دانلود رایگان مقاله روش سنجش کرنش برای تعیین عوامل شدت تنش مواد ارتوتروپیک

Abstract

A theoretical frame work is developed for strain gage based determination of mixed mode (KI/KII) stress intensity factors (SIFs) in slant edge cracked plate (SECP) made of orthotropic materials. Using three parameter strain series around the crack tip and appropriate stress functions, the present formulation shows that mixed mode SIFs in orthotropic materials could be determined using only four strain gages. A finite element based methodology is developed to determine the upper bound on the radial location (rmax) of strain gages ensuring accurate determination of SIFs. Proposed technique is applied to numerical simulation of [02/90]2S and [0/±45/90]S glass-epoxy SECP laminates to demonstrate accurate determination of mixed mode SIFs by placing the gages within rmax. Results from the present work provide clear guidelines in terms of number of strain gages and their suggested locations for accurate determination of mixed mode SIFs in orthotropic materials.

4. Conclusions

A simple, robust and practically feasible strain gage technique has been developed for the first time for the accurate determination of mixed mode SIFs (KI and KII) in orthotropic laminates. The proposed theoretical framework not only allows determination of mixed mode SIFs (KI and KII) using strain gages in orthotropic materials but also allows to calculate the valid radial locations of the strain gages ensuring accurate determination of KI and KII. As the proposed strain gage technique depends on three parameter representation, it allows the gages to be placed reasonably far away from the crack tip. Further, the proposed technique needs only four strain gages for determination of mixed mode SIFs. A finite element based methodology is also developed to evaluate the extent of radial locations of the strain gages ðrmaxÞ which ensure accurate determination of KI and KII for orthotropic laminates. Numerical experimentations have been performed on ½02=90 2S and ½0= 45=90 S glass- epoxy SECP laminates to validate the developed theory. Results show that the strains computed at points within rmax follow the theoretical predictions which validate the proposed method. It was observed that rmax depends both on the crack inclination angle (w) and on the relative crack length (a=b). Up to w ¼ 45, rmax remains almost same but beyond that rmax shows a sharp decrease. For a given w, rmax initially increases with the increase in a=b and then decreases. Numerical simulations show that while the computed values of KI and KII obtained from the simulated readings of strain gages placed within rmax are highly accurate, a very high error ({>}29%) results when the gages are placed outside rmax. Simulations have been carried out to show the robustness of the proposed method over a range of crack inclination angles. An extremely important recommendation from the present study is that while conducting strain gage based experiments, the radial locations where the strain gages need to be placed are dependent on the crack configurations (relative crack size and crack angle) and arbitrarily placing the strain gages will lead to highly erroneous results. The present work provides a robust method for prior determination of such optimal locations for a given configuration. The proposed method will be immensely useful for experimental stress analysts in accurate determination of mixed mode SIFs in orthotropic composites using strain gages as the rmax value for a given configuration could be easily calculated using a simple FEA.