Discussion on “A Mixed Mode Crack Growth Model Taking Account of Fracture Surface Contact and Friction” by Bian Et al. (2006)

A mixed-mode fatigue crack growth model with taking account of fracture surface contact and friction was developed recently by Bian et al. (2006), in reference to the general three-dimensional tensile stress solution for an elastic elliptical crack that was given by Kassir and Sih (1975). However, this general stress solution contains an error, and thus all equations for the fatigue crack growth model proposed by Bian et al. (2006) involve the error. The correct three-dimensional stress field for the elastic elliptical crack is then presented, and three fatigue crack growth models are corrected and expressed as simple functions in this paper.     

Finite element analysis of three dimensional crack growth by the use of a boundary element sub model

A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering structure.     

A thin cracked layer bonded to an elastic half-space under an antiplane concentrated load

The antiplane elasticity problem for a thin cracked layer bonded to an elastic half-space under an antiplane concentrated load is considered. The fundamental solution is obtained as a rapidly convergent series in terms of the complex potentials via iterations of Möbius transformation. The singular integral equation with a logarithmic singular kernel is derived to model a crack problem that can be solved numerically in a straightforward manner. The dimensionless mode-III stress intensity factors obtained for various crack inclinations and crack lengths are discussed in detail and provided in graphic form. A strip problem with an arbitrarily oriented crack is also considered.     

On the fracture behavior of a Zener–Stroh crack with plastic zone correction in three-phase cylindrical composite material

With crack tip plastic zone correction, stress investigation on the fracture behavior of a Zener–Stroh crack in three-phase composite was carried out. A Zener–Stroh crack (in the matrix phase) is near a circular inclusion, with the three-phase cylindrical composite model used to represent the composite material. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. The Dugdale model of small scale yielding is used to introduce a thin strip of yielded plastic zone each crack tip. The physical problem is formulated into a set of singular integral equations, using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function. The singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements using Erdogan and Gupta’s method with some iterative numerical procedures.     

裂尖具线性分布约束应力的运动裂纹模型及其解析解

以恒定速度运动的Griffith裂纹解析解为著名的Yoffe解。静止裂纹的条状屈服模型即Dugdale模型,将其推广到运动裂纹模型时发现,当裂纹运动速度跨越Rayliegh波速时,裂纹张开位移COD趋于(∞,且表现为间断。通过在裂尖引入一个约束应力区及两个速度效应函数,假设约束应力为线性分布,采用复变函数方法,求得动态应力强度因子SIF与裂纹张开位移COD的解析解。新的结果,在Rayleigh波速下裂纹张开位移连续且为有限值。给出裂纹张开位移的一些数值结果,获得了一些有意义的结论。     

A generalized crack problem in plane elasticity

The plane isotropic elasticity problem of a simple curvilinear crack with non-coincident edges (contrary to the idealization usually made) is considered. The maximum opening between the edges of the crack may be as great as 0.2 of the crack length. For the solution of this problem, the model of replacing the real crack by a continuous distribution of poles (concentrated forces and edge dislocations) along a single are lying between the real crack edges is introduced. The problem is reduced to an almost singular integral equation and an approximate method for its numerical solution is proposed. An application to the case of a symmetric crack in an infinite plane medium under uniform loading at infinity is also made.     

An explicit elastic solution for a brittle film with periodic cracks

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.     

Stochastic analysis of fatigue crack growth for metallic structures

In order to estimate the statistical variability of fatigue crack growth in metallic structures, a stochastic model is proposed by combining stochastic theory with experimental results. A stochastic differential equation is derived from the stochastic model for fatigue crack growth. By using the solution of the stochastic differential equation, some distribution functions related to fatigue crack growth were derived. Sample functions of fatigue crack growth time histories have been simulated as random processes.     

Bridge-toughening analysis of the penny crack in a fiber reinforced composite with interfacial effect

A fracture mechanics analysis of bridge effect on a fiber reinforced composite containing a penny crack is presented. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castingliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using iteration solution of the Fredholm integral equation of the second kind. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is presented and its error analysis is performed, which demonstrated the approximation solution to be appropriate. A parametric study of the influence of the length, interfacial shear modulus, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out.     

A THEORETICAL AND EXPERIMENTAL STUDY OF ENVIRONMENTAL HYDROGEN-ASSISTED SHORT FATIGUE CRACK GROWTH IN AN Al-Li ALLOY

Abstract— The initiation and propagation of fatigue cracks in an Al-Li 8090 alloy in a vapour environment of 0.6 M NaCl solution was investigated. A severe degradation of the resistance to short crack growth was exhibited. Preliminary work carried out to establish the susceptibility of the material to hydrogen embrittlement demonstrated a close correlation between the deformation mode of this alloy and hydrogen absorption. The combination of highly localized slip and highly localized hydrogen fugacity creates a high susceptibility to hydrogen-assisted crack growth.
On the basis of current micro-mechanical models, it is suggested that hydrogen trapping induces a reduction of the friction stress acting in the crack tip plastic zone. Consequently, enhanced plasticity at the crack tip due to the decrease in friction stress leads to an increase in crack growth rate.
An exact solution for a surface crack in a semi-infinite plane is obtained based on a dislocation crack model. Using this solution a computer method is developed to calculate the time-dependent short crack growth rate and fatigue lifetime. Both solutions show good correspondence with the experimental results.