حل بسته برای میدان های الاستیک حاصل از حرکت یک نابجایی پیچی دارای سرعت ثابت بر روی مسیری مستقیم الخط با راستایی دلخواه

نوع مقاله: پژوهشی

نویسنده

دانشکده مهندسی عمران، دانشگاه صنعتی خواجه نصیرالدین طوسی

10.24200/j30.2020.54889.2681

چکیده

مطالعه ی حاضر به تعیین میدان های الاستیک ناشی از یک نابجایی پیچی که بر روی مسیری مستقیم الخط با راستایی دلخواه در یک محیط نامتناهی همسانگرد در حال حرکت است اختصاص یافته است. در اینجا فرض می شود که این نابجایی با سرعتی ثابت و البته کمتر از سرعت انتشار امواج برشی در محیط حرکت می کند. در این تحلیل در چارچوب یک توصیف میکرومکانیکی، از مفهوم کرنش ویژه برای بیان هندسه ی نابجایی مذکور بهره برده خواهد شد. پس از صورت بندی معادلات حاکم بر مسأله، از تبدیل فوریه ی دو بعدی استفاده کرده و برای اولین بار برای میدان های تغییر مکان و کرنش الاستیک مسأله ی در دست بررسی، حل بسته ارائه می شود. نتایج حاصله به خوبی گویای اثر راستای حرکت نابجایی و نیز سرعت آن بر روی میدان های الاستیک ایجاد شده در محیط هستند.

کلیدواژه‌ها


عنوان مقاله [English]

Closed-form solutions for the elastic fields due to the motion of a screw dislocation at a constant velocity along a linear path with an arbitrary direction

نویسنده [English]

  • Mohammad Rasoul Delfani
Faculty of Civil Engineering, K. N. Toosi University of Technology
چکیده [English]

The present study has been dedicated to the determination of the elastic fields due to the motion of a screw dislocation that moves along a linear path with an arbitrary direction in an infinitely extended isotropic medium. It has also been assumed that the dislocation moves at a constant velocity less than the speed of shear waves in the medium. In the present analysis, from the viewpoint of micromechanics, the dislocation has been described by virtue of the concept of eigenstrain. The expression of such an eigenstrain field includes a constant which will be determined in the sequel of the analysis by applying the jump condition of the displacement on the slip plane of the dislocation. After the representation of the governing field equations of the problem, a two-dimensional Fourier transform is utilized and, then, the closed-form solutions are obtained for the displacement and elastic strain fields of the delineated problem, for the first time. Subsequently, two special cases of the problem, the one pertinent to the motion of the dislocation along its slip plane and the other associated with its motion perpendicular to such plane are addressed. The derived expressions show that the strain field of the problem has a singularity at the dislocation core. The obtained results demonstrate that, at different velocities and in different directions of motion, the displacement field of the problem suffers from a constant discontinuity on the slip plane of the dislocation. Moreover, it has been shown that, at distances far away from the slip plane of the dislocation, the components of the strain field vanish. The presented results, in addition, exhibit the effect of the direction of the motion of the dislocation and its velocity on the induced elastic fields. Specifically, it has been shown that, with an increase in the velocity of the dislocation, the magnitudes of the components of the induced strain field become larger.

کلیدواژه‌ها [English]

  • Screw dislocation
  • elastic field
  • uniform motion
  • eigenstrain