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Stress concentration around of pin-loaded hole in unidirectional multi-layered metallic matrix composite material

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Abstract

The objective of this study is to examine the stress concentration factor around a pin-loaded hole in a metallic matrix composite material, analytically and numerically. It is assumed that all unidirectional fibers lie in the metallic matrix while the shear stress in fibers is discarded. To generally derive the equilibrium equation for all fibers and the metallic matrix, the previous shear-lag theory had been improved and the extension in the metallic matrix was considered. Afterwards, the equilibrium equation was solved by the eigenvalue method while the displacement field and stress distribution around the pin-loaded hole were computed. Having calculated stress concentration factors and the displacement field in a unidirectional multi-layered composite material, we compared the analytical results with those numerical values from other references. Additionally, the effect of the pin’s diameter, as well as the edge-hole distance on maximum stress concentration factor was investigated. To recapitulate, it is seen that the modified shear-lag theory can simulate the mechanism of the load transfer between metallic matrices.

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Abbreviations

τ :

Shear stress

Φ:

Nondimensional parameter (Eq. (6))

A f :

Cross-sectional of the circular fibers

Γ:

Nondimensional parameter (Eq. (13))

γ :

Nondimensional parameter (Eq. (13))

δ :

Fiber spacing

ξ :

Non-dimensional coordinate along direction of circular fibers

Ψ:

The number of layers

Θ:

Nondimensional parameter (Eq. (16))

λ :

Eigen-value

ς :

Distance between any two successive columns of circular fibers

β :

Vertical distance between fibers and matrix

Ω:

Nondimensional parameter (Eq. (5))

α :

Horizontal distance between fibers and matrix

C :

Unknown constants

d :

Fiber diameter

D :

Unknown constants

e :

Distance from laminate edge to pinhole center

E :

Unknown constants

E f :

The modulus elasticity of fibers

E m :

The modulus elasticity of matrix

G m :

Matrix shear modulus

M :

The number of fibers in lamina

m :

Total of fiber in each layer

n :

Fiber number

N :

The total number of fibers

P :

Dimensionless load

p :

Load

n :

Fiber number

N :

The total number of fibers

P :

Dimensionless load

p :

Load

Q :

Nondimensional parameter (Eq. (5))

q :

The number of layers

R :

Eigenvector

U n :

Dimensionless fiber displacement

u :

Fiber displacement

w :

Laminate with

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Authors and Affiliations

  1. Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Sajjad Dehghanpour & Keivan Hosseini Safari

  2. Department of Mechanical Engineering, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Farzan Barati & Mohammadmahdi Attar

Authors
  1. Sajjad Dehghanpour
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  2. Keivan Hosseini Safari
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  3. Farzan Barati
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  4. Mohammadmahdi Attar
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Corresponding author

Correspondence to Keivan Hosseini Safari.

Additional information

Recommended by Associate Editor Kyeongsik Woo

Keivan Hosseini Safari received his Ph.D. degree in Mechanical Engineering from K.N.Toosi University of Technology, Iran, in 2012. He is currently an Assistant Professor in Islamic Azad University, Iran. His research areas cover impact dynamics, high strain rate deformation and viscoelasticity, viscoplasticity in polymers and composite material.

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Dehghanpour, S., Safari, K.H., Barati, F. et al. Stress concentration around of pin-loaded hole in unidirectional multi-layered metallic matrix composite material. J Mech Sci Technol 33, 4891–4898 (2019). https://doi.org/10.1007/s12206-019-0929-2

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  • DOI: https://doi.org/10.1007/s12206-019-0929-2

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