Artykuły w czasopismach: „Crack tip element”

1

Liu, C. H., and Jui-Hsiang Lin. "Finite Element Analysis of Interface Cracks Using Multiple Point Constraints." Journal of Strain Analysis for Engineering Design 41, no. 4 (May 1, 2006): 311–21. http://dx.doi.org/10.1243/03093247jsa112.

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A finite element technique to analyse closed-mode interface cracks is proposed in this study. Stress boundary conditions for a closed-tip model are transformed into multiple point constraints (MPCs) for nodal displacements. These constraints are imposed upon the finite element solutions to simulate closed-tip stress fields in crack-tip elements. This technique can deal with small as well as large crack-tip contact zones, and no special elements other than the standard quarter-point elements are needed. Since stresses approach infinity at the crack tip in a quarter-point element, dominant terms are used in deriving MPCs for nodal displacements. Fracture parameters are obtained by using the virtual crack extension method, and numerical results are in good agreement with analytical results.

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2

Yan, Xiangqiao. "An Efficient and Accurate Numerical Method of Stress Intensity Factors Calculation of a Branched Crack." Journal of Applied Mechanics 72, no. 3 (May 1, 2005): 330–40. http://dx.doi.org/10.1115/1.1796449.

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Based on the analytical solution of Crouch to the problem of a constant discontinuity in displacement over a finite line segment in an infinite elastic solid, in the present paper, the crack-tip displacement discontinuity elements, which can be classified as the left and the right crack-tip elements, are presented to model the singularity of stress near a crack tip. Furthermore, the crack-tip elements together with the constant displacement discontinuity elements presented by Crouch and Starfied are used to develop a numerical approach for calculating the stress intensity factors (SIFs) of general plane cracks. In the boundary element implementation, the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called the hybrid displacement discontinuity method (HDDM). Numerical examples are given and compared with the available solutions. It can be found that the numerical approach is simple, yet very accurate for calculating the SIFs of branched cracks. As a new example, cracks emanating from a rhombus hole in an infinite plate under biaxial loads are taken into consideration. The numerical results indicate the efficiency of the present numerical approach and can reveal the effect of the biaxial load on the SIFs. In addition, the hybrid displacement discontinuity method together with the maximum circumferential stress criterion (Erdogan and Sih) becomes a very effective numerical approach for simulating the fatigue crack propagation process in plane elastic bodies under mixed-mode conditions. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the HDDM. Crack propagation is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented.

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3

Lenkovskiy, T. M., V. V. Kulyk, Z. A. Duriagina, R. A. Kovalchuk, V. G. Topilnytskyy, V. V. Vira, T. L. Tepla, O. V. Bilash, and K. I. Lishchynska. "An effective crack tip region finite element sub-model for fracture mechanics analysis." Archives of Materials Science and Engineering 2, no. 87 (October 1, 2017): 56–65. http://dx.doi.org/10.5604/01.3001.0010.7446.

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Purpose: To create an effective in engineering strength calculation three-dimensional submodel of the near crack tip region in solids for hi-fidelity analysis of their stress-strain state by the finite element method. Design/methodology/approach: To create a volume near the crack tip, regular threedimensional 20-node prismatic isoparametric elements and 15-node special elements with edge length of 12.5 μm with shifted nodes in order to simulate the singularity of stress at the crack tip were used. Using these two types of elements, a cylindrical fragment of diameter of 100 μm was built. In its base is a 16-vertex polygon, and its axis is the crack front line. In the radial direction the size of the elements was smoothly enlarged by creating of 5 circular layers of elements, and in the axial direction 8 layers were created. For convenience of the sub-model usage, the cylindrical fragment was completed by regular elements to a cubic form with edge size 400 μm. For the sub-model approbation, the full-scale three-dimensional models of standard specimens with cracks were built. The stress intensity factor K at normal tension was calculated assuming small scale yielding conditions in a plane between 4th and 5th layers of special elements on the basis of analysis of displacement fields near the crack tip. Findings: An effective three-dimensional sub-model of the near crack tip region is proposed. The sub-model was used to obtain the dependence of the stress intensity factor on the relative crack length at normal tension for four types of standard specimens. The obtained dependences show excellent correlation with known analytical solutions. Research limitations/implications: The concept of finite element meshing at threedimensional modelling of the near crack tip region for high-fidelity stress-strain state analysis was generalized. A sub-model of the near crack tip region was created and used to determine the stress intensity factor at normal tension of four types of standard specimens. It is shown that the proposed methodology is effective for precise analysis of the stressstrain state of solids with cracks within the framework of linear fracture mechanics. Practical implications: By applying the generalized approach and the proposed threedimensional sub-model of the near crack tip region, one can determine the stress-strain state of structure elements and machine parts when analysing their workability by the finite element method. Originality/value: An effective finite-element sub-model for the stress-strain state analysis in the vicinity of the crack tip within the framework of the linear fracture mechanics is proposed.

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4

Zhong, Zhi Peng, Shui Wan, and Lin Yun Zhou. "A new Interface Element Method on Computation of the Interface Crack Propagation Energy Release Rate." Applied Mechanics and Materials 204-208 (October 2012): 4573–77. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4573.

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A new interface element method was proposed to calculate the strain energy release rates(SERR) based on the virtual crack closure technique (VCCT). A Lagrange multiplier was introduced between the node pair at crack tip to obtain the internal forces. Then from the VCCT, the SERR was solved by using the forces and displacements near the crack tip. Examples for stationary cracks under the two typical cases are given. Meanwhile, the relationship curves between crack energy release rate and the length of crack, plate depths were plotted respectively.The example shows that the interface element used to calculate the SERR is simple, efficient, and highly accurate in analysis of 2D crack growth problems, and without requiring the special singularity element or collapsed element at crack tip.

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5

Selvadurai, A. P. "Nonlinear mechanics of cracks subjected to indentation." Canadian Journal of Civil Engineering 33, no. 6 (June 1, 2006): 766–75. http://dx.doi.org/10.1139/l06-019.

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The paper presents the application of a boundary element technique to study the behaviour of plane cracks that are located at corner regions of an elastic solid and open during indentation. In particular, the surfaces of the planes on which indentation takes place also exhibit Coulomb frictional responses and degradation in the friction angle with plastic energy dissipation. An incremental boundary element formulation, in which special singularity elements model the behaviour at the crack tip, is used to examine the crack problems. The methodology is applied to investigate the mode I stress intensity factor at the crack tip located at the base of a V-notch in a test specimen.Key words: indented cracks, boundary element modelling, Coulomb friction, stress intensity factors

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6

Chu, Seok Jae, and Cong Hao Liu. "Finite Element Simulation of Stable Fatigue Crack Growth Using Critical CTOD Determined by Preliminary Finite Element Analysis." Advanced Materials Research 891-892 (March 2014): 1675–80. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.1675.

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Finite element simulation of stable fatigue crack growth using critical crack tip opening displacement (CTOD) was done. In the preliminary finite element simulation without crack growth, the critical CTOD was determined by monitoring the ratio between the displacement increments at the nodes above the crack tip and behind the crack tip in the neighborhood of the crack tip. The critical CTOD was determined as the vertical displacement at the node on the crack surface just behind the crack tip at the maximum ratio. In the main finite element simulation with crack growth, the crack growth rate with respect to the effective stress intensity factor range considering crack closure yielded more consistent result. The exponents m in the Paris law were determined.

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7

Choi, Hyeon Chang. "The Prediction of Fatigue Crack Opening Behavior Using Cyclic Crack Tip Opening Displacement by Finite Element Analysis." Key Engineering Materials 324-325 (November 2006): 295–98. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.295.

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An elastic-plastic finite element analysis (FEA) is performed to examine the opening behavior of fatigue crack, where the contact elements are used in the mesh of the crack tip area. The relationship between fatigue crack opening behavior and cyclic crack tip opening displacement was studied in the previous study. In this paper, we investigate the effect of the element size when predict fatigue crack opening behavior using the cyclic crack tip opening displacement obtained from FEA. The cyclic crack tip opening displacement is well related to fatigue crack opening behavior.

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8

Hai, Gong, Yi Bin, Wu Yunxin, Liao Zhiqi, Liu Yaoqiong, and Du Fei. "Integral Aircraft Wing Panels with Penetration Cracks: The Influence of Structural Parameters on the Stress Intensity Factor." Applied Sciences 10, no. 12 (June 16, 2020): 4142. http://dx.doi.org/10.3390/app10124142.

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The finite element model of integral wing panels with central penetration cracks under bending load was established, and the crack propagation process of the aircraft panel was simulated. The stress intensity factor (SIF) of the crack tip during crack propagation under varying conditions of crack length and panel structural parameters was determined. The effects of the panel structure parameters and crack size on the crack tip SIF were obtained. The regression analysis of the finite simulation element results has been performed and a regression model of SIF at the crack tip of the integral panel has been established, the determination coefficient of the regression model is 0.955.

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9

Hinneh, Perry, and Pi Hua Wen. "Displacement Correlation Technique for Interface Crack by FEM." Key Engineering Materials 713 (September 2016): 346–49. http://dx.doi.org/10.4028/www.scientific.net/kem.713.346.

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Interface crack is evaluated using modified quarter point crack tip displacement method. Quarter point elements around the crack tip were employed in the Finite Element (ABAQUS) analysis to determine the near crack tip grid point displacements. In this study, a technique is adopted in which the crack opening displacement of the near crack tip grid point is forced to satisfy a known constraint. The linear term in the distance around the crack tip is reduced to zero. The complex stress intensity factor for interface crack is determined using the quarter point and the displacement correlation technique. It is well observed that FEM produce a less reliable displacement approximation around interface crack tip. However, this report will show that the use of near crack tip open displacement as determined by the standard finite element method can be utilised to give satisfactory result for the interface stress intensity factors K1 and K2.

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10

Gray, L. J., A. V. Phan, Glaucio H. Paulino, and T. Kaplan. "Improved quarter-point crack tip element." Engineering Fracture Mechanics 70, no. 2 (January 2003): 269–83. http://dx.doi.org/10.1016/s0013-7944(02)00027-9.

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11

Liu, C. H., and Chunta Huang. "Oscillatory crack tip triangular elements for finite element analysis of interface cracks." International Journal for Numerical Methods in Engineering 58, no. 12 (2003): 1765–83. http://dx.doi.org/10.1002/nme.831.

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12

Jayaswal, K., and I. R. Grosse. "Finite element error estimation for crack tip singular elements." Finite Elements in Analysis and Design 14, no. 1 (August 1993): 17–35. http://dx.doi.org/10.1016/0168-874x(93)90076-3.

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13

Choi, Hyeon Chang, and Hyeon Ki Choi. "A Study on the Relationship between Fatigue Crack Growth Behavior and Cyclic Crack Tip Opening Displacement." Key Engineering Materials 326-328 (December 2006): 1051–54. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1051.

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The relationship between fatigue crack growth behavior and cyclic crack tip opening displacement is studied. An elastic-plastic finite element analysis (FEA) is performed to examine the growth behavior of fatigue crack, where the contact elements are used in the mesh of the crack tip area. We investigate the relationship between the reversed plastic zone size and the changes of the cyclic crack tip opening displacement along the crack growth. The cyclic crack tip opening displacement is related to fatigue crack opening behavior.

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14

Chung, Kwang Hwa, J. S. Kim, J. S. Kim, and Young Jin Kim. "Three-Dimensional Elastic-Plastic Finite Element Analysis of Biaxially Loaded Cracked Plates." Key Engineering Materials 261-263 (April 2004): 699–704. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.699.

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Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE)analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and cracked tip stresses for biaxially loaded plate with a through-thickness crack and semi-elliptical surface crack. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.

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15

Kim, H. S., K. S. Kim, and Young Seog Lee. "Finite Element Simulation of Crack Propagation Under Mixed Mode Loading Condition Using Element Removing Method." Key Engineering Materials 345-346 (August 2007): 501–4. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.501.

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In this study, we introduce an approach which simulates crack propagation under mixedmode loading condition. In comparison with the conventional element removing method which eliminates any element that satisfies a prescribed failure criterion near the crack tip, the present approach selects a set of elements ahead of the crack tip on the crack growth direction and removes them one by one when the element meets a prescribed failure criterion. Compact tension shear (CTS) specimens of type 304 stainless steel were used for failure testing. Finite element simulation has been carried out to simulate crack profiles and compared with observed ones. Results showed the proposed element removing algorithm is useful for crack growth simulation under mixed mode loading condition. The experimentally measured crack growth profile is in an agreement with the predicted ones.

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Ramalho, L. D. C., J. Belinha, and R. D. S. G. Campilho. "A New Crack Propagation Algorithm Combined with the Finite Element Method." Journal of Mechanics 36, no. 4 (April 1, 2020): 405–22. http://dx.doi.org/10.1017/jmech.2020.1.

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ABSTRACTThe prediction of crack propagation is an important engineering problem. In this work, combined with triangular plane stress finite elements, a new remeshing algorithm for crack opening problems was developed. The proposed algorithm extends the crack iteratively until a threshold maximum crack length is achieved. The crack propagation direction is calculated using the maximum tangential stress criterion. In this calculation, in order to smoothen the stress field in the vicinity of the crack tip, a weighted average of the stresses of the integration points around the crack tip is considered. The algorithm also ensures that there are always at least eight elements and nine nodes surrounding the crack tip, unless the crack tip is close to a domain boundary, in which case there can be fewer elements and nodes around the crack tip.Four benchmark tests were performed showing that this algorithm leads to accurate crack paths when compared to findings from previous research works, as long as the initial mesh is not too coarse. This algorithm also leads to regular meshes during the propagation process, with very few distorted elements, which is generally one of the main problems when calculating crack propagation with the finite element method.

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17

Fu, Qiang, Sinan Yi, Boyang Chen, Tinh Quoc Bui, Xiaofei Hu, and Weian Yao. "A crack-tip element for modelling arbitrary crack propagations." Theoretical and Applied Fracture Mechanics 105 (February 2020): 102422. http://dx.doi.org/10.1016/j.tafmec.2019.102422.

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Liu, Wen Hui, Hao Huang, Zhi Gang Chen, and Da Tian Cui. "Simulation of Crack Tip Plasticity Using 3D Crystal Plasticity Theory." Advanced Materials Research 291-294 (July 2011): 1057–61. http://dx.doi.org/10.4028/www.scientific.net/amr.291-294.1057.

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To investigate the plasticity distribution of microstructurally small crack tip in FCC crystals, the crack tip opening displacment(CTOD), crack tip plastic zone and maximum plastic work for stationary microstructurally small cracks were calculated with the three dimensional crystal plasticity finite element theory, which was implemented in the finite element code ABAQUS with the rate dependent crystal plasticity theory code as user material subroutine. Results show that crystallographic orientation has significant influence on CTOD and maximum plastic work. The CTOD and maximum plastic work in hard orientation are larger than that in soft orientaion under the displacement controlled boundary condition, which means that crack in hard orientation is more likely to extend than that in soft orientaion. The high-angle grain boundary shows a tendency to reduce crack extension, and the dislocation ahead of the crack tip becomes blocked by high-angle grain boundary.

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Xu, Hua, Lu Feng Yang, and Zhen Ping She. "Mode-III Stress Intensity Factor by Williams Element with Generalized Degrees of Freedom." Advanced Materials Research 487 (March 2012): 242–46. http://dx.doi.org/10.4028/www.scientific.net/amr.487.242.

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Williams series are developed for mode III cracks, based on which the displacement field is defined in the singular region around the crack tip. The Williams element with generalized degrees of freedom (GDOFs) is proposed for analysis of stress intensity factor (SIF) of mode III crack. The SIF at the crack tip can be evaluated analytically by one of the undetermined constants of the Williams element. The influence of the relative length of the crack on the SIF is investigated. Three important parameters for the Williams element, including the radial scale factor, the number of subelements and the terms of the Williams series, are discussed in detail. Numerical example shows that the Williams element is of accuracy and efficiency.

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20

Kunter, K., T. Heubrandtner, B. Suhr, and R. Pippan. "A hybrid crack tip element containing a strip-yield crack-tip plasticity model." Engineering Fracture Mechanics 129 (October 2014): 3–13. http://dx.doi.org/10.1016/j.engfracmech.2014.07.023.

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Alshoaibi, Abdulnaser M., and Yahya Ali Fageehi. "Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method." Metals 11, no. 1 (January 6, 2021): 98. http://dx.doi.org/10.3390/met11010098.

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The finite element method (FEM) is a widely used technique in research, including but not restricted to the growth of cracks in engineering applications. However, failure to use fine meshes poses problems in modeling the singular stress field around the crack tip in the singular element region. This work aims at using the original source code program by Visual FORTRAN language to predict the crack propagation and fatigue lifetime using the adaptive dens mesh finite element method. This developed program involves the adaptive mesh generator according to the advancing front method as well as both the pre-processing and post-processing for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip is characterized by the stress intensity factor associated with the rate of crack growth. The quarter-point singular elements are constructed around the crack tip to accurately represent the singularity of this region. Under linear elastic fracture mechanics (LEFM) with an assumption in various configurations, the Paris law model was employed to evaluate mixed-mode fatigue life for two specimens under constant amplitude loading. The framework includes a progressive analysis of the stress intensity factors (SIFs), the direction of crack growth, and the estimation of fatigue life. The results of the analysis are consistent with other experimental and numerical studies in the literature for the prediction of the fatigue crack growth trajectories as well as the calculation of stress intensity factors.

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Roesler, Jeffery R., and Lev Khazanovich. "Finite-Element Analysis of Portland Cement Concrete Pavements with Cracks." Transportation Research Record: Journal of the Transportation Research Board 1568, no. 1 (January 1997): 1–9. http://dx.doi.org/10.3141/1568-01.

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It was verified that finite-element modeling could be successfully used to analyze concrete pavements with partial-depth cracks. An existing finite-element program, ILLI-SLAB, was modified (ILSL97) to allow for partial-depth crack analysis. To model a partial-depth crack, a special line spring element was added to the finite-element code. The line spring elements mimic the behavior of a crack by acting as a rotational hinge between two continuous slabs. By using available fracture mechanics techniques, a relationship was derived between the amount of moment load transfer across a crack and the crack depth. This analytical solution was then used to formulate the element stiffness matrix for the line spring element. The deflections predicted by the new finite-element program are correct, but the stresses in the vicinity of the crack tip needed to be corrected to match the stress singularity zone in front of cracks. Several example problems were used to verify the proposed finite-element model, and an example of a typical highway loading condition was analyzed.

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Wang, Xue Zhi, Hao Fei Zou, Shu Wen Zheng, Yuan Li, and Jun Yu Liu. "Finite Element Simulation and Comparison of Hydraulic Splitting Fracturing Test of Concrete." Applied Mechanics and Materials 678 (October 2014): 551–55. http://dx.doi.org/10.4028/www.scientific.net/amm.678.551.

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I-II mixed mode fracture under two kinds of load manners was carried out, and it was also simulated by the ANSYS, and the test results and the simulation results were compared and analyzed, and the reasonableness of the model built and the effectiveness of test were verified. The failure process of fracture under the loading could be judged through the development of the crack tip combined with the stress nephogram and strain nephogram when cracks initiation at crack tip, and it provided the basis for the crack damage judgment.

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Dong, Jianwei, Weichi Pei, Hongchao Ji, Haiyang Long, Xiaobin Fu, and Hailong Duan. "Fatigue crack propagation experiment and numerical simulation of 42CrMo steel." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 14 (March 5, 2020): 2852–62. http://dx.doi.org/10.1177/0954406220910458.

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42CrMo steel is widely used in ultrahigh-strength structures such as low-speed heavy-duty gears. Mastering the fatigue crack propagation law has important significance for predicting structural fatigue life. Firstly, the fatigue crack propagation experiment is used to obtain the upper and lower thresholds value of type I fatigue crack propagation of 42CrMo steel compact tensile specimen under the alternating load of stress ratio R = 0.1. The Paris formula describing the relationship between the fatigue crack propagation rate and the crack tip stress intensity factor between the upper and lower thresholds value is obtained. Scanning electron microscopy was used to observe the microscopic features of different stages of fatigue fracture. The results show that the twin boundary can provide a place for crack initiation; the defects in the material can promote the initiation and extension of fatigue cracks. The fatigue crack propagation of 42CrMo steel compact tensile specimens was numerically simulated by the finite element method. The relationship between the crack tip stress intensity factor and the crack length was obtained. The analysis results show that the crack tip stress intensity factor calculated by the plane finite element method differs slightly from the experimental results during the stable extension stage. After correction, the correlation coefficient between the numerical simulation correction value and the crack tip stress intensity factor value obtained by the experiment is 0.9926. Finally, the fatigue crack propagation rate corresponding to the crack tip stress intensity factor in the finite element results is calculated by the Paris formula and briefly analyzed. Compared with the experimental results, it shows that the numerical simulation is consistent with it, indicating the accuracy of the numerical simulation method, which can effectively predict the initiation and propagation of fatigue cracks in 42CrMo steel compact tensile specimens.

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Davidson, B. D., Hurang Hu, and R. A. Schapery. "An Analytical Crack-Tip Element for Layered Elastic Structures." Journal of Applied Mechanics 62, no. 2 (June 1, 1995): 294–305. http://dx.doi.org/10.1115/1.2895931.

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A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.

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Frehner, Marcel, and Stefan M. Schmalholz. "Finite-element simulations of Stoneley guided-wave reflection and scattering at the tips of fluid-filled fractures." GEOPHYSICS 75, no. 2 (March 2010): T23—T36. http://dx.doi.org/10.1190/1.3340361.

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The reflection and scattering of Stoneley guided waves at the tip of a crack filled with a viscous fluid was studied numerically in two dimensions using the finite-element method. The rock surrounding the crack is fully elastic and the fluid filling the crack is elastic in its bulk deformation behavior and viscous in its shear deformation behavior. The crack geometry, especially the crack tip, is resolved in detail by the unstructured finite-element mesh. At the tip of the crack, the Stoneley guided wave is reflected. The amplitude ratio between reflected and incident Stoneley guided wave is calculated from numerical simulations, which provide values ranging between 43% and close to 100% depending on the type of fluid filling the crack (water, oil or hydrocarbon gas), the crack geometry (elliptical or rectangular), and the presence of asmall gas cap at the cracktip. The interference of incident and reflected Stoneley guided waves leads to a node (zero amplitude) at the tip of the crack. At other positions along the crack, this interference increases the amplitude. However, the exponential decay away from the crack makes the Stoneley guided wave difficult to detect at a relatively short distance away from the crack. The part of the Stoneley guided wave that is not reflected is scattered at the crack tip and emitted into the surrounding elastic rock as body waves. For fully saturated cracks, the radiation pattern of these elastic body waves points in every direction from the crack tip. The emitted elastic body waves can allow the detection of Stoneley guided wave-related resonant signals at distances away from the crack where the amplitude of the Stoneley guided wave itself is too small to be detected.

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Duong, C. N., and J. Yu. "The hybrid crack-tip element approach to thermo-elastic cracks." International Journal of Solids and Structures 35, no. 36 (December 1998): 5159–71. http://dx.doi.org/10.1016/s0020-7683(97)00252-7.

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Zheng, Weiling, and Christos Kassapoglou. "Energy method for the calculation of the energy release rate of delamination in composite beams." Journal of Composite Materials 53, no. 4 (July 5, 2018): 425–43. http://dx.doi.org/10.1177/0021998318785952.

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An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model.

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LIU, G. R., N. NOURBAKHSHNIA, L. CHEN, and Y. W. ZHANG. "A NOVEL GENERAL FORMULATION FOR SINGULAR STRESS FIELD USING THE ES-FEM METHOD FOR THE ANALYSIS OF MIXED-MODE CRACKS." International Journal of Computational Methods 07, no. 01 (March 2010): 191–214. http://dx.doi.org/10.1142/s0219876210002131.

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This paper presents a general formulation for simulating the singular stress field at the vicinity of the crack-tip for linear fracture mechanics problems, based on the edge-based smoothed finite element method (ES-FEM) settings. This novel "singular ES-FEM" makes use of the unique feature offered by the ES-FEM that only the assumed displacement values (not the derivatives) are required to compute the stiffness matrix of the discretized system. The present singular ES-FEM method uses a basic mesh of linear triangular elements and a layer of novel "five-noded crack-tip elements" sharing the crack-tip node. The five-noded crack-tip element has one additional node on each of the edges connected to the crack-tip, and the locations of the "edge-node" can be arbitrary. A number of examples are analyzed and the results demonstrate that the present singular ES-FEM is generally softer and much more accurate than the existing FEM. The stress intensity factors obtained using the singular ES-FEM are very stable for different area-integration paths designed around the crack-tip. The present singular ES-FEM is found an excellent alternative to the standard FEM for fracture problems.

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Ismail, Al Emran, Ahmad Kamal Ariffin, Shahrum Abdullah, Mariyam Jameelah Ghazali, and Ruslizam Daud. "Mode III Stress Intensity Factors of Surface Crack in Round Bars." Advanced Materials Research 214 (February 2011): 192–96. http://dx.doi.org/10.4028/www.scientific.net/amr.214.192.

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This study presents a numerical investigation on the stress intensity factors (SIF), K of surface cracks in round bars that were obtained under pure torsion loadings or mode III. ANSYS finite element analysis (FEA) was used to determine the SIFs along the crack front of surface cracks embedded in the solid circular bars. 20-node isoparametric singular elements were used around the crack tip by shifting the mid-side node ¼-position close to a crack tip. Different crack aspect ratio, a/b were used ranging between 0.0 to 1.2 and relative crack depth, a/D were ranged between 0.1 to 0.6. Mode I SIF, KI obtained under bending moment was used to validate the proposed model and it was assumed this proposed model validated for analyzing mode III problems. It was found that, the mode II SIF, FII and mode III SIF, FIII were dependent on the crack geometries and the sites of crack growth were also dependent on a/b and a/D.

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31

Yang, Shang Yang, Xi Guang Gao, and Long Yun Zhang. "Transient Analysis on Reflective Crack of Highway Semi-Rigid Pavement Caused by Temperature Change." Key Engineering Materials 744 (July 2017): 163–68. http://dx.doi.org/10.4028/www.scientific.net/kem.744.163.

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The asphalt surface crack fracture mainly includes load cracks and non-load cracks. The former is due to the weight of the vehicle itself causing excessive fatigue weight, therefore, this crack is also known as road load fatigue crack. Non-load crack is affected by nature factors such as temperature and humidity, which makes the road structure cracking. In this paper, finite element method is used to analyze the transient temperature field, and on this basis, the temperature stress simulation of pavement structure is carried out. The stress intensity factor of asphalt surface crack tip is analyzed by finite element method. The results show that the modulus of the surface and the base layer and the increase of the temperature coefficient of the base layer will lead to the increase of the stress intensity factor of the crack tip. The temperature coefficient of the surface layer has no obvious effect on the stress intensity factor. In addition, increasing the thickness of the surface layer can effectively reduce the stress intensity factor at the crack tip. The paper also concludes that the gravel base can effectively slow down the expansion of the road refection crack.

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32

Benyahia, F., A. Albedah, Bel Abbès Bachir Bouiadjra, and M. Belhouari. "J Integral Computation for Repaired Cracks with Bonded Composite Patch in Aircraft Structures." Key Engineering Materials 577-578 (September 2013): 341–44. http://dx.doi.org/10.4028/www.scientific.net/kem.577-578.341.

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In this study, the three-dimensional and nonlinear finite element method is used to estimate the performances of bonded composite repairs of metallic cracked aircraft structures by analyzing the J integral and at the crack tips of repaired cracks for single and double symmetric patches. Several calculations have been realized to extract the plasticized elements around the crack tip. The obtained results show that composite repair reduces significantly the J integral at the crack tip which can improve the fatigue life of aircraft structures. It was also shown that the double symmetric patch has a considerable beneficial effect on the repair performance compared to the single patch.

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33

Kumar, V., and M. D. German. "Studies of the Line-Spring Model for Nonlinear Crack Problems." Journal of Pressure Vessel Technology 107, no. 4 (November 1, 1985): 412–20. http://dx.doi.org/10.1115/1.3264475.

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This paper presents an investigation of the line-spring model (LSM) of Rice and Levy as applied to nonlinear crack problems. A J2 deformation theory of plasticity formulation of a LSM for obtaining the fully plastic crack solutions is first described in the framework of a shell finite element method. Results are obtained for 2-D axial and circumferential cracks in cylinders and are compared against those developed by detailed finite element crack tip analyses. Discrepancies are found in the case of axially cracked cylinders under internal pressure. To overcome this problem a modified approach, termed the continuum-LSM, is presented, and its finite element implementation is described in some detail. It is shown that in contrast to the shell-LSM, the results obtained by the continuum-LSM for internally pressurized axially cracked cylinders are in close agreement with detailed finite element crack-tip calculations. Lastly, a discussion on the fully plastic analysis of surface cracks by the LSM is also given.

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34

Yan, Xiangqiao. "A special crack tip displacement discontinuity element." Mechanics Research Communications 31, no. 6 (November 2004): 651–59. http://dx.doi.org/10.1016/j.mechrescom.2004.05.001.

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35

Zeng, Dan, Noriko Katsube, Jinmiao Zhang, and Wole Soboyejo. "Hybrid crack-tip element and its applications." Finite Elements in Analysis and Design 38, no. 4 (February 2002): 319–35. http://dx.doi.org/10.1016/s0168-874x(01)00087-7.

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36

Jiang, C. P., and Y. K. Cheung. "A special bending crack tip finite element." International Journal of Fracture 71, no. 1 (1995): 57–69. http://dx.doi.org/10.1007/bf00019341.

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Mi, Y., and M. H. Aliabadi. "Discontinuous crack-tip elements: Application to 3D boundary element method." International Journal of Fracture 67, no. 3 (June 1994): R67—R71. http://dx.doi.org/10.1007/bf00016267.

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38

Potjananapasiri, Kobsak, Sutthisak Phongthanapanich, Paritud Bhandhubanyong, and Pramote Dechaumphai. "Combined Adaptive Finite Element Method and J-Domain Integral Technique for Crack Problems." Key Engineering Materials 340-341 (June 2007): 459–64. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.459.

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An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near a crack tip. The domain integral technique is utilized as the J-integral solution scheme with the 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure to a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Two benchmark problems are analyzed to evaluate the efficiency of the combined procedure.

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39

Yeh, Meng Kao, and Chien Ming Kao. "Finite Element Analysis of Stress Concentration at Rounded Crack Tip with Different Physical Parameters." Applied Mechanics and Materials 481 (December 2013): 230–34. http://dx.doi.org/10.4028/www.scientific.net/amm.481.230.

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This paper investigates the effect of physical parameters of a rounded crack on the stress concentration near crack tip. The depth and radius at the crack tip are the two physical parameters concerned in this study. The finite element method was used to evaluate the stress value at the crack tip for a silicon chip with a tiny crack under tensile stress. Element type, shape and physical parameters of crack were varied to study their effect on the stress concentration near the crack. The simulation results were compared with the theoretical value, and the better physical parameters as well as the element type, element shape were discussed.

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40

Charalambides, P. G., P. A. Mataga, R. M. McMeeking, and A. G. Evans. "Steady-State Mechanics of a Growing Crack Paralleling an Elastically Constrained Thin Ductile Layer." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S267—S270. http://dx.doi.org/10.1115/1.3120824.

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The steady-state near tip mechanics of brittle cracks growing under mixed mode conditions parallel and at close proximity to a thin ductile layer in a sandwich specimen morphology are examined. The plastic dissipation in the elastically constrained ductile layer is determined analytically through an approximate method and numerically via rigorous finite element calculations. Sensitivity studies regarding the effects of plasticity, layer thickness and crack location are presented. Thus, crack shielding characteristics are addressed and relationships between the remote (Gapp) and near tip (Gtip) energy release rates are established. The associated crack tip phase angle ψtip is extracted numerically via the method of finite elements. The above analysis is used to interpret experimental data for a sapphire/gold/sapphire system obtained using the plane strain four-point flexure model specimen geometry.

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41

Chen, Yu Hui, Xiao Xiang Yang, and Shun Cong Zhong. "Finite Element Analysis of Four Fracture Mechanism in the Thermal Barrier Coating." Advanced Materials Research 933 (May 2014): 187–91. http://dx.doi.org/10.4028/www.scientific.net/amr.933.187.

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With the development of high temperature protective material, thermal barrier coatings are used in the field of aircraft and industrial steam turbine. They have characteristics of complex structure and long-term work in high temperature environment, etc. Because of multilayer material physical properties mismatch, oxidation, interface roughness, creep stress and so on, the coatings system is easy to produce cracks, expand and link near the interface of coating during thermal cycling. By establishing I, II, III, IV four numerical models of crack fracture mechanisms, assuming that the thickness of oxidation layer is constant, considering the influence of interface roughness and material properties mismatch in the process of thermal cycling, it gets the results of residual stress field near the crack and the influence of the interface. Compared to the presence of defects, four kinds of crack failure mechanisms are analyzed. Energy release rate is calculated by the virtual crack closure method, which can conclude the cracks of I, IV tip stress concentration phenomena are obvious, crack II is easy to expand, due to the temperature load, crack III does not appear stress concentration phenomenon at the tip.

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42

Liu, He Guo, Jun Lei, Peng Bo Sun, and Qing Sheng Yang. "Boundary Element Analysis for Piezoelectric Cracks by an Interaction Integral." Advanced Materials Research 1120-1121 (July 2015): 1390–94. http://dx.doi.org/10.4028/www.scientific.net/amr.1120-1121.1390.

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In this paper, an interaction integral is applied to evaluate the crack-tip field intensity factors for piezoelectric cracks by using BEM. Based on this, the fracture parameters for different crack configurations and loading conditions are analyzed in details for both the center crack and edge crack problem. According to the present results, the path-independent behavior of the interaction integral is verified. The comparison of the I-integral results with those by the J-integral and the displacement interpolating methods shows a good agreement.

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43

Sima, Yu Zhou, and Fu Zhou Wang. "Analysis of Multi-Crack Growth in Asphalt Pavement Based on Extended Finite Element Method." Advanced Materials Research 588-589 (November 2012): 1926–29. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.1926.

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An extended finite element method (XFEM) for multiple crack growth in asphalt pavement is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modeled by finite element with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Finally, the propagation path of the cracks in asphalt pavement under different load conditions is presented.

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AN, X. M., G. W. MA, H. H. ZHANG, and L. X. LI. "AN IMPROVED FINITE ELEMENT METHOD FOR CRACKS WITH MULTIPLE BRANCHES." International Journal of Computational Methods 09, no. 03 (September 2012): 1250043. http://dx.doi.org/10.1142/s0219876212500430.

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The conventional finite element method is improved to tackle complex cracks with multiple branches. The parasitic nodes are introduced to the nodes whose nodal support is completely cut by the crack surfaces, while the nodes whose supports contain crack tips inside are accordingly enriched by the crack tip functions. The principle to set parasitic nodes is regulated, and the relation to the previous methods is dissected. The formulation of the present method is derived, and numerical experiments are conducted. The results show that the present method can treat complex cracks conveniently and efficiently, and the unknowns have a clear physical interpretation.

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45

Li, Yuan, and Gang-Feng Wang. "Influence of Surface Tension on Mixed-Mode Cracks." International Journal of Applied Mechanics 07, no. 05 (October 2015): 1550070. http://dx.doi.org/10.1142/s1758825115500702.

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Surface tension inherently exists on free surface, and its effect becomes quite important at sharp crack tip. In the present paper, we investigate the influence of surface tension on mixed-mode cracks by finite element method. It is found that surface tension significantly alters the stress fields and J-integral around crack tip, depending on the profile of crack tip. Generally, surface tension decreases the J-integral and thus enhances material toughness, especially for sharp crack. Based on the criteria of energy release rate, the critical stress intensity factor (SIF) for brittle materials is also determined. Surface tension yields an enhanced critical SIF for mixed-mode cracks, and more significant strengthening effect is obtained for Mode-I crack than for Mode-II crack. Moreover, an analytical expression is advanced to characterize the influence of surface tension on fracture, which shows a good agreement with numerical calculations.

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46

Zhang, J. Z., Xiao Dong He, X. Song, and Shan Yi Du. "Elastic-Plastic Finite Element Analysis of the Effect of the Compressive Loading on the Crack Tip Plasticity." Key Engineering Materials 324-325 (November 2006): 73–76. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.73.

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An elastic-plastic finite element analysis of the effect of the compressive loading on crack tip plasticity is presented. Two center-cracked panel specimens with different crack lengths are analysed under tension-compression loading. The size and shape of the crack tip reverse plastic zone, the crack opening profiles of the crack tip for short (0.1 mm) and long crack (2 mm) have been studied. The analysis shows that the compressive loading has a significant contribution towards the crack tip plasticity.

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Wei, Gao Feng, Hong Fen Gao, and Hai Hui Jiang. "Stress Intensity Factor for Interfacial Cracks in Bi-Materials Using Incompatible Numerical Manifold Method." Advanced Materials Research 327 (September 2011): 109–14. http://dx.doi.org/10.4028/www.scientific.net/amr.327.109.

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Incompatible numerical manifold method (INMM) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement. This paper describes the application of INMM to bi-material interfacial crack. The two dimensional near-tip asymptotic displacement functions are added to the trial function approximation. This enables the domain to be modeled by manifold elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The INMM facilitates the incorporation of the oscillatory nature of the singularity within a conforming manifold element approximation. The complex stress intensity factors for bi-material interfacial cracks are numerically evaluated. Good agreement between the numerical results and the analytical solutions for benchmark interfacial crack problems is realized.

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Kuna, Meinhard. "Finite Element Analyses of Cracks in Piezoelectric Structures." Key Engineering Materials 348-349 (September 2007): 629–32. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.629.

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A review is given about FEM-techniques to compute the coupled electromechanical boundary value problem of cracks in piezoelectric structures under static and dynamic loads. To calculate the relevant fracture parameters very precisely and efficient, the following numerical techniques are presented: i) Special singular crack tip elements, ii) Modified crack closure integral, iii) Computation of electromechanical J-integral and iv) Usage of interaction integrals. Special emphasis is devoted to different electric crack face boundary conditions. The accuracy, efficiency and applicability of these techniques are examined by various example problems and discussed with respect to their advantages and drawbacks for practical applications.

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Truong, Thien Tich, and Bang Kim Tran. "APPLICATION OF QUARTER-POINT SINGULAR ELEMENT IN FINITE ELEMENT METHOD TO SIMULATION OF CRACK TIP BEHAVIOR." Science and Technology Development Journal 13, no. 2 (June 30, 2010): 5–13. http://dx.doi.org/10.32508/stdj.v13i2.2113.

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Fracture mechanics is a new branch in engineering. The development of modern mathematical background with different numerical methods has supported fracture mechanics to solve many complex fracture problems in practice effectively. This article introduces the application of quarter - point singular element in finite element method to simulate crack tip behavior in two dimensional problems. The ANSYS and FRANC2D programs are used to compute stress intensity factor, simulate the stress and displacement fields near crack tip and simulate crack propagation. The calculation results are compared with analytical results and the results in other articles.

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Choi, Hyeon Chang. "A Study on the Relationship between Fatigue Crack Opening Behavior and Reversed Plastic Zone Size." Key Engineering Materials 297-300 (November 2005): 66–71. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.66.

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A relationship between fatigue crack opening behavior and the reversed plastic zone size is studied. An elastic-plastic finite element analysis (FEA) is performed to examine the opening behavior of fatigue crack. The contact elements in this analysis are adopted in the mesh of the crack tip area. The smaller element size than reversed plastic zone size is used for evaluating the distribution of reversed plastic zone. In the author’s previous results, the FEA could predict the crack opening level, which the size of crack tip elements was in proportion to the theoretical reversed plastic zone size. It is found that the calculated reversed plastic zone size is related to the theoretical reversed plastic zone size and crack opening level. The calculated reversed plastic zone sizes are almost equal to the reversed plastic zone size considering crack opening level obtained by experimental results. It is possible to predict the crack opening level from the reversed plastic zone size calculated by the FEA. We find that the experimental crack opening levels correspond with the opening values of crack tip contact nodes on the calculated reversed plastic zone.

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