How to Enhance Efficiency and Accuracy of the Over-Deterministic Method Used for Determination of the Coefficients of the Higher-Order Terms in Williams Expansion

2012 ◽  
Vol 245 ◽  
pp. 120-125 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Fracture Behavior ◽  
Accurate Determination ◽  
Higher Order ◽  
Elastic Behavior ◽  
Deterministic Method ◽  
Effective Utilization ◽  
Higher Order Terms ◽  
Enhance Efficiency ◽  
Extended Zone

Using higher-order terms of the Williams expansion is necessary for assessment of fracture behavior of quasi-brittle materials. Multi-parameter fracture mechanics enables more accurate determination of the stress/displacement field even in a larger distance from the crack tip, thus the extended zone with non-elastic behavior typical for this kind of material can be well described. The so-called over-deterministic method (ODM) seems to be a suitable tool for the higher-order terms coefficients calculation, but its utilization exhibits some limitations. Therefore, extensive analyses have been performed in order to summarize recommendations regarding the mesh sensitivity, boundary conditions influence, etc. List of pieces of advice and author’s experiences presented in the end of this work should contribute to more accurate and effective utilization of the ODM.

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.

scholarly journals Probabilistic-Deterministic Method of Rescaling Ship Manoeuvring Simulation Data Defining Parameters of Fairway Bends

2018 ◽  
Vol 1 (1) ◽  
pp. 127-133
Author(s):  
Stanisław Gucma ◽  
Rafał Gralak
Keyword(s):  
Accurate Determination ◽  
Scaling Up ◽  
Maximum Length ◽  
Deterministic Method ◽  
Simulation Data ◽  
Ship Manoeuvring

Abstract The article presents a method of scaling up existing simulation tests results from ships with parameters L1, B1 (length and breadth) determining a safe waterway bend width (d1) to specify a width (d2) safe for ships with other dimensions L2, B2. This method enables accurate determination of the safe fairway width (d) in case it has been planned to increase maximum length and width of vessels without carrying out relatively expensive simulation tests. The method was used in designing the parameters of the modernized Swinoujscie-Szczecin fairway.

Accurate Description of Near-Crack-Tip Fields for the Estimation of Inelastic Zone Extent in Quasi-Brittle Materials

2012 ◽  
Vol 525-526 ◽  
pp. 529-532 ◽  
Author(s):  
Václav Veselý ◽  
Jakub Sobek ◽  
Lucie Šestáková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element ◽  
Order Term ◽  
Higher Order ◽  
Fe Analysis ◽  
Displacement Fields ◽  
Deterministic Method ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
Higher Order Term ◽  
Selection Of

A description of stress and displacement fields by means of the Williams power series using also higher-order terms is the focus of this paper. Coefficients of this series are determined via the over-deterministic method from the results of conventional finite element (FE) analysis. A study is conducted into the selection of the FE node set whose results are processed in this regression technique. Coefficients up to the twelfth term were determined with high precision. The effect of the position of the FE node set on the accuracy of the values of the higher-order term coefficients is reported.

The Dynamic Three-Parameter Method for Determination of Stress-Intensity Factors From Dynamic Isochromatic Crack-Tip Stress Patterns

1980 ◽  
Vol 47 (4) ◽  
pp. 795-800 ◽  
Author(s):  
H. P. Rossmanith
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Correction Term ◽  
Crack Tip ◽  
Higher Order ◽  
Parameter Method ◽  
Intensity Factors ◽  
Higher Order Terms ◽  
Stress Patterns

Correction methods for the determination of dynamic stress-intensity factors from isochromatic crack-tip stress patterns are developed within the framework of a Westergaard-type stress-function analysis where higher-order terms of the series expansions of the stress functions are retained. The addition σox to the extensional stress σx, is regarded as a first correction term, and the far-field correction term which is proportional to r1/2 is referred to as the β-correction. The β-term represents effects that are due to particular loading systems and situations including finite specimen boundaries. The associated method to determine K can be termed a three-parameter method since it contains K, α, and β as parameters. The correction methods, i.e., velocity correction and higher-order term corrections, permit modification of the “static” crack velocity versus stress-intensity factor (c-K) relationship by correcting the static K for the influence of crack speed and higher-order terms. The results show that both corrections assist the interpretation of current photoelastic c-K-data even though the crack speeds do not exceed one third of the shear wave speed.

Determination of Fracture Behavior under Biaxial Loading of Kevlar 149

2015 ◽  
Vol 766-767 ◽  
pp. 1127-1132 ◽  
Author(s):  
S. Manigandan
Keyword(s):  
Fracture Behavior ◽  
Biaxial Loading ◽  
High Strength ◽  
Flame Resistance ◽  
Flat Plates ◽  
Standard Size ◽  
Effective Utilization ◽  
Different Types ◽  
Effective Reinforcement

The high crystalline fiber Kevlar 149 has a major industrial application and it is extensively used in aerospace industries due to its significant properties of ultra-high modulus, high strength, low density, high flame resistance. Kevlar 149 has an advantage over K 49, since it absorbs less moisture and has high compression strength [3]. In order to explore the vast application, this paper investigates the fracture response of the Kevlar material computationally, when they are subjected to biaxial loading in both tensile and compression. This loading is done to understand the response of the Kevlar how far they poor in compression and rich in tensile. The fiber induced with epoxy is to form as an effective reinforcement. Here the fiber taken as Kevlar 149 & K-49 and the epoxy resin. For easy understanding a sample of two flat plates is considered as a composite structure of standard size, which under goes the biaxial loading computationally using Abaqus/CAE. The pictorial data’s are taken from the post processing study and the data’s can be used to investigate the fracture mechanism of Kevlar 149 & K-49, under different types of strain loading. The output results of Kevlar 149 is compared with K-49 to analyze the behavior of fiber undergoes the biaxial loading both compressive and tensile and also the merits and effective utilization of K-149. It is suggested that this method can be applied to other type of composite materials.

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