Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

Zappalorto, Michele; Lazzarin, P.

doi:10.1007/s10704-008-9185-7

Cited by 31 publications

(24 citation statements)

References 46 publications

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“…Neuber's law, which forms the basis for the present model, is strictly applicable only for small-scale yielding, wherein the inelastic zone size is small compared to the notch size and the net-section width [19,20]. However, we find, surprisingly, that the resulting SCFs and stress distributions in bluntly-notched CMCs are in excellent agreement with the FEA results even for large-scale and net-section inelasticity.…”

Section: Preliminariessupporting

confidence: 59%

Stress distributions in bluntly-notched ceramic composite laminates

Rajan

Zok

2014

Composites Part A: Applied Science and Manufacturing

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a b s t r a c tWe present a methodology for determining stress distributions ahead of blunt notches in plates of fiberreinforced ceramic-matrix composites subject to uniaxial tensile loading, accounting for the effects of inelastic straining due to matrix cracking. The methodology is based on linear transformations of the corresponding elastic distributions. The transformations are derived from adaptations of Neuber's law for stress concentrations in inelastic materials. Comparisons are made with results computed by finite element analysis using an idealized (bilinear) form of the Genin-Hutchinson constitutive law for ceramic composite laminates. Effects of notch size and shape as well as the post-cracking tangent modulus are examined. The comparisons show that, for realistic composite properties, the analytical solutions are remarkably accurate in their prediction of stress concentrations and stress distributions, even in cases of large-scale and net-section inelasticity. Preliminary assessments also demonstrate the utility of the solution method in predicting the fields under multiaxial stressing conditions.

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Section: Preliminariessupporting

confidence: 59%

Stress distributions in bluntly-notched ceramic composite laminates

Rajan

Zok

2014

Composites Part A: Applied Science and Manufacturing

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“…In a recent paper the present authors (Zappalorto and Lazzarin 2007) carried out an analytical study on the elastic-plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material was thought of as obeying an elastic perfectly-plastic or a strain hardening law.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, revisiting Glinka and Molski's Equivalent Strain Energy Density, these factors have been used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case. In Zappalorto and Lazzarin (2007) the attention was mainly focused on the stress components inside the plastic core, ahead of the notch tip, rather than in the outer elastic region; for this reason it has been used a leading-order-term formulation for the stress distribution. Not only the calculations related to the maximum plastic stress, but also those for the strain energy density over a control volume were fully confined within the plastic zone.…”

Section: Introductionmentioning

confidence: 99%

Plastic notch stress intensity factors for pointed V-notches under antiplane shear loading

Lazzarin

Zappalorto

2008

Int J Fract

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The paper deals with a work-hardening, elastic-plastic, stress analysis of pointed V-notches under antiplane shear deformation loading both under small and large scale yielding. Stress and strain field intensities are expressed in terms of plastic Notch Stress Intensity Factors, which are analytically linked to the corresponding linear elastic ones under small scale yielding. The near tip stress and strain fields are then used to give closed-form expressions for the Strain Energy Density over a circular sector surrounding the notch tip, and for the J-integral parameter, both as a function of the relevant plastic NSIFs, these expressions being valid both under small and large scale yielding

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“…Rounded crack tip elasticity solutions have typically employed series expansions of the linear elastic elliptical hole solution near one end of a semimajor axis or equivalently the vertex of a parabola [9,26,30]. These approximations recover as special cases the linear elastic mode I crack solution as the eccentricity of the ellipse approaches unity.…”

Section: Introductionmentioning

confidence: 99%

Linear Elastic Solutions for Slotted Plates

Unger

2011

J Elast

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Two-dimensional problems of finite-length blunted cracks cut into infinite plates subject to remote tractions are solved using complex variable theory. The slot geometry is composed of two flat surfaces connected by rounded ends. This special geometrical shape was derived by Riabouchinsky in the study of two-dimensional ideal fluid flow around parallel plates. The simpler antiplane slotted plate problem is addressed initially for this geometry. From this exact solution, the equivalent of a Westergaard stress potential is found and applied to the two other principal modes of fracture, which are plane elasticity problems. For a plate subject to uniform radial tension at infinity, an analytical solution is obtained that will reduce to the familiar mode I singular crack solution as the separation between the parallel faces of the slot becomes zero. For finite-width mode I slots, the rounded ends have tensile tractions which terminate at the adjoining flat surfaces of the slot, which remain traction-free. In this respect, the finite-width mode I slot problem resembles a Barenblatt cohesive zone model of a plane crack or a Dugdale plastic strip model of a plane crack, although the tractions will vary in magnitude along the slot ends rather than remaining uniform as in the former type of crack problems. Similarly, in the case of the finite-width mode II slot problem, the rounded ends of the slot have shear tractions, while the flat surfaces remain load-free. A distinguishing feature of the mode II slot solution over the mode I slot problem is that the maximum in-plane shear stress is constant along the rounded ends of the slot. Because of this, those particular regions of the boundary can represent incipient plastic yield based on either the Mises or Tresca yield condition under plane strain loading conditions. In this way, the problem resembles the plastic strip models of Dugdale, Cherepanov, Bilby-Cottrell-Swinden, and others. Notably, the mode III slot problem also has a constant maximum shear stress along the curved portions of the slot, while the entire slot boundary remains traction-free, unlike the mode II slot problem. Consequently, the mode III slot problem represents both a generalization of the standard mode III crack problem geometry, while simultaneously satisfying the boundary conditions of a plastic strip model.

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Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

Cited by 31 publications

References 46 publications

Stress distributions in bluntly-notched ceramic composite laminates

Stress distributions in bluntly-notched ceramic composite laminates

Plastic notch stress intensity factors for pointed V-notches under antiplane shear loading

Linear Elastic Solutions for Slotted Plates

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