Modelling the failure of orthotropic materials subject to biaxial loading

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The Dugdale crack model is generalized to the case of plane strain. The governing equations are set up to determine the stresses in the plastic zone. Numerical results from specific problems are analyzed and compared with those for plane stress state and other cases. A relationship between the crack model and K I -T theory is established in the case of small-scale yielding at the crack tip Keywords: Dugdale crack model, generalized model, plane strain, fracture toughness, T-stresses, plastic zone, plane stress state, small-scale yielding Introduction. Classical fracture mechanics, either linear or nonlinear, is based on a one-parameter estimate of the limiting state of a body with a mode I crack. For example, Griffith-Irwin-Orowan theory [31,33,40] considers an asymptotic field of elastic stresses at the crack tip and describes the limiting state by only the stress intensity factor (SIF) K I or energy release rate G I . Nonlinear fracture mechanics based on the Cherepanov-Rice J-integral proceeds from the singularity of the asymptotic stress field in a nonlinearly elastic material [19,32,41].The intensive experimental investigations initiated almost immediately after the above concepts had been put forward revealed that the fracture characteristics depend on specimen geometry and loading conditions, as shown by the dependence of the maximum SIF on the thickness of the specimen, the ratio of the crack length to its width, etc. [16,17]. In this connection, much effort went to the development of standards for determining fracture toughness K IC in the case of plane strain. The weaknesses of the one-parameter approach made themselves evident later, in analyzing the influence of two-axis loading on the limiting state of a cracked body [13,20]: this theoretical approach did not confirmed the experimentally revealed effect of the homogeneous normal stresses along the crack on the maximum SIF.The above-mentioned and other facts are indicative of the limitation of the one-parameter approach to the description of quasibrittle fracture. Two factors influencing the limiting state of cracked bodies attracted the attention of researchers: constrained plastic strains in different stress-strain states (SSSs) at the crack front and regular (according to the elastic solution) terms of the stress field. However small the plastic zone at the crack tip, the stresses at the boundary of the elastic and plastic zones are always finite, and the effect of regular terms may be significant. Obviously, a closed-form elastoplastic solution for a mode I crack would account for these factors. Such analytical solutions are as yet unavailable, however; and researchers have to use crack models to simplify the distribution of stresses and strains and the form of the plastic zone.Recently, the following nonclassical approaches have been developed: -the criteria of plasticity theory and various numerical methods of analyzing the plastic zone at the crack periphery [16,27];-criteria of local buckling near cracks [2, 13]; -more complete description of ...

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confidence: 99%

“…This generalization is based on the concept of fracture process zone at the crack tip and an additional strength condition for this zone. The approach was used in [9,10] to study the fracture of elastic and viscoelastic orthotropic plates made of composites and subjected to biaxial loading.…”

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confidence: 99%

Two-Parameter Model of a Mode I Crack in an Elastoplastic Body under Plane-Strain conditions

Kaminskii

Galatenko

2005

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“…Obviously, the integral in (2.3) can be evaluated in finite form as D ® ¥, which corresponds to a single cut [3]. The size of the fracture process zones is defined as follows [1]: Figure 1a shows the size of the fracture process zone d l / as a function of the distance D l / between cracks for p y / s 0 = 0.5.…”

Section: Limiting State Of An Orthotropic Plate With a Periodic Row Omentioning

confidence: 99%

“…Of special interest is to study the behavior of structural members made of anisotropic materials, which is confirmed by [11][12][13][14]. In [3], the Dugdale model was generalized to anisotropic materials by considering biaxial external loading, and the fracture problem for an orthotropic plate with a single rectilinear crack was solved. The paper [1] solves a similarly formulated problem for an orthotropic elastoplastic plate with a periodic row of collinear cracks under biaxial loading.…”

Section: Introductionmentioning

confidence: 99%

Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

Bogdanova

2008

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A modified d c -model is used to study the limiting state of an orthotropic plate weakened by a periodic row of collinear cracks and satisfying a general failure criterion. The failure mechanism of the plate is analyzed. A study is made of the effects of the degree of orthotropy, the biaxiality of external loading, and the geometrical parameters on the fracture process zones at the crack tips and the limiting state of the plate. The safe loading of an orthotropic viscoelastic plate with a periodic row of collinear cracks is examined. The effect of the rheological parameters on the safe-load region is studied Keywords: fracture, periodic row of cracks, orthotropic material, biaxial loading, safe loading Introduction. Modeling the fracture of materials under biaxial loading has specific features noted in many studies. This resulted in various approaches to the description of the external load acting along the crack line [6][7][8][9][10]. Of special interest is to study the behavior of structural members made of anisotropic materials, which is confirmed by [11][12][13][14]. In [3], the Dugdale model was generalized to anisotropic materials by considering biaxial external loading, and the fracture problem for an orthotropic plate with a single rectilinear crack was solved. The paper [1] solves a similarly formulated problem for an orthotropic elastoplastic plate with a periodic row of collinear cracks under biaxial loading. In the present paper, we analyze the limiting state of a viscoelastic orthotropic plate with a periodic row of collinear cracks under biaxial loading.1. Crack in an Orthotropic Material: A Model. Consider a thin orthotropic plate with a periodic row of collinear cracks aligned with one of the orthotropy axes. The experiments and their analysis performed in [8,15,16] show that fracture process zones occur ahead of the crack front and have different structures in different materials (these are zones with partially destroyed fibers in composites, crazes in polymers, plastic zones in metals, etc.). Assume that the limiting state of a material inside the fracture process zones can be described by a general failure criterion:

“…It is also assumed that the external load s x q ¥ = , if compressive, does not reach the critical level that causes local instability around a crack [3]. Our model is experimentally validated in [6].…”

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confidence: 99%

A mesomechanical fracture model for an orthotropic material with different tensile and compressive strengths

Kaminsky

Bogdanova

2009

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The paper addresses a fracture problem for an orthotropic cracked plate made of a material with different tensile and compressive strengths and subjected to biaxial loading. The problem is solved using a micromechanical fracture model proposed earlier by the authors. It is assumed that the fracture of the material in the fracture process zones at the crack front is described by the Gol'denblat-Kopnov failure criterion. Strength curves for an orthotropic cracked plate with different strength and fracture-toughness parameters are plotted Keywords: fracture, orthoropic material, process zone, plane stress state, biaxial loading, ultimate strength Introduction. The development of linear fracture mechanics and some divisions of nonlinear fracture mechanics was completed in the second half of the 20th century. Linear fracture mechanics based on the Griffith-Irwin theory and the concept of stress intensity factors as well as nonlinear fracture mechanics based on the Cherepanov-Rice theory and the concept of J-integral are macrotheories because they do not look into the physics of the fracture of materials. For this reason, fracture mechanics for these theories deals only with the macromechanical properties of materials.The past years have seen the development of the two-level approach, which, at the macrolevel, employs methods of solid mechanics for the major portion of a cracked body and, at the second level, models physical features of materials to study the fracture process at the crack front where the material appears partially damaged. This approach is currently known as fracture mesomechanics [2,12]. Methods of fracture mesomechanics make it possible to study fracture processes in various natural and man-made materials such as rocks, timber, concrete, ceramics, polymers, composites, and others. Of particular interest is the fracture of anisotropic materials [8][9][10][11].Experiments show that fracture process zones in thin plates are in many cases narrow and wedge-shaped areas located on the continuation of cracks and made of a partially damaged, discontinuous material [5,13]. These experimental data were used in [6] to model a fracture process. As the Leonov-Panasyuk-Dugdale model, this model considers a fracture process zone as a slit with self-balanced compressive stresses applied to its faces. Contrastingly, the parameters of our model are determined from a failure criterion for the material in the fracture process zone. This allows considering the stresses acting along the crack plane, which is impossible with the Leonov-Panasyuk-Dugdale model. This model [6] and the Gol'denblat-Kopnov failure criterion [1] are used here to study the fracture of a thin orthotropic cracked plate made of a material with different tensile and compressive strengths. Among such materials are concrete, reinforced concrete, rocks, and some composites.