Fatigue crack growth simulations of 3-D linear elastic cracks under thermal load by XFEM

doi:10.1007/s11709-015-0304-z

Frontiers of Structural and Civil Engineering

2015, Vol. 9

Issue (4): 359-382 https://doi.org/10.1007/s11709-015-0304-z

本期目录

Fatigue crack growth simulations of 3-D linear elastic cracks under thermal load by XFEM

Himanshu PATHAK¹,Akhilendra SINGH^2,^*(

),I.V. SINGH³,S. K. YADAV³

1. Department of Mechanical Engineering, Shiv Nadar University, Gautam Budha Nagar 201314, India
2. Department of Mechanical Engineering, IIT Patna, Patna 800013, India
3. Department of Mechanical and Industrial Engineering, IIT Roorkee, Roorkee 247667, India

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Abstract：

This paper deals with the fatigue crack growth simulations of three-dimensional linear elastic cracks by XFEM under cyclic thermal load. Both temperature and displacement approximations are extrinsically enriched by Heaviside and crack front enrichment functions. Crack growth is modelled by successive linear extensions, and the end points of these linear extensions are joined by cubic spline segments to obtain a modified crack front. Different crack geometries such as planer, non-planer and arbitrary spline shape cracks are simulated under thermal shock, adiabatic and isothermal loads to reveal the sturdiness and versatility of the XFEM approach.

Key words： 3-D cracks fatigue life Paris law thermal load XFEM

收稿日期: 2015-04-01 出版日期: 2015-11-26

Corresponding Author(s): Akhilendra SINGH

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2015, 9(4): 359-382.
Himanshu PATHAK,Akhilendra SINGH,I.V. SINGH,S. K. YADAV. Fatigue crack growth simulations of 3-D linear elastic cracks under thermal load by XFEM. Front. Struct. Civ. Eng., 2015, 9(4): 359-382.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-015-0304-z
https://academic.hep.com.cn/fsce/CN/Y2015/V9/I4/359

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p ( x ) = complete basis vector
a = set of unknown coefficient
N j = Lagrange shape functions
u j = field variable for the continuous part of domain
a j = additional degree of freedom associated with Heaviside function
H ( x ) = Heaviside function
c j α = additional DOFs associated with the four asymptotic enrichment functions
n = set of all nodes in the mesh
n s = set of all nodes associated with the crack surface
n t = set of nodes associated with the crack front
q = heat flux vector
Q = heat source
k = thermal conductivity
σ = Cauchy stress tensor
b = Body force per unit volume
∇ s = symmetric gradient operator
C = isotropic fourth order tensor
T = temperature field
ε = strain vector
ε T = thermal strain vector
T r e f = reference temperature
α = thermal expansion coefficient
I = second order identity tensor
K = global stiffness matrix
f = force vector
E = Young’s modulus
ν = Poisson's ratio
Ν i = finite element shape function
ψ = additional enrichment function
f ( x ) = vector between the point x and its projection on the crack surface
Γ c r = crack surface
φ ( x ) = signed distance function
( X , Y , Z ) = global Cartesian coordinate system
( ξ 1 , ξ 2 , ξ 3 ) = curvilinear coordinate system
( r , θ ) = polar coordinate system
( ξ , η , ζ ) = natural coordinate system
( K I , K I I a n d K I I I ) = stress intensity factors
W s = strain energy density
δ 1 j = Kronecker delta function
θ c = crack growth direction
K I C = fracture toughness
m = Paris exponent
C = Paris constant

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