Propagation of Cracks in Metals under the Action of Hydrogen and Long-Term Static Loading
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PROPAGATION OF CRACKS IN METALS UNDER THE ACTION OF HYDROGEN AND LONG-TERM STATIC LOADING O. E. Andreikiv and O. V. Hembara
UDC 669.778
We propose a computational model of crack growth caused by the action of hydrogen and longterm static loads. The model is based on the energy criterion of fracture of materials. As a result, we deduce the expression for the crack growth rate as a function of the load, size of the initial crack, and physicochemical and strength characteristics of the material. The theoretical curve reveals satisfactory agreement with the experimental data.
The existing models of crack growth in metals under the action of static loads and hydrogen [1–3] are, as a rule, too complicated for application in the engineering practice. In what follows, we propose a computational model of hydrogen-assisted crack growth based on the energy criterion of fracture of materials generalized to the case of influence of hydrogen. Generalization of the Energy Criterion of Propagation of Macrocracks in Metal Bodies Under the Action of Hydrogen-Containing Media and Long-Term Static Loads We consider an isotropic elastoplastic body Ω with boundary Γ weakened by a planar macrocrack S0 with smooth contour L0 subjected to the action of uniformly distributed forces P perpendicular to the plane of the crack and a hydrogen-containing medium. Our aim is to determine the subcritical crack growth rate. According to the law of conservation of energy [4–7], the sum of the work A˙ of the forces P per unit time and the thermal energy Q˙ conveyed to the body per unit time is equal to the rate of growth of the sum of the kinetic energy K, internal energy W, and fracture energy Π of the body as the area of the crack increases by S : ˙ A˙ + Q˙ = K˙ + W˙ + Π,
(1)
where the overdots denote the total derivatives of the corresponding quantities with respect to time t. The area of the crack S changes with time and ∂S(t ) ≥ 0. ∂t The quantities A, Q, K, W, and Π are functions of S and t. Hence, Eq. (1) takes the form ∂( A + Q − K − W − Π) ∂S ∂( A + Q − K − W − Π) + = 0, ∂S ∂t ∂t
(2)
whence we get the following law of changes in the crack area: Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Lviv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 3, pp. 29–33, May–June, 2005. Original article submitted January 31, 2005. 1068–820X/05/4103–0309
© 2005
Springer Science+Business Media, Inc.
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O. E. A NDREIKIV
∂( A + Q − K − W − Π) ⎡ ∂( A + Q − K − W − Π) ⎤ − 1 ∂S , = − ⎢⎣ ⎥⎦ ∂t ∂t ∂S
AND
O. V. HEMBARA
(3)
where ∂A = ∂S
∫ σij n j
Γ
∂ui dΓ + ∂S
∫ ρFi
Ω
∂ ∂K = 0.5 ∂S
∂Π = 2 ∫ γ 0 dS , ∂S S
∂ui dV , ∂S
(∫
Ω
ρ ui ui dV ∂S
∂Q = ∂S
),
∂q
∫ ∂Si ni dΓ ,
Γ
d ∫ W0 dV ∂W Ω , = ∂t dt
qi and Fi are the components of the vectors of heat flow and bulk forces, nj are the components of the unit vector of outer normal to the surface Γ, ρ is density, γ0 is the energy consumption per unit area of the newly formed crack surface, σij and ui are, respectively, the components of the stress te
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