Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

2019 ◽  
Vol 24 (10) ◽  
pp. 3216-3230 ◽  
Author(s):  
S Kozinov ◽  
A Sheveleva ◽  
V Loboda
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Behavior ◽  
Compressive Loading ◽  
Closed Form Solution ◽  
Industrial Applications ◽  
Shear Loading ◽  
Form Solution ◽  
Applied Loading

A closed-form solution is constructed for a bi-material consisting of two piezoelectric (or piezoelectric and dielectric) half-planes, which are periodically bonded along the interface and can partially contact along the initially unbonded parts. Under compressive loading, the size of the frictionless contact zone is usually quite large; in some cases the interface is completely closed. Such a situation is frequently observed in industrial applications. Since the periodic bonding of two different materials is extremely widespread, it is very important to study the influence of the mutual material properties of the composite and the applied loading on the size and shape of the opened regions, as well as the stress intensity factor at the bonding points. To formulate the problem, the electromechanical factors are presented through piecewise analytic functions, so that the problem in question is reduced to the combined periodic Dirichlet–Riemann problem, which is solved exactly. The obtained solution provides explicit formulas for the mechanical stresses and displacements along the interface and allows one to find the dependence of the contact zones and the stress intensity factor on the ratio of the bonded parts of the interface to the period for the different values of applied loading and materials.

An Closed Form Solution for Antiplane Problem of Doubly Periodic Non-Uniform Cracks

2006 ◽  
Vol 324-325 ◽  
pp. 311-314
Author(s):  
Yao Ling Xu ◽  
Wen Feng Tan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mapping Technique ◽  
Inhomogeneous Materials ◽  
Antiplane Problem ◽  
Microstructure Parameters

Inhomogeneous materials with doubly periodic non-uniform cracks under antiplane shear is dealt with. By using conformal mapping technique and elliptic function theory, the stress field and stress intensity factor at the tip of each crack are derived in closed form. Numerical examples show the influences of some microstructure parameters of crack distribution on stress intensity factor.

Estimation of Stress Intensity Factor for Circumferential Through-Wall Cracked Elbows Subjected to In-Plane Bending

2015 ◽  
Author(s):  
Han-Bum Surh ◽  
Jong Wook Kim ◽  
Min Kyu Kim ◽  
Min-Gu Won ◽  
Moon Ki Kim ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Form Solution ◽  
Accurate Estimation ◽  
Wide Range ◽  
Plane Bending ◽  
Geometric Variables

The stress intensity factor (SIF) is the major fracture mechanics parameter in LEFM concept. Since the SIF can be used for not only calculation of J-integral based on the GE/EPRI and reference stress method but also evaluation of fatigue crack growth, an accurate estimation of the SIF is an important issue for the piping in nuclear power plant. Recently, there is a need to develop the SIF solution which can cover wide geometric variables since there are on-going efforts that are developing next generation reactors in Korea, which is designed to thin-walled structures. For the through-wall cracked straight pipes, many researchers have proposed the SIF solutions which can cover wide range of wall thickness. However, since only limited solutions have been proposed yet for the through-wall cracked elbows, a research related to the SIF estimation for the elbows with wide geometric variables should be performed. In this study, the extended SIF solution for circumferential through-wall cracked elbows subjected to in-plane bending is proposed as the tabulated form through the finite element (FE) analyses. Wide elbow geometries are selected to range between 5 and 50 of Rm/t and range between 2∼20 of Rb/Rm. The existing solutions are then reviewed by comparing with the FE results. Furthermore, effects of geometric variables on the SIF are addressed through systematic investigation of FE based SIF results. These investigated results are expected to contribute to the development of closed form solution for the circumferential through-wall cracked elbows subjected to in-plane bending.

scholarly journals The Part-Through Surface Crack in an Elastic Plate

1972 ◽  
Vol 39 (1) ◽  
pp. 185-194 ◽  
Author(s):  
J. R. Rice ◽  
N. Levy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Strain ◽  
Surface Crack ◽  
Unit Length ◽  
Mathematical Formulation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bending Loads

An elastic analysis is presented for the tensile stretching and bending of a plate containing a surface crack penetrating part-through the thickness, Fig. 1. The treatment is approximate, in that the two-dimensional generalized plane stress and Kirchhoff-Poisson plate bending theories are employed, with the part-through cracked section represented as a continuous line spring. The spring has both stretching and bending resistance, its compliance coefficients being chosen to match those of an edge cracked strip in plane strain. The mathematical formulation reduces finally to two-coupled integral equations for the thickness averaged force and moment per unit length along the cracked section. These are solved numerically for the case of a semi-elliptical part-through crack, with results compared to a simple but approximate closed-form solution. Extensive results are given for the stress intensity factor at the midpoint of the part-through crack for both remote tensile and bending loads on the plate. These results indicate that the stress-intensity factor is substantially lower, in general, than for a similarly loaded strip in plane strain with a crack of the same depth.

The Importance of the Mode II Term on the Analysis of Angled Cracks in Unidirectional Carbon Fiber Composites

2021 ◽  
Author(s):  
Jacob Biddlecom ◽  
Garrett J. Pataky
Keyword(s):  
Stress Intensity Factor ◽  
Regression Analysis ◽  
Stress Intensity ◽  
Carbon Fiber ◽  
Intensity Factor ◽  
Fiber Composites ◽  
Shear Loading ◽  
Mode Ii ◽  
Carbon Fiber Composites ◽  
Displacement Fields

Abstract Carbon fiber reinforced polymers (CFRP) have been used in many high-performance applications where strength to weight ratio is an important characteristic. The goal of this research was to analyze the effects of Mode II, also known as shear loading, on the displacement fields surrounding a crack for unidirectional carbon fiber composites. Tensile and fatigue experiments were conducted on angled unidirectional CFRP coupled with digital image correlation (DIC) to analyze the full field displacement. Angled CFRP cracks experienced mixed mode loading which required addition insight due to the complex stresses on the fiber/matrix interface. The experimental displacement fields acquired from DIC were used as inputs for an anisotropic regression analysis to determine the mode I and mode II stress intensity factor ranges. The results from the regression analysis were used to predict the displacement fields around a crack. When comparing the experimental results with the predicted results, the inclusion of Mode II increased the agreement between predicted and experimental displacement fields around a crack tip for two different fiber orientation angles. Crack growth rate analysis and analytical stress intensity factor ranges were used to expand on the agreement of the results as well as bring to light CFRP specific fracture mechanisms that lead to disagreements.

Research on Fracture Behavior of a Cracked Film-Substrate Medium

2006 ◽  
Vol 324-325 ◽  
pp. 903-906
Author(s):  
Bao Liang Liu ◽  
Xian Shun Bi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Boundary Element Method ◽  
Intensity Factor ◽  
Boundary Element ◽  
Fracture Behavior ◽  
Thickness Ratio ◽  
Film Substrate ◽  
Substrate Medium ◽  
Element Method

This study gives the problem of a crack in the film oriented perpendicular to the film-substrate interface with the crack tip terminating at the interface. Based on Beuth’s theory, three-dimensional model is simplified to plane strain problems, which obtains fracture mechanisms of a cracked film-substrate medium by applying the boundary element method(BEM). The method aptly resolves the problem involving stress concentration and, further, that this study develops the multi-region boundary element method and applies it to evaluate the cracked film-substrate medium. It shows that the stress intensity factor is affected by the different elastic mismatches and the thickness ratio of the film and the substrate. These results indicate: 1) The stress intensity factor has remarkable increased with the decrease of the thickness ratio of the film and the substrate. The effect of the fracture behavior of film is negligible when the thickness ratio of the film and the substrate is above 10, therefore, it is treated as thin film; 2) The stress intensity factor will decrease with the increase of α ( −1 pα p +1) for β = 0 and β =α / 4 , where α and β are called Dundurs parameters. What’s more, this paper studies the special condition of the film-substrate medium, which is the analysis of the fracture of the absence of any elastic mismatch between the film and the substrate, i.e.α=β=0, and revision of the formula of Xia and Hutchinson is put forward for the stress intensity factor of the deep crack problems by comparing to the former conclusions of Y.Murakami.

Finite Element Fracture Mechanics Study of Pre-Northridge Connections

2006 ◽  
Vol 324-325 ◽  
pp. 1007-1010 ◽  
Author(s):  
Hong Bo Liu ◽  
Chang Hai Zhai ◽  
Yong Song Shao ◽  
Li Li Xie
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Behavior ◽  
Integral Approach ◽  
J Integral ◽  
Finite Element Analyses ◽  
Element Analysis ◽  
Weld Root

The objective was to quantify the variation of stress intensity factor to weld root flaw sizes in steel frame connections. Finite-element analyses were used to study fracture toughness in welded beam-column connections. Investigations of fracture behavior mainly focused on the standard pre-Northridge connection geometry. Finite element analysis was performed using the ANSYS computer program. Stress intensity factor was calculated through a J-integral approach. Results show that stress intensity factor is not uniform and is largest in the middle of beam flange. Stress intensity factor increases nearly linear with the increase of flaw size. Backing bars have little effect on weld fractures.

scholarly journals Hole Defects Affect the Dynamic Fracture Behavior of Nearby Running Cracks

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
R. S. Yang ◽  
C. X. Ding ◽  
L. Y. Yang ◽  
P. Xu ◽  
C. Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Dynamic Fracture ◽  
Fracture Behavior ◽  
Dynamic Stress ◽  
Crack Path ◽  
Dynamic Stress Intensity Factor ◽  
Experimental System ◽  
Intersection Area

Effects of defects on the dynamic fracture behavior of engineering materials cannot be neglected. Using the experimental system of digital laser dynamic caustics, the effects of defects on the dynamic fracture behavior of nearby running cracks are studied. When running cracks propagate near to defects, the crack path deflects toward the defect; the degree of deflection is greater for larger defect diameters. When the running crack propagates away from the defect, the degree of deflection gradually reduces and the original crack path is restored. The intersection between the caustic spot and the defect is the direct cause of the running crack deflection; the intersection area determines the degree of deflection. In addition, the defect locally inhibits the dynamic stress intensity factor of running cracks when they propagate toward the defect and locally promotes the dynamic stress intensity factor of running cracks when they propagate away from the defect.

Analysis of a Curved Interfacial Crack Between Viscoelastic Foam and Anisotropic Composites Under Antiplane Shear

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1573-1579
Author(s):  
Heoung Jae Chun ◽  
Sang Hyun Park
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Composite Materials ◽  
Intensity Factor ◽  
Hilbert Problem ◽  
Crack Problem ◽  
Interfacial Crack ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Stiffness Coefficients

The analysis of curved interfacial crack between viscoelastic foam and anisotropic composites was conducted under antiplane shear loading applied at infinity. In the analysis, in order to represent viscoelastic behavior of foam, the Kelvin-Maxwell model was incorporated and Laplace transform was applied to treat the viscoelastic characteristics of foam. The curved interfacial crack problem was reduced to a Hilbert problem and a closed-form asymptotic solution was derived. The stress intensity factors in the vicinity of the interfacial crack tip were predicted by considering both anisotropic characteristics of composites and viscoelastic properties of foam. It was found from the analysis that the stress intensity factor was governed by material properties such as shear modulus and relaxation time, and increased with the increase in the curvature as well as the ratio of stiffness coefficients of composite materials. It was also observed that the effect of fiber orientation in the composite materials on the stress intensity factor decreased with the increase in the difference in stiffness coefficients between foam and composite.

Sign in / Sign up

Export Citation Format

Share Document