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Size effect analysis of open-hole glass fiber composite laminate using two-parameter cohesive laws

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Abstract

The nominal strength of structures made of quasibrittle materials shows a noticeable decrease or increase in brittleness with respect to the increase in structure dimension; this is the well-known size effect on strength. The present study aims to analyze and experimentally validate the size effect on laminate composite glass fibers using cohesive laws. This work not only correlates the nominal strength with the size of the failure processing zone but also relates the size of the failure processing zone at failure load to the specimen dimension and geometry. Our study provides a useful tool that enables engineers to obtain a set of design charts that relate the nominal strength of the structure to the size and shape of the specimen. Moreover, it aims to apply a new method to study the effect of structure size on the tensile strength of fiber polymer composite. The results of nominal strength are validated using a matrix of experimental work, and they agree very well with the experimental data. The other fracture properties are compared using an extended finite element method. The output of the analysis is a valuable graph that gives the nominal strength of the open-hole specimen.

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Abbreviations

\({\rho_{{\rm{Cr}}}^{{\rm{theoretical}}}}\) :

Calculated relative specimen size

β w :

Normalized hole radius or hole width ratio, geometric factor

β i :

Parameter \({\beta_{i} =-\frac{2}{\pi}\left[{\sin ^{-1}\left( {\frac{C_{i}}{d}}\right)-\sin^{-1}\left({\frac{b_{i}}{d}}\right)}\right]\frac{F_{3} F_{4}}{F_{1} F_{2}}}\)

K t :

Stress concentration factor

σ n :

The nominal applied stress, mean stress at failure plane

σ u :

Un-notch strength

\({\overline{\rho}_{{\rm{Cr}}}}\) :

Transformation function

\({\overline{\sigma}_{{\rm{C}}}}\) :

Normalized cohesive law

ℓ Cr :

Irwin’s characteristic length

ℓ FPZ :

Crack length ahead of the hole radius

\({\rho_{{\rm{Cr}}}^{{\rm{Experimental}}}}\) :

Experimental relative specimen size

\({\overline{{w}}}\) :

Normalized crack opening

σ Zero :

Residual stress at maximum crack opening displacement

\({{b}_{{i,j}} ,{C}_{{i,j}}}\) :

Dimension for partially loaded cracks, i, j = 1,2

d :

Half length of crack (hole) pulse FPZ

E :

Laminate’s Young’s modulus

F 1 :

Hole correction factor

F 2 :

Width correction factor

F 3 :

Partially loaded hole correction factor

F 4 :

Partially loaded width correction factor

f i :

Operator functions \({f_{ij} =\frac{2}{E}\sqrt{d^{2}-x_{i}}F_1 F_2}\)

f ij , G(x i , x j ):

Influence functions that are independent of the crack geometry and loading conditions

G IC :

Mode I surface release energy

Ks:

Stress intensity factor due to remote stress

K σ :

Stress intensity factor due to crack face stress

R :

Hole radius

S :

Remote applied stress

S n :

Normalized nominal strength

W :

Specimen width

w c :

Critical crack opening

W i :

Unite crack opening displacement

X i,j :

Coordinate locates for element (i) or (j)

α ij :

Operator vector

θ ℓ :

Dimensionless length of (ℓ fpz), mm

λ :

Normalized crack length (normalized hole radius)

ρ CR :

Relative specimen size

σ ij :

Cauchy stresses

ξ :

Material type correction factor

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, South Valley University, Qena, 83521, Egypt

    Y. Mohammed, Mohamed K. Hassan & A. M. Hashem

  2. Production Engineering and Design Department, Faculty of Engineering, Minia Universities, Minia, 61111, Egypt

    H. Abu El-Ainin

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  1. Y. Mohammed
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  2. Mohamed K. Hassan
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  4. A. M. Hashem
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Mohammed, Y., Hassan, M.K., El-Ainin, H.A. et al. Size effect analysis of open-hole glass fiber composite laminate using two-parameter cohesive laws. Acta Mech 226, 1027–1044 (2015). https://doi.org/10.1007/s00707-014-1150-0

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