Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

2006 ◽  
Vol 22 (2) ◽  
pp. 148-155 ◽  
Author(s):  
Junhua Zhao ◽  
Wanlin Guo ◽  
Chongmin She ◽  
Bo Meng
Keyword(s):  
Crack Front ◽  
Three Dimensional ◽  
Elliptical Crack ◽  
Stress Fields ◽  
Elastic Plates

Three-Dimensional Stress Fields of Elastic Interface Cracks

1991 ◽  
Vol 58 (4) ◽  
pp. 939-946 ◽  
Author(s):  
T. Nakamura
Keyword(s):  
Interface Crack ◽  
Crack Front ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Stress Fields ◽  
Interface Fracture ◽  
Experimental Investigations ◽  
Mode Iii ◽  
Critical Energy Release Rate ◽  
Phase Angles

Various aspects of stress fields near an interface crack in three-dimensional bimaterial plates are investigated. Due to the nature of the resulting deformation field, three-dimensional effects are more critical in a bimaterial plate than in a homogeneous plate. In the close vicinity of the crack front, the stress field is characterized by the asymptotic bimaterial K-field, and its domain size is a very small fraction of a plate thickness. Unlike a homogeneous case, the asymptotic field always consists all three modes of fracture, and an interface crack must propagate under mixed-mode conditions. Furthermore, computational results have shown that the two phase angles representing the relative magnitudes of the three modes strongly depend on the bimaterial properties. It has been also observed that a significant antiplane (Mode III) deformation exists along the crack front, especially near the free surface. Since experimental investigations have shown that critical energy release rate Gc is highly dependent on the phase angles, accurate prediction of the interface fracture behavior requires not only the G distribution but also the variations of phase angles along the crack front.

Modified Strip Model for Analyzing the Line Heating Method-Part 1: Elastic Plates

1991 ◽  
Vol 35 (02) ◽  
pp. 172-182
Author(s):  
Jong Gye Shin ◽  
Amiram Moshaiov
Keyword(s):  
Strain Field ◽  
Three Dimensional ◽  
Past Research ◽  
Stress Fields ◽  
Transient Temperature ◽  
Heating Process ◽  
Elastic Strip ◽  
Elastic Plates ◽  
Line Heating ◽  
Heating Method

The line heating method can be most useful in the automation of plate forming and for removal of undesired residual distortions during shipbuilding. The three-dimensional transient temperature and stress fields complicate the problem of simulating the line heating process. In past research efforts, a strip model taken perpendicular to the heated line was used. However, recent experimental and theoretical works have demonstrated the need for a different model. Recognizing that the existing strip model cannot be used effectively in the analysis of the stress-strain field during the line heating process, a modified strip model is suggested. In Part 1 of this paper, the concept of a modified strip is introduced by developing a theory for an elastic modified strip. The results of selected examples show that the modified strip model gives excellent results for elastic plates in comparison with a regular strip model. In Part 2 (to be published in a later issue of JSR), the theory is extended to the thermo-elastic-plastic modified strip. The concept of a modified elastic strip may have other useful applications and therefore is highlighted separately.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals The effect of the outlet angle β2 on the thermomechanical behavior of a centrifugal compressor blade

2020 ◽  
Vol 29 (1) ◽  
pp. 1-8
Author(s):  
Ahmed Allali ◽  
Sadia Belbachir ◽  
Ahmed Alami ◽  
Belhadj Boucham ◽  
Abdelkader Lousdad
Keyword(s):  
Mechanical Behavior ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Complex Form ◽  
Compressor Blade ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Mechanical Fatigue ◽  
Outlet Angle ◽  
The Impact

AbstractThe objective of this work lies in the three-dimensional study of the thermo mechanical behavior of a blade of a centrifugal compressor. Numerical modeling is performed on the computational code "ABAQUS" based on the finite element method. The aim is to study the impact of the change of types of blades, which are defined as a function of wheel output angle β2, on the stress fields and displacements coupled with the variation of the temperature.This coupling defines in a realistic way the thermo mechanical behavior of the blade where one can note the important concentrations of stresses and displacements in the different zones of its complex form as well as the effects at the edges. It will then be possible to prevent damage and cracks in the blades of the centrifugal compressor leading to its failure which can be caused by the thermal or mechanical fatigue of the material with which the wheel is manufactured.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

Sign in / Sign up

Export Citation Format

Share Document