Subcritical crack growth in a polymer composite

Kaminskii, A. A.; Гаврилов, Д. А.; Markov, V. A.

doi:10.1007/bf01273666

Cited by 8 publications

(15 citation statements)

References 2 publications

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“…Equation (9) follows from Eqs. (14) and (22) (1) is a rather complicated computational procedure (Appendix A.2). Moreover, this procedure is not standardized as is, for example, that for Taylor coefficients.…”

Section: Branched Operator Continued Fraction Interpretation and Convmentioning

confidence: 99%

On the application of branched operator continued fractions for a boundary problem of linear viscoelasticity

Kaminsky

Selivanov

2006

Int Appl Mech

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In solving linear viscoelastic problems for composite materials, the problem arises of representing a multivariable operator function. To resolve this problem, the method of operator continued fractions is generalized to the case of a multivariable operator function. The method is based on the theory of branched continued fractions. Branched operator continued fractions are considered. Using the convolution theorem, fractions can be represented in terms of operators of basic class. This representation makes it possible to effectively solve boundary problems of linear viscoelasticity Keywords: branched continued fraction, Volterra integral operator, branched operator continued fraction 1. Problem Formulation. The classical Boltzman-Volterra theory of linear viscoelasticity, which appeared at the end of the 19th century, is extensively being used at present because of the need to study deformation in structures made of various viscoelastic composite materials. Methods of solving boundary problems are based on the Volterra principle. The principle suggests reducing the problem solution to the representation of a multivariable operator function in terms of a linear operator of basic class.The viscoelastic properties of materials are modeled by integral Volterra operators

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Section: Branched Operator Continued Fraction Interpretation and Convmentioning

confidence: 99%

On the application of branched operator continued fractions for a boundary problem of linear viscoelasticity

Kaminsky

Selivanov

2006

Int Appl Mech

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“…Fracture mechanics is based on failure models that include two basic elements: a crack model, which gives an idea of the form and edge structure of the crack, and a failure criterion, which is a condition whereby the crack begins to grow. To study the long-term fracture of polymeric composites, the authors of [1,2,7] proposed a modified δ c -model. According to this model, the fracture process zone is modeled by a cut on the continuation of the crack; the size of this zone is assumed constant during crack growth.…”

Section: Features Of Modeling Cracked Compositesmentioning

confidence: 99%

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

Kaminskii

Selivanov

2004

Int Appl Mech

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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.Keywords: viscoelastic composite material, operator continued fraction, crack growth, cyclic load 1. Viscoelastic Anisotropic Material. The stress-strain state of many polymers and polymeric composites is described by the linear rheological relations, even for high stress levels. Therefore, the stress-strain analysis of such materials is based on the linear theory of viscoelasticity. One of the alternatives of this theory that has recently received wide acceptance is based on the Boltzmann principle. According to this principle, the system of constitutive equations in the quasistatic theory of viscoelasticity is similar to the system of constitutive equations in the linear theory of elasticity, except for Hooke's law. The physical relations of linear viscoelasticity are similar to the physical relations of linear elasticity where the elastic anisotropy constants are replaced by integral operators. The stress-strain relationship for a linear viscoelastic medium are defined based on the Boltzmann principle aswhere ε kl and σ kl are the strain and stress components; and A ijkl * is the viscoelastic analog of the stiffness tensor. If the rheological characteristics of a viscoelastic composite are time independent (nonaging material), some viscoelastic operator M * acting on a time function has the following integral form (Volterra operator of the second kind):where M is the corresponding elastic constant; M(θ) is the relaxation function. Such functions are determined experimentally mainly for anisotropic media with certain symmetry. This reduces the number of independent creep functions. Features of Modeling Cracked Composites.A typical feature of matrix composites of regular microstructure is the anisotropy of their macroscopic physicomechanical properties. Despite the variety of reinforcement schemes, the relationship between the strain and creep components is the main concern in describing the mechanical properties of the composite. The deformation mode of the composite can be predicted in two ways. One is to consider a reinforced material as a structure (microapproach). The complexity of the mathematical microstructural description of deformation is mainly due to inhomogeneity whose degree depends on the relative fractions of the phases and differences between their properties. Strongly

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“…The experimental justification of this criterion is given in [2,5] for a great number of polymer materials and composites on their basis.…”

Section: [P(t)l(t)]=qp(t){(?lmentioning

confidence: 99%

“…According to the theory of precritical development of cracks in viscoelastic bodies [2][3][4][5], the process of crack propagation is described by corresponding integral equations in each of the above-mentioned stages of its slow precritical development.…”

Section: Equations Of Slow Precritical Crack Growthmentioning

confidence: 99%

“…A theory of precritical propagation of cracks in anisotropic viscoelastic materials, describing the process of long-term failure of some types of composites, is presented in [2][3][4][5][6]. It is based on a modified 8 c-model of failure [3], constructed within the framework of the concept of a constant size of the prefailure region near the front of a growing crack.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Long-term failure of a layered viscoelastic composite material with a crack under a time-dependent load

Kaminskii¹,

Selivanov²

2000

Mech Compos Mater

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Subcritical crack growth in a polymer composite

Cited by 8 publications

References 2 publications

On the application of branched operator continued fractions for a boundary problem of linear viscoelasticity

On the application of branched operator continued fractions for a boundary problem of linear viscoelasticity

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

Long-term failure of a layered viscoelastic composite material with a crack under a time-dependent load

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