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.

scholarly journals Propagation conditions of an eccentric crack in a semi-circular disk loaded in I+II mixed mode

2020 ◽  
Vol 310 ◽  
pp. 00017
Author(s):  
Lucie Malíková ◽  
Petr Miarka ◽  
Hana Šimonová
Keyword(s):  
Fracture Mechanics ◽  
Analytical Solution ◽  
Stress Field ◽  
Mixed Mode ◽  
Circular Disk ◽  
Field Approximation ◽  
Three Point Bending ◽  
Higher Order Terms ◽  
Eccentric Crack ◽  
The Individual

Multi-parameter fracture mechanics concept is applied to investigate crack propagation conditions during a three-point bending (3PB) test performed on an asymmetrical semi-circular disk under I+II mixedmode loading. The asymmetry is represented by an eccentricity of the angled crack as well as by different distances of both supports during the 3PB test from the middle of the specimen. The Williams series expansion is used for the crack-tip stress field approximation and fracture response of the crack is assessed by means of the combination of the numerical and analytical solution. Comparison between the individual configurations is carried out and discussion on the importance of the higher-order terms considered in the Williams expansion for various cases of asymmetry is presented.

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.

Estimation of the Zone of Failure Extent in Quasi-Brittle Specimens with Different Crack-Tip Constraint Conditions from Stress Field

2013 ◽  
Vol 592-593 ◽  
pp. 262-265 ◽  
Author(s):  
Václav Veselý ◽  
Jakub Sobek ◽  
Petr Frantík ◽  
Michal Štafa ◽  
Lucie Šestáková ◽  
...  
Keyword(s):  
Stress Field ◽  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Crack Tip ◽  
Bending Test ◽  
Stress Fields ◽  
Three Point Bending ◽  
Higher Order Terms ◽  
Crack Tip Constraint

A multi-parameter fracture mechanics concept based on the Williams power series is applied on novel cracked specimen geometries utilizing combined boundary conditions of the wedge splitting and the three-point bending test. Crack tip stress fields for various configurations (causing different constraint conditions at the crack tip and thus also different fracture process zone extents) are numerically investigated and subsequently analytically reconstructed using developed procedure. An importance of using higher order terms of the Williams series is demonstrated.

Micro-crack tip fracture of commercial grade aluminum under mixed mode loading

1999 ◽  
Vol 31 (2) ◽  
pp. 119-130 ◽  
Author(s):  
J.B Sha ◽  
J Sun ◽  
Z.J Deng ◽  
H.J Zhou
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Mixed Mode Loading ◽  
Commercial Grade

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.

Convergence Study on Application of the Over-Deterministic Method for Determination of Near-Tip Fields in a Cracked Plate Loaded in Mixed-Mode

2012 ◽  
Vol 249-250 ◽  
pp. 76-81 ◽  
Author(s):  
Lucie Šestáková ◽  
Václav Veselý
Keyword(s):  
Mixed Mode ◽  
Brittle Materials ◽  
Higher Order ◽  
Displacement Fields ◽  
Deterministic Method ◽  
Crack Behavior ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
Convergence Study

Multi-parameter description of crack behavior in quasi-brittle materials offers still enough space for investigations. Several studies have been carried out by the authors in this field [1-3]. One part of the publications by the authors (this work included) contain analyses of the accuracy, convergence and/or tuning of the over-deterministic method that enables determination of the coefficients of the higher-order terms in Williams expansion approximating the stress and displacement fields in a cracked body without any complicated FE formulations. These intermediate studies should bring together a list of recommendations how to use the ODM as effectively as possible and obtain reliable enough values of coefficients of the higher-order terms. Thus, the stress/displacement field can be determined precisely even in a larger distance from the crack tip, which is crucial for assessment of the fracture occurring in quasi-brittle materials.

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