Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element

2004 ◽  
Vol 125 (3/4) ◽  
pp. 207-225 ◽  
Author(s):  
Q.Z. Xiao ◽  
B.L. Karihaloo ◽  
X.Y. Liu
Keyword(s):  
Mixed Mode ◽  
Direct Determination ◽  
Higher Order ◽  
Higher Order Terms ◽  
Hybrid Crack Element ◽  
Crack Element

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.

Direct Determination of Glyphosate and its Metabolite AMPA in Soil Using Mixed-Mode Solid-Phase Purification and LC-MS/MS Determination on a Hypercarb Column

2019 ◽  
Vol 102 (3) ◽  
pp. 952-965 ◽  
Author(s):  
Pei Zhang ◽  
Mick Rose ◽  
Lukas Van Zwieten
Keyword(s):  
Mixed Mode ◽  
Crop Production ◽  
Solid Phase ◽  
Direct Determination ◽  
Correlation Coefficients ◽  
Grain Production ◽  
Internal Standards ◽  
Aminomethylphosphonic Acid ◽  
Lc Tandem Ms

Abstract Background: Although glyphosate is widely used in agriculture, information on its residue level in soils remains scarce partly because of the difficulty in its analysis. Objective: Develop and validate a method to directly analyze glyphosate and its metabolite aminomethylphosphonic acid (AMPA) in soil. Method: Soils were extracted with 0.6 M KOH solution, and coextracted interferences were removed using a mixed-mode Bond Elut Plexa PAX®. The extracts were analyzed by LC-tandem MS fitted with a Hypercarb column and isotope-labeled (13C,15N) glyphosate and AMPA were used as internal standards. Results: LOQs were 0.05 mg/kg for both glyphosate and AMPA in soils. Correlation coefficients were ≥0.99, residuals were below 20%, and calibrations were linear in the range 0.02–1.0 μg/mL. The method was validated on five contrasting soils (Vertosol, Calcarosol, Chromosol, Sodosol, and Tenosol) commonly used for grain production in Australia. The recoveries for glyphosate and AMPA in the soils were 96–121 and 91–118%, respectively, with RSD in the range of 3–16%. Conclusions: This paper presents using the validated method in analysis glyphosate and AMPA in soils collected from crop production paddocks in Australia. The survey data showed that glyphosate and AMPA were detected in all collected soils, with concentrations ranging between 0.05 and 1.2 mg/kg. Highlights: The study demonstrates that the mixed-mode solid-phase extraction is effective in removing interferences and validates the use of Hypercarb as an alternative stationary phase for glyphosate and AMPA analysis from soils.

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.

scholarly journals MULTIPARAMETRIC ANALYSIS OF THE STRESS FIELD NEAR THE CRACK TIP

2017 ◽  
Vol 21 (10) ◽  
pp. 52-76
Author(s):  
L.V. Stepanova ◽  
P.S. Roslyakov
Keyword(s):  
Asymptotic Expansion ◽  
Stress Field ◽  
Mixed Mode ◽  
Infinite Plate ◽  
Higher Order ◽  
Analytical Determination ◽  
Mixed Mode Loading ◽  
Complete Asymptotic Expansion ◽  
Higher Order Terms ◽  
Crack Tips

The paper is devoted to analytical determination of coefficients of the Williams asymptotic expansion of the stress field in the neighborhood of two collinear crack tips in an infinite plate under mixed mode loading. On the basis of the Kolosof-Muskhelishvili approach the complete asymptotic expansion of the stress field in the vicinity of the crack tips of two collinear cracks of equal lengths under mixed mode loading is derived. The analysis of the higher order terms in the asymptotic expansion series is performed. It is clear that it is necessary to take into account the higher order terms.

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