Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

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.

scholarly journals 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

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.

Detailed Crack-Tip Stress Field Description in a Specimen Subjected to Mixed-Mode Loading

2013 ◽  
Vol 577-578 ◽  
pp. 317-320 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Mixed Mode ◽  
Crack Tip ◽  
Analytical Description ◽  
Initial Crack ◽  
Propagation Direction ◽  
Mixed Mode Loading ◽  
Crack Propagation Direction ◽  
Higher Order Terms ◽  
Accurate Stress

A mixed-mode cracked configuration is investigated using the multi-parameter fracture mechanics concept based on the analytical description of the stress/displacement field near a crack tip by means of the Williams series expansion. It is shown that using only one (singular) parameter as it is usual for brittle materials is not sufficient if the accurate stress distribution also further from the crack tip shall be known. Tangential stress distribution in various distances from the crack tip is presented and importance of the higher-order terms of the Williams expansion emphasized. Moreover, initial crack propagation direction is investigated by means of the MTS criterion and utilization of its generalized form is discussed.

Accounting for Constraint in Probabilistic Fracture Mechanics Analysis of Welds in Floating Production, Storage and Off-Loading (FPSO) Vessels

2003 ◽  
Author(s):  
Jens P. Tronskar
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
North Sea ◽  
Failure Probability ◽  
Crack Tip ◽  
Probabilistic Fracture Mechanics ◽  
Crack Tip Constraint

Revision 4 of the British Energy R6 document: “Assessment of the integrity of structures containing defects” provides methods to allow for loss of crack tip constraint for shallow weld flaws. The document also provides methods to estimate upper-bound values of the through thickness residual stress distribution for a range of common weld joint configurations. The present paper presents results of analyses where approaches to modify the R6 Option 1 or 2 failure assessment diagrams (FADs) for loss of crack tip constraint pertaining to primary and non-uniform residual stress have been applied. The modified FAD were formulated for probabilistic fracture mechanics analyses of semi-elliptical surface cracks located at transverse deck welds of Floating Production, Storage and Off-loading (FPSO) vessels designed to operate in the North Sea. The objective was to study the influence on the failure probability of modifying the FAD for constraint and allowing for non-uniform residual stress. Another objective was to study the influence of constraint correction on the combined fatigue and fracture failure probability for the vessels subjected to wave loading. Material and weld tensile properties and fracture toughness distributions for input to the probabilistic fracture mechanics analyses were obtained from testing of welded panels prepared using welding procedures for actual FPSO fabrication. The loading conditions were derived based on North Sea wave data pertaining to the offshore field where the FPSO is operating. The stresses were obtained from global FE analysis and fitted Weibull long-term and extreme value distributions. The results of the analyses demonstrate clearly the importance of correcting for crack tip constraint pertaining to both primary and secondary stress and to allow for non-uniform residual stress for shallow surface flaws of known crack heights. However, in combination with fatigue crack growth the effects become less prominent as the failure probability is governed by the uncertainty in the parameters of the crack growth relationship and the long-term stress distribution.

Utilization of Williams’ Power Series for Estimation of Crack Behavior under Mixed-Mode Loading

2019 ◽  
Vol 827 ◽  
pp. 203-208
Author(s):  
Lucie Malíková ◽  
Petr Miarka ◽  
Hana Šimonová
Keyword(s):  
Fracture Mechanics ◽  
Mixed Mode ◽  
Crack Tip ◽  
Field Approximation ◽  
Bending Test ◽  
Mixed Mode Loading ◽  
Three Point Bending ◽  
Crack Behavior ◽  
Higher Order Terms ◽  
Specific Fracture

Multi-parameter fracture mechanics concept has been applied to investigate crack behavior under mixed-mode loading, particularly in a semi-circular bending disc. The so-called Williams’ series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behavior, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams’ expansion in fracture criteria can be helpful. The attention is devoted to the analysis of the influence of various distances between the supports during the three-point bending test on the results of the further crack propagation direction.

Application of the Williams Expansion near a Bi-Material Interface

2017 ◽  
Vol 754 ◽  
pp. 206-209 ◽  
Author(s):  
Lucie Malíková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Tip ◽  
Higher Order ◽  
Simplified Model ◽  
The Finite Element Method ◽  
Material Interface ◽  
Higher Order Terms ◽  
Element Method ◽  
Crack Tip Stress

A simplified model of a crack approaching a bi-material interface is modelled by means of the finite element method in order to investigate the significance of the higher-order terms of the Williams expansion for the proper approximation of the opening crack-tip stress near the bi-material interface. The discussion on results is presented and the importance of the higher-order terms proved.

Influence of Boundary Conditions on Higher Order Terms of Near-Crack-Tip Stress Field in a WST Specimen

2011 ◽  
Vol 488-489 ◽  
pp. 399-402 ◽  
Author(s):  
Václav Veselý ◽  
Lucie Šestáková ◽  
Stanislav Seitl
Keyword(s):  
Stress Field ◽  
Boundary Conditions ◽  
Numerical Study ◽  
Higher Order ◽  
Wedge Splitting Test ◽  
Splitting Test ◽  
Higher Order Terms ◽  
Test Geometry ◽  
Finite Element Package ◽  
Stress And Deformation

A precise description of the stress and deformation fields in a cracked body is provided using multi-parameter fracture mechanics based on the approximation of the fields by means of the Williams’ power series. This paper presents a detailed analysis of the stress field in a wedge-splitting test geometry specimen aimed at the calculation of coefficients of the higher order terms (up to 14) of the Williams’ expansion. The numerical study is conducted with the use of a conventional finite element package; however, for processing of the results an over-deterministic method is employed. Special attention is paid to the influence of boundary conditions of the test geometry on the values of the coefficients of the higher order terms of the Williams’ series. The results are compared to data from the literature; a strong effect of the boundary conditions is observed.

Higher order terms in asymptotic elastoplastic mode-III crack tip solutions

1991 ◽  
Vol 90 (1-4) ◽  
pp. 139-153 ◽  
Author(s):  
N. Aravas ◽  
D. A. Blazo
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Higher Order Terms
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