Stress Field for a Coated Triangle-Like Hole Problem in Plane Elasticity

2019 ◽  
Vol 36 (1) ◽  
pp. 55-72 ◽  
Author(s):  
S. C. Tseng ◽  
C. K. Chao ◽  
F. M. Chen
Keyword(s):  
Stress Field ◽  
Edge Dislocation ◽  
Coating Layer ◽  
Infinite Plate ◽  
Material Constant ◽  
Plane Elasticity ◽  
Analytical Continuation ◽  
Shape Factors ◽  
Trapping Mechanism ◽  
The Matrix

ABSTRACTThe stress field induced by an edge dislocation or a point force located near a coated triangle-like hole in an infinite plate is provided in this paper. Based on the method of analytical continuation and the technique of conformal mapping in conjunction with the alternation technique, a series solution for the displacement and stresses in the coating layer and the matrix is obtained analytically. Examples for the interaction between an edge dislocation and a coated triangle-like hole for various material constant combinations, coating thicknesses and shape factors are discussed. The analysis discovers that the so-called trapping mechanism of dislocations is more likely to exist near a coated triangle-like hole. The result shows that the dislocation will first be repelled by the coating layer and then attracted by a hole when the coating layer is slightly stiffer than the matrix. However, when the coating layer is sufficiently thin, the dislocation will always be attracted by a hole even the coating layer is stiffer than the matrix.

Analysis of the M-Integral in Plane Elasticity

2004 ◽  
Vol 71 (4) ◽  
pp. 572-574 ◽  
Author(s):  
Y. Z. Chen ◽  
Kang Yong Lee
Keyword(s):  
Stress Field ◽  
Infinite Plate ◽  
Plane Elasticity ◽  
Physical Stress ◽  
Paper Analysis ◽  
Elasticity Solution ◽  
Large Circle ◽  
Applied Forces ◽  
The Difference ◽  
M Integral

In this paper, analysis of the M-integral in plane elasticity is carried out. An infinite plate with any number of inclusions and cracks and with any applied forces and remote tractions is considered. To study the problem, the mutual work difference integral (abbreviated as MWDI) is introduced, which is defined by the difference of works done by each other stress field on a large circle. The concept of the derivative stress field is also introduced, which is a real elasticity solution and is derived from the physical stress field. It is found that the M-integral on a large circle is equal to a MWDI from the physical stress field and a derivative stress field. Finally, the expression for M-integral on a large circle is obtained. The variation for the M-integral with respect to the coordinate transformation is addressed. An illustrative example for the use of M-integral is presented.

Invariant properties of the stress in plane elasticity and equivalence classes of composites

1992 ◽  
Vol 438 (1904) ◽  
pp. 519-529 ◽  
Keyword(s):  
Stress Field ◽  
Functional Dependence ◽  
Matrix Material ◽  
Plane Elasticity ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Isotropic Composite ◽  
Compliance Tensor ◽  
The Matrix

Attention is drawn to the invariance of the stress field in a two-dimensional body loaded at the boundary by fixed forces when the compliance tensor S(x) is shifted uniformly by S 1 (λ, - λ), where λ is an arbitrary constant and S 1 ( k,u )is the compliance tensor of a isotropic material with two-dimensional bulk and shear moduli k and μ . This invariance is explained from two simple observations: first, That in two dimensions the tensor S (1/2, -1/2) acts to locally rotate the stress by 90° and the second that this rotated field is the symmetrized gradient of a vector field and therefore can be treated as a strain. For composite materials the invariance of the stress field implies that the effective compliance tensor S * also gets shifted by S 1 l( (λ, - λ) when the constituent moduli are each shifted by S (λ, - λ). This imposes constraints on the functional dependence of S * on the material moduli of the components. Applied to an isotropic composite of two isotropic components it implies that when the inverse bulk modulus is shifted by the constant 1/λ and the inverse shear modulus is shifted by — 1/λ, then the inverse effective bulk and shear moduli undergo precisely the same shifts. In particular it explains why the effective Young’s modulus of a two-dimensional media with holes does not depend on the Poisson’s ratio of the matrix material.

Solution for elliptic inclusion in an infinite plate with remote loading and Eshelby’s eigenstrain of polynomial type

2021 ◽  
pp. 108128652110600
Author(s):  
YZ Chen
Keyword(s):  
Stress Field ◽  
Complex Variable ◽  
Infinite Plate ◽  
Inclusion Problem ◽  
Elliptic Inclusion ◽  
Inherent Difficulty ◽  
Polynomial Type ◽  
Stress Components ◽  
The Matrix ◽  
Remote Loading

In this paper, a particular inhomogeneous inclusion problem is studied. In the problem, Eshelby’s eigenstrain takes the type [Formula: see text], where m+ n = 2, and the remote loadings [Formula: see text], [Formula: see text] are applied. In the solution, the complex variable method is used. The continuity conditions along the interface of the matrix and the inclusion are formulated exactly. Because the stress field is no longer uniform in inclusion in this case, the studied problem has an inherent difficulty. After some manipulation, the final result for stress components [Formula: see text], [Formula: see text] and [Formula: see text] in inclusion are obtainable. In the present study, [Formula: see text], [Formula: see text] and [Formula: see text] are no longer uniform.

Formation of carbon Cottrell atmospheres and their effect on the stress field around an edge dislocation

2017 ◽  
Vol 129 ◽  
pp. 16-19 ◽  
Author(s):  
Osamu Waseda ◽  
Roberto GA Veiga ◽  
Julien Morthomas ◽  
Patrice Chantrenne ◽  
Charlotte S. Becquart ◽  
...  
Keyword(s):  
Stress Field ◽  
Edge Dislocation ◽  
Cottrell Atmospheres

An Edge Dislocation in a Three-Phase Composite Cylinder Model With a Sliding Interface

2002 ◽  
Vol 69 (4) ◽  
pp. 527-538 ◽  
Author(s):  
X. Wang ◽  
Y.-p. Shen
Keyword(s):  
Edge Dislocation ◽  
Arbitrary Point ◽  
Circular Inclusion ◽  
Composite Cylinder ◽  
Phase Form ◽  
Sliding Interface ◽  
Three Phase ◽  
Cylinder Model ◽  
The Matrix ◽  
Perfect Interface

An exact elastic solution is derived in a decoupled manner for the interaction problem between an edge dislocation and a three-phase circular inclusion with circumferentially homogeneous sliding interface. In the three-phase composite cylinder model, the inner inclusion and the intermediate matrix phase form a circumferentially homogeneous sliding interface, while the matrix and the outer composite phase form a perfect interface. An edge dislocation acts at an arbitrary point in the intermediate matrix. This three-phase cylinder model can simultaneously take into account the damage taking place in the circumferential direction at the inclusion-matrix interface and the interaction effect between the inclusions. As an application, we then investigate a crack interacting with the slipping interface.

On prismatic and bending bifurcations of fiber-reinforced elastic membranes under swelling with application to aortic aneurysms

2021 ◽  
pp. 108128652110587
Author(s):  
Murtadha J. Al-Chlaihawi ◽  
Heiko Topol ◽  
Hasan Demirkoparan ◽  
José Merodio
Keyword(s):  
Axial Loading ◽  
Material Constant ◽  
Exponential Model ◽  
Aortic Aneurysms ◽  
Orthotropic Materials ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
The Matrix ◽  
Elastic Membranes ◽  
Fiber Winding

The influence of swelling on prismatic and bending bifurcation modes of inflated thin-walled cylinders under axial loading is examined. The bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure, and swelling is provided. We consider orthotropic materials with two preferred directions which are mechanically equivalent and symmetrically disposed. The mechanical behavior of the matrix is described by a swellable isotropic model. The isotropic material is augmented with two functions that are equal, each one of them accounting for the existence of a unidirectional reinforcement. Two reinforcing models that depend only on the stretch in the fiber direction are considered: the so-called standard reinforcing model and an exponential one. The analysis of bifurcation modes for these models under the conditions at hand may establish the connection with modeling of the normal and diseased aorta in arterial wall tissue. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of prismatic and bending bifurcations are investigated. It is shown that for membranes without fibers, prismatic bifurcation is not feasible. On the other hand, bending bifurcation is more likely to occur for swollen cylinders. However, for a particular model of fiber-reinforced membranes, the standard model, there exists a domain of deformation values together with material constant values that may trigger prismatic bifurcation. The exponential model does not allow prismatic bifurcations. Both models allow bending bifurcation and may or may not trigger it depending on the deformation together with material parameters.

Analytical-Numerical Determination of Stress Distribution around a Tip of Polygon-Like Inclusion

2016 ◽  
Vol 713 ◽  
pp. 94-98
Author(s):  
Ondřej Krepl ◽  
Jan Klusák ◽  
Tomáš Profant
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Numerical Procedure ◽  
Plane Elasticity ◽  
Necessary Condition ◽  
Singular Stress ◽  
Reliable Assessment ◽  
Generalized Stress Intensity Factors ◽  
Stress Behaviour

A stress distribution in vicinity of a tip of polygon-like inclusion exhibits a singular stress behaviour. Singular stresses at the tip can be a reason for a crack initiation in composite materials. Knowledge of stress field is necessary condition for reliable assessment of such composites. A stress field near the general singular stress concentrator can be analytically described by means of Muskhelishvili plane elasticity based on complex variable functions. Parameters necessary for the description are the exponents of singularity and Generalized Stress Intensity Factors (GSIFs). The stress field in the closest vicinity of the SMI tip is thus characterized by 1 or 2 singular exponents (1 - λ) where, 0<Re (λ)<1, and corresponding GSIFs that follow from numerical solution. In order to describe stress filed further away from the SMI tip, the non-singular exponents for which 1<Re (λ), and factors corresponding to these non-singular exponents have to be taken into account. Analytical-numerical procedure of determination of stress distribution around a tip of sharp material inclusion is presented. Parameters entering to the procedure are varied and tuned. Thus recommendations are stated in order to gain reliable values of stresses and displacements.

Interfacial Stresses of a Coated Square Hole Induced by a Remote Uniform Heat Flow

2020 ◽  
Vol 12 (06) ◽  
pp. 2050063
Author(s):  
S. C. Tseng ◽  
C. K. Chao ◽  
F. M. Chen
Keyword(s):  
Heat Flow ◽  
Shape Factor ◽  
Coating Layer ◽  
Infinite Plate ◽  
Interfacial Stress ◽  
Graphical Form ◽  
Shear Stresses ◽  
Interfacial Stresses ◽  
Uniform Heat ◽  
Square Hole

This paper presents an analytical solution of a coated square hole embedded in an isotropic infinite plate under a remote uniform heat flow. Based on conformal mapping, analytic continuation theorem and the alternation technique, temperature and stress functions are derived in a compact series form. Results of temperature contours and interfacial stresses are validated using the finite element method. The comparison indicates the high accuracy of the proposed method. Numerical results of both the interfacial normal and shear stresses for different properties and geometric parameters of a coated layer are provided in a graphical form. The results indicate that the interfacial stresses are highly dependent on the thermal expansion coefficient, thickness of the coating layer and shape factor of the coated square hole. In conclusion, the interfacial shear stresses exhibit a significant increase at the corners with abrupt geometrical changes, which would cause the delamination of the coating layer system. Furthermore, increasing the thickness of the coating layer and the shape factor results in a higher interfacial stress.

scholarly journals The Preparation and Research on the Electromagnetic Shielding Effectiveness of T-ZnO@Ag/Silicone Rubber Composites

2019 ◽  
Vol 26 (2) ◽  
pp. 205-209 ◽  
Author(s):  
Jingkai NIE ◽  
Guangke WANG ◽  
Dong HOU ◽  
Fu GUO ◽  
Yu HAN
Keyword(s):  
Coating Layer ◽  
Electromagnetic Shielding ◽  
Shielding Effectiveness ◽  
Rubber Composites ◽  
Chemical Plating ◽  
Agno3 Solution ◽  
Rubber Composite ◽  
The Matrix ◽  
Micro Structures ◽  
Electromagnetic Shielding Effectiveness

This study first conducted surface modification of Ag-plated Tetrapod-like zinc oxide (T-ZnO) whiskers with the use of dopamine and prepared Ag-plated T-ZnO whiskers (T-ZnO@Ag) by means of chemical plating, in which AgNO3 solutions with different concentrations were used during the preparation. Micro-structures of the prepared T-ZnO@Ag powders were examined to evaluate the effect of AgNO3 concentration on Ag plating performance. Subsequently, conductive Si rubber samples were prepared, the T-ZnO@Ag powders were used as fillers, and the effectiveness of the related electromagnetic shielding was investigated in detail. The results showed that using AgNO3 solution with a concentration of 20 g/L, a continuous Ag coating-layer was observed on the surface of T-ZnO whiskers. It was evident that, when used as fillers, T-ZnO@Ag has a conductive threshold and when the mass fraction of the fillers exceeded 50 %, the T-ZnO@Ag whiskers that were uniformly dispersed in the matrix formed interconnected conductive paths. In this condition, the electromagnetic shielding effectiveness of the prepared T-ZnO@Ag/Si rubber composite reached up 90 dB.

An Edge Dislocation in a Three-Phase Composite Cylinder Model

1991 ◽  
Vol 58 (1) ◽  
pp. 75-86 ◽  
Author(s):  
H. A. Luo ◽  
Y. Chen
Keyword(s):  
Edge Dislocation ◽  
Stable Equilibrium ◽  
Phase Model ◽  
Composite Cylinder ◽  
Two Phase ◽  
Trapping Mechanism ◽  
Three Phase ◽  
Cylinder Model ◽  
Stable Equilibrium Position ◽  
The Stability

An exact solution is given for the stress field due to an edge dislocation embedded in a three-phase composite cylinder. The force on the dislocation is then derived, from which a set of simple approximate formulae is also suggested. It is shown that, in comparison with the two-phase model adopted by Dundurs and Mura (1964), the three-phase model allows the dislocation to have a stable equilibrium position under much less stringent combinations of the material constants. As a result, the so-called trapping mechanism of dislocations is more likely to take place in the three-phase model. Also, the analysis and calculation show that in the three-phase model the orientation of Burgers vector has only limited influence on the stability of dislocation. This behavior is pronouncedly different from that predicted by the two-phase model.

Sign in / Sign up

Export Citation Format

Share Document