The penny-shaped crack in three-dimensional electrostriction

1969 ◽  
Vol 20 (6) ◽  
pp. 966-974 ◽  
Author(s):  
William E. Warren
Keyword(s):  
Three Dimensional ◽  
Penny Shaped Crack ◽  
Shaped Crack

A Survey of Macro-Microcrack Interaction Problems

2000 ◽  
Vol 53 (5) ◽  
pp. 117-146 ◽  
Author(s):  
Vera Petrova ◽  
Vitauts Tamuzs ◽  
Natalia Romalis
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Crack Location ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Microcrack Interaction ◽  
The Impact ◽  
The Continuum ◽  
Model Approach

The results obtained on the problem of the interaction between a large crack and an array of microcracks or other microdefects are reviewed. The following problems are considered: interaction of main crack with microcracks in the two-dimensional case at tensile, shear or combined stress state; a closure of macro or microcracks as a result of their interaction, and the influence of this phenomenon on the stress intensity factor; the thermal cracking of an elastic solid caused by the macro-microcracks interaction and cracks closure; the interaction of a crack with an array of small pores or rigid inclusions; three-dimensional problems of the interaction of a penny-shaped crack with small penny-shaped microcracks. Discussed analytical results are based on the asymptotic analysis and the series solution to systems of singular integral equations describing the interaction of the macrocrack and microdefects. The series solutions were obtained with respect to the small parameter representing the ratio of micro- to macrocrack sizes. Throughout the review, the known solutions on the crack interaction are surveyed. The comparison with solutions to other relevant problems such as an interaction of semi-infinite crack with an array of finite cracks is given. The impact of a close crack location, and a comparison with relevant results of the continuum model approach are discussed. This review article includes 332 references.

Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

2010 ◽  
Vol 81 (6) ◽  
pp. 685-700 ◽  
Author(s):  
Qun Li ◽  
Andreas Ricoeur ◽  
Meinhard Kuna
Keyword(s):  
Three Dimensional ◽  
Piezoelectric Body ◽  
Penny Shaped Crack ◽  
Shaped Crack

Three-Dimensional Elastic Problem of a Penny-Shaped Crack in an Elastic Layer Sandwiched Between Dissimilar Materials

2018 ◽  
Vol 2018 (0) ◽  
pp. G0300401
Author(s):  
Kotaro MIURA ◽  
Makoto SAKAMOTO ◽  
Koichi KOBAYASHI ◽  
Jonas A. PRAMUDITA ◽  
Yuji TANABE
Keyword(s):  
Elastic Layer ◽  
Three Dimensional ◽  
Dissimilar Materials ◽  
Elastic Problem ◽  
Penny Shaped Crack ◽  
Shaped Crack

Modeling of Threshold Strength in Cylindrical Ceramic Structures

2005 ◽  
Vol 72 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Fjo´la Jo´nsdo´ttir ◽  
Glenn E. Beltz ◽  
Robert M. McMeeking
Keyword(s):  
Ceramic Body ◽  
Three Dimensional ◽  
Element Model ◽  
Ceramic Composites ◽  
Strength Distribution ◽  
Penny Shaped Crack ◽  
Ceramic Components ◽  
Threshold Strength ◽  
Shaped Crack ◽  
Residual Compression

Recently, three-dimensional structured ceramic composites with large threshold strengths (i.e., stress below which there is zero probability of failure) have been fabricated utilizing an architecture consisting of relatively stress-free, elongated prismatic domains, separated by thin compressive walls. We build upon prior work on laminate architectures, with the common feature that these structures are all susceptible to fracture. Typically, these three-dimensional structures consist of thin shells of mullite that surround alumina. Cracks, originating from large flaws within the ceramic body, are arrested by the surrounding compressive layers until a specific stress level is attained (i.e., the threshold strength), resulting in a truncation of the strength distribution in the flaw region. A preliminary stress intensity solution has shown that this arrest is caused by a reduction of the crack driving force by the residual compression in the compressive walls. This solution also predicts that the threshold strength is dependent not only on the magnitude of the residual compression in the walls but also on the dimensions of both phases. A finite element model is presented that utilizes a penny-shaped crack in the interior of such a structure or half-penny-shaped crack emanating from the edge of such a structure. Ongoing analytical and experimental work that is needed to more fully understand this arrest phenomenon and its application towards the development of reliable, damage-tolerant ceramic components are discussed.

Transient Thermoelastic Fields in a Transversely Isotropic Infinite Solid With a Penny-Shaped Crack

1987 ◽  
Vol 54 (4) ◽  
pp. 854-860 ◽  
Author(s):  
N. Noda ◽  
F. Ashida
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transient Heat Conduction ◽  
Thermoelastic Problem ◽  
Conduction Equation ◽  
Thermal Stress Field ◽  
Penny Shaped Crack ◽  
Shaped Crack

The present paper deals with a transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid with a penny-shaped crack. A finite difference formulation based on the time variable alone is proposed to solve a three-dimensional transient heat conduction equation in an orthotropic medium. Using this formulation, the heat conduction equation reduces to a differential equation with respect to the spatial variables. This formulation is applied to attack the transient thermoelastic problem for an axisymmetric transversely isotropic infinite solid containing a penny-shaped crack subjected to heat absorption and heat exchange through the crack surface. Thus, the thermal stress field is analyzed by means of the transversely isotropic potential function method.

Dynamic Analysis of a Piezoelectric Material with an Impermeable Penny-Shaped Crack under Pure Torsional Wave

2007 ◽  
Vol 345-346 ◽  
pp. 433-436
Author(s):  
Zeng Tao Chen
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Transient Wave ◽  
Total Displacement ◽  
Penny Shaped Crack ◽  
Shaped Crack

A torsional transient wave was assumed acting at infinity on the piezoelectric body with an embedded penny-shaped crack. Appropriate governing equations and boundary conditions have been built within the three-dimensional electroelasticity. The total displacement field was simply considered as the combination of two parts, one related to incident waves inducing an oscillating motion, and another with the scattered waves. An electric impermeable crack was assumed to simplify the mathematical analysis. The problem was formulated in terms of integral transforms techniques. Hankel transform were applied to obtain the dual integral equations, which were then expressed to Fredholm integral equations of the second kind.

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