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1.
Stable growth of penny-shaped crack in viscoelastic composite material under time-dependent loading 总被引:1,自引:0,他引:1
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. 相似文献
2.
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. 相似文献
3.
The delayed fracture of a viscoelastic plate with a rectilinear mode I crack under a time-dependent load is studied. The plate is made of a laminated composite with an isotropic elastic reinforcing component and a viscoelastic matrix. The composite is modeled by an orthotropic homogeneous linearly viscoelastic medium with some averaged characteristics. To determine the viscoelastic characteristics of the composite, the Volterra principle and the method of continued fractions are used. The study is made within the framework of the theory of delayed fracture for viscoelastic bodies. 相似文献
4.
G. V. Gavrilov 《International Applied Mechanics》2004,40(1):77-82
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 相似文献
5.
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
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 1, pp. 82–92, January 2007. 相似文献
6.
G. V. Gavrilov 《International Applied Mechanics》2010,46(4):422-428
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 相似文献
7.
The problem of long-term fracture of an aging reinforced composite array having hexagonal symmetry and weakened by a flat
circular macrocrack is considered based on the Boltzmann-Volterra principle and the theory of long-term fracture of viscoelastic
bodies. The array is under the action of stationary tensile forces applied at infinity and normal to the crack plane. The
Maslov-Arutyunyan operator is used to describe the aging strain properties of the array. The irrational functions of integral
Volterra operators obtained during the solution are determined by expanding them into continued fractions. The crack growth
equations derived are numerically solved for a specific material (ferroconcrete). Curves of the rupture life of the composite
array, kinetics of crack growth, and safe loading are presented.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 35, No. 12, pp. 72–79, December, 1999. 相似文献
8.
N. A. Abrosimov N. A. Kulikova 《Journal of Applied Mechanics and Technical Physics》2011,52(1):132-140
A method for identifying the material parameters of the constitutive relations of viscoelastic and elastoplastic deformation
for isotropic and homogeneous composite materials is developed based on minimizing the mismatch between the results of numerical
and experimental modeling of unsteady deformation of structural elements made of the materials studied. The method is tested
and shown to be effective in determining the viscoelastic and elastoplastic characteristics of models for the nonlinear deformation
of impulsively loaded isotropic and composite circular plates. 相似文献
9.
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. 相似文献
10.
An efficient method is proposed to determine the deformation function of a viscoelastic material from experimental data. The
deformation function is assumed to be an integral operator with Rabotnov's fractional-exponential kernel or a sum of such
kernels. This representation enables effective use of the method of operator continued fractions. To illustrate the method,
deformation data for polymethylmethacrylate are used. The viscoelastic characteristics of a composite based on this material
are obtained using the method of operator continued fractions
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 41–50, August 2005. 相似文献
11.
12.
M. F. Selivanov 《International Applied Mechanics》1999,35(2):165-169
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. 相似文献
13.
14.
David E. Walrath 《Experimental Mechanics》1991,31(2):111-117
Viscoelastic response of a unidirectional aramid fiber-reinforced epoxy was measured. Procedures to measure all five time-dependent material properties necessary to describe behavior of a transversely isotropic continuous-fiber unidirectional lamina were implemented. The Iosipescu shear method was used to measure in-plane and interlaminar shear viscoelastic response. Applicability of the Schapery single-integral nonlinear viscoelastic constitutive model to describe time-dependent mechanical behavior of a laminated composite material containing two viscoelastic phases was explored. Linear and nonlinear viscoelastic parameters for this two-viscoelastic constituent composite were measured and data summaries are presented in the paper. The time-dependent behavior of this two-viscoelastic constituent composite material was found to be complex, but the Schapery nonlinear viscoelastic model did adequately fit the response of such a composite to uniaxial applied loads.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10. 相似文献
15.
I. V. Andrianov H. Topol D. Weichert 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(11):999-1007
In A fibre-reinforced 2D composite material with elastic fibres and viscoelastic, isotropic matrix is studied. Starting from
the solution of a reference-problem with elastic matrix material the elastic matrix parameters are substituted by their viscoelastic
correspondents in the Laplace domain. For simplification the time-dependent solution is approximated by using limiting value
theorems that give information about the time-dependent solution for t → 0 and t → ∞. Then the method of asymptotically equivalent functions is used and illustrated with examples of a steel fibre in a PMMA
matrix. The analytical solutions are compared with their numerical counterparts. In summary it can be stated that this paper
is a further contribution to the vast literature about the application of the correspondence principle to the solution of
special problems of the linear viscoelasticity. 相似文献
16.
Analysis of mode Ⅲ crack perpendicular to the interface between two dissimilar strips 总被引:2,自引:1,他引:1
M. S. Matbuly 《Acta Mechanica Sinica》2008,24(4):433-438
The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor. 相似文献
17.
G. V. Gavrilov 《International Applied Mechanics》2007,43(8):903-911
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
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 92–101, August 2007. 相似文献
18.
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
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 89–97, September 2006. 相似文献
19.
20.
A new method is proposed to solve some problems of linear viscoelasticity for anisotropic bodies. The method uses a branching continued fraction to approximate an irrational multivariable function. Such an approach allows obtaining a linear operator as an approximation of a multivariable operator function. The deformation of a cracked composite body with a plastic matrix is analyzed as an example. Both composite components are assumed to exhibit viscoelastic properties 相似文献