ÇENTİKLİ ELEMANLARIN KIRILMASININ BİR KONTROL ALGORİTMASI KULLANILARAK STABİLİZASYONU

Abstract

Çatlak yayılımı, yük etkisine maruz yarı-gevrek malzemelerin davranışını belirleyen önemli bir mekanizmadır. Çatlak yayılımı çok aniden ortaya çıkabilmekte ve bu da bazı problemlerin analizinde sayısal dengesizliklere ve kusurlara neden olabilmektedir. Bu davranış kendini sayısal sonucun ıraksaması yani bütün yük yerdeğiştirme eğrisinin elde edilememesi olarak veya yük-yerdeğiştirme eğrisinde sıçrama şeklinde gösterir. Bu çalışmada çatlak yayılmasının bütün yük-yer değiştirme eğrisinin elde edilmesinde sayısal sorunlar yarattığı, snap-back (geri tepme) davranışında olduğu gibi, durumlar için bir kontrol algoritması uygulanması verilmiştir. Kontrol tekniğinin performansı tek çentikli levhaya uygulanan doğrudan çekme deneyi, çentikli kirişlerde üç noktalı eğilme deneyi ve iki çentikli levhaların karışık kırılma modu testi simüle edilerek gösterilmiştir. Bu çalışma, kontrol algoritmasının bu tür problemler için kararlı bir çözüm yolu üretebildiğini göstermiştir. Bu yöntem herhangi bir kullanıcı tanımlı alt rutine ihtiyaç duymadan mevcut ticari sonlu eleman kodlarında kolayca uygulanabilir.

Keywords

• Kontrol algoritması
• Kırılma
• Sonlu Elemanlar Yöntemi
• Yarı-gevrek
• Snap-back (geri tepme).

STABILIZATION OF NOTCHED ELEMENTS' FRACTURE BY USING A CONTROL ALGORITHM

Abstract

Crack propagation is a significant mechanism for quasi-brittle materials under applied loading. It can occur very suddenly and causes numerical instabilities and deficiencies in some problems. This behavior manifest itself as non-convergence solutions i.e. the inability to obtain the entire load-displacement curve or jumps in the load displacement curve. In this study, a control technique is implemented to obtain the whole load–displacement curve when crack propagation causes severe numerical instabilities such as snap-back behavior. The performance of the control technique was demonstrated by simulating uniaxial tension test of pre-notched plate, three-point bending test of a notched beam and mixed-mode test of a notched plate. This study shows that the control algorithm is able to produce a stable solution path for these kinds of problems. This method can be easily implemented in available commercial finite element codes without the need for any user defined subroutines.

Keywords

• Control algorithm
• Fracture
• Finite Element Method
• Quasi-brittle
• Snap-back.

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