Question

(17 points) During a percutaneous angioplasty the vessel wall is expanded by inflating a balloon. At a certain moment during inflation the internal pressure was at p 0.2 MPa-while the internal radius of the vessel wall increased by 10% from 1 .5 m m. At the same state, the wall thickness decreased from 0.31 mm down to 0.28 mm, Assuming that the tength of the balloon and the length of the vessel wall in contact with the balloon do not change. Further, you can assume that the vessel wall properties can be approximated as LEHI that follows Hook's law with a known Young's modulus of E-8 MPa and a Poisson ratio of v 0.33 a) What is the strain in the circumferential direction at the inner surface of the vascular wall (point A)? b) What is the strain in the axial direction at the inner surface of the vascular-wall? c) Calculate the stress in circumferential and axial direction at point A. Given ,-(111)(1-2) Pi oz

Answer 1

For pressure vessel wall at inner surface Initially radius, Ri Final radius, R_f = R_i + 10/100 times Ri = 1.1 Ri [As radius increased by 10%] P_i = 0.2 Mpa E = 8 Mpa V = 1/3 = 0.33 (a) strain in circumferential direction at inner side. Sigma_yy = change in radius/Initial radius = R_f - R_i/R_i = (1.1 - 1) R_i/Ri E_yy = 0.1 b) Sigma_xx = -(sigma_xx - v sigma_xy)/E = -(1 - v) sigma_yy/E \r\n = -1(1 - 0.33) Sigma_yy = -(1 - 0.33) times 0.1 [sigma_xx = sigma-yy = P_i R i/t] [therefore sigma_y/elementof_0 = Sigma_yy] stress in x y direction and strain will be o opposite nature as that is in y - direction. Sigma_xx = -0.67 times 0.1 Sigma_xx = -0. (c) Sigma_yy = Sigma_yy times E (By Hooke's law therefore epsilon = sigma/E or sigma = epsilon E] sigma = 0.1 times 8 sigma_yy = 0.8 Mpa