Growth of a penny-shaped crack with a nonsmall fracture process zone in a composite

The paper studies the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load. The composite has hexagonal symmetry and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled as a transversely isotropic homogeneous viscoelastic medium with effective characteristics. The crack is in the isotropy plane. The ring-shaped fracture process zone at the crack front is modeled by a modified Dugdale zone with time-dependent stresses. The viscoelastic properties of the matrix are characterized using a resolvent integral operator. Use is made of Volterra's principle, the method of operator continued fractions, and the theory of precritical crack growth in viscoelastic bodies. The problem is reduced to nonlinear integral equations. Numerical results are obtained for certain components of the composite, constant volume fractions, and different fracture strengths Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 45–51, August 2008.     

Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 13–22, October 2008.     

Influence of cyclic loading on crack growth kinetics in a viscoelastic orthotropic plate made of a composite material

The kinetics of crack growth in a viscoelastic orthotropic plate made of a composite material is analyzed. The external load is the superposition of a cyclic load and a constant tensile load. The level of the tensile load is assumed to exceed the amplitude of the cyclic load. The kinetic curves are compared with the constant tension curves. The effect of the cyclic component is studied.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 116–122, September 2004.     

Growth of a mode II crack in an orthotropic plate made of a viscoelastic composite material

The growth of a straight mode II crack in a viscoelastic orthotropic plate is examined. The plate material is modeled by a viscoelastic anisotropic medium. The shear displacement in the fracture process zone is determined as a function of time using the corresponding elastic solution, the Volterra principle, and the method of operator continued functions. The time dependence of the crack length is constructed as integral equations of three phases of stable growth. The solution of these equations gives kinetic curves __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 89–97, September 2006.     

Influence of buckling of a tension plate with an edge crack on fracture characteristics

Local buckling and fracture of plates with an edge crack under tension are studied. The crack is at an arbitrary angle to the load line. The relationship between the crack-growth initiation stress and the bending strain is established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 113–116, May 2006.     

大体积混凝土等效裂纹断裂模型研究

根据大比尺混凝土紧凑拉伸与楔入劈拉试验成果,将裂纹在稳定扩展中断裂有程区应力分布与相应的变形（张开度ω）联系起来,通过“归一化”处理,得到了大体积混凝土断裂过程区长度的解析表达式,建立了大体积混凝土Ⅰ型断裂破坏的等效裂纹断裂模型。     

On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 14–23, February 2006.     

Subcritical stable growth of a penny-shaped crack in an aging viscoelastic body with cylindrical anisotropy

The paper studies the subcritical stable growth of a penny-shaped mode I crack in an aging linear viscoelastic body with cylindrical anisotropy under tensile loads applied at infinity. The equations of quasistatic crack growth are derived using the Volterra principle for a modified Dugdale model and the critical crack opening displacement as a failure criterion. The kernel of the operator that describes the viscoelastic crack opening is found using operator-valued continued fractions. As an example, the subcritical stable growth of a crack in a specific material is studied numerically __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 82–92, January 2007.     

Study of the plastic zone near a crack in an anisotropic body

The plastic zone at a crack tip in a finite anisotropic body is studied. A boundary-value problem is formulated in terms of the components of the covariant displacement vector for small strains. Particular attention is given to the case of plain strain. In this case, a numerical solution is found for a long rectangular body with a central crack under tension. As a result, conditions for the occurrence and development of a plastic zone at the crack tip are established. A plastic zone on the lateral surface of the body is discovered. How both zones extend and coalesce is elucidated. The effect of anisotropy on the occurrence of a plastic zone is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 29–44, July 2006.     

Formation of the plastic zone in an anisotropic body with a crack

The influence of the length of a mode I crack on the plastic zone in an anisotropic body under hard loading is studied. The case of a generalized plane stress state is examined. A boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, the additional plastic zone on the lateral face of the body, and the merged plastic zone Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 36–52, September 2008.     

Stability of a viscoelastic plate in fluid flow

The stability of an infinite viscoelastic plate on an elastic foundation in a viscous incompressible flow is studied. The Navier-Stokes system is linearized for an exponential velocity profile. The problem is reduced by a Fourier-Laplace transform to a system of ordinary differential equations, whose solution is found in the form of convergent series. The roots of the dispersion relation that characterize the stability of the system are found numerically. The effect of the viscosities of the fluid and the plate on the stability of the waves propagating upstream and downstream is studied. The results are compared with available data on the stability of a viscoelastic plate in an ideal fluid flow. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 66–74, July–August, 2006.     

Nonlinear vibrations of a viscoelastic plate with concentrated masses

The problem of vibrations of a viscoelastic plate with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate, the action of the concentrated masses is taken into account using Dirac δ-functions. The problem is reduced to solving a system of Volterra type ordinary nonlinear integrodifferential equations using the Bubnov-Galerkin method. The resulting system with a singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature formulas. The effect of the viscoelastic properties of the plate material and the location and amount of concentrated masses on the vibration amplitude and frequency characteristics is studied. A comparison is made of numerical calculation results obtained using various theories. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007.     

Refinement of the plastic-zone boundary in the vicinity of a crack tip for the quasiviscous and viscous types of fracture

A refined solution of the elastoplastic problem of an insulated mode I crack in a thin plate of reasonably large dimensions is obtained. Estimates of the plastic zone in the vicinity of the crack tip are given for quasiviscous and viscous types of fracture.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 126–132, January–February, 2005     

Formation of a plastic zone in an anisotropic body under loads acting along a crack

The effects of tension and compression along a crack on the plastic zone in a finite anisotropic body under plane strain are studied. The formation pattern for the plastic zone with increasing load is established by numerically solving a boundary-value problem for each of the cases. In particular, a new plastic zone is revealed. It occurs at the crack face under a compressive load of certain magnitude. How this plastic zone interacts with that at the crack tip is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 3–19, May 2007.     

An analytically-numerical approach for the analysis of an interface crack with a contact zone in a piezoelectric bimaterial compound

An interface crack with an artificial contact zone at the right-hand side crack tip between two dissimilar finite-sized piezoelectric materials is considered under remote mixed-mode loading. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical loads, the stress intensity factors at the singular points are obtained. As a particular case of this solution, the contact zone model (in Comninou’s sense) is derived. A simple transcendental equation and an asymptotic formula for the determination of the real contact zone length are derived. The dependencies of the contact zone lengths on external load coefficients are illustrated in graphical form. For a particular case of a short crack with respect to the dimensions of the bimaterial compound, the numerical results are compared to the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.     

Dynamic stability of a viscoelastic plate with concentrated masses

The paper addresses the geometrically nonlinear problem of dynamic stability of a viscoelastic plate with concentrated masses. The Bubnov-Galerkin method based on polynomial approximation is used to reduce the problem to a system of nonlinear Volterra-type integro-differential equations with singular relaxation kernels. This system is solved by numerical method based on quadrature formulas. The critical loads are found and their dependence on the arrangement and number of concentrated masses is studied for a wide range of mechanical and geometrical parameters of the plate. The choice of a relaxation kernel for dynamic problems for viscoelastic thin-walled plate-like structures is justified. Results produced by different theories are compared __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 109–118, February 2008.     

Transformation toughening of a ceramic in stable crack growth under plane stress conditions

A finite element study of stable crack growth in ceramics that can undergo a stress-induced martensitic phase transformation is performed under plane stress and small scale transforming conditions. The finite element method is based on the continuum model developed by Budiansky et al. (Int. J. Solids Structures 19, 1983). To guarantee the subcritical transformation behavior without loss of ellipticity of the governing equations, the possibility of strain localization is first re-examined. It is found that the plane stress conditions greatly favor transformation instability in that supercritical transformation occurs when the bulk modulus ¯B during transformation is below –G/3, instead of –4G/3 for three-dimensional or plane strain cases, whereG is the shear modulus. Next, transient crack extension under continuously increasing tensile load is simulated by a node release technique. Transformation zones and crack growth resistance curves are obtained.     

Dynamic bending of a symmetric piezoelectric laminated plate with a through crack

The dynamic theory of linear piezoelectricity is applied to analyze the scattering of time harmonic flexural waves by a through crack in a symmetric piezoelectric laminated plate subjected to electric field loading. An incident wave giving rise to moments symmetric about the crack plane is considered. Piezoelectric layers are added to the upper and lower surfaces. Classical lamination theory is extended to include dynamic piezoelectric effects. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, the solution of which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor vs. frequency is computed and the influence of the electric field on the normalized values is displayed graphically.     

An electrically conducting interface crack with a contact zone in a piezoelectric bimaterial

A plane problem for an electrically conducting interface crack in a piezoelectric bimaterial is studied. The bimaterial is polarized in the direction orthogonal to the crack faces and loaded by remote tension and shear forces and an electrical field parallel to the crack faces. All fields are assumed to be independent of the coordinate co-directed with the crack front. Using special presentations of electromechanical quantities via sectionally-analytic functions, a combined Dirichlet–Riemann and Hilbert boundary value problem is formulated and solved analytically. Explicit analytical expressions for the characteristic mechanical and electrical parameters are derived. Also, a contact zone solution is obtained as a particular case. For the determination of the contact zone length, a simple transcendental equation is derived. Stress and electric field intensity factors and, also, the contact zone length are found for various material combinations and different loadings. A significant influence of the electric field on the contact zone length, stress and electric field intensity factors is observed. Electrically permeable conditions in the crack region are considered as well and matching of different crack models has been performed.