Applied Mathematics and Mechanics

, Volume 5, Issue 2, pp 1209–1219 | Cite as

Fatigue crack propagaion under mixed mode loading

  • Cao Gui-xin
  • Ju Ding-yi


Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under uniaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β0 for an inclined crack. It is also shown that it is more convenient to express the Paris equation by means of crack lengthprojected on the x—axis, ax rather than the actual length, a itself. The crack trajectory due to cyclic loading is predicted. β0 is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β0 exceeds 30°.


Fatigue Crack Crack Growth Rate Fatigue Crack Growth Fatigue Crack Propagation Fatigue Crack Growth Rate 
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Half-length of inclined crack


Length of the half length of inclined crack when jected on the x-axis


Crack growth increment


Rate of fatigue crack propagation


Rate of fatigue crack propagation when projected along the x-axis


Variables in Sih's strain energy density factor equation

C, m

Coefficient and exponent in Paris equation respectively


Opening, sliding and tearing mode stress intensity factors factors respectively


Stress intensity factor range


Stress intensity factor range in Sih's equation


Stress intensity factor range when crack length is projected on the x-axis


Threshold stress intensity factor range


Strain energy density factor range


Crack angle, which is the angle made by crack plane with the loading axis


Value of β of the original inclined crack


Function of β0


Angle between the direction of a certain point on the crack trajectory and the horizontal axis


Direction of crack growth with respect to crack plane


Shear modulus


Poisson's ratio


Stress range


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Copyright information

© HUST Press 1984

Authors and Affiliations

  • Cao Gui-xin
    • 1
  • Ju Ding-yi
    • 1
  1. 1.Department of Mechanical EngineeringEast China Institute of Chemical TechnologyShanghai

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