Issue 60

H. Benzineb et al., Frattura ed Integrità Strutturale, 60 (2022) 331-345; DOI: 10.3221/IGF-ESIS.60.23

an opening (tensile) mode where the crack surfaces move directly apart. Mode II is a sliding (in-plane shear) mode where the crack surfaces slide over one another in a direction perpendicular to the leading edge of the crack. Mode III is a tearing (antiplane shear) mode where the crack surfaces move relative to one another and parallel to the leading edge of the crack. Mode I is the most common load type encountered in engineering design. Different subscripts are used to designate the stress intensity factor for the three different modes. The stress intensity factor for mode I is designated K I and applied to the crack opening mode. The mode II stress intensity factor K II , applies to the crack sliding mode and the mode III stress intensity factor K III applies to the tearing mode. These factors are formally defined as [26]:       0 lim 2 , 0 I yy r K r r       0 lim 2 , 0 II yx r K r r (8)       0 lim 2 , 0 III yz r K r r

   I K a

(9)







   2 4

 



sec

1 0.025 0.06

2

where, K I =Stress intensity factor β = Geometry factor α = 2a/W 2a = Crack length W = Width of the plate σ = Force applied Where the factor β is used to relate gross geometrical features to the stress intensity factor



2

a

        a b

   1

0.326

b

2

   

   



  a

K

(10)

I

a b



1

Crack in a finite plate under mode I loading. The generalized form for mode II stress intensity factor can be expressed as: The Mode II stress intensity factor K II is derived using the following equation [27],          1 II K a sin cos

(11)

The second part of this work shows the effect of temperature on the behavior of the corroded and cracked aluminum plate with an inclined crack in mixed mode (mode I+ mode II). The evolution of the stress intensity factor (K I +K II ) for several angles of crack inclination and the three types of composite patch was shown in Fig. 14. The analysis of these curves obtained for the circular shape allows the observation of the effect of the crack inclination. It can be seen that the increase in the angle of the crack inclination leads to a decrease in the values of the sum (K I +K II ) for all the types of composite patch used. As for the second observation concerning the type of patch, the values of (K I +K II ) obtained for boron/epoxy are better than those of (graphite/epoxy and glass/epoxy). For the angle of inclination θ =30 o and for Δ T=0 o C (T=20°C), the value for boron/epoxy of (K I +K II ) is 7 MPa.m 1/2 but for graphite/epoxy (K I +K II )=9.75MPa.m 1/2 and for Glass/epoxy the value of (K I +K II ) 7.75 MPa.m 1/2. Therefore, the following conclusions can be as follows

342