Numerical study of crack growth in porous media: Effect of elliptical porosity parameters

Document Type : Research Article

Authors

1 M.Sc. in rock mechanic, Engineering Faculty, University of Zanjan, Zanjan, Iran

2 Department of Mining, Material and Metallurgy, Faculty of engineering, University of Zanjan, Zanjan, Iran

3 Assistant Professor in Mining Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

Abstract

Summary
Recent developments in eXtended Finite Element Method (XFEM) opened new avenues through crack propagation problems. However, in most researches, exact porosities are not considered or are just replaced with some circular pores. This means the effects of the shape, location, and arrangement of the porosities are less evaluated. In this study, by considering the porosity as an elliptical pore, parameters such as elliptical shape, relative location, and arrangement of pores are studied. The results revealed that this kind of considerations can improve the accuracy of crack growth modeling through porous media.
 
Introduction
The shape and location of a pore have a significant effect on the cracks' growth and propagation in porous media. Due to the concentration of stress around these discontinuities, tensile cracks are created and coalesced leading to the final failure in the sample. Since these kinds of tests in pore-scale are practically hard to implement in the laboratory, numerical computation of these behaviors is of great importance to correctly understand this phenomenon. In recent years, the use of XFEM, which eliminates the need for remeshing along the crack path, has been extensively developed and used by many researchers. However, due to the complex shape of the porous structure, even in numerical modeling, they either are not considered or their shape is assumed to be circular. We, in this study, will go a step forward in this limitation by assuming an elliptic shape for porosities.
 
Methodology and Approaches
In this article, the effect of shape, location, and arrangement of elliptical porosity on crack growth is numerically modeled. By placing these porosities beside and in front of the crack, the stress distribution, stress intensity factor variation, and maximum resistance of the sample are investigated.
 
Results and Conclusions
The results showed that for the equal size of pores if the vertical elliptical pore is located in front of the crack, its destructive effect is about 20% more than the horizontal elliptical pore. Also, when the porosity is located beside the crack, by increasing the angle between the horizontal axis with the direction of the large ellipse diameter (here we call it α), the stress intensity factor decreases from 1 to 0.94 and reduces the crack propagation in the porous sample. In addition, we defined the angle between the horizontal axis and the line joining the centers of the two porosities as β and evaluated the effect of the porosity shape and its location on crack growth in more complex models (i.e., models containing two elliptical porosities). By increasing the α and β from 0o to 90o, the maximum strength of the sample decreases by 18.12%, and the von Mises stress value increases from 0.154 to 0.922 MPa. However, the results revealed that the effect of β on crack growth is greater than α.

Keywords

Main Subjects

Full Text

مواد ترد به‌طور طبیعی دارای ناپیوستگی­های متعددی ازجمله ترک، درزه و تخلخل بوده که خصوصیات مکانیکی و مقاومتی آن‌ها را کاهش داده و بر نحوه وقوع شکست در آن‌ها تأثیر بسزایی دارد ]3-1[. به‌عنوان‌مثال رفتار سنگ­ها، به‌طورمعمول تحت تأثیر رفتارهای میکرومکانیکی ناشی این ناپیوستگی­ها قرار می­گیرد. به‌طور خاص در مواد متخلخل، هندسه، شکل و نحوه چیدمان تخلخل‌ها مؤلفه‌های بسیار تعیین‌کننده‌ای در نحوه گسترش ترک و مقاومت نهایی سنگ، به شمار می­آیند [4، 5]. بسیاری از مطالعات آزمایشگاهی نشان داده‌اند که شروع و گسترش ترک، از ناپیوستگی­هایی که از پیش در نمونه وجود داشته‌اند، آغاز می‌شود [6، 7]. ازاین‌رو، مطالعه نحوه توزیع تنش، چگونگی شروع و گسترش ترک و مقاومت بیشینه در مواد متخلخل، بسیار مهم است. بررسی و ارزیابی فرآیند انتشار ترک در سنگ­های متخلخل، می­تواند برای طراحی بهتر پروژه‌های ژئومکانیکی و پایش پایداری سازه­های مهندسی، بسیار کاربردی باشد [8]. ازآنجایی‌که ارزیابی آزمایشگاهی گسترش ترک و تغییر مقاومت در سنگ‌های متخلخل، بسیار دشوار است، روش­های عددی به‌عنوان یک راهکار مناسب برای بررسی چنین مواردی به‌حساب می‌آیند. روش‌های عددی مختلفی برای بررسی رشد ترک و شکست در مواد ترد ارائه‌شده است [9]. در این میان، روش اجزا محدود توسعه‌یافته[i] (XFEM)، به علت ویژگی­های منحصربه‌فرد و توانایی بالا در سال‌های اخیر موردتوجه پژوهشگران متعددی قرارگرفته است [10، 11]. ازجمله چالش­ها و معایب عمده­ی روش اجزا محدود استاندارد، مش­بندی دوباره دامنه موردمطالعه در مدل­سازی رشد ترک و نیز صرف هزینه محاسباتی بالا در موقعیت ناپیوستگی‌ها (محاسبه تکینگی در نوک ترک) است که استفاده از آن را در برخی از مسائل مکانیک شکست، محدود می­سازد. عدم در نظر گرفتن هندسه ناپیوستگی‌ها در مش‌بندی دامنه و نیز عدم نیاز به مش‌بندی دوباره آن به‌واسطه رشد ترک، ازجمله قابلیت‌های عمده روش کارآمد اجزا محدود توسعه‌یافته محسوب می­شود. درروش XFEM، از روش اجزا محدود استاندارد بدون استفاده از المان­های تکینه[ii] و با استفاده از توابع غنی­ساز[iii] که از حل تحلیلی میدان تنش در پیرامون ناپیوستگی و ترک استخراج می‌شوند، استفاده می‌شود. بااین‌حال، اضافه کردن درجات آزادی (غنی­سازی) گره‌هایی از مش که با ناپیوستگی در ارتباط است، شبیه‌سازی تکینگی و ناپیوستگی­ها را در این روش، امکان‌پذیر می­کند. در این روش، موقعیت نوک ترک و بدنه ترک را می‌توان در هر مرحله از رشد ترک یافت و درنتیجه المان‌هایی که باید غنی‌سازی شوند را به‌درستی انتخاب نمود [12].


[i] eXtended Finite Element Method (XFEM)

[ii]Singular elements

3 Enrichment functions

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Journal of Analytical and Numerical Methods in Mining Engineering
Volume 11, Issue 27
July 2021
Pages 79-92

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History

  • Receive Date: 13 November 2020
  • Revise Date: 29 January 2021
  • Accept Date: 15 March 2021

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