Asymptotic analysis of crack interaction with free boundary

Dyskin, Arcady; Germanovich, L. N.; Устинов, К. Б.

doi:10.1016/s0020-7683(99)00063-3

Cited by 46 publications

(51 citation statements)

References 14 publications

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“…Also, for a very large ratio c/ h, the aperture's square root tip behavior is confined to a very small region. For more detailed discussion of the asymptote's changing nature, the reader may refer to [Dyskin et al 2000]. Additionally, we note that the values of K II in Figure 2 differ by a factor of about 2 from those of [Bunger and Detournay 2005], while the respective values of K I agree, approximately.…”

Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 75%

“…Srivastava and Singh [1969] analyzed the effect of a penny-shaped crack on the stress field in a semiinfinite solid. Other researchers have studied the fracture mechanisms of subsurface cracks under different loading conditions, for example, contact, wear, and indentation [Komvopoulos 1996;Ma and Hwang 1996;Goshima and Soda 1997;Dyskin et al 2000;Zhang et al 2002;2005;Feng and Xu 2006]. Fleming and Suh [1977] studied how surface traction helped propagate a horizontal subsurface crack.…”

Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 99%

“…Bunger and Detournay [2005] and Zhang et al [2002;2005] studied the asymptotic behaviors of penny-shaped hydraulic cracks. Dyskin et al [2000] employed the beam and dipole asymptotic approaches to analyze the interaction of a crack with parallel free boundaries. Despite the extensive interest, however, the community has not produced efficient methods for deriving the SIFs of subsurface cracks due to the crack-free surface interaction [Ma et al 2005].…”

Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 99%

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Fracture mechanics analysis of three-dimensional ion cut technology

Feng

Wang

et al. 2007

JOMMS

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The recently established ion cut technology enables accurate fabrication of silicon-on-insulator (SOI) wafers and has found some other significant applications. We study fracture mechanics of the technology when directly cutting a wafer into a desired surface morphology. First, we describe integral transformbased methods for calculating the stress intensity factors of subsurface cracks embedded in a semiinfinite solid. Because the crack and the free surface interact, the crack tip fields are generally of I-II mixed mode. We derive solutions for plane-strain or axisymmetrical configurations. We then analyze the suggested three-dimensional ion cut method using the fracture criterion for kinking propagation of a mixed-mode crack. To illustrate the approach, we consider circular hole and straight groove surface patterns.

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Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 75%

Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 99%

Section: Integral Transform Methods For Subsurface Cracksmentioning

confidence: 99%

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Fracture mechanics analysis of three-dimensional ion cut technology

Feng

Wang

et al. 2007

JOMMS

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“…The results were obtained on the base of solution of the matrix Wiener-Hopf problem [14], which was extended to describe displacements. The extraction of the coefficient 22 a for this case was made before [15], [16]. 3-D case was considered in [17].…”

Section: Calculating Coefficients Of Matrix Of Elastic Clampingmentioning

confidence: 99%

On influence of substrate compliance on delamination and buckling of coatings

Устинов

2015

Engineering Failure Analysis

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Abstract. Problems related to delamination of coatings from substrates and their buckling are widely investigated due to importance of the problem for application in industry, particularly in micro-and nano-electronics and biology. The problem was addressed by many authors by using both analytical and numerical approaches. Here the model is developed that treats the delaminated part of the coating as a plate with a special attention given to the boundary conditions, which are supposed in the form of the generalized elastic clamping, i.e. it is supposed that components of displacements and angle of rotation at the point of clamping are related to the acting total force and total moment by means of 3x3 matrix of elastic coefficients. Knowing the coefficients of this matrix allows determining parameters of buckling such as the critical stress, energy release rate due to further delamination, amplitude of buckling. A few variants of analytical models to determine the coefficients of this 3x3 matrix were considered and discussed. Both the cases of isotropic and anisotropic coating and substrate are considered. The solution for some matrix coefficients was obtained with the help of Fourier transform and WienerHopf technique. On the base of the obtained solution it is shown that the difference between the obtained critical stress and the critical stress of a rigidly clamped plate can be defined by a single nondimensional parameter, which is a combination of the elastic constants of the coating and substrate, and the ratio of delamination length to coating thickness. The results correlate well with the results obtained using the FEM model. IntroductionThe interest to effects, related to coatings delaminations causes by importance of the problem for such fields as micro-and nanoelectronics, biology, medicine. Number of studies is devoted to the problem e.g. , and energy release rates along and across the delamination front as well were found. The delaminated part of coating was considered as a clamped plate, which corresponds to rigid substrates. However, detailed studies yield that, from the one hand, the condition of rigid clamping are not satisfied exactly even for absolutely rigid substrates [5], and, from the other hand, on the base of numerical calculations it is said [6], [7] that even for substrates tree times softer then coating the condition of rigid clamping yields acceptable errors. The last statement has to be accepted with cautions, because the influence of delamination size, importance of which being confirmed by other studies [5], [8], was not investigated in [6]. Influence of the substrate rigidity was studied by [4][5][6], however without paying attention to the influence of the delamination width to the critical stress. The analysis of influence of both substrate compliance and delamination width on the critical stress was performed in [5]. The delamination

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“…More recent work has been concerned with developing numerical algorithms to simulate three-dimensional propagation of hydraulic fractures in layered strata [5,7,12,46,47,53]; this is in contrast to earlier work where approximate solutions were found for simple fracture geometries [1,8,28,33,45,48,55]. A substantial difference between hydraulic fracturing and other studies of fracture (see [22,49,52]) is the coupling with the equations for the fluid and fracture geometry. Most models in hydraulic fracturing only consider planar fractures rather than kinked or curved cracks [13,41,42].…”

mentioning

confidence: 99%

An Asymptotic Framework for Finite Hydraulic Fractures Including Leak‐Off

Mitchell¹,

Kuske²,

Peirce³

2007

SIAM J. Appl. Math.

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Abstract. The dynamics of hydraulic fracture, described by a system of nonlinear integrodifferential equations, is studied through the development and application of a multiparameter singular perturbation analysis. We present a new single expansion framework which describes the interaction between several physical processes, namely viscosity, toughness, and leak-off. The problem has nonlocal and nonlinear effects which give a complex solution structure involving transitions on small scales near the tip of the fracture. Detailed solutions obtained in the crack tip region vary with the dominant physical processes. The parameters quantifying these processes can be identified from critical scaling relationships, which are then used to construct a smooth solution for the fracture depending on all three processes. Our work focuses on plane strain hydraulic fractures on long time scales, and this methodology shows promise for related models with additional time scales, fluid lag, or different geometries, such as radial (penny-shaped) fractures and the classical Perkins-Kern-Nordgren (PKN) model.

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Asymptotic analysis of crack interaction with free boundary

Cited by 46 publications

References 14 publications

Fracture mechanics analysis of three-dimensional ion cut technology

Fracture mechanics analysis of three-dimensional ion cut technology

On influence of substrate compliance on delamination and buckling of coatings

An Asymptotic Framework for Finite Hydraulic Fractures Including Leak‐Off

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