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Distribution of crack-tip stresses during fatigue loading with an overload event: role of initial crack-tip shape, plastic compressibility and material softening

Pandey Satyabrat, Khan Debashis, Alam Intaf

Journal of Theoretical and Applied Mechanics

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2021

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Vol. 59 nr 2

239--250

EN

This paper deals with the influence of initial crack-tip shape, plastic compressibility and material or strain softening on near-tip stress-strain fields for mode I crack when subjected to fatigue loading with an overload event under plane strain and small scale yielding conditions. A finite strain elastic-viscoplastic constitutive equation with a hardening-softening- -hardening hardness function is taken up for simulation. For comparison, a bilinear hardening hardness function is also considered. It has been observed that the near-tip crack opening stress yy, crack growth stress xx, and hydrostatic stresses are noticeably controlled by the initial crack tip shape, plastic compressibility, material softening as well as the overload event. The distribution pattern of different stresses for a plastically compressible hardening- -softening-hardening solid appears to be very unusual and advantageous as compared to those of traditional materials. Therefore, the present numerical results may guide material scientists/engineers to understand the near-tip stress-strain fields and growth of a crack in a better way for plastically compressible solids, and thus may help to develop new materials with improved properties.

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Generalized thermal microstretch elastic solid with harmonic wave for mode-I crack problem

Lotfy Khaled, El-Bary Alaa Abd, Allan Mohamed, Ahmed Marwa H.

Archives of Thermodynamics

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2020

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Vol. 41, no 2

147--168

EN

A general model of the equations of generalized thermo-microstretch for an infinite space weakened by a finite linear opening mode-I crack is solved. Considered material is the homogeneous isotropic elastic half space. The crack is subjected to a prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, using mathematical analysis with the purview of the Lord-Şhulman (involving one relaxation time) and Green-Lindsay (includes two relaxation times) theories with respect to the classical dynamical coupled theory (CD). The harmonic wave method has been used to obtain the exact expression for normal displacement, normal stress force, coupled stresses, microstress and temperature distribution. Variations of the considered fields with the horizontal distance are explained graphically. A comparison is also made between the three theories and for different depths for the case of copper crystal.

3

Revisiting the Reflected Caustics Method : the Accurate Shape of the “Initial Curve”

Markides Ch. F., Kourkoulis S. K.

Engineering Transactions

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2013

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Vol. 61, iss. 4

265–-287

EN

The shape of the “initial curve”, i.e. the locus of material points, which if properly illuminated provide (under specific conditions) the “caustic curve”, is explored. Adopting the method of complex potentials improved formulae for the shape of the “initial curve” are obtained. Application of these formulae for two typical problems, i.e. the mode-I crack and the infinite plate with a finite circular hole under uniaxial tension, indicates that the “initial curve” is in fact not a circular locus. It is either an open curve or a closed contour, respectively, the actual shape of which depends also on the in-plane displacement field.