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

Kaminskii, A. A.; Selivanov, M. F.

doi:10.1007/bf02262810

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…The method is more efficient when the function can be expanded into a proper continued fraction. Note that such a fraction can be derived from the Taylor-series expansion of the function [6]. In this case, the convergents of the expansion possess a "fork" property: the exact value of the function is between the values of two sequential convergents [5].…”

Section: Applying the Methods Of Operator Continued Fractionsmentioning

confidence: 98%

A Method for Determining the Viscoelastic Characteristics of Composites

Kaminskii

Selivanov

2005

Int Appl Mech

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An efficient method for determining the deformation function of a composite is discussed. The method is based on a fractional exponential representation of the deformation functions of the composite components. The viscoelastic solution is obtained using the Volterra principle. The deformation function is represented as a function of a base operator. Thus, the problem is solved by approximating the deformation function by a continued fraction and applying the method of operator continued fractions. A computational procedure is detailed and illustrated using data on longitudinal relaxation of polymethylmethacrylate. As an example, the deformation of a polymethylmethacrylate-based fibrous composite with viscoelastic properties is analyzed Introduction. Extensive use of polymers and polymer-based composites entails intensive development of the theory of viscoelasticity needed to solve practical deformation problems for composites and boundary-value problems for materials with time-dependent stress-strain state. Typical properties of these materials are relaxation (decreasing stresses at constant strains) and creep (increasing strains at constant stresses). To describe the deformation of viscoelastic materials, Boltzmann proposed a theory of hereditary viscoelasticity based on the superposition principle. According to this theory, the equation relating the strains and stresses in a linear nonaging viscoelastic material under uniaxial loading and isothermal conditions reads

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Section: Applying the Methods Of Operator Continued Fractionsmentioning

confidence: 98%

A Method for Determining the Viscoelastic Characteristics of Composites

Kaminskii

Selivanov

2005

Int Appl Mech

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“…The singular equations in [1] are valid in the neighborhood of r << l. By increasing the neighborhood around the crack tip, we can more accurately determine the fringe order and SIF ( ) K . The simultaneous solution of the equations of orthotropic photoelasticity and fracture mechanics of materials with cracks yields the relationship between the fringe orders m and K, as was shown in [16].…”

Section: Introductionmentioning

confidence: 98%

“…To determine the stress intensity factors (SIFs) around cracks propagating from the edges of a hole in elastic isotropic plates, use is made of numerical [1,3], theoretical-and-experimental [2], and experimental [8] methods. The major results in the field have been obtained in the static case.…”

Section: Introductionmentioning

confidence: 99%

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Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

2011

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The stress-strain state near cracks on the boundary of a circular hole in a linear elastic orthotropic composite plate under tension is analyzed. The distribution of stress intensity factors (SIFs) at the crack tip is found from photoelectric measurements. The dependence of the SIFs on the ratio of crack length to hole radius and on the mechanical properties of the material is established Keywords: photoelasticity, orthotropic composite plate, circular hole with two edge cracks, tension, stress intensity factor Introduction.Theoretical and experimental studies of the stress distribution in composite structural members (plates and shells with stress concentrators (holes, cracks)) are addressed in [1, 3, 6, 7, 11-16, etc.)].To determine the stress intensity factors (SIFs) around cracks propagating from the edges of a hole in elastic isotropic plates, use is made of numerical [1, 3], theoretical-and-experimental [2], and experimental [8] methods. The major results in the field have been obtained in the static case. Solutions to dynamic problems for anisotropic bodies with stress concentrators obtained by the photoelastic method can be found in [12][13][14][15].We will use photoelastic measurements to study the stress distribution around cracks on the boundary of a hole in linear elastic fiber-reinforced composite plates under a tensile force normal to the cracks. Use will be made of a procedure that produces more accurate results than in [16]. The mathematical model discussed below allows us to increase the neighborhood around the crack tip to improve the accuracy of determining the fringe orders and, hence, the SIFs.1. Problem Formulation. Procedure of Analysis. To describe the mechanical and optical behavior of the composite, we will assume that it is homogeneous and anisotropic. Consider a photoelastic plate under creep.The orthotropic plate is weakened by a crack on an interval ( ) 2l of the x-axis aligned with the principal axis of orthotropy of the material (Fig. 1). The plate is subject to a tensile force P = const applied far from the stress concentrator. In the case of plane stress state, the components of the stress tensor s s t

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“…Even at normal temperature, they show viscoelastic behavior [15]. Experimental data [3,4,10,12] suggest that the fracture of such materials largely depends on their rheological properties and may occur at low stresses as a slowly growing crack. Efficient experimental nondestructive methods for the quantitative assessment of the damage of anisotropic materials under loading, especially in the plastic range, are yet to be developed.…”

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Photoelastic modeling of the fracture of viscoelastic orthotropic plates with a crack

2010

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The well-known equations of photoelasticity of linear viscoelastic bodies are used to describe the photoelastic behavior of a viscoelastic orthotropic plate with a crack. Expressions for the stress intensity factors (SIFs) at the crack tip are obtained using photoelastic measurements. The time dependence of the SIFs is analyzed and shown to be determined by the angles between directions of the crack and tension Keywords: photoelasticity, viscoelastic orthotropic plate with a crack, tension, stress intensity, fracture Introduction. Intensive loading causes early damage of the material of structural members due to the growth of existing and the initiation of new submicro-and microdefects. In many fibrous composites, such processes mainly occur at the fiber-matrix interface. Even at normal temperature, they show viscoelastic behavior [15]. Experimental data [3,4,10,12] suggest that the fracture of such materials largely depends on their rheological properties and may occur at low stresses as a slowly growing crack. Efficient experimental nondestructive methods for the quantitative assessment of the damage of anisotropic materials under loading, especially in the plastic range, are yet to be developed.Among the direct nondestructive methods that could be used to study the kinetics of damage growth, the acoustic-emission method is the most promising [1]. A review of literature on the use of this method for the evaluation of accumulated damage shows that some well-known data are empirical, which significantly limits their use [14].The photoelastic method makes it possible to determine stresses and strains and also their distribution in anisotropic optically sensitive materials with accuracy sufficient for engineering [9,13].Solutions to nonstationary problems of fracture mechanics for anisotropic bodies with stress concentrators obtained by the dynamic photoelastic method can be found in [17-22, etc.].We will outline a technique for the determination of the stress intensity factors (SIFs) near cracks in linear viscoelastic materials based on photoelastic measurements. We will discuss results on the variation in the SIFs during precritical crack growth.1. Problem Formulation and Method of Analysis. Consider a plate made of a linear viscoelastic fibrous composite and having a central crack. The crack is parallel to the direction of preferential reinforcement of the orthotropic composite (Å Å

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

Cited by 5 publications

References 6 publications

A Method for Determining the Viscoelastic Characteristics of Composites

A Method for Determining the Viscoelastic Characteristics of Composites

Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

Photoelastic modeling of the fracture of viscoelastic orthotropic plates with a crack

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