Linear Crack Research Articles

An investigation on a two-dimensional problem of Mode-I crack in a thermoelastic medium

In this work, we consider a two-dimensional dynamical problem of an infinite space with finite linear Mode-I crack and employ a recently proposed heat conduction model: an exact heat conduction with a single delay term. The thermoelastic medium is taken to be homogeneous and isotropic. However, the boundary of the crack is subjected to a prescribed temperature and stress distributions. The Fourier and Laplace transform techniques are used to solve the problem. Mathematical modeling of the present problem reduces the solution of the problem into the solution of a system of four dual integral equations. The solution of these equations is equivalent to the solution of the Fredholm’s integral equation of the first kind which has been solved by using the regularization method. Inverse Laplace transform is carried out by using the Bellman method, and we obtain the numerical solution for all the physical field variables in the physical domain. Results are shown graphically, and we highlight the effects of the presence of crack in the behavior of thermoelastic interactions inside the medium in the present context, and its results are compared with the results of the thermoelasticity of type-III.

Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems

The displacement discontinuity method (DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue, enlightened by the mapped finite element method (FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM (MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.

Radiographically recognizable? An investigation into the appearance of osteomalacic pseudofractures

Pseudofractures, lucent bands that occur due to a build-up of osteoid, are a key feature of osteomalacia. In paleopathology, pseudofractures are often marked by small, linear cracks in the cortex of the bone surrounded by irregular, bony spicule formation. Radiography can be used to help diagnose pseudofractures, both clinically and in paleopathology. A detailed understanding of the radiographic appearance of pseudofractures and their development is, therefore, necessary to aid a diagnosis of vitamin D deficiency. The present study examined the clinical literature to determine current ideas on the appearance of pseudofractures with the aim of applying this knowledge to paleopathology. A radiographic study of the characteristics of pseudofractures was performed on five individuals with clear skeletal features of osteomalacia from archaeological sites in Canada and the United Kingdom dating to the medieval period (5th to 15th centuries) and the 18th to 19th century. Results show that the radiographic appearance of pseudofractures could potentially reveal information about the cause of the deficiency and the chronicity of pseudofractures. This type of information has the potential to further our understanding of the lived experiences of archaeological individuals with osteomalacia.

Experimental research on resistance of infrared optical windows to erosion caused by ice particle impact

The erosion resistance of infrared optical windows was studied experimentally using ice particles of 2mm diameter. Single ice particles were accelerated to approximately Mach 4.7 using a two-stage light gas gun. Sapphire and zinc sulfide infrared optical windows were tested. The windows were impacted repeatedly until a linear or circumferential crack was found. From the normal impact tests, it was found that uncoated and AR-coated infrared windows have similar erosion characteristics. Damage threshold curves were determined from the test data to characterize the erosion resistance of the windows. From oblique impact tests, it was found that resistance to erosion from normal and oblique impacts is related by a trigonometric function based on damage threshold velocity (DTV).

Torsion of circular anisotropic beam with two linear cracks, weakened with a circular cavity

Various components made of anisotropic materials (plast-mass, glass material, etc.) have been widely used in the production of modern mechanisms and machinery. Precise calculation of these elements, constituting the design, holds great importance. In general, fracture and distribution are essential issues in safety calculations. In this study, torsion of a beam with an S oblast having outer and inner constraints as L2 and L1 circles with R2 and R1 radii, respectively, is investigated.

Reliability analysis of wind turbines under non‐Gaussian wind load

SummaryBased on translation models, both Gaussian and non‐Gaussian wind fields are generated using the harmony superposition method for examining the reliability of a typical wind turbine at operational and parked conditions. Using the blade aerodynamic model and multibody dynamics, wind turbine responses are calculated and then probability characteristics are analyzed in details. The short‐term extreme response distribution is estimated by the average conditional exceedance rate method at each mean wind speed bin, and the long‐term extreme response distribution is then determined by further integrating the short‐term extreme response distribution conditional on wind speed with the distribution of mean wind speed. Additionally, crack initiation life and crack propagation life are evaluated using the linear cumulative damage theory and linear crack propagation theory, respectively. The results indicate that non‐Gaussian characteristics of wind inflows have a noticeably greater influence on both extreme response and fatigue damage, and the Gaussian assumption cannot suit wind turbine in complex terrain.

Method to analyse multiple site damage fatigue before and after crack coalescence

The Multiple Site Damage is a phenomenon that appears in e.g. aircraft fuselages and weld geometries. This article introduces a method for solving the Multiple Site Damage fatigue in a 2D specimen. The cases studied are for Linear Elastic Fracture Mechanics situations, isotropic materials and crack growth governed by the Paris Law regime. Already known fracture mechanics concepts are merged together in an innovative algorithm that increases computational efficiency by optimizing the number of Finite Element Analyses necessary for fatigue calculations. A new approach to crack coalescence is presented by using the application limit of Linear Elastic Fracture Mechanics. Comparisons with analytical, experimental and other software results have shown the reliability of this method for several cases. A final explanatory example of a plate with multiple cracks and a hole shows the capabilities of the method proposed.

Predictions of fracture load, crack initiation angle, and trajectory for V-notched Brazilian disk specimens under mixed mode I/II loading with negative mode I contributions

In this paper, first the fracture load, the crack initiation angle and the crack trajectory are experimentally measured for the round-tip V-notched Brazilian disk specimen made of polymethyl-methacrylate under compressive-shear loading. Then, the fracture load and the crack initiation angle are predicted by using the extended finite element method on the basis of the linear cohesive crack criterion. The fracture trajectory of the round-tip V-notched Brazilian disk specimens is also estimated by means of the extended finite element method and the incremental methods. Both the experimental observations and the theoretical fracture models indicate that although the notch bisector line is under compressive-shear loading, one half of the notch border still sustains tensile stresses and fracture takes place from this half. A very good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.

Theoretical and numerical prediction of crack path in the material with anisotropic fracture toughness

The crack path in the anisotropic medium is studied theoretically and numerically in this paper, with focusing on the effects of the anisotropic fracture toughness. A weak plane model is adopted to characterize the anisotropic fracture toughness and the maximum energy release rate criterion (MERR) is chosen to predict the crack path. We prove that the crack deflecting direction in a weak plane material, theoretically, only relates to the weak plane direction, the weakness of the plane, and the ratio of stress intensity factors before crack extending. Two critical weakness ratios are found: one is for that the weak plane captures all cracks for any loading state; the other is for that the weak plane traps the crack once it is deflected to the plane. To further numerically study the complex crack path in an anisotropic medium, the extended finite element method (XFEM) embedded MERR criterion and weak plane model is developed, in which a mesh independent piecewise linear crack formulation is proposed to capture the curved crack path. By modeling the three point bending loading test, the influences of the weak plane angles and the weaknesses on crack path deflection are studied, and periodically oscillatory crack path behaviors are found as observed in experiments. Further more, the crack extending through multiple layers of weak plane material and isotropic material is numerically studied, which shows that the crack diffracts at the material interface, and the crack path in the anisotropic toughness material is rougher than in the isotropic material. The presented work in this paper will be helpful to understand and control the crack path in the rocks as well as other anisotropic materials.

A continuous–discontinuous hybrid boundary node method for solving stress intensity factor

A novel boundary type meshless method called continuous–discontinuous hybrid boundary node method is proposed in this paper, in which the enriched discontinuous shape function is developed to solve linear elastic crack problems. Firstly, the whole boundary is divided into several individual segments, and variables on each one of those segments are interpolated, respectively. For continuous segments, radial point interpolation method is employed. In regard to discontinuous segments, the enriched discontinuous basis functions combining with radial point interpolation method are developed for simulating the discontinuity of displacement and stress field on surfaces of crack, and the near tip asymptotic field functions are employed for simulating the high gradient of stress field around crack tip, so that high accuracy and discontinuity property of a crack can be easily described. Stress intensity factors are calculated directly using displacement extrapolation by displacement field near crack tip. Some numerical examples are shown that the present method is effective and can be widely applied in some practical engineering.

Explicit relationship between electrical and topological degradation of polymer-supported metal films subjected to mechanical loading

For a comprehensive characterization of mechanical reliability of metallization layers on polymer substrates, both electrical and mechanical degradation should be taken into account. Although it is evident that cracking of a conductive film should lead to electrical degradation, the quantitative relationship between the growth of electric resistance and parameters of the induced crack pattern has remained thus far unexplored. With the help of finite element modelling, we were able to find an explicit and concise expression which shows that electrical resistance grows with the fourth order of the crack length and second order of the areal crack density. The discovered relationship was verified by comparison with the experimental results of tensile testing of polymer-supported thin metal films. The presented model is independent of the length scale and can be applied to films with different thicknesses as long as Ohm's law is valid. It is demonstrated that the linear crack density is an ambiguous parameter, which does not properly capture the development of a crack pattern. For the unambiguous characterization of the intensity of a crack pattern, a universal dimensionless factor is proposed. The presented results show that there is a wide range of possible crack patterns which do not lead to electrical failure of a conductive film that can be used for the failure-free design of flexible electronic devices.

Effects of the 2016 Kumamoto earthquakes on the Aso volcanic edifice

Large earthquakes occurred in the central part of Kumamoto Prefecture on April 14–16, 2016, causing severe damage to the northern segment of the Hinagu faults and the eastern segment of the Futagawa faults. Earthquake surface ruptures appeared along these faults and on the Aso volcanic edifice, which in turn generated landslides. We conducted landform change analysis of the central cones of Aso volcano by using satellite and aerial photographs. First, we categorized the topographical changes as surface scarps, arc-shaped cracks, and linear cracks. Field survey indicated that landslides caused the scarps and arc-shaped cracks, whereas faulting caused the linear cracks. We discovered a surface rupture concentration zone (RCZ) formed three ruptures bands with many surface ruptures and landslides extending from the west foot to the center of the Aso volcanic edifice. The magmatic volcanic vents that formed during the past 10,000 years are located along the north margin of the RCZ. Moreover, the distribution and dip of the core of rupture concentration zone correspond with the Nakadake craters. We conclude that a strong relationship exists between the volcanic vents and fault structures in the central cones of Aso volcano.Graphical abstract.

Influences on morphology and biomechanics in rabbit’s femur cortex of ovariectomy

Objective To investigate the influences on the femur cortex of the rabbit after ovariectomy and its mechanism. Methods Eighty 6 months-old female pure New Zealand rabbits were divided into two groups: 40 rabbits in ovariectomy group and 40 in sham-operation group. The weight averaged 2.2±0.28 kg. Four weeks and 8 weeks after operation, a series of tests were performed in both groups concerning the number, the volume, the rate and the maximal load of cortical bone porosity. The number, the length and the density of linear crack in rabbit femur cortex were documented after repetitive application of minor trauma. Results Micro-CT demonstrated that both on week 4 and 8 after operation, the number, the volume and the rate of cortical bone porosity were all significantly higher in ovariectomy group than that of the control group. Four weeks after operation, the biomechanical test showed the significantly lower average maximal load of rabbit femur in ovariectomy group (1 892.60±59.09) than that of in control group (1 949.25±53.12) (P=0.003). Eight weeks after operation, the average load of both groups decreased to some extent, which was 1 944.55±41.76 in control group and 1 692.40±85.08 in ovariectomy group respectively (P=0.000). However, the average maximal load of ovariectomy group decreased more significantly. Having application of repetitive minor trauma to the bone, the number, the length and the density of linear crack of cortical bone were 3.40±1.67, 216.80±17.60 μm and 0.40±0.08/mm2 in ovariectomy group, and 2.00±1.17, 160.45±16.89 μm and 0.29±0.13/mm2 in control group 4 weeks later. And after 8 weeks, they were 5.15±1.18, 334.60±13.94 μm and 0.35±0.10/mm2 in ovariectomy group, and 3.10±1.37, 182.10±9.80 μm and 0.24±0.09/mm2 in control group. The number, the length and the density of linear crack of cortical bone were all significantly higher in ovariectomy group than that of in control group both on week 4 and on week 8 after operation. Conclusion Ovariectomy increases the porosity of cortical bone of rabbit, destroys its biological property, accelerates the fatigued damage and delays the healing process. These changes may be attributed to fracture and delayed union after fracture. Key words: Rabbits; Ovariectomy; Femur; Biomechanics

The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study

In this work, the natural neighbor radial point interpolation method (NNRPIM) is extended to the numeric analysis of crack propagation problems. Here, the advanced discretization meshless technique is combined with a linear elastic crack growth algorithm. The algorithm simulates the crack propagation by displacing iteratively the crack tip, which consequently requires a local remeshing. In each iteration, it is estimated the stress state in the crack tip and afterwards the direction of the crack propagation is obtained considering the maximum circumferential stress criterion.The required local remeshing does not represent a numeric difficulty for the NNRPIM. The main advantage of the NNRPIM is its capability to fully discretize the problem domain using only an unstructured nodal distribution. Being a truly meshless method, the NNRPIM is able to define autonomously the nodal connectivity and the background integration mesh.The classic NNRPIM formulation permits to enforce the nodal connectivity by means of two kind of influence-cells: first degree influence-cells or second degree influence-cells. This work investigates the influence of the nodal connectivity on the simulated crack propagation path. Thus, demanding benchmark crack propagation examples are studied and the obtained results are compared with reference solutions available in the literature.

Moment tensor analysis of transversely isotropic shale based on the discrete element method

In this study, the moment tensor of transversely isotropic shale was analyzed using a discrete element method-acoustic emission model (DEM-AE model). Firstly, the failure modes of the shale obtained from the acoustic emission (AE) events and physical experiments were compared. Secondly, the relationships between AE events and seismic magnitudes, and AE events and the resulting cracks were analyzed. Finally, a moment tensor T-k chart describing the seismic source was introduced to demonstrate the differences in the transversely isotropic shale. The results showed that, for different anisotropy angles, a linear logarithmic relationship existed between the cumulative AE events and the seismic magnitude in the concentration area of the AE events. A normal distribution was observed for the number of AE events as the seismic magnitude changed from small to large. The moment tensor T-k chart indicated that the number and proportion of linear tension cracks in the shale were highest. When θ=30°, the peak seismic magnitude was at a minimum. The average seismic magnitude in the concentration area of the AE events was also relatively small. Points close to the U=−1/3V line and the number of cracks included in a single AE event were at a minimum, and the corresponding peak stress also reached its lowest level. In contrast, when θ=90°, all related parameters were contrary to the above θ=30° case. The DEM-AE model and the moment tensor T-k chart are suitable for analyzing the distribution of shale cracks appearing during the loading process. This study can provide constructive references for future research on the fracturing treatment of shale.

Lamb Waves in a Perpendicularly Cracked, Poroelastic Plate

In this paper, we continue our work on the propagation of Lamb waves in a poroelastic infinite strip containing a linear crack. In the previous work, the crack was placed horizontal to the upper and lower surfaces and moreover, there was zero pressure on the upper and lower surfaces, a physically impossible situation. In the present paper, the crack is situated perpendicular to the side and situated at the origin. A step stress is applied to the crack surface resulting in transient behavior. By using the Fourier transform and Laplace transform methods, we arrive at dual integral equations. From this formulation, we subsequently obtain, by reduction, a Fredholm integral equation of the second kind. This equation is solved numerically, and the dynamic stress intensity factor is shown graphically.

Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig3-CNS (NMM) element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig3-CNS (NMM) element can be considered as a development of both the Trig3-CNS element and the numerical manifold method (NMM). Inheriting all the advantages of Trig3-CNS element, calculations using Trig3-CNS (NMM) element can obtain higher accuracy than Trig3 element without extra degrees of freedom (DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig3-CNS (NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper, complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig3-CNS (NMM) element. Numerical results show that the Trig3-CNS (NMM) element is prominent in modeling complex crack problems.

Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique (Duflot and Bordas, 2008) is used to quantify the interpolation error. Based on this error distribution, four strategies relying on two different mesh optimality criteria are compared. The first aims at homogenizing the error distribution. The second minimizes the total number of elements given a target global error level. We study the behaviour of these criteria in the context of cracks treated by an X-FE approach. In particular, we investigate the convergence rates at the element-level depending its enrichment type. We conclude on the most suitable refinement criterion and propose and verify a strategy for mesh adaptation on 3D damage tolerance assessment problems.

Safe life approach considering creep-fatigue interaction and Weibull statistics for crack growth evaluation based on field feedback applied to a GT first stage blade

The increased flexibility that the energy market requires makes the service condition of gas turbine (GT) components more and more critical in terms of creep-fatigue interaction. A new lifing strategy has been developed in order to evaluate the expected life of blades and vanes in this demanding service condition taking into consideration creep-fatigue interaction. The developed lifing methodology has been applied to the first stage blade of an Ansaldo Energia F-class GT and the life map has been compared with the available field feedback. With this procedure crack initiation in the base material is considered as the lifing criteria. So, the critical locations have been correctly identified and the number of predicted cycles correspond to service experience. The available field feedback has been treated by using Weibull statistics. The statistical treatment of crack size for the critical locations provides a crack initiation evaluation that is in good agreement with the lifing strategy. Moreover, the available field feedback on the first stage blade allows the correlation of the linear crack size with its depth. This relationship has been used to define the maximum allowable crack length for safe operation of this component.

A Fast and Adaptive Road Defect Detection Approach Using Computer Vision with Real Time Implementation

Road defect is one of the most important factors for traffic accident. Therefore, these defects should be corrected as soon as possible. It usually occurs cracks, rutting, and potholes in road surface. These errors are based on the fact that people have recognized and fixed these errors in our day. But if these errors are not corrected in a short time, the size of the error grows day by day. There are various methods used to detect road errors in the literature. One of these methods is the use of computer vision. There are various types of roads in real life. Since the studies in the literature have been carried out only by taking into account one type of road, the accuracy rates decrease when these studies are used in different types of roads. In the study carried out, different roads have been made adaptive by the operations performed in the detection of road errors from the received images. Images taken from the camera on a vehicle are used for the study. The study applied is ensured to have high accuracy rates in different types of roads via customization. In the second stage, the image blurred by using median filter and the unprocessed images are collected, and the darkest parts of the image are brought into the forefront. The image is converted into a binary image and improved by mathematical morphological operations. As a result of the operations performed, which of the five classes including un-cracked roads, superficial crack, crocodile crack, linear crack and transverse crack the roads belong to is determined. In the study carried out, the fact that it is fast and that its accuracy rates are good indicate that it can be used in real life.