Relevant bibliographies by topics / Crack-tip asymptotic expansion

Academic literature on the topic 'Crack-tip asymptotic expansion'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Crack-tip asymptotic expansion"

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Gerasimova, T. E., P. N. Lomakov, and L. V. Stepanova. "NUMERICAL PHOTOMECHANICS: NUMERICAL PROCESSING OF PHOTOELASTICITY EXPERIMENTS AND ITS APPLICATION TO THE PROBLEMS OF FRACTURE MECHANICS PROBLEMS." Vestnik of Samara University. Natural Science Series 19, no. 9.2 (June 6, 2017): 63–73. http://dx.doi.org/10.18287/2541-7525-2013-19-9.2-63-73.

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On the basis of photoelasticity method the experimental study of near crack tip stressed strain state in specimens under mixed loading conditions is performed. Carried out experimental investigation allows to obtain coefficients of full asymptotic expansions of stress and displacement fields in the vicinity of the crack tip and alos to find coefficients of highest approach in Williams full asymptotic expansion.
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Dai, Yao, Xiu Fa Yan, Chang Qing Sun, and Wei Tan. "The Crack-Tip Higher Order Asymptotic Fields for a Mode III Crack in a Functionally Gradient Material." Advanced Materials Research 33-37 (March 2008): 713–18. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.713.

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Crack-tip higher order stress and displacement fields for a mode III crack along the direction of property variation in a functionally gradient material (FGM), which has a power variation of shear modulus along the gradient direction, are obtained through the asymptotic analysis. The asymptotic expansions of crack tip stress fields are derived to explicitly bring out the influence of non-homogeneity on the structure of the stress field. The analysis reveals that only the higher order terms in the expansion are influenced by the material non-homogeneity. Moreover, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly and theoretically account for non-homogeneity effects on crack tip stress fields.
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Stepanova, L. V., and P. S. Roslyakov. "MULTIPARAMETRIC ANALYSIS OF THE STRESS FIELD NEAR THE CRACK TIP." Vestnik of Samara University. Natural Science Series 21, no. 10 (May 15, 2017): 52–76. http://dx.doi.org/10.18287/2541-7525-2015-21-10-52-76.

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The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof-Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.
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Dai, Yao, and Xiao Chong. "The Higher Order Crack Tip Fields for Physical Weak-- Discontinuous Crack of FGM Plate with Reissner’s Effect." Advanced Materials Research 664 (February 2013): 841–45. http://dx.doi.org/10.4028/www.scientific.net/amr.664.841.

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The physical weak-discontinuous problem of an interfacial crack between homogeneous material and functionally graded materials (FGMs) is studied based on Reissner’s plates considering transverse shear deformation effect. The crack-tip higher order asymptotic fields of homogeneous materials and FGMs regions are obtained by the asymptotic expansion method, respectively. Finally, the whole crack tip high order fields are assembled and given. The results provide a theoretical basis for solving interfacial crack problems of FGMs plates and their engineering application.
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Stepanova, L. V., and V. S. Dolgikh. "EXPERIMENTAL DETERMINATION OF COEFFICIENTS OF A MULTIPARAMETER DECOMPOSITION OF FIELD OF CRACK TIP STRESSES: PHOTOELASTICITY METHOD." Vestnik of Samara University. Natural Science Series 23, no. 1 (September 20, 2017): 59–68. http://dx.doi.org/10.18287/2541-7525-2017-23-1-59-68.

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The purpose of this study is multiparameter asymptotic analysis of the stress field in the immediate vicinity of the crack tip in a linearly elastic material and construction of complete asymptotic expansion of M. Williams stress field in the vicinity of the crack tip. Multiparametric analysis of the stress field is based on the polarization-optical methods of mechanics of a deformable solid (the method of photoelasticity). Digital processing of the results of optoelectronic measurements performed on a series of samples with cracks and notches is carried out. Different classes of samples from optically sensitive materials, in particular a sample with two collinear cracks under conditions of normal detachment, were considered. A set of programs has been prepared that makes it possible to determine the scale (amplitude) multipliers of complete asymptotic expansion of M.Villiams for the stress field at the crack tip. Using the basic law of photoelasticity, first five coefficients of complete asymptotic expansion of M. Williams are calculated. The results of the experiments are compared with the available analytical solution. It is shown that the results of processing optoelectronic measurements are in good agreement with the analytical solution obtained for an infinite plate with two collinear cracks.
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Dai, Yao, Jun Feng Liu, Lei Zhang, Xiao Chong, and Hong Qian Chen. "Higher Order Crack-Tip Fields of Reissner’s Linear Functionally Graded Materials Plates." Advanced Materials Research 549 (July 2012): 914–17. http://dx.doi.org/10.4028/www.scientific.net/amr.549.914.

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Reissner’s plate bending fracture theory with consideration of transverse shear deformation effects is adopted for the crack problem of functionally graded materials (FGMs) plates. Assume that the crack is perpendicular to the material property gradient. By applying the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to Williams’ solutions of homogeneous materials are obtained.
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Dai, Yao, Shi Min Li, Peng Zhang, and Xiao Chong. "The Higher Order Asymptotic Fields for Anti-Plane Oblique Crack with Physical Weak-Discontinuity." Advanced Materials Research 217-218 (March 2011): 1309–13. http://dx.doi.org/10.4028/www.scientific.net/amr.217-218.1309.

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An arbitrarily oriented anti-plane crack with its tip at the physical weak-discontinuous line of the structure which is made up of homogeneous material and functionally graded materials (FGMs) is studied. The analytic solution of the higher order crack tip fields (similar to the Williams’ solution of homogenous material) is obtained by applying the asymptotic series expansion. When non-homogeneous material parameters are degenerated, the solutions become the same as the asymptotic crack tip fields of the homogeneous material. Therefore, the solutions are the basic results of non-homogeneous fracture mechanics, and provide a theoretical basis for solving the fracture problems of one common structure with physical weak-discontinuity.
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Dai, Yao, Jun Feng Liu, Xiao Chong, and Lei Zhang. "The Crack-Tip Higher Order Field of Power-Law FGMs Plates with Reissner’s Effect for Crack Parallel to Material Property Gradient." Advanced Materials Research 664 (February 2013): 821–24. http://dx.doi.org/10.4028/www.scientific.net/amr.664.821.

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Reissner’s plate bending fracture theory with consideration of transverse shear deformation effects is adopted for the crack problem of power-law functionally graded materials (FGMs) plates. Assume that the crack is parallel to the material property gradient. By applying the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to Williams’ solutions of homogeneous materials are obtained.
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Dai, Yao, Lei Zhang, Xiao Chong, and Chun Fang Xue. "The Higher Order Crack-Tip Field of Circumferential Crack for Reissners FGMs Cylindrical Shell." Advanced Materials Research 791-793 (September 2013): 754–57. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.754.

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Reissners shell theory is employed to analyze the circumferential crack problem for FGMs cylindrical shell by using the asymptotic expansion method. The higher order crack tip fields for circumferential FGMs cylindrical shell which is similar to Williams solution are obtained.
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Dai, Yao, Lei Zhang, Jun Feng Liu, Xiao Chong, and Hong Qian Chen. "The Higher Order Asymptotic Crack-Tip Field for Reissner’s Linear Functionally Graded Shell." Advanced Materials Research 549 (July 2012): 826–29. http://dx.doi.org/10.4028/www.scientific.net/amr.549.826.

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The eigen-problem of a crack in functionally graded Reissner’s spherical shell is analyzed. By adopting the asymptotic expansion method, the higher order crack tip asymptotic fields which are similar to the Williams’ solutions of plane crack problems in homogenous materials are obtained. The grade direction is assumed to be parallel to the crack. The results can be widely adopted in numerical analysis, experimental investigation and the engineering application of FGM shell structure.
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Dissertations / Theses on the topic "Crack-tip asymptotic expansion"

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He, Zhuang. "Effect of 3D stress states at crack front on deformation, fracture and fatigue phenomena." Thesis, 2016. http://hdl.handle.net/2440/105077.

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Theoretical, numerical and experimental studies involving elastic plate components, weakened by through-the-thickness cracks and subjected to loading parallel to the plane of the plate, are often based on plane stress or plane strain simplifications. These simplifications essentially reduce the dimensionality of the physical three-dimensional problem and enable the achievement of effective analytical and numerical solutions for many important practical problems. The influence of various three-dimensional effects, such as the variation of stresses across the plate thickness, effects of the three-dimensional corner (vertex) singularities and coupling of fracture modes II and III, on the deformation and stresses near the crack front are at present largely ignored or viewed as negligible for all practical purposes. As a result of this view, the outcomes of experimental studies and fracture tests are also commonly analysed within the framework of the plane theories of elasticity. Nevertheless, a number of theoretical and experimental studies over the past two decades have demonstrated that the predictions made within these theories can be unsatisfactory and the effect of three-dimensional stress states at the crack front on deformation, fatigue and fracture of plate components can be significant. This thesis aims to elucidate the role of three-dimensional stress states in the deformation, fracture and fatigue phenomena further. The main outcomes of this thesis are: (1) the development and validation of a simplified method for the evaluation of the fatigue crack front shapes and their effect on the steady-state fatigue crack growth rates in plate components; (2) investigation of the effect of three-dimensional corner (vertex) singularities on the stress intensities and displacement field near the crack front; and (3) development and validation of a new experimental approach for the evaluation of mode I and mode II stress intensity factors from the measurement of the out-of-plane displacements in the near crack tip region, which are affected by three-dimensional effects, and, in particular, by the 3D corner (vertex) singularity. This new research is important in many engineering contexts. For example, the new theoretical model, which takes into account the actual shape of the crack front, can be utilised in advanced fatigue life calculations, as well as in failure investigations. The latter is possible as the shape of the fatigue crack front can now be related to the parameters of fatigue loading. The new experimental approach developed in this thesis can be useful in fracture characterisation of thick plate components with through-cracks. This approach specifically addresses the situation when the Kdominance zone, or William’s solution convergence domain, are relatively small. In this case, the data extraction region can be affected by the three-dimensional stress states leading to significant errors in the evaluation of the stress intensity factors when using traditional approaches. This thesis is presented in the form of a compendium of published papers that are the summation of the research undertaken by the author. The five articles which form the main body of the thesis are united by a common theme, which is the investigation of three-dimensional effects near the crack front on stresses and displacements, fracture and fatigue phenomena. Two appendices are also included; they represent a compilation of the candidate’s publications related to the main topic of the thesis.
Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Mechanical Engineering, 2016.
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Book chapters on the topic "Crack-tip asymptotic expansion"

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Broese, Carsten, Jan Frischmann, and Charalampos Tsakmakis. "Mode-I and Mode-II Crack Tip Fields in Implicit Gradient Elasticity Based on Laplacians of Stress and Strain. Part II: Asymptotic Solutions." In Nanomechanics [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.93618.

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We develop asymptotic solutions for near-tip fields of Mode-I and Mode-II crack problems and for model responses reflected by implicit gradient elasticity. Especially, a model of gradient elasticity is considered, which is based on Laplacians of stress and strain and turns out to be derivable as a particular case of micromorphic (microstrain) elasticity. While the governing model equations of the crack problems are developed in Part I, the present paper addresses analytical solutions for near-tip fields by using asymptotic expansions of Williams’ type. It is shown that for the assumptions made in Part I, the model does not eliminiate the well-known singularities of classical elasticity. This is in contrast to conclusions made elsewhere, which rely upon different assumptions. However, there are significant differences in comparison to classical elasticity, which are discussed in the paper. For instance, in the case of Mode-II loading conditions, the leading terms of the asymptotic solution for the components of the double stress exhibit the remarkable property that they include two stress intensity factors.
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Conference papers on the topic "Crack-tip asymptotic expansion"

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Profant, T., J. Sládek, V. Sládek, and M. Kotoul. "Assessment of amplitude factors of asymptotic expansion at crack tip in flexoelectric solid under mode I loadings." In Engineering Mechanics 2022. Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague, 2022. http://dx.doi.org/10.21495/51-2-317.

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Yuan, F. G., and S. Yang. "Asymptotic Crack-Tip Fields in an Anisotropic Plate Subjected to Bending Moments and Transverse Shear Loads." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1157.

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Abstract Asymptotic crack-tip fields in an anisotropic plate under bending moments and transverse shear loads including the effect of transverse shear deformation is presented. Utilizing the Reissner variational principle, the equilibrium equations and stress resultant-displacement relations are obtained. Assuming the displacement and stress resultant are in a separation of variable form, it is found that the equations governing crack-tip fields of an anisotropic plate bending are analogous to those governing generalized plane deformation of a composite. Thus the Stroh formalism can be used to characterize the crack-tip fields of the anisotropic plate and the energy release rate can be expressed in a real form in terms of stress intensity factors. The degenerated case of isotropic plates is also presented. Finally, the coefficients of the asymptotic expansion can be obtained from the J-integral method and Betti’s reciprocal theorem together with the auxiliary fields.
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Stepanova, Larisa, and Pavel Roslyakov. "Complete Williams asymptotic expansion of the stress field near the crack tip: Analytical solutions, interference-optic methods and numerical experiments." In MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2016): Proceedings of the 10th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Author(s), 2016. http://dx.doi.org/10.1063/1.4967050.

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Duan, Chuanjie, and Shuhua Zhang. "Two Parameter J-A Estimation for Weld Centerline Cracks in Welded Single-Edge Cracked Plate Under Tensile Loading." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95392.

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Abstract This work examines the J–A two-parameter characterization of elastic–plastic crack front fields for weld centerline cracks under tensile loading. Extensive finite element analyses (FEA) have been conducted to obtain solutions of constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for the stress field near the tip of mode-I crack, for modified boundary layer (MBL) model and welded single-edge cracked plate (SECP). Solutions of the constraint parameter A were obtained for the material following the Ramberg-Osgood power law. The crack geometries analyzed include shallow and deep cracks, and remote tension loading levels cover from small-scale to large-scale yielding conditions. The effects of weld material mismatch and weld width on crack tip constraint were considered in the FEA. A constraint parameter AM, only caused by material strength mismatch, is defined and its parametric equation was obtained. The total constraint in the bi-material weldment can be predicted by adding together AM and A in the homogeneous material. Good agreements were achieved for welded SECP specimen with different crack size and weld width from small-scale to large-scale yielding conditions. This methodology would be useful for performing constraint-based elastic-plastic fracture analyses of other welded test specimens.
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Muju, Sandeep. "Crack Propagating in a Bimaterial Functionally Graded Multilayered Composite Media." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1184.

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Abstract The macroscopically anisotropic homogenization of a multilayered composite implicitly assumes that the spatial wavelength of material inhomogeneity is smaller than the macroscopic quantity of interest and hence, is a reasonable approximation of the bulk behavior [1]. However, close to the crack tip, gradients in field quantities are strongly influenced by the local heterogeneity, which the anisotropic homogenization fails to capture. Thus, given the insights from a homogenized continuum study, the next level of refinement is to study the effect of inhomogeneity on crack driving force. Asymptotic studies of cracks perpendicular and parallel to a bimaterial interface and in a layer between two materials have been very widely researched over the past two decades. Recently the advent of the use of functionally gradient materials (FGM) in composites, nano-composites and other multi-material structural systems has spurred interest in the fracture mechanics of such inhomogeneous materials. The problems considered in the literature typically assume a functional form for the material property variation, usually in one direction only, and calculate the driving force at the crack tip for a crack at some orientation to the direction of variation. The interest in FGM’s is due to their superior performance as interfacial layers in general and in particular in high temperature applications. Discontinuities in material properties between joined material constituents act as stress concentrators, especially due to thermal expansion mismatches under thermal processing or service loads. The use of a FGM as an interfacial layer smooths the discontinuity and reduces the stress concentrations. In this paper an analytic solution for the effect of periodic inhomogeneity on crack driving force is studied. Via Williams eigenfunction expansion approach it is seen that, for continuously differentiable moduli inhomogeneity the nature of the stress singularity at the crack tip is the same as in a homogeneous media, though the eigenvalue (Stress Intensity Factor) does depend on the inhomogeneity [1]. In order to study the effect of layered inhomogeneity on the Stress Intensity Factor(s), the Bueckner-Rice weight function approach for homogeneous media [2–3] is incorporated here to study the layered media problem. In this chapter the moduli perturbation approach, [4], is further extended to the case of multilayered media, especially in a functionally gradient material sense. It is shown that to the first order, the effect of moduli inhomogeneity, residual stresses and inelastic strains on crack tip stress intensity factor are superposable. The results provide insight into the influence of residual stress and periodic moduli inhomogeneity on effective crack driving force for cracks propagating through multilayered bimaterial media. Further, this method in general allows one to study thermoelastic crack problems in complex heterogeneous media, alleviating difficulties associated with some of the traditional methods.
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Pochiraju, Kishore. "An Atlas of Asymptotically Singular Stress Fields in Axisymmetric Fiber Push-Out Model." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1173.

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Abstract Extracting fiber-matrix interface properties from single fiber push-out experimentation results requires careful micro-mechanical modeling. The axisymmetric concentric cylinder model is widely used to determine stress and damage state in the fiber, matrix, and at the interface. Several mechanics models developed for analyzing this model recognize the existence of asymptotically singular local regions for analyzing the stress fields in fiber push-out, but a comprehensive description of the nature of these stress fields and estimates for the regions of their influence is not available. Early work by Zak has shown that plane strain singularities which are separable in radial and angular directions dominate in the axisymmetric model at regions close to the point of singularity. Later efforts characterized the power of the radial singularity and angular variations of the singular stress fields in the model. In this paper the qualitative and quantitative nature of the singular stress fields, their regions of dominance, and scaling of the stress intensity with applied load for several fiber-matrix interface conditions are described. The presented results are obtained using a local-global matching technique which uses combined asymptotic and finite element methods to determine the stress fields in the local regions. The results are presented for both edge/corner singularities and for crack tip singularities in the model. The fiber radius and fiber volume fraction are considered as the geometric parameters. The material mismatch effects are considered using a wide spectrum of Dundurs mismatch parameters. Several interface conditions including perfectly bonded, partially cracked, debonding with frictional sliding of the crack tips and the oscillatory bi-material singularities are considered. Two different loading conditions, namely the thermal residual stresses and the push-in displacement loads are considered. The paper focuses on the local stress fields as determined by the first and second (when singular) terms of the asymptotic expansion and their scaling with applied loading. The paper provides an atlas of the nature of the stress singularities (power of the stress singularity, mode mixity, the angular variation, and region of dominance) and the approximate stress intensity factors in the model for the two loading types for most practical fiber-matrix combinations, interface frictions and model geometric parameters.
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