Higher order asymptotic field at the moving crack tip

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

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The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1015.97 ◽

2014 ◽

Vol 1015 ◽

pp. 97-100

Author(s):

Yao Dai ◽

Xiao Chong ◽

Ying Chen

Keyword(s):

Piezoelectric Materials ◽

Electric Displacement ◽

Interfacial Crack ◽

Crack Tip ◽

Higher Order ◽

Functionally Graded ◽

Linear Functions ◽

Intensity Factors ◽

Crack Tip Fields ◽

Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

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Features of Dynamic Deformation of an Elastoviscoplastic Material in the Vicinity of a Moving Crack Tip

Mechanics of Solids ◽

10.3103/s0025654420060151 ◽

2020 ◽

Vol 55 (6) ◽

pp. 885-891

Author(s):

N. D. Verveiko ◽

S. E. Krupenko ◽

A. I. Shashkin

Keyword(s):

Dynamic Deformation ◽

Crack Tip ◽

Moving Crack

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Asymptotic fields near a moving crack tip

Dynamic Fracture Mechanics ◽

10.1017/cbo9780511546761.005 ◽

1990 ◽

pp. 152-220

Keyword(s):

Crack Tip ◽

Moving Crack ◽

Asymptotic Fields

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The Higher Order Crack Tip Fields of Exponential Gradient FGMs Plates with Reissner’s Effect

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.278-280.491 ◽

2013 ◽

Vol 278-280 ◽

pp. 491-494

Author(s):

Yao Dai ◽

Xiao Chong

Keyword(s):

Asymptotic Expansion ◽

Crack Tip ◽

Expansion Method ◽

Higher Order ◽

Functionally Graded ◽

Transverse Shear Deformation ◽

Plate Bending ◽

Graded Materials ◽

Fundamental Significance ◽

Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials (FGMs) plates for a crack perpendicular to material gradient. The crack-tip higher order asymptotic fields of FGMs plates are obtained by the asymptotic expansion method. This study has fundamental significance as Williams’ solution.

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Experimental determination and finite element analysis of coefficients of the multi-parameter Williams series expansion in the vicinity of the crack tip in linear elastic materials. Part I

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.4.20 ◽

2020 ◽

pp. 237-249

Author(s):

L. V Stepanova

Keyword(s):

Series Expansion ◽

Digital Image ◽

Power Series Expansion ◽

Crack Tip ◽

Higher Order ◽

Accurate Estimation ◽

Principal Stresses ◽

Isochromatic Fringe ◽

Higher Order Terms ◽

Fringe Patterns

This study aims at obtaining coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and in the semi-circular notched disk under bending by the use of the digital photoelasticity method. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give a more accurate estimation of the near-crack-tip stress, strain and displacement fields and extend the domain of validity for the Williams power series expansion. The program is specially developed for the interpretation and processing of experimental data from the phototelasticity experiments. By means of the developed tool, the fringe patterns that contain the whole field stress information in terms of the difference in principal stresses (isochromatics) are captured as a digital image, which is processed for quantitative evaluations. The developed tool allows us to find points that belong to isochromatic fringes with the minimal light intensity. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of the stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The iterative procedure of the over-deterministic method is utilized to find the higher order terms of the Williams series expansion. The procedure is based on the consistent correction of the coefficients of the Williams series expansion. The first fifteen coefficients are obtained. The experimentally obtained coefficients are used for the reconstruction of the isochromatic fringe pattern in the vicinity of the crack tip. The comparison of the theoretically reconstructed and experimental isochromatic fringe patterns shows that the coefficients of the Williams series expansion have a good match.

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