Literature Review
2.3 Strain gage techniques for determination of mixed mode I/II SIFs
Very limited amount of published work is available on applications of strain gage techniques for determination of mixed mode I/II SIFs for isotropic materials.
The very first work in this direction was due to Dally and Berger [42] who extended DS technique to the mixed mode strain field for the determination of static SIFs KI and KII in isotropic materials. More number of parameters was employed in their method as compared to DS technique so that the strain gages could be placed at grater distances from the crack tip. Due to the use of multiparameter strain field representation, the region of strain field was increased substantially but at the same time more number of strain gages was required to find the unknown coefficients. Two ten element strip gages were pasted on both sides of crack axis in a slant edge cracked plate made of aluminum alloy at equal angle and at equal radius form crack tip to capture corresponding positive and negative strains. No guidelines or procedure was suggested on valid or optimal radial locations for strain gages. It appears that the placement of strip gages, from the crack tip was probably based on their intuition/past experience. It is clear that since they employed strip gages some of the gages may be at the optimal locations and others may be at unacceptable locations. The SIFs were obtained by graphical extrapolation technique. The SIFs obtained by experimental techniques were compared with both numerical result and published result. An error of about 16.4% in KI and 29% in KII were reported when they compared their experimental values with the published data. In the present investigation, henceforth, Dally and Berger [42] mixed mode technique is termed as DB technique throughout the present investigation.
Kondo et al. [43] proposed a strain gage method for determination of mixed mode SIFs of sharp notched strips. In this technique it was necessary to position the strain gage along more than two different directions for determination of mixed mode SIFs. They employed two strip gages containing five elements for measuring strain along two rays from the bisector angle of the notch. The radial locations of each strain gage were selected based on the theory given by Dally and Sanford [22] for minimizing the averaging errors in gages. No procedure was discussed for valid or
optimal radial locations of strain gages. The experimental results of mode I and mode II SIFs were consistently smaller than the theoretical results and within 10%
difference for various notch angles and shapes.
Another strain gage technique for determination of mixed mode SIFs was proposed by Dorogoy and Rittel [44] using strain gage rosettes instead of single element gages. The procedure for obtaining the SIFs was presented using numerical studies on a slant edge cracked plate and no experimental results were reported. They observed from the numerical analysis that the radial location of rosette was an important factor in accurate measurement of SIFs. They recommended that the rosette should be placed as close as possible to the crack tip but out side the plastic zone and three dimensional effects which clearly demands knowledge of unknown SIFs. From the numerical example, they suggested the use of two strain gage rosettes at the same angle and linearly extrapolate their results for obtaining reasonably accurate mixed mode SIFs.
Multiphase material interfaces are found in many applications. The interface between the two materials is a plane of low strength. Fracture starts along the interface. The determination of fracture toughness of bimaterial interface is important in advanced material systems. It is represented by a complex SIF which is a combination of both tensile and shear effect that are intrinsically linked and therefore inseparable. Therefore, both mode I and mode II SIFs are required to represent the complex SIF. As a consequence some strain gage techniques have also been developed for bimaterial systems.
Ricci et al. [45] were first to apply the strain gage technique to determine complex SIFs in bimaterial system of PSM-1 and aluminum under quasi-static loading. Singular radial strain field equations were derived from stress field equations.
In their technique mixed mode SIFs were determined using singular or leading strain field terms without considering subsequent higher order terms. As a consequence, the two SIFs were determined using only two strain gages which were necessarily to be placed within the singularity dominated zone. From a series of parametric studies they decided that the radial distance more than or equal to half the specimen thickness was sufficient to measure the strain accurately without affected by strain gradient,
plasticity and three dimensional effects. However, no explanation was provided as the selected radial distance was within the singularity dominated zone or not i.e., within the realm of selected strain terms. They reported that the mixed mode SIFs KI and KII obtained by strain gage method deviated from theoretical values by 11% and 4%
respectively.
Marur and Tippur [46] developed a strain gage technique for determination of complex SIF in bimaterial systems. As in the case of Ricci et al. [45] technique, only singular strain terms were considered for representation of strain field ahead of the crack tip. Unlike Ricci et al. [45], Marur and Tippur [46] considered both the radial and hoop strains for the determination of mixed mode SIFs and therefore a strain rosette was employed for experimental determination of SIFs. They selected the radial distance for the strain gages from the parametric studies presented by Ricci et al. [45]
and no explanation was provided as to whether the selected radial distances were within the singularity dominated zone or not. The angular position of the rosette was selected based on conditioning of the coefficient matrix and to maximize the sensitivity of the measurements. The results corresponding to static and dynamic loading conditions showed that the complex SIFs obtained by strain gage method were in agreement with the finite element estimations.
Ricci et al. [47] extended the strain gage technique developed by Ricci et al.
[45] for subsonic dynamic loading conditions of isotropic-isotropic bimaterial systems. They selected the radial distance for the strain gages from the parametric studies presented by Ricci et al. [45] and no explanation was provided as to whether the selected radial distances were within the singularity dominated zone or not. The angular position was again based on the parametric study which maximized the sensitivity of strain measurement. Results obtained using their strain gage technique were in agreement with the photoelastic results.
Ricci et al. [48] extended their strain gage technique presented in Ref. [47] to isotropic- orthotropic bimaterial interface. Again they selected the radial distance for the strain gages from the parametric studies presented by Ricci et al. [45] and no explanation was provided as to whether the selected radial distances were within the
singularity dominated zone or not. As stated earlier, these locations were selected to avoid three dimensional and plasticity effects at the crack tips. For the experiments, four strain gages were mounted in a row. The orientation of strain gages were decided based on peak strain profile. Results showed that the complex SIF obtained by strain gage method was in agreement with results obtained by photoelasticity method.
To the best of author’s knowledge the very early attempt on determination of optimal strain gage locations corresponding to the DS technique was proposed by Kaushik and Murthy [49]. Their estimation was based on the extent of applicability of assumed strain distribution in the DS technique. Although, the proposed technique was applicable for all configurations, it is observed that their approach resulted into highly inconsistent and over estimated values optimal gage locations. No experimental study was conducted for verification of the estimated gage locations.
Due to erroneous estimations, many important results were obscured.