In the present study the asymptotic analysis of the multi-parameter Williams series expansion of the stress-strain state in the vicinity of seven different configurations is performed. The aim of the asymptotic analysis is to educate the sensitivity of different cracked and notched configurations to the number of kept terms in Williams series expansion. It is shown that all configurations with the concentrated forces possess the more sensitivity to the number of terms in the truncated Williams series expansions and, therefore, require the more terms in the series expansion. The cracked configurations with distributed loadings are less sensitive to the number of terms in Williams series expansion. As a whole, it is demonstrated that high order terms have principal role in the description of the stress-strain in the vicinity of the crack tip.

Comparative analysis of stress state in the vicinity of the crack-tips and notches using truncated williams series expansion

The photoelastic method is an experimental technique that combines optics and mechanics for a stress analysis. The photoelastic phase-shifting technique is different from the moiré, holography, and speckle phase-shifting techniques, which only need to measure one parameter. The photoelastic phase-shifting technique needs to assess isoclinic and isochromatic parameters, which affect each other, seriously hindering the development of the phase-shifting photoelasticity method. First, the interaction between the isoclinic and isochromatic parameters is analyzed in detail. Secondly, an algorithm is proposed to adjust the mutation and obtain the correct isoclinic parameter affected by the isochromatic parameter. This method can effectively eliminate the influence of the isochromatic parameter. The isoclinic parameter is consistent with the theoretical value, which verifies the effectiveness of this method. Finally, the photoelastic method uses the proposed algorithm to test the stress at different positions of the turbine blade root. Moreover, the bearing capacity of the turbine blade root is analyzed to provide support for the safe use and optimization design of the turbine.

Algorithm and its application for automatic measurement of the full-field isoclinic parameter by digital phase-shifting photoelasticity.

Investigation of constantly and transiently propagating cracks in functionally graded materials by dynamic photoelasticity

To analyze the stress of functionally graded materials (FGMs) through an experiment, transparent homogeneous FGMs (THFGMs) with similar theoretical and physical properties need to be created. This study developed such THFGMs and proposed a method for determining their stress intensity factors (SIFs) and T-stresses via photoelastic experiments. The Young’s modulus and Poisson’s ratio of these THFGMs linearly change along the physical variation direction, and the shear modulus varies almost linearly. The SIFs and T-stresses were obtained for the central and edge cracks in finite rectangular FGM plates with linear variations in the shear modulus under constant density along the direction of the crack under mode I loading. The SIFs and T-stresses can be obtained using the exponential and linear variation in the stress fields, even if the physical properties of FGM plates show linear variation in the shear modulus. The characteristics of the experimental SIFs obtained in this study generally agree with those of theoretical SIFs reported in previous research. For center crack tips, the SIFs at the hard right crack tip were greater than those at the soft left crack tip. For edge crack tips, when a/W 0.35, the SIFs were greater than the homogeneous materials. The experimental T-stresses for the center crack agreed well with the numerical T-stresses reported in previous research. For the edge crack, when a/W ≤ 0.3, the experimental T-stresses agreed with the numerical T-stress, but when a/W ≥ 0.4, considerable differences were observed between the experimental and numerical T-stresses. Where a(a) denotes the crack length for edge cracks or half the crack length for center cracks, and W is the width of the specimen. Experimental results coincide well with those reported in the literature, except for the T-stresses for edge crack when a/W > 0.3. Therefore, the THFGMs, which are new FGMs developed in this study, can be effectively used in experimental fracture analysis.

Ji Sik Kim

Papers

Fabrication of transparent homogeneous functionally graded materials and crack analysis by photoelasticity