مدلسازی عددی فرآیند انحلال رسوبات کروی در آلیاژها با روش دیفرانسیل کوادریچر (DQM)
محورهای موضوعی : فصلنامه علمی - پژوهشی مواد نوین
نوذر انجبین
1
(بخش مهندسی مواد- دانشگاه شیراز)
کلید واژه: مدلسازی عددی, انحلال رسوب, روش دیفرانسیل کوادریچر, روش جبهه ثابت, مسئله با مرز متحرک,
چکیده مقاله :
پیش بینی سینتیک انحلال رسوب در فرایند های متالورژیکی مختلف نظیر جوشکاری، عملیات همگن سازی و پیشگرم کردن آلیاژهای رسوب سخت شونده حائز اهمیت است. مسئله انحلال رسوب کروی در زمره مسائل با مرزهای متحرک است و تابحال حل تحلیلی دقیق برای آن ارایه نشده است. در تحقیق پیش رو یک مدل عددی بر مبنای روش دیفرانسیل کوادریچر برای حل مسئله انحلال رسوب با هندسه کروی در زمینه ای با ابعاد متناهی ارایه شده است. در مدل پیشنهاد شده سینتیک انحلال بصورت تابعی از کسر حجمی رسوب، غلظت عنصر آلیاژی در زمینه و رسوب، غلظت تعادلی در فصل مشترک رسوب/زمینه و نیز دمای عملیات آنیل بیان شده است. همگرایی مدل عددی ارایه شده در حل مسئله انحلال از طریق بررسی اثر اندازه گام زمانی و تعداد نقاط شبکه بر نتایج حل عددی، مورد ارزیابی قرار گرفته است. همچنین دقت مدل پیشنهادی از طریق مقایسه نتایج مدل با نتایج یک مدل تحلیلی تقریبی و نیز داده های آزمایشگاهی مورد بررسی قرار گرفته است. نتایج بدست آمده نشان می دهد که مدل عددی ارایه شده حتی با تعداد نقاط شبکه کم، نیز همگرا بوده و انطباق خوبی با داده های آزمایشگاهی مربوط به انحلال رسوب کروی حین عملیات آنیل هم دما دارد.
Prediction of the dissolution kinetics of precipitates is important in various metallurgical processes such as welding, homogenization, and preheating of the age hardenable alloys. The problem of spherical particle dissolution is a moving boundary problem, which has no exact solution yet. In the present study, a numerical model based on the differential quadrature method is presented to solve the problem of precipitate dissolution with spherical geometry in a matrix with finite dimensions. In the proposed model, the dissolution kinetics is expressed as a function of the volume fraction of the precipitate, the concentration of the alloying element in the matrix, and precipitate, equilibrium concentration at the precipitate /matrix interface, and the annealing temperature. The convergence of the presented numerical model in solving the dissolution problem is evaluated by examining the effect of time step size and number of grid points on the numerical solution results. The accuracy of the proposed model is also evaluated by comparing the model results with the results of an approximate analytical model as well as experimental data. The results show that the proposed model converges even with a low number of grid points and is in good agreement
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