The purpose of this paper is to investigate the stress concentration factor(SCF) for an internally pressurized cylinder with hole and based on detailed three -dimensional elastic FE analysis, a new comprehensive set of formulas for SCFs are proposed. These stress concentration factors are presented and discussed as a function of the ratio of cylinder diameter to the thickness of cylinder and hole diameter. The first ratio “D/100t” is equal to 1, 1.25 , 1.5, 1.75, 2, 2.5, 2.75, 3, 3.25 and 3.5 and the second ratio “D/10d”, cylinder internal diameter to the hole diameter, varies from 0.6, 0.9, 1.2, 1.5, 1.8, 2, 2.3, 2.7,3.1 and 3.5. Results are also presented for SCF of longitudinal, circumferential and Von Mises stresses. Keywords : pressure vessel, stress concentration, finite element method, parameter identification Described Stress Concentration Factors of an Internally Pressurized Cylinder with Hole by New Formulas Copyright ⓒ 2016 IJCRM | Page 22 | function of the ratio of the cylinder internal diameter to the thickness of cylinder D/100t, and the hole’s diameter D/10d. FINITE ELEMENT MODELLING AND GEOMETRY 2.1. Geometry Fig. 1 shows sketch and notation of the cylindrical vessel with hole. Figure1. Geometry and notation of cylindrical vessel with hole The main cylinder has a mean diameter, D, thickness, t, and hole diam eter, D. The ranges of geometry parameters included in this study are shown in table 1. Table 1.Range of geometrical parameters D/100t 1 1.25 1.5 1.75 2 2.5 2.75 3 3.25 3.5 D/10d 0.6 0.9 1.2 1.5 1.8 2 2.3 2.7 3.1 3.5 The constitutive law used was homogeneous, isotropic and linear elastic. The pressure, P, was considered to act on the inner surface of the cylinder. The material properties used I the FE analysis were: E= 2.07x105 MPa and a Poisson’s ratio of 0.3, as empl oyed in Ref. [25], was used throug hout the calculation in order to be able to make a complete comparison with the results reported therein, including and especially the particular comparison for the so called SCF formula as proposed in this work. 2.2. FE Analysis In this study the softwar e used was ANSYS and as the maximum stress around the hole region should be measured from the FE analysis, the number of elements around it would be an important parameter. So regions around hole use relatively refined meshing. This mesh is believed to acc urately represent the geometry, being minimal without losi ng information [26]. In this work the internal pressure is fixed and used in every case. As shown in table 1, a wide range of thickness and hole diameter ratios were analysed and the maximum longitudinal, circumferential and Von Mises stresses around hole can be easily determined from elastic FE analyses, from which the stress concentration factors can be determined by using the following expressions relatively: 𝐾𝑡 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 =𝐾𝑡𝑙=𝜎max 𝑙 𝜎𝑛𝑜𝑚 𝑙 1 𝐾𝑡 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 =𝐾𝑡𝑐=𝜎𝑚𝑎𝑥 𝑐 𝜎𝑛𝑜𝑚 𝑐 2 𝐾𝑡 𝑣𝑜𝑛𝑚𝑖𝑠𝑒𝑠 =𝐾𝑡𝑣=𝜎𝑚𝑎𝑥 𝑣 𝜎𝑛𝑜𝑚 𝑣 3 RESULT AND DISCUSSION 3.1. Results and formulas for SCFs The calculation to determine the SCFs for the case treated in this analysis were perform ed by computing the maximum stress indicated in equations 1, 2 and 3. Fig. 2 -7 shows the significant Described Stress Concentration Factors of an Internally Pressurized Cylinder with Hole by New Formulas Copyright ⓒ 2016 IJCRM | Page 23 | influence of D/100t and D/10d on the magnitude of the SCFs. As expected, the values of SCFs increase with increasing D/100t ratios and decrease with increa sing D/10d. Also as shown in figures, the D/100t ratio has linear influence on SCFs, but the D/10d ratio has nonlinear influence on there and the SCFs are more sensitive on D/10d in little values. The equations for the longitudinal, circumferential and Von -Mises SCFs in cylinders were developed as a function of D/100t and D/10d by curve fitting the finite element analysis results. These equations are given by the following, respectively: 𝐾𝑡𝑙&𝐾𝑡𝑐&𝐾𝑡𝑣=𝐴 𝐷 10𝑑 2 +𝐵 𝐷 10𝑑 +𝐶 4 That for longitudinal SCF the parameters A, B and C are defined as: 𝐴=0.01 𝐷 100𝑡 2 +0.8 𝐷 100𝑡 +0.4 5 𝐵=0.044 𝐷 100𝑡 2 −0.2 𝐷 100𝑡 −1.29 (6) 𝐶=−0.016 𝐷 100𝑡 2 +0.019 𝐷 100𝑡 +1.03 (7) And for circumferential SCF, the parameters A, B and C are described as: 𝐴=−0.095 𝐷 100𝑡 2 +2.38 𝐷 100𝑡 +0.6 (8) 𝐵=−0.02 𝐷 100𝑡 2 +0.197 𝐷 100𝑡 −1.56 (9) 𝐶=0.008 𝐷 100𝑡 2 −0.35 𝐷 100𝑡 +3.26 (10) And for von -mises SCF, the parameters A, B and C are determined as: 𝐴=−0.108 𝐷 100𝑡 2 +2.74 𝐷 100𝑡 +0.66 (11) 𝐵=−0.0216 𝐷 100𝑡 2 +0.206 𝐷 100𝑡 −1.58 (12) 𝐶=0.009 𝐷 100𝑡 2 −0.4 𝐷 100𝑡 +3.78 (13) These equations were designed to be used in lieu of the graphs and charts to easily compute the stress concentration factors Described Stress Concentration Factors of an Internally Pressurized Cylinder with Hole by New Formulas Copyright ⓒ 2016 IJCRM | Page 24 | Figure 2.Longitudinal stress concentration factors with various ratio of D/10d Figure 3.Circumferential stress concentration factors with various ratio of D/10d Figure 4. Von-Mises stress concentration factors with various ratio of D/10d Described Stress Concentration Factors of an Internally Pressurized Cylinder with Hole by New Formulas Copyright ⓒ 2016 IJCRM | Page 25 | Figure 4. Longitudinal stress concentration factors with various ratio of D/100t Figure 6. Circumferential stress concentration factors with various ratio of D/100t Figure 7. Von-Mises stress concentration factors with various ratio of D/100t 3.2. Checking the validity of the proposing equation to existing literature Table 2 shows a comparison of the longitudinal stress concentration factors around hole in pressurized cylinder vessel in three different cases. Our analysis results are in good agreement with the Described Stress Concentration Factors of an Internally Pressurized Cylinder with Hole by New Formulas Copyright ⓒ 2016 IJCRM | Page 26 | experimental analysis in existing literature [27]. The errors between the results obtained fr om formulas and experimental tests are about max. 9.8%. Table2. Longitudinal stress concentration factor around the hole in three cases D D T D/100t D/10d KtL (test) KtL (formula) Error 1 2 3 1000 1000 1000 125 167 142.8 4.08 2.86 3.23 2.45 3.5 3.1 0.8 0.59 0.7 4.8 7.2 6.4 4.37 7.87 5.99 9.8% 8.5% 6.8% CONCLUSION In this work based on detailed 3D elastic F.E. analysis a new comprehension set of formulas for SCFs in an internally pressurized cylinder with hole are proposed. The results from these comprehensive formulas with the experimental results in existing literature are compared. Charts and formulas were developed as a function of the cylinder diameter to thickness of cylinder (D/100t) and hole diameter (D/10d). We recommend the following: I. Insert the hole stress concentration factors chart and formulas presented in this paper in the ASME code, sec. VIII Div.3 so that they are readily accessible for their use in fatigue strength evaluation in pressurized cylinder. II. Investigate the longitud inal, circumferential and von -mises stress distribution in plastic range around the hole in pressurized cylinder. III. Investigate the effects and formulas for pressurized cylinder with elliptical hole and other kind of discontinuity.