Stress intensity factor for cracks in bonded dissimilar materials (original) (raw)
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Stress Intensity Factors for a Crack in Bonded Dissimilar Materials Subjected to Various Stresses
Universal Journal of Mechanical Engineering, 2019
The modified complex variable function method with the continuity conditions of the resultant force and displacement function are used to formulate the hypersingular integral equations (HSIE) for an inclined crack and a circular arc crack lies in the upper part of bonded dissimilar materials subjected to various remote stresses. The curve length coordinate method and appropriate quadrature formulas are used to solve numerically the unknown crack opening displacement (COD) function and the traction along the crack as the right hand term of HSIE. The obtained COD is then used to compute the stress intensity factors (SIF), which control the stability behavior of bodies or materials containing cracks or flaws. Numerical results showed the behavior of the nondimensional SIF at the crack tips. It is observed that the nondimensional SIF at the crack tips depend on the various remote stresses, the elastic constants ratio, the crack geometries and the distance between the crack and the boundary.
Applied Mathematical Modelling, 2019
In this paper, numerical solutions of multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.
Stress Intensity Factors for Crack Problems in Bonded Dissimilar Materials
Journal of Engineering and Technological Sciences, 2020
The problem of inclined cracks subjected to normal and shear stress in bonded dissimilar materials was formulated. The modified complex potentials function method was used to formulate the hypersingular integral equations. The obtained system of hypersingular integral equations was solved numerically using the appropriate quadrature formula. The stress intensity factors at the crack tips depend on the elastic constant's ratio and crack geometries.
Interaction between Two Inclined Cracks in Bonded Dissimilar Materials subjected to Various Stresses
IOP Conference Series: Materials Science and Engineering, 2020
This paper deals with the interaction between two inclined cracks in the upper part of bonded dissimilar materials subjected to various stresses which is normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress. This problem is formulated into hypersingular integral equations (HSIE) by using modified complex potentials (MCP) with the help of continuity conditions of the resultant force and displacement functions where the unknown is the crack opening displacement (COD) function and the tractions along the crack as the right hand terms. Then, the curve length coordinate method and appropriate quadrature formulas are used to solve numerically the obtained HSIE to compute the stress intensity factors (SIF) in order to determine the stability behavior of materials containing cracks. Numerical results showed the behavior of the nondimensionalSIF at the cracks tips. It is observed that the various stresses and the elastic constants ratio are influences to...
Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings
Symmetry
A new mathematical model is developed for the analytical study of two cracks in the upper plane of dissimilar materials under various mechanical loadings, i.e., shear, normal, tearing and mixed stresses with different geometry conditions. This problem is developed into a new mathematical model of hypersingular integral equations (HSIEs) by using the modified complex potentials (MCPs) function and the continuity conditions of the resultant force and displacement with the crack opening displacement (COD) function as the unknown. The newly obtained mathematical model of HSIEs are solved numerically by utilizing the appropriate quadrature formulas. Numerical computations and graphical demonstrations are carried out to observe the profound effect of the elastic constants ratio, mode of stresses and geometry conditions on the dimensionless stress intensity factors (SIFs) at the crack tips.
Stress intensity factor for bonded dissimilar materials weakened by multiple cracks
Applied Mathematical Modelling, 2020
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • The inclined or circular arc cracks in both upper and lower parts of bonded dissimilar materials are formulated. • The modified complex potential methods are used to formulate the hypersingular integral equations. • This hypersingular integral equations is solve numerically using the appropriate quadrature formula • The stress intensity factors at the crack tips depend on the elastic constants ratio and cracks geometries.
Computational Methods for Differential Equations, 2020
In this paper, numerical solutions of multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.
Computational Methods for Differential Equations, 2020
In this paper, numerical solutions of multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.
Stress intensity factors for bonded two half planes weakened by thermally insulated cracks
Acta Mechanica, 2020
The thermally insulated inclined or circular arc cracks problems subjected to axial stress in the upper part of bonded two half planes are considered. The modified complex potential function method with the continuity conditions of the resultant force, displacement, and heat conduction functions is used to develop the new system of hypersingular integral equations (HSIEs) for the problems. The new system of HSIEs is solved numerically for the unknown crack opening displacement function and the known traction along the crack as the right-hand term using the appropriate quadrature formulas. Numerical results for the nondimensional stress intensity factors (SIFs) at all cracks tips are presented. A comparison between the nondimensional SIFs for cracks with and without thermal influence is also given The N. M. A. Nik Long would like to thank the Ministry of Education Malaysia for financial support by the Fundamental Research Grant Scheme with Project Number 5540269.
Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity
Mathematical Problems in Engineering, 2015
The interaction between the inclined and curved cracks is studied. Using the complex variable function method, the formulation in hypersingular integral equations is obtained. The curved length coordinate method and suitable quadrature rule are used to solve the integral equations numerically for the unknown function, which are later used to evaluate the stress intensity factor. There are four cases of the mode stresses; Mode I, Mode II, Mode III, and Mix Mode are presented as the numerical examples.