a new way for landslide detection is proposed to achieve effective detection and identification of hazards. This paper takes the landslide as the data set, carries on the noise reduction, the image expansion, and the image segmentation processing to the image, and extracts the object region information. The quantitative description of the azimuth displacement and displacement change of the crack curve is completed in this paper. This method is suitable for 3D simulation model, sand and stone model, soil model, and the sliding test results of Panzhihua Flight Field, which proves that the design method is effective. Experiments show that when sliding occurs, the texture and color become chaotic, the usual mountain becomes more in the regular state, and the extraction of features is very different. The method has better recognition effect for the hillside covered with vegetation, the recognition time is short, and the recognition rate can reach 90%.

Pavement crack detection using non‐local theory and iterative sampling

Crack is a common form of road distress and a key study of an intelligent transportation system. However, automatic pavement crack detection is a very challenging task due to noisy texture background, intensity inhomogeneity, and topology complexity. In this paper, a new pavement crack detection algorithm to address these issues is proposed. First, non-local block matching strategy and local statistical mean are put together to generate the probability map of cracks, which has advantages on automatic threshold choosing and strong resistance to intensity inhomogeneity. Second, an iterative seed points sampling algorithm is proposed, which makes full use of the area and shape of connected regions where the seeds lie in, thus exploiting high reliable crack seeds for following curves extraction. Finally, a minimum spanning tree (MST) is adopted to connect points into crack curves and employ a crack growth method to find out the cracks, which is specified to deal with complex topology of cracks. For parameters, a robust and optimal parameters selection rule is obtained by data driven method. The algorithm is compared with other state-of-the-art algorithms on two datasets. The experiment result shows that the proposed method has a better detection performance on F 1 $F1$ -measure score over other methods.

Pavement crack detection using hessian structure propagation

Pavement images are widely used in transportation agencies to detect cracks accurately so that the best proper plans of maintenance and rehabilitation could be made. Although crack in a pavement image is perceived because the intensity of crack pixels contrasts with that of the pavement background, there are still challenges in distinguishing cracks from complex textures, heavy noise, and interference. Unlike the intensity or the first-order edge feature of crack, this paper proposes the second-order directional derivative to characterize the directional valley-like structure of crack. The multi-scale Hessian structure is first proposed to analytically adapt to the direction and valley of cracking in the Gaussian scale space. The crack structure field is then proposed to mimic the curvilinear propagation of crack in the local area, which is iteratively applied at every point of the crack curve to infer the crack structure at the gaps and intersections. Finally, the most salient centerline of the crack within its curvilinear buffer is exactly located with non-maximum suppression along the perpendicular direction of crack. The experiments on large numbers of images of various crack types and with diverse conditions of noise, illumination and interference demonstrate the proposed method can detect pavement cracks well with an average Precision, Recall and F-measure of 92.4%, 88.4%, and 90.4% respectively. Also, the proposed method achieves the best performance of crack detection on the benchmark datasets among methods that also require no training and publicly offer the detection results for every image.

Curve‐based crack detection using crack information gain

Crack detection provides valuable information concerning the location, extent, type, and severity for structural health monitoring of civil infrastructures. Due to the influence of uneven lighting and imaging noise, as well as the debris, various textures, and materials of the different civil structure, detecting cracks in the surface images of civil infrastructures remains challenging in that there are many false positives and defragmentation of the crack curve. In this paper, an information-based crack detection method is developed to robustly characterize and detect cracks on a curve-by-curve basis. Crack information gain (CIG) is defined to characterize the information of a local patch's being cracked. With the proposed model of estimating crack depth, the information-based crack descriptor CIG is calculated by statistically modeling the probabilistic distribution of crack depth. Secondly, crack curves of different saliency are progressively detected by iteratively searching the salient string of pixels, regardless of the small gaps between fragments of the crack curve. Finally, crack curves are validated by examining the variation of CIG along the crack curve. The experimental results on a diverse set of images of different civil infrastructures demonstrate the generalizability of the proposed method, and the overall performance on each dataset outperforms the state-of-the-art available methods with 2.9% improvement. The proposed method has potential for the quantitative evaluation of cracks on a meaningful curve basis.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

Strong imposing Dirichlet boundary conditions remain a challenge for eXtended Finite Element Methods (XFEMs) or eXtended Isogeometric Analysis (XIGA) of discontinuous problems. Moreover, the physical meaning of the additional Degrees of Freedom (DOFs) in the displacement expression of XFEMs or XIGA is not clarified. To address these issues, we proposed a new method that combines XIGA and B++ splines for modeling the fracture behaviors of single and multiple cracks in 2D elasticity solids. We adopt the overlapping trimming curves to represent the crack curves. The control points that the basis functions are non-zeros for the penetrating elements in XIGA are changed into the double-layer collocation points on the crack curves in our proposed method. In doing so, the DOFs of control points of the elements penetrated by the crack in the XIGA are replaced by those of the double-layer collocation points on the crack curves. The movement of the crack edges is simulated by the displacement of collocation points. Thus, the physical meaning of the DOFs of the elements penetrated by the cracks is clarified. As the basis functions of the collocation points on the crack boundary satisfy the Kronecker delta property, the presented method allows strong imposing Dirichlet boundary conditions on the crack edges. The stress intensity factors (SIFs) are calculated by adopting the interaction integral technology. Numerical examples verify the accuracy of the proposed method.

Unique solvability of an equilibrium problem for a Kirchhoff-Love plate with a crack along the boundary of a flat rigid inclusion

A new model of an equilibrium problem for a Kirchhoff-Love plate with a flat cylindrical rigid inclusion and an interfacial crack is considered. As in previous works, we consider a rigid inclusion defined with the help of a cylindrical surface, but unlike the known models relating to the crack theory, we suppose that traces of derivatives of vertical displacements (deflections) satisfy certain boundary conditions. These conditions determine constant angles of normal fibers along an entire flat cylindrical inclusion. The interfacial crack is located on the boundary of the rigid inclusion. A condition of mutual non-penetration of opposite crack faces is given as an inequality on the crack curve. We prove the existence and uniqueness of a solution for this variational problem.

Pavement Crack Detection from Mobile Laser Scanning Point Clouds Using a Time Grid.

This paper presents a novel algorithm for detecting pavement cracks from mobile laser scanning (MLS) data. The algorithm losslessly transforms MLS data into a regular grid structure to adopt the proven image-based methods of crack extraction. To address the problem of lacking topology, this study assigns a two-dimensional index for each laser point depending on its scanning angle or acquisition time. Next, crack candidates are identified by integrating the differential intensity and height changes from their neighbors. Then, morphology filtering, a thinning algorithm, and the Freeman codes serve for the extraction of the edge and skeleton of the crack curves. Further than the other studies, this work quantitatively evaluates crack shape parameters: crack direction, width, length, and area, from the extracted crack points. The F1 scores of the quantity of the transverse, longitudinal, and oblique cracks correctly extracted from the test data reached 96.55%, 87.09%, and 81.48%, respectively. In addition, the average accuracy of the crack width and length exceeded 0.812 and 0.897. Experimental results demonstrate that the proposed approach is robust for detecting pavement cracks in a complex road surface status. The proposed method is also promising in serving the extraction of other on-road objects.

Fracture path of cracks emigrating from two circular holes under blasting load

In rock excavating and mining, blasting a row of circular holes is a common practice. It is often observed that cracks emanating from two adjacent holes tend to avoid each other when closely approached and form a hooked or butterfly-shaped loops. Five crack models were designed in this paper to study the propensity of forming the hook pattern. The five models are to simulate geometric imperfection in the field or laboratory for the two borehole case. Using the T-stress at the crack tip, the incremental crack growth method is adopted to simulate the crack propagation paths. The results showed that: (1) the T-stress values calculated from the first two models are negative, indicating curving (or hooking) cannot occur, (2) the T-stress at the crack tip is positive in the third model, and therefore crack curving (or hooking) may occur, (3) unlike the first three models, the fourth and fifth models are mixed mode I/II crack geometries and the mode II stress intensity factor dictates the crack curving direction, (4) the hook pattern would indeed happen under certain conditions.

Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack

We consider equilibrium problems for a cracked composite plate with a thin cylindrical rigid inclusion. Deformation of an elastic matrix is described by the Timoshenko model. The plate is assumed to have a through crack that does not touch the rigid inclusion. In order to describe mutual nonpenetration of the crack faces we impose a boundary condition in the form of inequality on the crack curve. For a family of appropriate variational problems, we analyze the dependence of their solutions on the location of the rigid inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on the solution space, while the location parameter of inclusion is chosen as the control parameter. The existence of a solution to the optimal control problem and a continuous dependence of the solutions in a suitable Sobolev space with respect to the location parameter are proved.

Research on crack monitoring at the trailing edge of landslides based on image processing

Currently, the frequency of landslides is increasing. Scientific monitoring methods are playing an essential role in effectively reducing landslide disasters. This paper proposes a method for identifying the cracks at the trailing edge of a landslide (TEL) based on image processing technology and adopts the custom interval median comparison algorithm (IMCA) to calculate the crack motion parameters. First, we perform a series of processes on the TEL images, including image preprocessing, Otsu’s algorithm processing, and Canny edge detection processing, to identify the outline of the TEL. Then, we propose using the azimuth and displacement to characterize the motion of the cracks and using the IMCA to calculate the changes before and after motion of any two groups of cracks. Finally, we design a computer program using a free and open-source widget toolkit (named QT platform) based on the calculation model that corresponds to the proposed method, and we apply the crack monitoring test to a 3D simulation model, a gravel model, a soil model, and a collapsed body of the Panzhihua Airport landslide in southwestern China. From the results, it can be assessed that the method can identify the outline of the TEL and calculate the azimuth and displacement of two crack curves before and after motion. These two parameters can describe the movement of the trailing edge cracks of the monitored landslide. Thus, this method can be used in early warning system for landslide hazards.

ПРОИЗВОДНАЯ ФУНКЦИОНАЛА ЭНЕРГИИ В ЗАДАЧЕ О РАВНОВЕСИИ ПЛАСТИНЫ КИРХГОФА ––– ЛЯВА С УСЛОВИЯМИ НЕПРОНИКАНИЯ ДЛЯ ИЗВЕСТНОЙ КОНФИГУРАЦИИ ИЗГИБА

Рассматриваются вариационные задачи теории упругости в области с разрезом, описывающие равновесие пластины с трещиной. Предполагается, что под действием определенных заданных нагрузок пластина имеет деформации с определенной заранее известной конфигурацией кромок вблизи трещины. На кривой в срединной плоскости, соответствующей трещине, заданы краевые условия в виде двух неравенств. В предположении, что параметр описывает возмущение трещины, находится производная функционала энергии по отношению к . Результаты получены для новых математических моделей с новыми краевыми условиями, описывающими специальный характер контактного взаимодействия кромок пластины. Equilibrium problems for elastic plates with a rectilinear crack are studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. Assuming that the parameter describes the crack perturbation, the derivative of the energy functional with respect to is found. The results are obtained for new mathematical models with new nonlinear boundary conditions describing special character of the mechanical contact interaction of the plate edges.

Structural fatigue investigation of transverse surface crack growth in rail steels and thermite welds subjected to in-plane and out-of-plane loading

This study investigates the structural fatigue crack growth behavior of observed transverse surface cracks in rail steel and thermite weld subjected to in-plane and out-of-plane loading. Stress Intensity Factor (SIFs) solutions were derived from finite element model analysis for transverse surface cracks located at five different crack initiation locations in the cross-section of rail steel and thermite weld. The SIFs were presented by the conventional geometry factor Y and weld magnification factor Mk solutions for rail steel and thermite weld. Fracture toughness and fatigue crack growth rate tests were conducted to determine the mechanical properties of thermite weld materials and are compared with reported data for rail steels (R260 and R350HT). Fatigue crack growth prediction algorithm was developed using the coupled root mean square integration approach and was compared with the conventional uncoupled two-degree of freedom approach for semi-elliptical surface crack growth in the depth and surface directions respectively. The fatigue crack growth algorithm and propagation life prediction provide valuable observations on the crack shape evolution. It proves that out-of-plane bending loading is a more significant failure mode as compared to in-plane bending loading for thermite weld joints at curve tracks. Fatigue crack propagation results provide fatigue stress range-life curves for weld-toe surface cracks initiated at the head-to-web region of thermite welded joint structure.