Question

A pressure vessel with an internal diameter of 2.1 m, and a wall thickness of 6mm, has a maximum working internal pressure of 0.6. 1 MPa. A through-thickness crack (Q=1), 5.3 mm in length is found during inspection. (i) Find the critical crack length that can be reached before failure occurs, and the corresponding number of cycles to failure. Kic = 50MN/m2 da 50 x 10-12 (A k)4.1 dN (ii) If the desired life cycle is N = 10,000, define the dimensions of four pressure vessels with a wall thickness and internal diameter suitable to withstand a similar fracture failure. NOTE: These four sets of dimensions must be varied and of a sensible value,

Answer 1

Solution Given data: Internal diameter, d 2-5 m. wall thickness , t Cmim OOO 6 M Maximcem working internal presscere, P = 0.61 MPa we know, stress Pd 4t 0.61 x 2.1 4 * 0.006 53.375 MPa Giren Kic 50 MN OMN/m2/2 :) Kic Qofta 1 x 53.375 x Tac. 50 0.93676 Stac (0.93676) 2 Tac

critical crack length, (0.93676) a. T ac 0.2793 m Number of cycles to failure, N 2|(9,59*- (2,5) (2-) che 7/2 where, ai initial crack size 5.3 0.0053 m Given thet, 4.1 da - 50x10" (AK) dn The Standad form of equation is da dN c (AK) SOx10-12 U n 4.1

Substituote the above value in equation o (24) CO-2793) 0.0053) (2-4 . u (2-4.1) – soro". (u** (83.379) "(a)(**) 36419.75 Number of cycles o failure, N = 36420 cycles = TOOOO cycles (Given data} 3 2-7 We know, - 2 (2) (a;) (2-n) C a on a12 Replace the value of o by pd 4t Pd 4t 0.61d 4 t MPa. 0.1525 d t N = 2 (a) (2-n).c 2" (0.1925 19 ana

(o2793) (3) (o.009) 4) 1 (42) - 12 (2-4) x SOO (1) 0.1525 d. 자 P t 10000 0.3184 1이다 41 ㅋ 14 9. 81734 x 10 + 10000 이. 31784 < 10'이 ㅋ V 41 d [ 10 8)734 x 10 * 479.71 +

The four set of dimension can be as follows Wall thickness (t) Internal diameter (d) d 2-4 m ;) + t = = 5mm t = 6 mm d=2.87 m シ ii t = 7 mm d 3. 36 m iv ) t - 8 mm d - 3.84 m