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A simple analytical crack tip opening displacement approximation under random variable loadings

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Abstract

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.

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Abbreviations

a :

Crack length at arbitrary time instant

α, β :

Calibration parameters considering hardening effect

E :

Young’s modulus

K max :

Maximum stress intensity factor

K min :

Minimum stress intensity factor

K max,mem :

SIF level corresponding to the largest monotonic zone size d f,mem

ΔK :

Stress intensity factor range

T :

Material hardening coefficient in a bilinear hardening model

R :

Stress ratio

d f :

Monotonic plastic zone size

d r,reloading :

Reversed plastic zone size during the reloading path

d f,mem :

The largest monotonic plastic zone size in the loading history

δ :

Crack tip opening displacement (CTOD)

δ max :

Maximum CTOD value at the previous σ max

δ min :

Minimum CTOD value at the previous σ min

δ min, m :

CTOD value at σ min, m

δ max, m :

CTOD value at σ max, m

σ min, σ max :

Minimum and maximum stress in one loading cycle

σ min, m :

mth minimum stress during the loading history

σ max,m :

mth maximum stresses during the loading history

σ y :

Material yield strength

Y :

Geometric correction factor

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Authors and Affiliations

  1. Clarkson University, Potsdam, NY, 13699, USA

    Yongming Liu

  2. Beijing Aeronautical Science and Technology Research Institute, Beijing, China

    Zizi Lu & Jifeng Xu

Authors
  1. Yongming Liu
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  2. Zizi Lu
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  3. Jifeng Xu
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Correspondence to Yongming Liu.

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Liu, Y., Lu, Z. & Xu, J. A simple analytical crack tip opening displacement approximation under random variable loadings. Int J Fract 173, 189–201 (2012). https://doi.org/10.1007/s10704-012-9682-6

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  • DOI: https://doi.org/10.1007/s10704-012-9682-6

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