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Effects of loading modes on reliability of cracked structures using FORM and MCS

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Abstract

Studying the reliability of cracked structures under different types of failure modes such as a mixture of Mode I and Mode II loadings has been of great importance in many applications. The purpose of this study is to evaluate the effects of different modes of loading, i.e. pure Mode I, pure Mode II and Mixed mode I/II loadings on the reliability of cracked structures via three typical case studies including 1st: through crack in a very wide plate, 2nd: cracked pressurized fuselage and 3rd: cracked fastener holes under actual geometries and loading conditions using the FORM, the fracture toughness and the equivalent SIF for Mixed mode I/II loading which is extracted by the Energy release rate model 1. The MCS was used to check the accuracy of the FORM. It was found that the failure probability decreases significantly as the loading mode changes from the pure Mode I to pure Mode II. This means that the reliability in the Mixed mode I/II loading is higher than that of pure Mode I and smaller than for pure Mode II. Also, it was concluded that the failure probability decreases with increasing of the angle of crack for the Mixed mode I/II loading conditions. The results indicated that the angle of crack and the applied stress are the two variables which have the most significant influence on the reliability.

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Abbreviations

K I , K II :

stress intensity factor (SIF) in Mode I and Mode II

K (I,II) :

equivalent SIF in Mixed mode I/II loading

K IC , K IIC :

fracture toughness in Mode 1 and Mode II

K (I,II)C :

fracture toughness in Mixed mode I/II loading

PF :

failure probability

SI Xi :

the sensitivity index of variable X i

β :

safety index or reliability index

σ Z :

standard deviation of variable Z

μ Z :

mean value of variable Z

S :

load normal variable

R :

resistance normal variable

Z :

new variable of limit state function

Φ:

cumulative distribution function for a standard normal variable

σ :

applied stress

a :

crack size

α :

dimensionless geometry correction factor

Beta :

angle between the normal plane to the crack and stress axis

C.O.V :

coefficient of variance

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Authors and Affiliations

  1. Department of Aerospace Engineering, Sharif University of Technology, Tehran, 11365-11155, Iran

    Ali Delbariani-Nejad & Saeed Adib Nazari

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  1. Ali Delbariani-Nejad
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  2. Saeed Adib Nazari
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Correspondence to Ali Delbariani-Nejad.

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Delbariani-Nejad, A., Nazari, S.A. Effects of loading modes on reliability of cracked structures using FORM and MCS. Int. J. Precis. Eng. Manuf. 18, 63–76 (2017). https://doi.org/10.1007/s12541-017-0008-5

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  • DOI: https://doi.org/10.1007/s12541-017-0008-5

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