• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.11-18
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• 2001

A simple and convenient method of analysis for obtaining the individual stress intensity factors in a three-dimensional mixed mode crack is proposed. The procedures presented here are based on the path independence of J integral and mutual or two-state conservation integral, which involves two elastic fields. The problem is reduced to the determination of mixed mode stress intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. Some numerical examples are presented to investigate the effectiveness and applicability of the method for a three-dimensional penny-shaped crack problem under mixed mode. This procedure is applicable to a three-dimensional mixed mode curved crack.

• International Journal of Precision Engineering and Manufacturing
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• v.1 no.2
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• pp.14-23
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• 2000

A numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three dimensional mixed mode crack. The method is based on the path independence of J and M integral and mutual or two-state conservation integral , which involves two elastic fields. Some numerical example are presented to investigate the effectiveness and applicability of the method for and axisymmetric crack and a three dimensional penny shaped crack problem under mixed mode.

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Smart Structures and Systems
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• v.19 no.2
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• pp.163-179
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• 2017

The axisymmetric buckling delamination of the Piezoelectric/Metal/Piezoelectric (PZT/Metal/PZT) sandwich circular plate with interface penny-shaped cracks is investigated. The case is considered where open-circuit conditions with respect to the electrical displacement on the upper and lower surfaces, and short-circuit conditions with respect to the electrical potential on the lateral surface of the face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. The sought values are presented in the power series form with respect to the small parameter which characterizes the degree of the initial imperfection. The zeroth and first approximations are used for investigation of stability loss and buckling delamination problems. It is established that the equations and relations related to the first approximation coincide with the corresponding ones of the three-dimensional linearized theory of stability of electro-elasticity for piezoelectric materials. The quantities related to the zeroth approximation are determined analytically, however the quantities related to the first approximation are determined numerically by employing Finite Element Method (FEM). Numerical results on the critical radial stresses acting in the layers of the plate are presented and discussed. In particular, it is established that the piezoelectricity of the face layer material causes an increase (a decrease) in the values of the critical compressive stress acting in the face (core) layer.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.39-50
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• 1999

특이 가중함수로 표현된 shepard interpolant와 일관조건을 사용하여 무요소법 형성함수를 도출하였다. 따라서 통상의 EFGM(Element Free Galerkin Method)과는 달리 변위로 주어지는 경계조건을 자연스럽게 부과할 수 있다. 수치계산 예로서 외팔보 문제를 다루었는데 보이론과 비교하여 매우 잘 맞는 결과를 보여주고, 유한요소법과의 결합도 자연스럽게 이루어짐을 보인다. 또 penny-shaped 균열을 다루는데, 응력확대계수는 균열 표면의 변위로부처 직접 계산하여 해석해와 비교한다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.10
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• pp.1009-1016
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• 2007

Finite element alternating method has been suggested and used effectively to obtain the fracture parameters in assessing the integrity of cracked structures. The method obtains the solution from alternating independently between the FEM solution for an uncracked body and the crack solution in an infinite body. In the paper, the finite element alternating method is extended in order to obtain the elastic-plastic stress fields of a three dimensional inner crack. The three dimensional crack solutions for an infinite body were obtained using symmetric Galerkin boundary element method. As an example of a three dimensional inner crack, a penny-shaped crack in a finite body was analyzed and the obtained elastc-plastic stress fields were compared with the solution obtained from the finite element analysis with fine mesh. It is noted that in the region ahead of the crack front the stress values from FEAM are close to the values from FEM. But large discrepancy between two values is observed near the crack surfaces.

• International Journal of Highway Engineering
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• v.6 no.1 s.19
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• pp.47-56
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• 2004

To determine the pure bond strength between substrate and its overlayed concrete material, a direct pull-off test method was introduced by using a bi-material cylinder with which a penny-shaped crack was mountained at its interface. First, to evaluate the stress magnification or concentration at the interface, the energy release rates of a penny-shaped interface crack in remote tension loading on a bi-material cylinder were determined in terms of different modulus ratios and undonded area ratios(crack ratios) using a commercial finite element program. Then the energy release rates were calibrated as non-dimensional values in consideration of structural dimensions and applied forces. And to evaluate whether this new pull-off test method gives sound test results, three different sizes of unbended area ratios were incorporated along their interface in bi-material cylinders(sulphur polymer concrete + old concrete). Test results showed that all specimens were broken off at their interfaces as intended. Also the FEM analyses and test results indicated that a bi-material specimen with unbended area ratio of 0.4$\sim$0.6 is suitable for best accurate testing.