scholarly journals On The Parameters of Geometric Constraints for Cracked Plates under Tension – Three-Dimensional Problems

2017 ◽  
Vol 22 (4) ◽  
pp. 901-919 ◽  
Author(s):  
M. Graba
Keyword(s):  
Fracture Toughness ◽  
Comparative Analysis ◽  
Crack Front ◽  
External Load ◽  
Three Dimensional ◽  
Geometric Constraints ◽  
Numerical Calculations ◽  
Cracked Plates ◽  
The Relationship ◽  
Actual Fracture

Abstract This paper provides a comparative analysis of selected parameters of the geometric constraints for cracked plates subjected to tension. The results of three-dimensional numerical calculations were used to assess the distribution of these parameters around the crack front and their changes along the crack front. The study also involved considering the influence of the external load on the averaged values of the parameters of the geometric constraints as well as the relationship between the material constants and the level of the geometric constraints contributing to the actual fracture toughness for certain geometries.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

2003 ◽  
Author(s):  
Y. Kim ◽  
Y. J. Chao ◽  
M. J. Pechersky ◽  
M. J. Morgan
Keyword(s):  
Fracture Toughness ◽  
Plane Strain ◽  
Crack Front ◽  
Testing Effect ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
J Integral ◽  
Η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

C-Specimen Fracture Toughness Testing: Effect of Side Grooves and η Factor

2004 ◽  
Vol 126 (3) ◽  
pp. 293-299 ◽  
Author(s):  
Y. Kim ◽  
Y. J. Chao ◽  
M. J. Pechersky ◽  
M. J. Morgan
Keyword(s):  
Fracture Toughness ◽  
Plane Strain ◽  
Crack Front ◽  
Testing Effect ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Compact Tension ◽  
Compact Tension Specimen ◽  
J Integral ◽  
Η Factor

Elastic-plastic crack front fields in arc-shaped tension specimens (C-specimens) were analyzed by a three-dimensional finite element method. The effect of side grooves on the ductile fracture behavior was investigated by studying the J-integral distribution, plane-strain constraint parameter, and development of plastic zones and comparing to experimental data. The applicability of the η factor (derived for use with compact tension specimens) for the calculation of J-integral values for the C-specimen was also investigated. The results show that side grooves promote and establish near plane strain conditions at the crack front in sub-size specimens. It was also found that a two-dimensional plane-strain analysis in conjunction with the standard American Society for Testing and Materials (ASTM) tests was sufficient to determine the fracture toughness values from side-grooved C-specimen. The results indicate the η factor for compact tension specimen as specified in the ASTM standards appears to produce reliable results for the calculation of J of C-specimens.

Effect of Various Side Grooves on 3D Crack-Front J-Integral for CT Specimens

2016 ◽  
Vol 853 ◽  
pp. 46-50 ◽  
Author(s):  
Xiang Qing Li ◽  
Chuan Xiao Wu ◽  
Jian Feng Mao ◽  
Shi Yi Bao ◽  
Zeng Liang Gao
Keyword(s):  
Fracture Toughness ◽  
Crack Front ◽  
Numerical Study ◽  
Three Dimensional ◽  
Element Model ◽  
Compact Tension ◽  
Test Method ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Strain Relationship

Three-dimensional (3D) elastic-plastic finite element model (FEM) is adopted to research the effect of side groove on the crack-front J-integral for different size of Compact Tension (CT) specimens. Although the side-grooved CT specimen is widely used in the existing test method, such as ASTM E1820-13, the test data of fracture toughness is varying with the various geometric parameters. Before FE calculation, the material properties of Q345 steel were obtained by uniaxial tensile test, especially for the true stress-strain relationship. In this paper, it focuses on the numerical study of geometric parameter effects on the fracture toughness. Toward this end, the commercial FE software of ABAQUS is adopted to calculate the J-integral. Since the side groove of CT specimen is so important to make the fracture test success, the various parameters of side groove is intensively analyzed for obtaining the accurate J-integral along the crack front, including the effects of the angle, depth and root radius. In fact, the side groove effect is so significant around the crack front that cannot be ignored in the J-integral calculation. Through rigorous FE investigation, the influence of the side groove on the fracture toughness testing is fully disclosed, and the appropriate side groove configuration is recommended accordingly.

On the Path and Area Jx1-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates

2009 ◽  
Vol 417-418 ◽  
pp. 421-424 ◽  
Author(s):  
A. Fernández Canteli ◽  
E. Giner ◽  
D. Fernández Zúñiga ◽  
J. Fernández Sáez
Keyword(s):  
Crack Front ◽  
Three Dimensional ◽  
Young Modulus ◽  
Simple Relation ◽  
Thin Plates ◽  
Elastic Behaviour ◽  
Specimen Thickness ◽  
Plane Stress Condition ◽  
Cracked Plates ◽  
Out Of Plane

In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is shown that the 2D plane stress condition is impossible in the close neighbourhood of a 3D crack front under elastic behaviour so that the consideration of an equivalent Young modulus E', used to find a simple relation between the J(s)-integral and KI for different constraint levels can be misleading.

Probabilistic PTS Analysis

2016 ◽  
Author(s):  
V. R. Bhimanadam ◽  
F. J. Blom
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Base Metal ◽  
Heat Affected Zone ◽  
Crack Front ◽  
Master Curve ◽  
Three Dimensional ◽  
Deterministic Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

This paper describes the effect of variability of fracture toughness of nuclear pressure vessels during a PTS event. The model used in this paper is based on the NESC-1 experiment. To determine the behavior of the surface breaking defect NRG performed three dimensional finite element calculations and subsequently extended these calculations to the probabilistic calculations. Three-dimensional finite-element model of the cladded cylinder was generated using ANSYS with semi-elliptical surface crack having a crack depth of 75 mm and a crack length of 205 mm. The cylinder specimen was subjected to thermal-shock and centrifugal loading conditions and analyzed with a themo-elastic-plastic material model and subsequently determined the fracture mechanics parameters (J and K) along the elliptical crack front as a function of time and temperature. The determined stress intensity factor K has been compared with the available cleavage fracture toughness (KJC) data with 50% fracture probability which has been obtained from the Master Curve according to BS7910. The comparison has been performed for the locations in the base metal as well as the locations in the heat affected zone. Deterministic analysis has been extended to probabilistic analysis to calculate the failure probability for the crack initiation at the locations in the base metal as well as the locations in the heat affected zone along the crack front by considering probabilistic distributions from Master Curve and FAVOR. Master Curve analysis through the ASME code case N-629 has been applied to the material. Results obtained from these two methods have been compared and also the results are used to compare the inherent safety factors in the deterministic analysis using RTNDT and Master Curve.

Three-Dimensional Crack Growth in Ductile Materials: Effect of Stress Constraint on Crack Tunneling

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Jianzheng Zuo ◽  
Xiaomin Deng ◽  
Michael A. Sutton ◽  
Chin-Shan Cheng
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
Crack Front ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Stress Constraint ◽  
Ductile Materials ◽  
Fracture Simulation ◽  
Crack Tunneling ◽  
Stable Tearing

Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially straight crack fronts. As a specimen is loaded monotonically, the midsection of the crack front will advance first, which will be followed by crack growth along the rest of the crack front, leading to the formation of a thumbnail shaped crack-front profile. From the viewpoint of fracture mechanics, crack tunneling will occur if the operating fracture criterion is met first in the midsection of the crack front, which may be due to a higher fracture driving force and∕or a lower fracture toughness in the midsection. A proper understanding of this fracture behavior is important to the development of a three-dimensional fracture criterion for general stable tearing crack growth in ductile materials. In this paper, the phenomenon of crack tunneling during stable tearing crack growth in a single-edge crack specimen is investigated by considering the effect of stress constraint on the fracture toughness. Crack growth in the specimen under nominally Mode I loading conditions is considered. In this case, crack tunneling occurs while the initially flat crack surface (which is normal to the specimen’s lateral surfaces) evolves into a final slanted fracture surface. A mixed-mode crack tip opening displacement (CTOD) fracture criterion and a custom three-dimensional (3D) fracture simulation code, CRACK3D, are used to analyze the crack tunneling event (but not crack slanting) in the specimen. Results of this investigation suggest that the critical CTOD value (which is the fracture toughness) has a clear dependence on the crack-front stress constraint Am (the constraint measure in this work is the stress triaxiality, which is the ratio of the mean normal stress to the von Mises effective stress). For simplicity, this dependence can be approximated by a straight line within the range of stress constraint values found, with the toughness decreasing as the constraint increases. It is found that crack tunneling in this case is mainly the result of a higher stress constraint (hence a lower fracture toughness) in the midsection of the crack front. Details of the crack growth simulation and other findings of this study will also be presented.

Crack Tunneling: Effect of Stress Constraint

2004 ◽  
Author(s):  
Jianzheng Zuo ◽  
Xiaomin Deng ◽  
Michael A. Sutton ◽  
C.-S. Cheng
Keyword(s):  
Fracture Toughness ◽  
Crack Growth ◽  
Crack Front ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Tunneling Effect ◽  
Stress Constraint ◽  
Ductile Materials ◽  
Crack Tunneling ◽  
Stable Tearing

Crack tunneling is a crack growth feature often seen in stable tearing crack growth tests on specimens made of ductile materials and containing through-thickness cracks with initially straight crack fronts. As a specimen is loaded monotonically, the mid-section of the crack front will advance first, which will be followed by crack growth along the rest of the crack front, leading to the formation of a thumb-nail shaped crack-front profile. From the viewpoint of fracture mechanics, crack tunneling will occur if the operating fracture criterion is met first in the mid-section of the crack front, which may be due to a higher fracture driving force and/or a lower fracture toughness in the mid-section. A proper understanding of this fracture behavior is important to the development of a three-dimensional fracture criterion for general stable tearing crack growth in ductile materials. In this paper, the phenomenon of crack tunneling during stable tearing crack growth in a single-edge crack specimen is investigated by considering the effect of stress constraint on the fracture toughness. Crack growth in the specimen under nominally Mode I loading conditions is considered. In this case, crack tunneling occurs while the initially flat crack surface (which is normal to the specimen’s lateral surfaces) evolves into a final slanted fracture surface. A mixed-mode CTOD fracture criterion and a custom three-dimensional fracture simulation code, CRACK3D, are used to analyze the tunneling and slanting process in the specimen. Results of this investigation suggest that the critical CTOD value (which is the fracture toughness) has a clear dependence on the crack front stress constraint (which is the ratio of the mean stress to the von Mises effective stress). This dependence seems to be linear within the range of stress constraint values found, with the toughness decreasing as the constraint increases. It is found that crack tunneling in this case is mainly the result of a higher stress constraint (hence a lower fracture toughness) in the midsection of the crack front. Details of the crack growth simulation and other findings of this study will also be presented.

Elastic-Plastic Deformation in Surface-Cracked Plates: Experiment and Numerical Analysis

1991 ◽  
Vol 58 (4) ◽  
pp. 895-903 ◽  
Author(s):  
Y.-Y. Wang ◽  
D. M. Parks ◽  
W. R. Lloyd ◽  
W. G. Reuter ◽  
J. Epstein
Keyword(s):  
Crack Front ◽  
Three Dimensional ◽  
Small Strain ◽  
J Integral ◽  
Cracked Plates ◽  
Theory Of Plasticity ◽  
Surface Displacements ◽  
Dominance Study ◽  
Eventual Loss ◽  
Global Deformation

Detailed three-dimensional nonlinear finite element (FE) analyses and experimental moire studies are performed on a plate containing a moderately deep part-through surface crack to establish limits of HRR-dominance. The plate is subjected to predominantly far-field tensile loading. The material under investigation is ASTM A710 steel, which was constitutively modeled by large deformation J2 flow theory of plasticity. The FE mesh was carefully constructed to resolve both crack front fields (such as J-integral and CTOD) and global fields (such as surface displacements, strains). By comparing the J-integral and CTOD results with an earlier HRR-dominance study using (small strain) deformation theory of plasticity, we found little effect of the different formulations on the crack front fields. The global deformation fields from the numerical simulation are in good agreement with our experimental results. The eventual loss of HRR-dominance is intimately related to the interaction of the global plastic flow fields with those of the crack front.

The number of employed as a macroeconomic indicator of working time dynamics

2020 ◽  
Vol 16 (5) ◽  
pp. 935-945
Author(s):  
I.A. Zaikova
Keyword(s):  
Comparative Analysis ◽  
Manufacturing Sector ◽  
Working Hours ◽  
Working Time ◽  
Labor Costs ◽  
Factors Affecting ◽  
Time Dynamics ◽  
Developed Economies ◽  
The Relationship ◽  
Macroeconomic Indicator

Subject. The working time of workers at any stage of economic development is a value reflecting the level of labor productivity. Any progress in productivity contributes to changes in the volume of labor costs and the number of employed. Depending on the relationship between the total volume of labor costs and the number of employed, the duration of working time per one worker may change (it may increase, decrease, or remain unchanged). Objectives. The study aims to confirm the importance of such a macroeconomic indicator as the number of employed in varying working hours. Methods. The study rests on the comparative analysis of countries with developed economies based on some indicators like dynamics of the working time fund, dynamics of the number of employed, average number of hours worked during the year per employee, etc. The analyzed timespan is 25 years (from 1991 to 2016). Results. The comparative analysis revealed that in the non-production sphere and the economy as a whole the macroeconomic determinants correlate so that the length of working time per worker reduces. When considering the analysis results for the manufacturing sector, no single trend was identified. Conclusions. One of the key factors affecting the change in working hours is the number of employed. The relationship between the working time fund and the number of employed directly determines the dynamics of working time per worker.

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