Study into the kinetics of a crack with a nonsmall fracture process zone in an aging viscoelastic plate

The subcritical growth of a mode I crack with nonsmall end zones in an aging viscoelastic plate under tensile loads applied at infinity is studied assuming that the fracture process zone is of constant length. The equations of incubation, transition, and major crack growth stages are obtained on the basis of the Volterra principle and critical crack opening criterion. The crack subcritical growth of a specific material is studied as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 92–101, August 2007.     

Subcritical crack growth in an aging plate with variable elastic modulus

The paper addresses subcritical growth of a crack in a thin isotropic plate made of an aging viscoelastic material with time-dependent elastic modulus. The behavior of the material is described by Arutyunyan’s creep theory. To simulate fracture, a modified Leonov–Panasyuk–Dugdale model and a critical crack opening displacement criterion are used. An equation describing the subcritical growth of the crack is derived assuming that Poisson’s ratio is constant. As an example, the critical loads are determined, and curves of subcritical crack growth are plotted for a specific material. The results are compared with the case of constant elastic modulus     

Subcritical Growth of an Internal Circular Crack in an Aging Viscoelastic Laminated Composite

Delayed fracture of a laminated composite under tensile loads applied at infinity is studied. The composite consists of alternating elastic and aging viscoelastic layers and contains an internal penny-shaped mode I macrocrack located in parallel to the layers. A modified Leonov–Panasyuk–Dugdale crack model and the critical crack-tip opening criterion constitute a fracture model. The subcritical crack growth equations are derived using the Volterra principle and the method of operator continued fractions. The laws governing delayed fracture are studied for a specific composite material     

Analyzing the Laws of Stable Subcritical Growth of Cracks in Polymeric Materials on the Basis of Fracture Mesomechanics Models. Theory and Experiment

The laws of stable crack growth are analyzed using fracture mesomechanics models for polymeric materials under long-term subcritical tension. A review is given of experimental and theoretical studies of crack-tip process zones. The studies were conducted using physical and mechanical methods and fracture mesomechanics models, allowing for the structural and rheological features of process zones. Theoretical and experimental results on the behavior of process zones are generalized and the theory of stable crack growth in viscoelastic polymers, which assumes the autonomy of the process zone during crack development, is justified     

Stable growth of penny-shaped crack in viscoelastic composite material under time-dependent loading

Considered is the long-term cracking of the three-dimensional fiber-reinforced viscoelastic composite with a plane penny-shaped crack under time-dependent loading. The composite has a hexagonal structure and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled by transversally isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. The crack propagation planecoincides with the plane of isotropy. A ring-shaped yield zone in front of the moving crack is modeled as a Dugdale's zone with time-dependent stresses. Crack growth under deformation of the composite occurs by application of a slowly increasing tensile load; it is normal to the plane of crack propagation. A convolution-type time operator describes the viscoelastic properties of the matrix material. Use is made of the Volterra principle and the theory of long-term cracking of viscoelastic bodies. The irrational function of integral operator associated with the viscoelastic crack opening expression is expanded into a continued fraction of operators. The solution is reduced to the nonlinear integral equations of crack growth. Numerical results are obtained for a specific material. Crack growth kinetics is discussed in connection with the onset of stable crack growth and crack border stress intensity factor.     

Initiation and stable growth of penny-shaped crack in aging viscoelastic transversally isotropic material

Considered is the long-term cracking of an aging transversally isotropic material containing a Mode I penny-shaped crack under remotely applied tensile stress. The aging material properties are described by the Boltzmann–Volterra’s linear theory for integral operators with non-difference kernels. It applied to wood, concrete, some polymers and rocks. Only the symmetric case is considered where the crack lies in the plane of isotropy. The modified Leonov–Panasyuk–Dugdale’s crack model is used with a constant process zone assuming that the critical opening displacement is the fracture criterion. Volterra’s principle is applied to derive the equations of subcritical crack growth. Numerical calculations are made for subcritical crack growth for the specific example of transversally isotropic material simulating the behavior of reinforced concrete.     

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.     

Viscoelastic Deformation of a Reinforced Plate with a Crack

The deformation of a viscoelastic reinforced composite is studied. The composite has an axis of elastic symmetry and consists of transversally isotropic fibers and a viscoelastic matrix, which differ by the volume concentration and mechanical characteristics. The material is modeled by a transversely isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. A plate fabricated from the composite in question is weakened by a through mode I crack and is subjected to constant tensile forces. The viscoelastic properties of the matrix material are described by a convolution operator. The Volterra principle is used to derive expressions for the viscoelastic characteristics and crack opening. The irrational function of the integral operator that describes the crack opening is expanded into an operator continued fraction and is represented as the sum of base operators     

裂纹尖端张开角准则的稳态裂纹扩展实验研究

ASTM和ISO已发布获得低约束条件下断裂性能和裂纹稳态扩展阻力曲线的标准,标准中采用多种试验方法确定临界裂纹张开角度来表征板材的裂纹稳态扩展。本文采用准静态裂纹扩展试验方法,通过摄像技术测定裂纹尖端张开角(CTOA),验证标准对1mm厚度2024-T3铝合金板稳态裂纹扩展行为的有效性。研究了试样构型、裂纹尺寸和是否疲劳预制裂纹对裂纹稳态扩展过程中CTOA的影响。试验结果表明:裂纹扩展2mm后,距离裂纹尖端1mm处的CTOA趋于一个恒定值6°,这个值与试样构型和裂纹长度无关;同时,不预制疲劳裂纹对CTOA值和试样的最大剩余强度影响较小。     

The delayed fracture of an isotropic viscoelastic plate with a microcrack under a varying load

The delayed fracture of an isotropic viscoelastic plate due to subcritical growth of a rectilinear microcrack of normal separation is studied. The paper deals with the development of the crack due to the stretching of the plate by uniformly distributed increasing and cyclic external loads applied perpendicularly to the crack line. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent integral operators of difference type, which describe the deformation of materials with time-dependent rheological properties. Numerical calculations are performed for resolvent integral operators with a kernel in the form of Rabotnov's fractional-exponential function. The kinetics of a crack with a tip zone commensurable with the crack length is studied. The results are compared with those obtained on the basis of the hypothesis on the thin structure of the crack tip. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 114–121, May, 2000.     

Fatigue and fracture of bovine dentin

In this paper, the fatigue and fracture properties of bovine dentin are evaluated usingin vitro experimental analyses. Double cantilever beam (DCB) specimens were prepared from bovine maxillary molars and subjected to zeroto-tension cyclic loads. The fatigue crack growth rate was evaluated as a function of the dentin tubule orientation using the Paris law. Wedge-loaded DCB specimens were also prepared and subjected to monotonic opening loads. Moiré interferometry was used to acquire the in-plane displacement field during stable crack growth, and the instantaneous wedge load and crack length were acquired to evaluate the crack growth resistance and crack tip opening displacement (CTOD) with crack extension. The rate of fatigue crack growth was generally larger for crack propagation occurring perpendicular to the dentin tubules. The Moiré fringe fields documented during monotonic crack growth exhibited non-linear deformation occurring within a confined region adjacent to the crack tip. Both the wedge load and CTOD response provided evidence that a fracture process zone contributes to energy dissipation during crack extension and that dentin exhibits a risingR-curve behavior. Results from this preliminary investigation are being used as a guide for an evaluation of the fatigue and fracture properties of human dentin.     

粘弹性介质中扩展裂纹与J积分

本文提出了在线弹性及粘弹性介质中扩展裂纹与路径无关的J~*积分,并给出了严密的证明。文中证明了J~*积分与扩展裂纹尖端的张开位移(动态COD)之间有简单的关系,同时利用J~*积分求得了粘弹性介质中变速扩展裂纹尖端的奇异性。当裂纹以常速扩展时,J~*积分与能量释放率、动应力强度因子之间也有简单的关系。利用这些关系,我们给出了动态COD与动应力强度因子之间的关系式。     

Subcritical growth of macrocracks in an aging orthotropic viscoelastic composite under static loads

The problem of subcritical crack growth in an aging orthotropic plate deformed across the reinforcing fibers by tension applied at infinity is solved on the basis of the theory of subcritical crack growth proposed by A.A. Kaminskii. Kinetic curves of crack growth are constructed for different volumes of reinforcing fibers and different ages of the binder. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 92–97, June, 1999.     

Specification of crack opening and surface sliding in orthotropic viscoelastic material

Modelling of crack opening and surface sliding in an orthotropic viscoelastic material is made by introducing two coefficients: one for the surface displacement and surface friction. The material possesses orthotropy in two dimensions and viscoelastic property consisting of a Kelvin element in series with a spring. The method of Laplace transform is applied to obtain a closed form solution to the problem. Explicit expressions of Mode I and II stress intensity factors are computed together with crack surface opening. Trade-off between the Mode I and II stress intensity factors depends on the nature of material orthotropy.     

Development of a crack with a considerable prefracture zone in a viscoelastic orthotropic plate under variable loads

The study is made of the delayed fracture of a viscoelastic orthotropic plate caused by subcritical advancement of a rectilinear microcrack, which is located along one of the orthotropic axes. The crack develops because of stretching of the plate by uniformly distributed increasing and cyclic external forces perpendicular to the crack line. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent integral operators of difference type, which describe the deformation of a material with time-dependent rheological properties. The analytical form of the kernel of an irrational function of a linear combination of the above integral operators is determined by the method of operator continued fractions. Numerical calculations are conducted for resolvent bounded integral operators with a kernel in the form of Rabotnov's fractional-exponential function. The kinetics of growth of a crack with tip regions commensurable with the crack length is studied. A comparison with the results obtained within the framework of the concept of the thin structure of the crack tip is given. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 121–129, June, 2000.     

Effects of humidity and temperature on subcritical crack growth in sandstone

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. The influences of the surrounding environmental conditions and rock fabric on subcritical crack growth in sedimentary rocks in air are yet to be clarified, while the nature of subcritical crack growth in igneous rocks has been studied well. In this study, the influences of temperature and relative humidity on subcritical crack growth in Berea sandstone, Shirahama sandstone and Kushiro sandstone were investigated in air. The load relaxation method of Double Torsion (DT) testing method was used to measure both crack velocity and stress intensity factor under a controlled temperature and relative humidity.Results show that the change of the crack velocity at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. On the other hand, we show that the crack velocity increased by several orders of magnitude when the relative humidity increased threefold or fourfold under a constant temperature at a given stress intensity factor. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. It is therefore necessary to consider the additional mechanisms for subcritical crack growth in sandstone. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in sandstone in air is affected remarkably by the relative humidity and the amount of clays in rock.     

Design of ceramic components using fracture mechanics concepts

Using linear elastic fracture mechanics concepts, a design lifetime diagram for an aluminum oxide insulator is developed. The stresses are given in terms of mechanical stress and temperature differences. Design considerations in the presence of subcritical crack growth are discussed as well as the statistical nature of the flaw populations in brittle solids. Depending on the nature of the environment, subcritical crack growth may or may not be important.     

MICROMECHANICS ANALYSIS ON EVOLUTION OF CRACK IN VISCOELASTIC MATERIALS

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Delayed fracture of an isotropic viscoelastic material with a crack under cyclic loading

The delayed fracture of an isotropic viscoelastic plate is examined as a process involving the subcritical propagation of a straight normal-rupture crack during fatigue loading. Calculations are based on the modified {ie165-1} of fracture, it being assumed that the size of the prefracture zone ahead of the moving crack remains constant. This zone is also assumed to be small compared to the size of the crack itself. Solutions for a time-dependent crack length are given both for media which undergo quasi-viscous flow (an integral operator with an Abelian kernel is used) and for media whose creep curves have a horizontal asymptote (an integral operator with a kernel in the form of the fractional-exponential function of Yu. N. Rabotnov is used). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 60–64, February, 1999.     

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.