Synergistic determination of mode I stress intensity factors using photoelastic experimental hybrid method

Abstract

Engineering components possess discontinuities such as cracks which develop during service while others exist due to structural and material defects. The physical discontinuities in mechanical structures lead to stress concentrations, which can trigger mechanical collapses and catastrophic failures of the structure. Stress field equations of fracture mechanics have been formulated to aid in determination of the critical fracture mechanics parameter namely; the stress intensity factors (SIFs) ahead of cracks. Mathematical formulations for fracture mechanics, however, are known to predict infinite values of stress near the crack tip because of the stress singularity at the crack tip and therefore, provide limited information. Further interpretations and a combination of results from different techniques are frequently required to obtain the complete stress condition. In order to accurately determine mode I stress intensity factors without reverting to supplemental techniques, photoelastic experimental hybrid method (PEHM) is utilized in this research. Hybrid methods synergizing mathematical, numerical and experimental data have been used with great success in experimental stress analysis. Its application in the current fracture mechanics problem shows that photoelastic experimental hybrid method stress intensity factors correspond well with those calculated from theoretical method. In addition, it is noted that varying the geometric condition 2a/W from 0.2 to 0.6 while maintaining constant load had the effect of changing K 1 /K 0 from 1.1 to 1.5.

A mathematical Theory of Elasticity for Photoelastic Experimental Hybrid Method

“…Now, it is worth noting that the equilibrium equations of (1) can be satisfied by introducing a stress function, F(x,y), which is related to the stresses as shown in equation (5);…”

“…The electrical resistance strain gage method in which gages are bonded onto the surface has been variously applied as an experimental stress analysis tool [4]. However, this method provides only point-to-point information and their use can be arduous if the number of gage locations becomes large [5]. Other methods such as holography and speckle method have also been used but require sophisticated optics [6].…”