Estimation of the SIF in FGM spherical pressure vessel

ABSTRACT

One of the key factors in the design of the spherical pressure vessels is the lack of study of the SIF in different modes of fracture. In the present research, the SIF evaluation in three modes of fracture was investigated in FGM spherical pressure vessel. The walls of the spherical vessel consisting of semi-elliptical and semi-circular cracks were considered. The simulation and numerical solutions of the problem were done in ABAQUS software. The modelling of FGM spherical vessel was done using the power function and the effect of crack angles on the SIF was evaluated under p, p_d and p_h. The obtained results illustrated that in homogeneous and FGM vessels, the variation of the SIF directly related to p, so that, with increasing p, the SIF also increases. Also, it was observed that the most variation in the SIF was associated with the ceramic phase of the wall of the vessel where the elastic modulus reduced. In addition, the minimum variation takes place in the steel phase of the wall where the elastic modulus increases. In addition, the results were indicated the minimum variation for this parameter relates to crack at = 90°.

Abbreviations: BEM: boundary element method; EFE: enriched finite element; EFGM: element-free Galerkin method; FEA: finite element analysis; FEM: finite element method; FEs: finite elements; FGMs: functionally graded materials; FG: functionally graded; GFEs: graded finite elements; ITM: interaction integral method; LEFM: linear elastic fracture mechanics; LFM: linear fracture mechanics; SIFs: stress intensity factors; WFs: weight functions; 3D: three dimensional; CWF: coefficients of weight function; SC: semi-circular; SE: semi-elliptical.

KEYWORDS:

• Fracture mechanics
• spherical pressure vessels
• FGM
• finite element method

Nomenclature

a	=	The crack length (edge and central cracks) (mm)
pd	=	Design pressure (MPa)
a, c	=	Dimensions for semi-elliptical and semi-circular cracks (mm)
ph	=	Hydrostatic pressure (MPa)
Dw	=	The average diameter (mm)
Ri	=	Internal radius (mm)
Ec	=	Ceramic elastic modulus (GPa)
Ro	=	External radius (mm)
Es	=	Steel elastic modulus (GPa)
t	=	Wall thickness (mm)
${\mathrm{K}}_{\mathrm{I},\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$	=	SIFs for three modes (opening, shearing, tearing) (MPa.m^0.5)
${\sigma }_{\mathrm{A}}:$	=	Applied stress (MPa)
pout	=	External pressure (MPa)
$\theta$	=	Location of the crack angles (radian)
pin	=	Internal pressure (MPa)
p	=	Internal pressure (MPa)
pm	=	Pressure in metal phase (MPa)
ρc	=	Ceramic density (kg/m3)
pc	=	Pressure in ceramic phase (MPa)
ρs	=	Steel density (kg/m3)
β, n	=	The constants of FG material (power function)

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

N. Habibi

N. Habibi is assistant professor of Solid Mechanics at University of Kurdistan in Iran. He joined the Mechanical Engineering Department in 2011. He received Ph.D. and M.Sc. in Mechanical Engineering from the Bu-ali Sina University in Iran (2011 and 2003). His current research interests are fracture mechanics, creep and stress analysis, fatigue life estimation, applied mathematics in mechanics, offshore structures, bolted and welding joints, adhesive and rivet joints, numerical methods in engineering, modeling of finite element and boundary element methods.

H. Bahrampour

H. Bahrampour is Graduated from the Master of Mechanical Engineering at University of Kurdistan in Iran. He received M.Sc. in Mechanical Engineering from Universityof Kurdistan in Iran (2020). His current research interests are fracture mechanics and simulation of crack in the pressure vessels and piping.