J Fail. Anal. and Preven. (2008)8: 41-47 2.18=107 .80 141·10 1,01·107 8.21*105 8.21=105 1.58*1 6.28106 Fig. 3(a) Distribution of the principal stress (internal of bend).(b) Distribution of the principal stress(extemal of bend).(c) Distribution of the on Misesl stress (internal of bend). (d) Distribution of the von Misesl stress(external of bend) pressure of (PD/4t)=36.4 MPa on the other end; D and t value induced by loading artificially, the principal stress is are the diameter and thickness of the surveyed pipe, 101 MPa. The von Mises stress is given in Fig 3(c)and(d) respectively. Youngs modulus for the material is given as and displays the peak stress of about 125 MPa. From above 80,000 MPa (N/mm) from tensile test, and Poisson's results, under actual operating conditions, the maximum ratio is assumed to be 0.3. In order to obtain reasonable and resultant stress loading on the pipe is a1= 125 MPa. This accurate results, the analysis of the thick-wall bend stress was used to evaluate residual life of the bent attached to straight ends is defined by three-dimensional sections (3D)cells. To incorporate the actual sizes and space with the results of accelerated test and stress analysi structure of the exposed pipe, the model was set using a the permitted stress [a] expressed is geometry model tool in NASTRAN software. The opti- mized finite element mesh method was employed after the d model was established Generally, the stress to cause failure may be consic Here n is safety factor (generally, 1. 2-1.65), and we take to be either yielding or rupture stress, depending the value of n=1.5. Therefore the bent section of the criteria used. The corresponding failure theories also main pipe has permitted stress, from redesign viewpoint sider two types of failure: reaching the ultimate tensile of: stress for rupture and reaching the Mises yield criterion for [o]=131/1.5=87.3 MPa yield failure. The calculated results were presented in form of principal stress(rupture)and Von Mises Compared with the maximum resultant stress derived from (yielding)simultaneously. The distributions of principal finite element analysi stress are given in Fig 3(a) and(b). Except for the peak d=87. 3 MPa <OT= 125 MPa 2 Springpressure of (PD/4t) = 36.4 MPa on the other end; D and t are the diameter and thickness of the surveyed pipe, respectively. Young’s modulus for the material is given as 180,000 MPa (N/mm2 ) from tensile test, and Poisson’s ratio is assumed to be 0.3. In order to obtain reasonable and accurate results, the analysis of the thick-wall bend attached to straight ends is defined by three-dimensional (3D) cells. To incorporate the actual sizes and space structure of the exposed pipe, the model was set using a geometry model tool in NASTRAN software. The opti￾mized finite element mesh method was employed after the model was established. Generally, the stress to cause failure may be considered to be either yielding or rupture stress, depending on the criteria used. The corresponding failure theories also con￾sider two types of failure: reaching the ultimate tensile stress for rupture and reaching the Mises yield criterion for yield failure. The calculated results were presented in the form of principal stress (rupture) and Von Mises stress (yielding) simultaneously. The distributions of principal stress are given in Fig. 3(a) and (b). Except for the peak value induced by loading artificially, the principal stress is 101 MPa. The von Mises stress is given in Fig. 3(c) and (d) and displays the peak stress of about 125 MPa. From above results, under actual operating conditions, the maximum resultant stress loading on the pipe is r1 = 125 MPa. This stress was used to evaluate residual life of the bent sections. With the results of accelerated test and stress analysis, the permitted stress [r] expressed is: ½r ¼ r550 C 105 n ð2Þ Here n is safety factor (generally, 1.2–1.65), and we take the value of n = 1.5. Therefore, the bent section of the main pipe has permitted stress, from redesign viewpoint of: [r] = 131=1.5 = 87.3 MPa ð3Þ Compared with the maximum resultant stress derived from finite element analysis: ½r ¼ 87:3 MPa\rT ¼ 125 MPa ð4Þ Fig. 3 (a) Distribution of the principal stress (internal of bend). (b) Distribution of the principal stress (external of bend). (c) Distribution of the von Misesl stress (internal of bend). (d) Distribution of the von Misesl stress (external of bend) J Fail. Anal. and Preven. (2008) 8:41–47 45 123