Test methodUtilizing digital image correlation to determine stress intensity factors
Introduction
Stress concentrations at discontinuities such as cracks may lead to early structural failure in railroads. The crack growth could be controlled if its fracture characteristics are understood. The problem becomes even more complicated when the edge cracks propagate in mixed mode conditions [1]. Modeling and simulation of railroad contacts can be used as a useful tool to understand their behavior. Railroad contacts can be simulated as a contact problem between a tilted wedge and a half-plane embodying an edge crack [2].
Digital image correlation (DIC) has become a very popular choice of experimental optical method [3], [4], [5]. DIC test setup is less complex compared to other methods such as shearography, moiré and caustics [6]. In addition, its vast applications in stress and strain analyses have made DIC a practical and valuable technique. In contrast to other optical methods, such as photoelasticity, DIC is applicable to both opaque and transparent materials, and its image processing does not entail fringe pattern analysis and phase-unwrapping [7].
The analysis of stresses transferred within various contact components is a critical mechanical design criterion. Therefore, a great number of investigations of contact problems in different geometries have been carried out [8], [9]. This design problem becomes escalated when one of the touching components becomes vulnerable due to the presence of discontinuities and cracks. The distribution of contact forces and displacement discontinuity of cracks in contact problems, as well as the effects of frictional forces on stress intensity factors (SIFs) have been greatly inspected [8], [9], [10], [11]. Nonetheless, there are few published studies on the effect of wedge tip angle on the SIFs for the contact problem.
The DIC method was first used at the University of South Carolina to measure displacement fields of loaded components by Peters and Ranson [12]. A few years later, Sutton et al. [13] improved the DIC technique and demonstrated its precision in obtaining strain fields. Since then, many researchers have been working on this field and further developed this method [14], [15]. Recently, Réthoré et al. [16], [17] developed another form of DIC method for crack analysis. Moreover, Sutton et al. [18] used a 3D DIC setup to demonstrate the effect of out-of-plane displacements on 2D DIC measurements.
Due to the sensitivity and precision of the DIC method, it has been widely used for different engineering problems [19]. Determining the SIFs is one of the most important applications of this method. SIFs could be determined by using displacement fields along with the finite element or finite deference method [20]. Yoneyama et al. [21] and Ju et al. [22] employed this method for the evaluation of mixed mode SIFs. Furthermore, DIC technique was employed to analyze 3D x-ray computed micro-tomographic images cracks to estimate SIFs [23].
In this study, effects of wedge tip angle and edge crack angle on the SIFs of a half plane under three different contact loads were studied. The results were also compared with those using photoelasticity and good agreement between the obtained SIFs was observed.
Section snippets
Sample preparation
Two polycarbonate plates of 240 × 60 × 4 mm were used. According to the provider, the polycarbonate had an elastic modulus of 2.4 GPa, a Poisson's ratio of 0.38, and a friction coefficient of 0.4. Crack lengths of 5 mm with a 0.2 mm width were machined into the specimens employing a 0.2-mm blade. The plate edge cracks were inclined at 60° and 90° with respect to the horizontal direction.
Four asymmetric tilted wedges made of CK45 steel (Mat.No. 1.1191, DIN Ck45, AISI 1045) were used. All of the
Results and discussion
Fig. 5, Fig. 6 represent the contour maps for the contact of the half plane with wedges labeled W1 and W4, respectively. A vertical force of 255 N was applied by the wedges to the specimens.
The calculated SIFs along with the relative difference between the SIFs obtained from DIC and photoelasticity methods are presented in Table 2, Table 3. The half plane with a 90° edge crack experienced a mixed mode fracture and retained both non-zero in-plane SIFs, KI and KII. However, the half plane
Conclusions
DIC method was utilized to evaluate SIFs in the contact problem between a half plane with an edge crack and an asymmetric tilted wedge. The effect of wedge tip angles on SIF values was studied for two different crack angles (60° and 90°) under three different force magnitudes. The results of DIC method were compared with the ones obtained from the photoelasticity technique and revealed that the relative difference between the SIF values obtained from the two methods was less than 3% for all the
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