scholarly journals An Investigation of Surface Stress on the Fracture Mechanics Behavior of Classical and Phase-Separating Planar Electrodes

2021 ◽  
Author(s):  
Seyed Ali Mahmoudy ◽  
Hamed Haftbaradaran
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Size Effects ◽  
Surface Stress ◽  
Lithium Ion ◽  
High Energy ◽  
Large Strains ◽  
Stress Theory

Although lithium-ion batteries have extensively been used in various applications because of their high energy capacity, fracture and failure, the by-products of large strains and stresses caused by fast charging and discharging need yet to be addressed. The size effects on the mechanical behavior of the nano-sized structures are significant; however, the classical elasticity theory may not consider such effects. On the other hand, surface stress theory, as a robust and potential theory, is suitable in considering size effects in nano-scale structures. Therefore, in this paper, in order to involve the surface stress effects on the fracture behavior of Li-ion batteries, the following steps are taken. Firstly, a phase-field model is used to determine the evolution of the concentration profile. Subsequently, the stress distribution is obtained by using the surface stress theory combined with chemical equations for a planar electrode. Afterward, by using the weight function method for an edge crack in the plate, the stress intensity factor is derived for all time steps and possible crack lengths during the process. It is found that with increasing phase boundary thickness parameter or decreasing phase-separation phenomenon, the surface mechanics parameters become more influential. Furthermore, in the presence of positive surface stress, the diffusion-induced stress distribution decreases, which in turn reduces the stress intensity factor. In addition, in this paper, the two states of surface stress are compared either for elastic or total strain. Concerning stresses and concentrations, the results indicate a big difference at the beginning of the deintercalation process showing, in particular, 2% for stresses, but the differences diminish gradually.

Universal Weight Function Consistent Method to Fit Polynomial Stress Distribution for Calculation of Stress Intensity Factor

2010 ◽  
Author(s):  
Douglas A. Scarth ◽  
Steven X. Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Wall Thickness ◽  
Function Method ◽  
Polynomial Equation ◽  
Evaluation Procedure ◽  
Weight Function Method

Procedures for analytical evaluation of flaws in nuclear pressure boundary components are provided in Section XI of the ASME B&PV Code. The flaw evaluation procedure requires calculation of the stress intensity factor. Engineering procedures to calculate the stress intensity factor are typically based on a polynomial equation to represent the stress distribution through the wall thickness, where the polynomial equation is fitted using the least squares method to discrete data point of stress through the wall thickness. However, the resultant polynomial equation is not always an optimum fit to stress distributions with large gradients or discontinuities. Application of the weight function method enables a more accurate representation of the stress distribution for the calculation of the stress intensity factor. Since engineering procedures and engineering software for flaw evaluation are typically based on the polynomial equation to represent the stress distribution, it would be desirable to incorporate the advantages of the weight function method while still retaining the framework of the polynomial equation to represent the stress distribution when calculating the stress intensity factor. A method to calculate the stress intensity factor using a polynomial equation to represent the stress distribution through the wall thickness, but which provides the same value of the stress intensity factor as is obtained using the Universal Weight Function Method, is provided in this paper.

RPV Structure Integrity Assessment With Surface Cracks Under PTS

2017 ◽  
Author(s):  
Wei Lu ◽  
Zheng He
Keyword(s):  
Fracture Toughness ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Thermal Shock ◽  
Surface Crack ◽  
Parameter Analysis ◽  
Integrity Assessment ◽  
Pressurized Thermal Shock

As one of the most critical barrier of pressurized-water reactor, Reactor Pressurized Vessel (RPV) is exposed to high temperature, high pressure and irradiation. During the lifetime of RPV, the core belt material will become brittle under the influence of neutron irradiation. The ductile-brittle transition temperature will increase and upper shelf energy will decrease. Thus the structure integrity evaluation of RPV concerning brittle fracture is one of the most important tasks of RPV lifetime management. The non-LOCA accident of Rancho Seco nuclear power plant in 1978 indicates that the emergent cooling transients the sudden cooling down may accompany with the re-pressurize of main loop. The combination of pressure loads and thermal loads may induce a large tensile stress in RPV internal surface, which is the so called pressurized thermal shock (PTS). Due to the existence of welding cladding on the inner surface of RPV, the discontinuity of stress distribution on the cladding-base interface of RPV wall will make calculation of stress-intensity-factor (SIF) difficult. In present research, a two dimensional axial-symmetrical model is built and Finite Element Method (FEM) is adopted to calculate the transient thermal distribution and stress distribution. The influence function method is adopted to calculate crack SIF. Stress distributions in the base and cladding are decomposed respectively and SIFs are calculated respectively to obtain the crack SIF. ASME method is used to calculate the fracture toughness. Present PTS program is validated by the comparative benchmark calculation (the International Comparative Assessment Study of Pressurized Thermal-Shock in Reactor Pressure Vessels). The calculated SIF from present program lies in the reasonable region of the comparing group results. A LOCA transient is investigated with a semi-elliptical surface crack on the RPV beltline region. The temperature and stress distribution along the vessel wall during the transient are given. The stress intensity factors at the deepest and interface point are given respectively. The integrity of RPV under PTS transient is evaluated by comparing stress intensity factor with fracture toughness. Results indicate that the stress intensity factor will not exceed the fracture toughness of the RPV material. The difference between the stress intensity factor and fracture toughness reach a minimum value at the crack tip temperature 20°C. Present research gives a reliable and efficient program to perform RPV structure integrity assessment with surface crack under PTS, which is suitable for further parameter analysis and probabilistic analysis.

The Correction of Stress Intensity Factor for Crack Growth Evaluation Under Steep Residual Stress Distribution and Steep Yield Strength Distribution

2013 ◽  
Author(s):  
Tetsuo Yasuoka ◽  
Yoshihiro Mizutani ◽  
Akira Todoroki
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Yield Strength ◽  
Crack Tip ◽  
Strength Distribution ◽  
Residual Stress Distribution ◽  
Growth Evaluation

Welds and heat affected zones have the distribution of the residual stress or the yield strength. The crack growth evaluation is conventionally conducted using stress intensity factor in those regions. However, the stress intensity factor may be invalid when the residual stress distribution or yield strength distribution changes in the vicinity of a crack tip. The reason is that the distributions around the crack tip affect the plastic zone size and the stress intensity factor inappropriately represents the stress state in the vicinity of a crack tip. In this study, the residual stress distribution and yield strength distribution was assumed along the crack propagation path and the validity of the stress intensity factor was discussed on that condition. As a result, the stress intensity factor tended to be invalid when the steep residual stress distribution or the steep yield strength distribution. When the steep distribution exists, the crack growth evaluation should be conducted using a parameter considering the elastoplastic behavior near the crack tip. For that purpose, the authors proposed new method of the plastic zone correction using a differential term of the stress intensity factor. The new method was demonstrated through the case study for stress corrosion cracking of nuclear power plants.

Stress Intensity Factors due to Residual Stresses in Thin-Walled Girth-Welded Pipes

1981 ◽  
Vol 103 (1) ◽  
pp. 66-75 ◽  
Author(s):  
E. F. Rybicki ◽  
R. B. Stonesifer ◽  
R. J. Olson
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Crack Growth ◽  
Residual Stress Distribution ◽  
Intensity Factors ◽  
Thin Walled Pipe ◽  
Thin Walled

The effect of a girth-weld-induced residual stress field on the linear elastic fracture mechanics of a thin-walled pipe is examined. The procedure for using the residual stress distribution to compute KI and KII for a circumferential crack which is growing radially is described. In addition to the two-pass girth weld, stress intensity factors are computed for a residual stress distribution in a flat plate and for a hypothetical residual stress state in a second thin-walled pipe. The computed stress intensity factor for the flat plate geometry and its residual stress distribution are compared with a solution from the literature as a check on the computational procedure. The through-the-thickness residual stress distribution due to the two-pass girth weld is similar to a half-cosine wave. For purposes of comparison, the hypothetical through-the-thickness distribution selected for the second pipe is similar to a full cosine wave. The stress intensity factor is presented as a function of crack depth for a crack initiating on the inner surface of the pipe. The redistribution of residual stresses due to crack growth is also shown for selected crack lengths. The study shows that residual stress-induced crack growth in pipes can be significantly different from that in flat plates due to the possibility of locked-in residual bending moments in the pipe. These locked-in moments can have effects similar to externally applied loads and can either promote or restrain crack growth. A residual stress distribution is illustrated in which crack growth, if initiated, would continue through the entire wall. Also, a residual stress distribution is illustrated for which the crack could arrest after a certain amount of growth.

Weight Function Method With Segment-Wise Polynomial Interpolation to Calculate Stress Intensity Factors for Complicated Stress Distributions

2012 ◽  
Author(s):  
Yinsheng Li ◽  
Hiroto Itoh ◽  
Kunio Hasegawa ◽  
Steven X. Xu ◽  
Douglas A. Scarth
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Polynomial Interpolation ◽  
Distribution Area ◽  
Stress Distributions ◽  
Weight Function Method

Many solutions of the stress intensity factor have been proposed in recent years. However, most of them take only third or fourth-order polynomial stress distributions into account. For complicated stress distributions which are difficult to be represented as third or fourth-order polynomial equations over the stress distribution area such as residual stress distributions or thermal stress distributions in dissimilar materials, it is important to further improve the accuracy of the stress intensity factor. In this study, a weight function method with segment-wise polynomial interpolation is proposed to calculate solutions of the stress intensity factor for complicated stress distributions. By using this method, solutions of the stress intensity factor can be obtained without employing finite element analysis or difficult calculations. It is therefore easy to use in engineering applications. In this method, the stress distribution area is firstly divided into several segments and the stress distribution in each segment is curve fitted to segment-wise polynomial equation. The stress intensity factor is then calculated based on the weight function method and the fitted stress distribution in each segment. Some example solutions for both infinite length cracks and semi-elliptical cracks are compared with the results from finite element analysis. In conclusion, it is confirmed that this method is applicable with high accuracy to the calculation of the stress intensity factor taking actual complicated stress distributions into consideration.

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.

Weight Function Method With Segment-Wise Polynomial Interpolation to Calculate Stress Intensity Factors for Complicated Stress Distributions

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Yinsheng Li ◽  
Kunio Hasegawa ◽  
Steven X. Xu ◽  
Douglas A. Scarth
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Distribution ◽  
Intensity Factor ◽  
Weight Function ◽  
Function Method ◽  
Polynomial Interpolation ◽  
Distribution Area ◽  
Stress Distributions ◽  
Weight Function Method

Many solutions of the stress intensity factor have been proposed in recent years. However, most of them take only third or fourth-order polynomial stress distributions into account. For complicated stress distributions which are difficult to be represented as third or fourth-order polynomial equations over the stress distribution area such as residual stress distributions or thermal stress distributions in dissimilar materials, it is important to further improve the accuracy of the stress intensity factor. In this study, a weight function method with segment-wise polynomial interpolation is proposed to calculate solutions of the stress intensity factor for complicated stress distributions. By using this method, solutions of the stress intensity factor can be obtained without employing finite element analysis or difficult calculations. It is therefore easy to use in engineering applications. In this method, the stress distribution area is firstly divided into several segments and the stress distribution in each segment is curve fitted to segment-wise polynomial equation. The stress intensity factor is then calculated based on the weight function method and the fitted stress distribution in each segment. Some example solutions for both infinite length cracks and semi-elliptical cracks are compared with the results from finite element analysis. In conclusion, it is confirmed that this method is applicable with high accuracy to the calculation of the stress intensity factor taking actual complicated stress distributions into consideration.

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