# DETERMINATION OF STRESS CONCENTRATION FACTOR FOR AN INFINITE 3D SOLID PLATE WITH A DEEP HYPERBOLIC GROOVE AND ANN APPLICATION

### Abstract

The stress concentration factor (SCF) is important for design of machine components. Especially designing machine components, some geometrical shapes may occur such as grooves, notches, holes and curves. Working components of machine are deformed. Thus, SCF should be thought when designing the machine equipment. Material selection is so important for stable system design which deals with the stress concentration. Generally, the reasons of SCF depend on the design features. In this research, a deep hyperbolic groove is analyzed in terms of SCF. There are several methods to examine the SCF. These methods can be named such as Numerical Analysis, Finite Element Analysis (FEA), Experimental Analysis, Artificial Neural Network (shortly ANN) Methods etc. One of them is known as ANN model which is used in this research. ANN model is used for determination of SCF for an infinite three-dimensional groove. Groove shape types and dimensions can be varied. This is impossible to do experiment or do numerical analysis for every each design shape. ANN is economical and useful method for determination of SCF. While use the some of data of numerical or experimental results, the other types of grooves SCF can be determined with high reliability. The ANN works with different learning algorithms. Neuron is the main element of ANN. The infinite plate is exposed to torsional loading. Meanwhile groove radius and differences of dimensions between two grooves are changed. Analytical, empirical (Peterson’s) and ANN model results have been obtained, and error calculations have been analyzed with using these results. ANN model demonstrates that, fast and accurate results can be obtained for SCF of hyperbolic groove.

### Downloads

### References

H. Liebowitz, H. Vanderveldt and R. J. Sanford, “Stress concentrations due to sharp notches,” Experimental Mecahanics, Vol. 7, 1967, p. 513-517

T. Nicholas, “High Cycle Fatigue: A Mechanics of Materials Perspective,” 1st ed., Elsevier, Oxford, 2006, pp. 213–238.

A. Dogrusadik, “Çentikli Parçaların Yorulma Ömürlerinin Saptanmasında Kullanılan Yöntemlerin Deneysel Tahkiki,” Istanbul Teknik Üniversitesi, 2009, Istanbul, 1–2.

D. Arola, C. L. Williams, “Estimating the fatigue stress concentration of machined surfaces,” International Journal of Fatigue, 24, 2002, pp. 923-930.

H Nisitani, N. Noda, “Stress concentration of a cylindircal bar wih a V-shaped circumferential Groove under torsion, tension or bending,” Engineering Fracture Mechanics, Vol. 20, 1984, pp. 743-766.

F. A. Mcclintock 1968. “A criterion of ductile fracture by the growth of holes,” J Appl Mech, 35, 1968, pp. 363–371.

J. R. Rice, D. M. Tracey, “On the ductile enlargement of voids in triaxial stress fields,” J. Mech Phys Solids, vol. 17, 1969, pp. 201–217.

J. W. Hancock and A. C. Mackenzie, “On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states,” J Mech Phys Solids, vol. 24, 1976, pp. 69–147.

P. W. Bridgman, “Studies in large plastic flow and fracture,” MA Harvard University Press, Cambridge, 1952, pp. 3–5.

J. W. Hancock and D. K. Brown, “On the role of strain and stress state in ductile Failure,” Journal of the Mechanics and Physics of Solids, vol. 31, 1983, pp. 1–24.

H. Neuber, “Elastischstrenge Lo¨sungen zur Kerbwirkung bei Scheiben und Umdrehungskorpern. ZAMM, vol. 13, 1933, pp. 439–442.

H. Neuber, “Kerbspannungslehre,” 2nd edition, 1958, pp. 159–163 (Springer-Verlag, Berlin).

W. D. Pilkey and D. F. Pilkey, “Peterson’s stress concentration factors,” 3rd edition, 2008, (Wiley, New York).

S. J. Hardy and N. H. Malik, Survey of post-Peterson stress concentration factor data,” Int. J. Fatigue, vol. 14, 1992, pp. 147–153.

A. Thum and O. Svenson, “Beanspruchung beimehrfacher Kerbwirkung,” Schweiz. Arch. Angew. Wiss. Techn, vol. 15, 1949, pp. 161–174.

A. Thum and O. Svenson, “Mehrfache Kerbwirkung: Entlastungskerben-U¨ berlastungskerben,” Z. VDI, vol. 92, 1950, pp. 225–230.

C. Weber, “Spannungsverteilung in Blechen mit mehreren kreisfo¨rmigen Lochern,” ZAMM, vol. 2, 1922, pp. 276–273.

A. Atsumi, “Stress concentrations in a strip under tension and containing an infinite row of semicircular notches,” Q. J. Mech. and Applied Math., XI(4), 1958, pp. 478–490.

M. P. Savruk and A. M. P. Kazberuk, “A plane periodic boundary-value problem of elasticity theory for a half-plane with curvilinear edge,” Mater. Sci., vol. 44, 2008, pp. 461–470.

N. K. Naik, “Photoelastic investigation of finite plates with multi-holes,” Mech. Res. Commun, vol. 15, 1988, pp. 141–146.

R. B. Heywoood, “Designing by photoelasticity,” 1st edition, 1952, pp. 202–205 (Chapman and Hall, London).

K. J. Schulz, “On the state of stress in perforated strips and plates,” Proc. Koninkl¨yke Nederlandsche Akadamie vanWetenschappen (Netherlands Royal Academy of Science), Amsterdam, Vol. 46–48, 1943-1945, pp. 282-292.

T. Slot, “Stress Analysis of Thick Perforated Plates,” Technomic Publishing Co., Doctoral thesis Westport, CT., 1972.

Özkan M T, Toktas I (2016). Determination Of The Stress Concentration Factor Kt İn A Rectangular Plate With A Hole Under Tensile Stress Using Different Methods Title. Materials Testing, 58(10), 839-847., Doi: 10.3139/120.110933 (Yayın No: 2867876)

Demir E, Toktas I, Özkan M T, Jabbar G (2015). Comparison With Different Models Of Bending Stress Analysis Of The Cantilever Beams Under Different Profile Section Materials And Loads. Social Gau Journal & Applied Sciences, 7(11), 173-182. (Yayın No: 1549735)

Demir E,Toktas I,Özkan M T,Jabbar G (2015). Comparison With Different Models Of Tensile And Compressive Stress Analysis On A Cantilever Beam Model. Social Gau Journal & Applied Sciences, 7(11), 183-194. (Yayın No: 1549749)

Özkan M T (2015). Surface Roughness During The Turning Process Of A 50crv4 Sae 6150 Steel And Ann Based Modeling. Materials Testing, 57(10), 889-896., Doi: 10.3139/120.110793 (Yayın No: 1549691)

Özkan M T,Eldem C,Sahin I (2014). Determination Of Notch Factor For Shafts Under Torsional Stress By The Help Of Artificial Neural Networks. Materiali İn Tehnologije / Materials And Technology, 48(1), 81-90. (Yayın No: 348892)

Özkan M T (2013). Experimental And Artificial Neural Network Study Of Heat Formation Values Of Drilling Boring Operations On Al 7075 T6 Workpiece. Indian Journal of Engineering & Materials Science, 20(4), 259-268. (Yayın No: 348417)

Özkan M T (2012). Notch Sensitivity Factor Calculationin The Design of Shafts Using Artificial Neural Network System. Education Science And Technology Part A: Energy Science And Research , 30(1), 621-630. (Yayın No: 348170)

*International Journal of Scientific Research in Information Systems and Engineering (IJSRISE)*,

*4*(1), 60-69. Retrieved from http://ijsrise.com/index.php/IJSRISE/article/view/15