The Stress Field and Intensity Factor due to Crazes Formed at the Poles of a Spherical Inhomogeneity

1994 ◽  
Vol 61 (4) ◽  
pp. 803-808 ◽  
Author(s):  
Z. M. Xiao ◽  
K. D. Pae
Keyword(s):  
Stress Intensity Factor ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Moduli ◽  
Superposition Principle ◽  
Numerical Examples ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Good Agreement

The problem of two penny-shaped crazes formed at the top and the bottom poles of a spherical inhomogeneity has been investigated. The inhomogeneity is embedded in an infinitely extended elastic body which is under uniaxial tension. Both the inhomogeneity and the matrix are isotropic but have different elastic moduli. The analysis is based on the superposition principle of the elasticity theory and Eshelby’s equivalent inclusion method. The stress field inside the inhomogeneity and the stress intensity factor on the boundary of the craze are evaluated in the form of a series which involves the ratio of the radius of the penny-shaped craze to the radius of the spherical inhomogeneity. Numerical examples show the interaction between the craze and the inhomogeneity is strongly affected by the elastic properties of the inhomogeneity and the matrix. The conclusion deduced from the numerical results is in good agreement with experimental results given in the literature.

An energy-based equivalent inclusion for the determination of nanocomposite behavior

2015 ◽  
Vol 22 (5) ◽  
Author(s):  
Yamen Maalej ◽  
Luc Dormieux ◽  
Eric Lemarchand
Keyword(s):  
Polymer Nanocomposites ◽  
Elastic Moduli ◽  
New Class ◽  
Inclusion Phase ◽  
Equivalent Inclusion ◽  
Mechanical And Physical Properties ◽  
The Matrix ◽  
Low Levels ◽  
Good Agreement

AbstractAchieving remarkable mechanical properties for very low levels of reinforcement, nanocomposites are nowadays a new class of materials with high potential. Thanks to the stiffening aspect of the interface region between the matrix and the inclusions, nanocomposites often exhibit improved mechanical and physical properties compared to the conventional composites reinforced with micron-sized particles. This paper presents a strategy based on the introduction of an equivalent inclusion phase that allows managing the ellipsoidal morphology of inhomogeneous inclusion nanophase in the determination of estimates for the homogenized elastic moduli. Application to clay-polymer nanocomposites is presented in the framework of the dilute scheme. The latter gives theoretical estimates in good agreement with experimental results reported in the literature.

Analysis of Crack-Inclusion Interaction in an Anisotropic Medium by Eshelby Equivalent Inclusion Method

2011 ◽  
Vol 268-270 ◽  
pp. 72-75 ◽  
Author(s):  
Xian Wei Zeng ◽  
Xi Luo
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Anisotropic Medium ◽  
Mode I ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
Inclusion Interaction ◽  
Eshelby Equivalent Inclusion Method

The problem of a semi-infinite crack in anisotropic medium interacting with a near-tip inclusion is analyzed by the Eshelby equivalent inclusion method. The change of mode I stress intensity factor due to crack-inclusion interaction is evaluated using a novel analytical solution for the model I stress intensity factor at the tip of a semi-infinite crack due to near-tip eigenstrains. Numerical results of the mode I stress intensity factor due to the presence of a near-tip circular inclusion are presented to show the influence of the elastic stiffness of an inclusion on the near-tip elastic field. The present scheme can be applied to calculate the stress intensity at a crack-tip in anisotropic media due to the interaction of inclusions with arbitrary shapes.

Structural Integrity of Penetration Nozzle of Reactor Pressure Vessel Head of PWR Plant

2008 ◽  
Author(s):  
Kiminobu Hojo ◽  
Naoki Ogawa ◽  
Yoichi Iwamoto ◽  
Kazutoshi Ohoto ◽  
Seiji Asada ◽  
...  
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Pressure Vessel ◽  
Structural Integrity ◽  
Complex Structure ◽  
Reactor Pressure Vessel ◽  
Reactor Pressure

A reactor pressure vessel (RPV) head of PWR has penetration holes for the CRDM nozzles, which are connected with the vessel head by J-shaped welds. It is well-known that there is high residual stress field in vicinity of the J-shaped weld and this has potentiality of PWSCC degradation. For assuring stress integrity of welding part of the penetration nozzle of the RPV, it is necessary to evaluate precise residual stress and stress intensity factor based on the stress field. To calculate stress intensity factor K, the most acceptable procedure is numerical analysis, but the penetration nozzle is very complex structure and such a direct procedure takes a lot of time. This paper describes applicability of simplified K calculation method from handbooks by comparing with K values from finite element analysis, especially mentioning crack modeling. According to the verified K values in this paper, fatigue crack extension analysis and brittle fracture evaluation by operation load were performed for initial crack due to PWSCC and finally structural integrity of the penetration nozzle of RPV head was confirmed.

Crack Tip Stress Analysis of the Steam Generator Dissimilar Steel Welded Joint under Residual Stress Field

2019 ◽  
Vol 795 ◽  
pp. 451-457
Author(s):  
Bao Yin Zhu ◽  
Xian Xi Xia ◽  
He Zheng ◽  
Guo Dong Zhang
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Numerical Method ◽  
Steam Generator ◽  
Welded Joint ◽  
Crack Tip ◽  
Residual Stress Field

An typical mode of a structural integrity failure in dissimilar steel welded joints. This paper aims at studying crack tip stress of a steam generator dissimilar welded joint under residual stress field with the method of interaction integral and XFEM. Firstly, the corresponding weak form is obtained where the initial stress field is involved, which is the key step for the XFEM. Then, the interaction integral is applying to calculate the stress intensity factor. In addition, two simple benchmark problems are simulated in order to verify the precision of this numerical method. Finally, this numerical method is applying to calculate the crack tip SIF of the addressed problem. This study finds that the stress intensity factor increases firstly then decreases with the deepening of the crack. The main preponderance of this method concerns avoiding mesh update by take advantage of XFEM when simulating crack propagation, which could avoid double counting. In addition, our obtained results will contribute to the safe assessment of the nuclear power plant steam generator.

scholarly journals Analysis of Line Contact Elastohydrodynamic Lubrication with the Particles under Rough Contact Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Keying Chen ◽  
Liangcai Zeng ◽  
Juan Chen ◽  
Xianzhong Ding
Keyword(s):  
Film Thickness ◽  
Rough Surface ◽  
Thickness Distribution ◽  
Traction Force ◽  
Elastohydrodynamic Lubrication ◽  
Equation System ◽  
Line Contact ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix

A numerical solution for line contact elastohydrodynamic lubrication (EHL) occurring on the rough surface of heterogeneous materials with a group of particles is presented in this study. The film thickness disturbance caused by particles and roughness is considered into the solution system, and the film pressure between the contact gap generated by the particles and the surface roughness is obtained through a unified Reynold equation system. The inclusions buried in the matrix are made equivalent to areas with the same material as that of the matrix through Eshelby’s equivalent inclusion method and the roughness is characterized by related functions. The results present the effects of different rough topographies combined with the related parameters of the particles on the EHL performance, and the minimum film thickness distribution under different loads, running speeds, and initial viscosities are also investigated. The results show that the roughness morphology and the particles can affect the behavior of the EHL, the traction force on a square rough surface is smaller, and the soft particles have more advantages for improving the EHL performance.

Elevated Temperature Neutron Measurements of Thermal Residual Stresses in a Sic Fibre Reinforced Al Alloy

1994 ◽  
Vol 376 ◽  
Author(s):  
Monica Ceretti ◽  
M. Kocsis ◽  
A. Lodini
Keyword(s):  
Residual Stresses ◽  
Al Alloy ◽  
Thermal Residual Stresses ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Al 7075 ◽  
Sic Whiskers ◽  
Stress Free State ◽  
Increasing Temperature

ABSTRACTThe main objective of the present investigation is to determine the evolution of residual stresses by neutron powder diffraction in an Al/SiC composite (Al 7075 reinforced by 27 vol.% SiC whiskers), originating from thermal treatment and mechanical loading. The results show that residual stresses in the matrix and in the reinforcement decrease in magnitude with increasing temperature and they reach the stress free state at the 'equivalent temperature'. As the temperature further increases, these stresses increase numerically in a reverse sense for both phases. The data obtained are analysed in terms of a simple model based on Eshelby's equivalent inclusion method.

A Model for Determining Crack Opening Stress Intensity Factor Ratio under Tri-Axial Stress State

2005 ◽  
Vol 297-300 ◽  
pp. 1572-1578
Author(s):  
Yu Ting He ◽  
Feng Li ◽  
Rong Shi ◽  
G.Q. Zhang ◽  
L.J. Ernst ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress State ◽  
Intensity Factor ◽  
Present Model ◽  
Axial Stress ◽  
Crack Opening ◽  
Factor Ratio ◽  
Crack Opening Stress ◽  
Good Agreement

When studying 3D fatigue crack growth behaviors of materials, to determine the crack opening stress intensity factor ratio is the key issue. Elastic-plastic Fracture Mechanics theory and physical mechanism of cracks’ closure phenomena caused by plastic deformation are employed here. A model for determining the crack opening stress intensity factor ratio under tri-axial stress state is presented. The comparison of the present model with available data and models shows quite good agreement.

The Effects of Residual Stress Distribution and Component Geometry on the Stress Intensity Factor of Surface Cracks

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Katsumasa Miyazaki ◽  
Masahito Mochizuki
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Stress Field ◽  
Crack Growth ◽  
Residual Stress Distribution ◽  
Surface Cracks ◽  
Intensity Factors

The stress intensity factor estimated by the appropriate modeling of components is essential for the evaluation of crack growth behavior in stress corrosion cracking. For the appropriate modeling of a welded component with a crack, it is important to understand the effects of residual stress distribution and the geometry of the component on the stress intensity factor of the surface crack. In this study, the stress intensity factors of surface cracks under two assumed residual stress fields were calculated. As residual stress field, a bending type stress field (tension-compression) and a self-equilibrating stress field (tension-compression-tension) through the thickness were assumed, respectively. The geometries of the components were plate and piping. The assumed surface cracks for those evaluations were a long crack in the surface direction and a semi-elliptical surface crack. In addition, crack growth evaluations were conducted to clarify the effects of residual stress distribution and the geometry of the component. Here, the crack growth evaluation means simulating increments of crack depth and length using crack growth properties and stress intensity factors. The effects of residual stress distribution and component geometry on the stress intensity factor of surface cracks and the appropriate modeling of cracked components are discussed by comparing the stress intensity factors and the crack growth evaluations for surface cracks under residual stress fields.

Complex Variable Green’s Functions for Crack-Microcracks Interactions

2011 ◽  
Vol 465 ◽  
pp. 123-128 ◽  
Author(s):  
M. Chabaat ◽  
H. Ayas
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Main Crack ◽  
Green's Functions ◽  
Green’S Functions ◽  
Complex Variables ◽  
Mode I ◽  
Micro Cracks

In this study, interaction between a main crack and a surrounding layer of micro cracks is considered. A stress field distribution induced during these interactions is obtained using Muskhelshvili’s complex variables formalism which relies on the Green's functions. The effect of amplification and shielding on the resulting stress field is shown, herein, through a study of mode I Stress Intensity Factor (SIF). To quantify these effects, orientations as well as positions of microcracks with respect to the main crack is taken into consideration. Obtained results are compared and agreed with those of other researchers.

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