Abstract
Kırılma, malzemelerin gerilme altında birden fazla parçalara ayrılması olarak tanımlanmaktadır. Kırılma tokluğu ise, çatlaklı bir malzemenin kırılmaya karşı direncini gösteren malzemelerin mekanik özelliklerinden biridir ve 𝐽−integral yöntemi, kırılma tokluğunun geometriden bağımsız ölçümünü veren bir yöntemdir. Bu çalışmada, izotropik özelliklere sahip kenar çatlaklı numune, farklı takviye açılarına sahip 45o merkez çatlaklı ortotropik özellikte dikdörtgen numune ve merkezinde farklı açılarda çatlaklar ihtiva eden izotropik özelliklere sahip kare numune için, 𝐽−integral’i değerleri ANSYS APDL kullanılarak tespit edilmiştir. ANSYS kullanılarak elde edilen sayısal sonuçlar, simgesel bir matematik yazılımı kullanılarak, analitik olarak ta elde edilerek, sayısal ve analitik sonuçlar mukayese edilmiştir. Sonuçta; 𝐽−integralin çatlak ucuna olan uzaklığına göre değişimi incelenmiş olup, sayısal ve analitik sonuçlar arasındaki hata payının % 0.0462 ile % 2.8149 arasında değiştiği tespit edilmiştir.
References
- Aleksic B , Milovic L. ,Grbovic A ,Hemer A., 2018. Experimental and numerical investigations of the critical values of J-integral for the steel of steam pipelines. Procedia Structural Integrity,13, 1589-1594.
- Balaban AC, Tee KF., 2019. Strain energy release rate of sandwich composite beams for different densities and geometry parameters. Theoretical and Applied Fracture Mechanics, 101,191-199.
- Chu SJ, Hong CS., 1990. Application of the Jk Integral to Mixed Mode Crack Problems for Anisotropic Composite Laminates. Engineering Fracture Mechanics, 35,1093-1103.
- Gibson RF., 1994. Principles of Composite Material Mechanics. New York, USA, McGraw–Hill.
- Gu L, Kasavajhala ARM, Zhao S., 2011. Finite Element Analysis of Cracks in Aging Aircraft Structures with Bonded Composite-Patch Repairs. Composites: Part B, 42, 3, 505-510.
- Lekhnitskii SG., 1963. Theory of Elasticity of an Anisotropic Elastic Body. San Fransisco, USA, Holden-Day.
- Lei J , Xu Y ,Gu Y ,Fan C., 2019. The generalized finite difference method for in-plane crack problems. Engineering Analysis with Boundary Elements, 98,147-156.
- Liu J, Sawa T., 2000. Stress Analysis and Strength Evaluation of Single Lap Band Adhesive of Dissimilar Adherends Subjected to External Bending Moment. J. Of Adhesion Science and Technology, 14, 67-92.
- Özdemir A., 2006. Seramik Malzemelerin Kırılma Tokluğu Değerlerinin Üç Boyutlu Sonlu Elemanlar Yöntemi İle Teorik Olarak Belirlenmesi. Yüksek Lisans Tezi, Dokuz Eylül Üniversitesi, İzmir, Türkiye.
- Patil K, Wadageri CS., 2016.Fracture Analysıs for Steel and Epoxy Materıal Plate With Edge Crack”. International Journal of Recent Trends in Engineering & Research,2, 2455-1457.
- Rice JR., 1968. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35,379-386.
- Tan CL, Gao YL., 1992.Boundary Element Analysis of Plane Anisotropic Bodies with Stress Concentrations and Cracks, Composite Structures,20,17-28.
- Vavrik D , Jandejsek I., 2014. Experimental evaluation of contour J integral and energy dissipated in the fracture process zone. Engineering Fracture Mechanics,129,14-15.
- Wang Y, Sun Y., 2005. A new boundary integral equation method for cracked 2-D anisotropic bodies. Engineering Fracture Mechanics,72, 2128–2143.
- Wen P, Aliabadi M., 1995. A contour integral for the evaluation of stress intensity factors. Appl. Math. Modelling,19,450-455.
Abstract
Fracture is defined as breaking of materials under stress and breaking them into more than one part. On the other hand, fracture toughness is one of the mechanical properties of materials showing the resistance of a material that has a crack and the 𝐽−integral method is a method that gives the geometry independent measurement of fracture toughness. In this study, the 𝐽−integral values were determined for a specimen which is a crack in its edge and having isotropic properties, a rectangular specimen which is orthotropic properties in addition to different reinforcement angles and having a 45o crack in its center and a square specimen which is the different cracks in its center and having isotropic properties using ANSYS APDL. Numerical results obtained using ANSYS were also obtained analytically by using a symbolic mathematics software and numerical and analytical results were compared. As a result; The variation of the 𝐽− integral with respect to the distance to the crack tip was investigated and it was found that the error margin between numerical and analytical results varied between 0.0462 % and 2.8149 %.
References
- Aleksic B , Milovic L. ,Grbovic A ,Hemer A., 2018. Experimental and numerical investigations of the critical values of J-integral for the steel of steam pipelines. Procedia Structural Integrity,13, 1589-1594.
- Balaban AC, Tee KF., 2019. Strain energy release rate of sandwich composite beams for different densities and geometry parameters. Theoretical and Applied Fracture Mechanics, 101,191-199.
- Chu SJ, Hong CS., 1990. Application of the Jk Integral to Mixed Mode Crack Problems for Anisotropic Composite Laminates. Engineering Fracture Mechanics, 35,1093-1103.
- Gibson RF., 1994. Principles of Composite Material Mechanics. New York, USA, McGraw–Hill.
- Gu L, Kasavajhala ARM, Zhao S., 2011. Finite Element Analysis of Cracks in Aging Aircraft Structures with Bonded Composite-Patch Repairs. Composites: Part B, 42, 3, 505-510.
- Lekhnitskii SG., 1963. Theory of Elasticity of an Anisotropic Elastic Body. San Fransisco, USA, Holden-Day.
- Lei J , Xu Y ,Gu Y ,Fan C., 2019. The generalized finite difference method for in-plane crack problems. Engineering Analysis with Boundary Elements, 98,147-156.
- Liu J, Sawa T., 2000. Stress Analysis and Strength Evaluation of Single Lap Band Adhesive of Dissimilar Adherends Subjected to External Bending Moment. J. Of Adhesion Science and Technology, 14, 67-92.
- Özdemir A., 2006. Seramik Malzemelerin Kırılma Tokluğu Değerlerinin Üç Boyutlu Sonlu Elemanlar Yöntemi İle Teorik Olarak Belirlenmesi. Yüksek Lisans Tezi, Dokuz Eylül Üniversitesi, İzmir, Türkiye.
- Patil K, Wadageri CS., 2016.Fracture Analysıs for Steel and Epoxy Materıal Plate With Edge Crack”. International Journal of Recent Trends in Engineering & Research,2, 2455-1457.
- Rice JR., 1968. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35,379-386.
- Tan CL, Gao YL., 1992.Boundary Element Analysis of Plane Anisotropic Bodies with Stress Concentrations and Cracks, Composite Structures,20,17-28.
- Vavrik D , Jandejsek I., 2014. Experimental evaluation of contour J integral and energy dissipated in the fracture process zone. Engineering Fracture Mechanics,129,14-15.
- Wang Y, Sun Y., 2005. A new boundary integral equation method for cracked 2-D anisotropic bodies. Engineering Fracture Mechanics,72, 2128–2143.
- Wen P, Aliabadi M., 1995. A contour integral for the evaluation of stress intensity factors. Appl. Math. Modelling,19,450-455.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | September 25, 2020 |
| Submission Date | December 3, 2019 |
| Published in Issue | Year 2020 Volume: 20 Issue: 4 |
