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
Article

Abstract

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°.

Keywords

Fatigue Crack Crack Growth Rate Fatigue Crack Growth Fatigue Crack Propagation Fatigue Crack Growth Rate 

Notation

a

Half-length of inclined crack

ax

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

Δa

Crack growth increment

da/dN

Rate of fatigue crack propagation

dax/dN

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

aij

Variables in Sih's strain energy density factor equation

C, m

Coefficient and exponent in Paris equation respectively

KIKIIKIII

Opening, sliding and tearing mode stress intensity factors factors respectively

ΔK

Stress intensity factor range

Δk

Stress intensity factor range in Sih's equation

ΔKx

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

ΔKth

Threshold stress intensity factor range

ΔS

Strain energy density factor range

β

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

β0

Value of β of the original inclined crack

f0)

Function of β0

γ

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

θ0

Direction of crack growth with respect to crack plane

μ

Shear modulus

v

Poisson's ratio

Δσ

Stress range

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    Paris, P. C. and F. Erdogan, A Critical Analysis of Crack Propagation Laws, J. Basic Eng., 85 (4), (1963), 528–534.Google Scholar
  2. (2).
    Erdogan F. and G. C. Sih, On the Crack Extension in Plates under Plane Loading and Transvers Shear,ibid, 85, (1963), 519–527.Google Scholar
  3. (3).
    Sih, G. C., Strain Energy Density Factor Applied to Mixed Mode Crack Problems, Int. J. Fract. 10, (1974), 305–322.Google Scholar
  4. (4).
    Iida, S. and A. S. Kobayashi, Crack Propagation Rate in 7075-T6 Plates under Cyclic Tensile and Transverse Shear Loading, J. Basic Eng., 91, (1969), 764–769.Google Scholar
  5. (5).
    Sih, G. C. and B. M. Barthelemy, Mixed Mode Fatigue Crack Growth Predictions, Eng. Fract. Mech, 13, (1980), 439–451.Google Scholar
  6. (6).
    Patel, A. B. and R. K. Pandey, Fatigue Crack growth under Mixed Mode Loading, Fatigue of Eng. Materials and Structure. 4 (1), (1981), 65–77.Google Scholar
  7. (7).
    National Research Institute of Aeronautics of China, Handbook of Stress Intensity Factors, Science Press, Beijing, (1981), 128–129. (in Chinese)Google Scholar
  8. (8).
    Otsuka, A., K. Mori and T. Miyata, The Condition of Fatigue Crack Growth in Mixed Mode Condition, Eng. Fract. Mech. 7, (1975) 429–439.Google Scholar

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

Personalised recommendations