Characteristics of the Elastic Field of a Rigid Line Inhomogeneity

1985 ◽  
Vol 52 (4) ◽  
pp. 818-822 ◽  
Author(s):  
Z. Y. Wang ◽  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Stress Field ◽  
Elastic Field ◽  
Square Root ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Rigid Line ◽  
Square Root Singularity ◽  
Inclined Loading ◽  
Explicit Expressions

Explicit expressions are obtained for the stress and displacement fields near the tip of a rigid line inhomogeneity subjected to an inclined loading. It is shown that the tip stress field, with a square-root singularity, differs in characteristics from that of a slit crack. New designations for the mode of deformation based on the fracture concept are presented and the inhomogeneity extension forces are calculated and discussed.

scholarly journals The critical influence of some “tiny” geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length

2021 ◽  
Vol 16 (59) ◽  
pp. 405-422
Author(s):  
Stavros K Kourkoulis ◽  
Christos Markides ◽  
Ermioni Pasiou ◽  
Andronikos Loukidis ◽  
Dimos Triantis
Keyword(s):  
Stress Field ◽  
Finite Width ◽  
Notch Radius ◽  
Displacement Fields ◽  
Geometrical Characteristics ◽  
Numerical Studies ◽  
Stress And Displacement Fields ◽  
Geometrical Features ◽  
Actual Stress

The role of some geometrical characteristics of the notches ma­chined in circular discs, in order to determine the mode-I fracture tough­ness of brittle materials, is discussed. The study is implemented both analyti­cally and numerically. For the analytic study advantage is taken of a recently intro­duced solution for the stress- and displacement-fields developed in a finite disc with a central notch of finite width and length and rounded corners. The vari­ation of the stresses along strategic loci and the deformation of the peri­me­ter of the notch obtained analytically are used for the calibration/validation of a flexible nu­mer­ical model, which is then used for a parametric investiga­tion of the role of geometrical features of the notched disc (thickness of the disc, length and width of the notch, radius of the rounded corners of the notch). It is con­cluded that the role of the width of the notch is of critical im­port­ance. Both the ana­lytic and the numerical studies indicate definitely that ignoring the ac­curate geo­metric shape of the notch leads to erroneous results concerning the actual stress field around the crown of the notch. Therefore, it is possible that misleading values of the fracture toughness of the material of the disc may be obtained.

The Stress Field Caused by a Circular Cylindrical Inclusion in a Transversely Isotropic Elastic Solid

2003 ◽  
Vol 70 (6) ◽  
pp. 825-831 ◽  
Author(s):  
H. Hasegawa ◽  
M. Kisaki
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Cylindrical Inclusion ◽  
Stress Distributions ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Isotropic Solid ◽  
Stress And Displacement Fields

Exact solutions are presented in closed form for the axisymmetric stress and displacement fields caused by a circular solid cylindrical inclusion with uniform eigenstrain in a transversely isotropic elastic solid. This is an extension of a previous paper for an isotropic elastic solid to a transversely isotropic solid. The strain energy is also shown. The method of Green’s functions is used. The numerical results for stress distributions are compared with those for an isotropic elastic solid.

Axisymmetric Stress Field Around Spheroidal Inclusions and Cavities in a Transversely Isotropic Material

1968 ◽  
Vol 35 (4) ◽  
pp. 770-773 ◽  
Author(s):  
W. T. Chen
Keyword(s):  
Stress Field ◽  
Linear Elasticity ◽  
Isotropic Material ◽  
Transversely Isotropic ◽  
Transversely Isotropic Material ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
The Matrix ◽  
Classical Linear Elasticity

A spheroidal inclusion is embedded in an elastic matrix composed of a different material. Both materials are transversely isotropic with the material property axes parallel to the geometric axis of the spheroid. At the interface, the two materials are bonded. The matrix is subjected to a uniform axisymmetric stress field at infinity. Explicit expressions for the stress and displacement fields in the inclusion and the matrix will be presented. The analysis is within the realm of classical linear elasticity.

scholarly journals Unconventional singularities and energy balance in frictional rupture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Efim A. Brener ◽  
Eran Bouchbinder
Keyword(s):  
Energy Balance ◽  
Square Root ◽  
Earthquake Physics ◽  
Macroscopic Theory ◽  
Scale Separation ◽  
Rate Dependent ◽  
Theoretical Predictions ◽  
Spatially Extended ◽  
Singularity Order ◽  
Square Root Singularity

AbstractA widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid. Here we develop a macroscopic theory that shows that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, and that even if this deviation is small, significant non-edge-localized rupture-related dissipation emerges. The physical origin of the latter, which is predicted to vanish identically in the crack analogy, is the breakdown of scale separation that leads an accumulated spatially-extended dissipation, involving macroscopic scales. The non-edge-localized rupture-related dissipation is also predicted to be position dependent. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed.

A Stress Singularity Parameter Approach for Evaluating the Interfacial Reliability of Plastic Encapsulated LSI Devices

1989 ◽  
Vol 111 (4) ◽  
pp. 243-248 ◽  
Author(s):  
T. Hattori ◽  
S. Sakata ◽  
G. Murakami
Keyword(s):  
Adhesive Strength ◽  
Evaluation Method ◽  
Stress Singularity ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Ni Alloy ◽  
Base Resin ◽  
Interfacial Reliability ◽  
Parameter Approach

Since the stress and displacement fields near a bonding edge show singularity behaviors, the adhesive strength evaluation method, using maximum stresses calculated by a numerical stress analysis such as the finite element method, is generally not valid. In this paper, a new method, which uses two stress singularity parameters, is presented for evaluating adhesive strength. This method is applied to several kinds of molded models, composed of epoxy base resin and Fe-Ni alloy sheets, and plastic encapsulated LSI models. Predictions about the initiation and extension of delamination are compared with the results of observations made by scanning acoustic tomography on these models.

Propagation and Opening of a Through Crack in a Pipe Subject to Combined Cyclic Thermomechanical Loading

1976 ◽  
Vol 98 (1) ◽  
pp. 17-25 ◽  
Author(s):  
T. R. Hsu ◽  
A. W. M. Bertels
Keyword(s):  
Bauschinger Effect ◽  
Thermal Loading ◽  
Thin Wall ◽  
Pipe Material ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Growing Crack ◽  
Cyclic Plastic Deformation ◽  
Cyclic Thermomechanical Loading ◽  
Thermoelastic Plastic

The present investigation deals with the propagation and opening of a single crack in a thin wall pipe subject to cyclic pressure and thermal loading. A thermoelastic-plastic analysis based on the finite element variational technique is used to calculate the stress and displacement fields in the vicinity of the growing crack. A special type of element known as a “breakable element” is developed to model the gradual propagation of the crack. Kinematic work hardening is included to account for the Bauschinger effect of the pipe material when subjected to cyclic plastic deformation.

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