M-integral analysis for microcrack-damaged anisotropic composite materials

2000 ◽  
Vol 70 (8-9) ◽  
pp. 625-634 ◽  
Author(s):  
J.-J. Han ◽  
Y.-H. Chen
Keyword(s):  
Composite Materials ◽  
Integral Analysis ◽  
Anisotropic Composite ◽  
M Integral

scholarly journals The flexural strength of anisotropic composite plates with free edges

2021 ◽  
Vol 21 (1) ◽  
pp. 26-34
Author(s):  
Ashot G. Akopyan ◽  
Keyword(s):  
Composite Materials ◽  
Stress State ◽  
Classical Theory ◽  
Solid Mechanics ◽  
Composite Plates ◽  
Operating Conditions ◽  
Plate Bending ◽  
Structural Elements ◽  
Engineering Structures ◽  
Anisotropic Composite

Modern technology shows increased demands on the strength properties of machines, their parts, as well as various structures, reducing their weight, volume and size, which leads to the need to use anisotropic composite materials. Finding criteria to determine the ultimate strength characteristics of structural elements, engineering structures is one of the urgent problems of solid mechanics. Strength problems in structures are often reduced to finding out the nature of the local stress state at the vertices of the joints of the constituent parts. The solution of this urgent problem for composite anisotropic plates can be found in this article, where the author continues the research in this area, extending them to the bending of anisotropic composite plates. The aim of the work is to study the limit stress state of anisotropic composite plates in the framework of the classical theory of plate bending. The outer edges of the plate are considered to be free. Using the classical theory of anisotropic plate bending in the space of physical and geometric parameters, the hypersurface equations determining the low-stress zones for the edge of the contact surface of a composite cylindrical orthotropic plate are obtained. Modern technological processes of welding, surfacing, soldering and bonding allow to produce structural elements of monolithic interconnected dissimilar anisotropic materials. The combination of different materials with qualities corresponding to certain operating conditions opens up great opportunities to improve the technical and economic characteristics of machines, equipment and structures. It can contribute to a significant increase in their reliability, durability, reduce the cost of production and operation. On this basis, the solution proposed in this work can be useful to increase the strength of composite materials.

The Interface Crack Between Dissimilar Anisotropic Composite Materials

1983 ◽  
Vol 50 (1) ◽  
pp. 169-178 ◽  
Author(s):  
S. S. Wang ◽  
I. Choi
Keyword(s):  
Composite Materials ◽  
Interface Crack ◽  
Hilbert Problem ◽  
Stress Singularity ◽  
Anisotropic Elasticity ◽  
Crack Model ◽  
Closed Crack ◽  
Anisotropic Composite ◽  
Interlaminar Crack ◽  
As Stress

The fundamental nature of an interface crack between dissimilar, strongly anisotropic composite materials under general loading is studied. Based on Lekhnitskii’s stress potentials and anisotropic elasticity theory, the formulation leads to a pair of coupled governing partial differential equations. The case of an interlaminar crack with fully opened surfaces is considered first. The problem is reduced to a Hilbert problem which can be solved in a closed form. Oscillatory stress singularities are observed in the asymptotic solution. To correct this unsatisfactory feature, a partially closed crack model is introduced. Formulation of the problem results in a singular integral equation which is solved numerically. The refined model exhibits an inverse square-root stress singularity for commonly used advanced fiber-reinforced composites such as a graphite-epoxy system. Extremely small contact regions are found for the partially closed interlaminar crack in a tensile field and, therefore, a simplified model is proposed for this situation. Physically meaningful fracture mechanics parameters such as stress intensity factors and energy release rates are defined. Numerical examples for a crack between θ and −θ graphite-epoxy composites are examined and detailed results are given.

The M-Integral Analysis for a Nano-Inclusion in Plane Elastic Materials Under Uni-Axial or Bi-Axial Loadings

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Tong Hui ◽  
Yi-Heng Chen
Keyword(s):  
Surface Effect ◽  
Continuum Theory ◽  
Elastic Materials ◽  
Hard Inclusion ◽  
Surface Parameters ◽  
Integral Analysis ◽  
Axial Tension ◽  
Soft Inclusion ◽  
Tension Loading ◽  
M Integral

This paper deals with the M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Based on previous works (Gurtin and Murdoch, 1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323; Mogilevskaya, et al., 2008, “Multiple Interacting Circular Nano-Inhomogeneities With Surface/Interface Effects,” J. Mech. Phys. Solids, 56, pp. 2298–2327), the surface effect induced from the surface tension and the surface Lamé constants is taken into account, and an analytical solution is obtained. Four kinds of inclusions including soft inclusion, hard inclusion, void, and rigid inclusions are considered. The variable tendencies of the M-integral for each of four nano-inclusions against the loading or against the inclusion radius are plotted and discussed in detail. It is found that in nanoscale the surface parameters for the hard inclusion or rigid inclusion have a little or little influence on the M-integral, and the values of the M-integral are always negative as they would be in macroscale, whereas the surface parameters for the soft inclusion or void yield significant influence on the M-integral and the values of the M-integral could be either positive or negative depending on the loading levels and the surface parameters. Of great interest is that there is a neutral loading point for the soft inclusion or void, at which the M-integral transforms from a negative value to a positive value, and that the bi-axial loading yields similar variable tendencies of the M-integral as those under the uni-axial tension loading. Moreover, the bi-axial tension loading increases the neutral loading point, whereas the bi-axial tension-compression loading decreases it. Particularly, the magnitude of the negative M-integral representing the energy absorbing of the soft inclusion or void increases very sharply as the radius of the soft inclusion or void decreases from 5 nm to 1 nm.

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