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Farklı çatlak boyuna sahip plakada gerilme yoğunluğunun nümerik ve sonlu elemanlar yöntemi ile analizi

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Abstract (2. Language): 
The stress intensity factor is a fundamental quantity that governs the stress field near the crack tip. The stress intensity factor depends on both the geometrical configuration and the loading conditions of the body. A number of methods have been used for the determination of stress intensity factors. They may be classified as theoretical (Westergaard semi-inverse method and method of complex potentials); numerical (Green's function, weight functions, boundary collocation, alternating method, integral transforms, continuous dislocations and finite elements methods), and experimental (photo elasticity, caustics, and combinations of these methods). The stress field in the neighborhood of a point of the border of an elliptical crack is a combination of the opening-mode, sliding-mode and tearing-mode, as for a through crack in a plate, and it is governed by the values of the corresponding stress intensity factors, KI , KII and KIII. These factors are independent of the coordinate variables and depend only on the position of the point at the crack front, the nature of loading and the crack geometry. Irwin presented a simplified model for the determination of the plastic zone attending the crack tip under small-scale yielding. He focused attention only on the extent along the crack axis and not on the shape of the plastic zone, for an elastic-perfectly plastic material. The universal availability of powerful, effective computational capabilities, usually based on the finite element method, has altered the use of and the need for stress concentration factors. Often a computational stress analysis of a mechanical device, including highly stressed regions, is shown, and the explicit use of stress concentration factors is avoided. Alternatively, a computational analysis can provide the stress concentration factor, which is then available for traditional design studies The elastic stress distribution of the case of an elliptical hole in an infinite-width thin element in uniaxial tension has been determined. At the edge of the elliptical hole, the sum of the stress components, σx and σy is given by the other investigators. Photo elastic tests of tension members with a transverse slit connecting two small holes are in reasonable agreemenet with the foregoing, take into consideration the accuracy limits of the photo elastic test. The “equivalent ellipse” concept ise useful for the ovaloid and other openings sach as two holes connected by a slit. A shape is enveloped by an ellipse (same major axis a and minor radius r) the KI values for the shape and equivalent ellipse may be nearly same. Aim of this study is to investigate, stress intensity factor (KI ) by using fem and theoretical formulations of rectangular plate with single edge crack. (KI ) was obtained for different crack length (a) and crack angle (θ), and results are compared. In addition, contour plot of stress field distribution was obtained for different normal stress (σy = 50, 75 and 100 MPa), at single edge crack plate. σx , σy , τ xy and von-Misses stress field distribution was investigated contour plot for different crack length a =1.00, 1.25 and 1.5 mm. By using empirical formulations and Ansys solutions were compared KI results, and among these Gross’s solution is considered to be best with finite element method (FEM) solution.
Abstract (Original Language): 
Gerilme şiddeti faktörü çatlak ucu yakınındaki gerilme alanı düzenleyen temel bir büyüklüktür. Gerilme şiddet faktörü de geometrik konfigürasyon ve cismin yükleme koşullarına bağlıdır. Farklı yöntemler kullanılarak bir dizi gerilme şiddeti faktörleri tespit edilmiştir. Bu yöntemler; teorik (Westergaard yarı ters yöntem ve karmaşık potansiyelleri yöntemi) sayısal (Green fonksiyonu, ağırlık fonksiyonları, sınır kollokasyon, yöntem alternatif dönüşümleri, integral, sürekli çıkık ve sonlu elemanlar yöntemleri) ve deney (fotoğraf esneklik, kostiklere ve bu yöntemlerin kombinasyonları) olarak sınıflandırılabilir. Bir eliptik çatlağın yakınındaki bir noktada oluşan gerilme alanı; açılma modu, düzlem içi kayma modu, düzlem dışı kayma modu olarak incelenmektedir. Bu faktörlerin koordine değişken bağımsızdır. Bu çalışmanın amacı tek kenarında çatlak bulunan dikdörtgen plakanın teorik hesaplamalar ve sonlu elamanlar metodunu kullanarak gerilme yoğunluğu faktörünü (KI ) incelemektir. Farklı çatlak boyu (a=1.00, 1.25 ve 1.5 mm) ve farklı açılar gerilme yoğunluğu elde edilmiş ve sonuçlar karşılaştırılmıştır. Ayrıca için gerilme (σy =50, 75 ve 100 MPa) altında plakanın gerilme yoğunluğu faktörü her iki yöntem ile elde edilmiştir. Söz konusu yükleme şartlarında, σx , σy , τ xy ve von-Mises gerilmeleri için plaka yüzeyinde ve çatlak civarında meydana gelen gerilme alan dağılımı grafikleri gösterilmiştir. Ampirik sonuçları, özellikle Gross tarafından geliştirilen formülasyon sonuçlarının ve Ansys kullanılarak elde edilen (KI ) sonuçlarıyla oldukça yakın değerler elde edilmiştir.

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