Experimental Mechanics

, Volume 45, Issue 1, pp 42–52 | Cite as

A new photoelastic model for studying fatigue crack closure

  • M. N. Pacey
  • M. N. James
  • E. A. Patterson


The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.

Key Words

Pholoelasticity in fatigue crack closure effective stress intensity factor Muskhelishvili genetic algorithm downhill simplex method 



Fourier series coefficients


mean difference between theoretical and experimental stress values


square root of −1


mapping function shape descriptor

r, θ

polar coordinates in the mapping plane


standard deviation in the difference between stress values


distance from the crack tip

x, y

Cartesian coordinates in the physical plane


complex coordinate in the physical plane


rigid body translation of the mapping plane


rigid body rotation of the mapping plane


mode I and II stress intensity factors


maximum value of stress intensity factor


pressure loading on the crack


mapping function length descriptor


shear loading on the crack


principal stress direction at infinity


material constant


Poisson's ratio

σ1, α

maximum principal stress at infinity

σ2, α

minimum principal stress at infinity


shear stress


mapping function


complex coordinate in the mapping plane


rigid body movement of the mapping plane

Ε, Γ

complex stress functions


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Copyright information

© Society for Experimental Mechanics 2005

Authors and Affiliations

  • M. N. Pacey
    • 1
  • M. N. James
    • 1
  • E. A. Patterson
    • 2
  1. 1.Department of Mechanical and Marine EngineeringUniversity of PlymouthPlymouthUK
  2. 2.Department of Mechanical EngineeringMichigan State UniversityE. LansingUSA

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