Fracture mechanics of materials under compression along cracks (survey). Structural materials

Guz, A. N.; Назаренко, В. М.

doi:10.1007/bf00889098

Cited by 11 publications

(6 citation statements)

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“…Since then, there have been numerous studies on the subject. These studies are reviewed in [47,49,55,56]. Relevant results were consistently considered in the monograph [44] and in many others publications listed in [49].…”

Section: Buckling (Delamination) Of Elastic and Viscoelastic Pates Wimentioning

confidence: 93%

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Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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Investigations of viscoelastic composite materials and structural members carried out using the TDLTSDB and initial-imperfection method are reviewed. The investigations address the internal and surface loss of stability of layered and fibrous composites, the loss of stability of plates, and the delamination (buckling) of plates with cracks. Each of these problems is reviewed separately. New areas of further research are proposed. The review focuses on the investigations carried out by the author and his students Keywords: buckling, crack, delamination, plate, instability, viscoelastic composite material 1. Introduction. As in [33,[41][42][43][44][45] and many other publications, by three-dimensional instability problems will be understood here instability problems investigated employing the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB). The investigations regarding the construction of the TDLTSDB are detailed in the paper [46] and in the monographs [33,[41][42][43]45]. It was noted there that the tendencies to construct the theory, which allows us (i) to describe the buckling phenomenon for a well-defined three-dimensional stress-strain state and (ii) to obtain reliable data on the critical parameters for thin-walled and massive structural elements, contributed to the creation of the TDLTSDB. Historically, the TDLTSDB began to be developed in the first half of the 20th century, and the basic TDLTSDB relations were obtained in [30, 31-33, 35, 38, 45, 63, 71-73, 80, 84, 85] using either a strict and exact approach based on the linearization of the exact and strict relations of the nonlinear three-dimensional theory or an approximate approach based on a physical and, in part, linearization of certain relations. Development and detailed analyses of the results from these investigations were presented in the monographs [41,42,45].In the second half of the 20th century, the main attention of researchers was focused on the solution to separate classes of TDLTSDB problems. At the same time, general aspects of the TDLTSDB were also developed. It should be noted that the results of these studies were the subject of many monographs such as [41][42][43][44][45] and were reviewed in many papers such as [28,46,47,49,52,55,56,58].It follows from the search of the foregoing and other numerous inquiries that the TDLTSDB was mainly applied to analyze the stability of structural members made of time-independent materials. Moreover, these investigations used the bifurcation (Euler) approach. The Euler approach is known to be generally unsuitable for investigating instability problems for structural elements made of time-dependent materials and subjected to external static loading. This is why a dynamic investigation method was suggested in [40,45] to examine these problems. Note that this method represents the sought quantities with a multiplier exp(iWt) and determines the critical parameters of the problems from the requirement ImW = 0. However, if the dynamic investigation method is applied with...

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Section: Buckling (Delamination) Of Elastic and Viscoelastic Pates Wimentioning

confidence: 93%

“…At the same time, general aspects of the TDLTSDB were also developed. It should be noted that the results of these studies were the subject of many monographs such as [41][42][43][44][45] and were reviewed in many papers such as [28,46,47,49,52,55,56,58].…”

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confidence: 99%

Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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“…Since the data obtained in [3-5, 22, 24-27, 62-66, 69, 80, 93] for near-surface cracks in hyperelastic, composite, and elastoplastic materials are very extensive and have already been covered in detail in [24,25] and the scope of the present publication is limited, we will restrict ourselves to spatial axisymmetric problems for composites as the most interesting, in our opinion, case.…”

Section: Governing Equationsmentioning

confidence: 99%

“…For elastoplastic materials, the characteristic equation has complex-conjugate roots n n 1 2 = . The generalization of the mathematics to the case of complex-conjugate roots (and use of complex-valued functions of real variable) is discussed in [8,25,72]. An incompressible isotropic elastoplastic model was used to describe the deformation of the material.…”

Section: Plastic Materialsmentioning

confidence: 99%

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Fracture and stability of materials and structural members with cracks: approaches and results

2004

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A new alternative approach to fracture problems for materials and structural elements with cracks is set out. It is based on the mechanism of local instability near defects. The approach is used to study the fracture of materials compressed along interacting cracks and the fracture of thin structural members with cracks under tension with allowance for local buckling.Introduction. The main question to answer by linear fracture mechanics, a well-established and widely accepted since, in looking into the possibility of further growth of existing cracks is whether the cumulative elastic energy is sufficient for additional surfaces of the defect to form. In Irwin's interpretation, this question is whether the integral characteristics of the stress-strain state at crack tips (stress intensity factors or crack opening displacement) achieve certain limit (critical) values under given loads.In some cases, however, this approach is a fortiori inapplicable, though intuition suggests that fracture (crack growth or fragmentation) may (and will actually) occur under increasing loads. Among such cases is primarily loads acting along cracks-the stress intensity factors appearing in failure criteria such as the Griffith-Irwin one (linear fracture mechanics) are equal to zero, and, hence, fracture does not occur. The buckling of cracked materials (under compression along near-surface cracks parallel to the free surface) is a widely known and well-described phenomenon (in particular, in laminated composites). The aforementioned pertains equally to parallel cracks along which loads act.It has long been known that local buckling triggers fracture [69]. Moreover, local buckling may strongly affect the classical linear fracture process by preceding it and frequently reducing the threshold levels of applied loads. This is particularly true of thin-walled structural members (plates and shells) where out-of-plane buckling precedes fracture.This paper cites results of solving nonclassical problems of fracture mechanics where local buckling either triggers fracture (loads parallel to crack surfaces) or strongly influences the fracture process by preceding it and altering the geometry of the element (thin-walled plate or shell).When the initial stresses are parallel to crack faces, there may be two classes of problems, depending on whether there is a field of additional stresses that are rather small compared with the initial stresses [8].If there is no such an additional filed, then we deal with fracture under compression along cracks. The approach used to solve such problems is based on the relations of three-dimensional linearized solid mechanics. The concept of fracture is this: local buckling near cracks triggers fracture. The process of fracture is initiated when the initial stresses reach critical levels (values corresponding to local instability). This approach (including the relations of linearized solid mechanics, the corresponding mathematical tool, and failure criteria) is detailed in [8][9][10][11][12]. The formulation of the b...

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Preliminary Consideration: Background, Approaches and Their Analysis

Guz

Bogdanov

Назаренко

2020

Advanced Structured Materials

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Fracture mechanics of materials under compression along cracks (survey). Structural materials

Cited by 11 publications

References 0 publications

Three-dimensional instability problems for viscoelastic composite materials and structural members

Three-dimensional instability problems for viscoelastic composite materials and structural members

Fracture and stability of materials and structural members with cracks: approaches and results

Preliminary Consideration: Background, Approaches and Their Analysis

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