Strength of compact sample made of elastoplastic structured material

Machine-building Engineering and Machine Science


DOI: 10.34759/vst-2022-3-200-208

Аuthors

Astapov N. S.*, Kurguzov V. D.**

Lavrentiev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia

*e-mail: nika@hydro.nsc.ru
**e-mail: kurguzov@hydro.nsc.ru

Abstract

The strength of compact sample at normal separation (fracture mode I) was studied within the framework of the Neuber–Novozhilov approach. A model of ideal elastoplastic material with ultimate relative elongation was selected as a model of a deformable solid. This class of materials includes, for example, low-alloyed steels applied in the structures operating at temperatures below the cold brittleness threshold.

The crack propagation criterion is formulated with the modified Leonov–Panasyuk–Dugdale model, which employs an additional parameter, namely the plasticity zone diameter (the pre-fracture zone width). The two-parameter (twinned) criterion for the crack quasi-brittle fracture in the elastoplastic material was formulated under conditions of small-scale yielding with the presence of the stresses field singularity in the vicinity of the crack tip. This twinned fracture criterion includes the deformation criterion, formulated in the crack tip, as well as force criterion, formulated in the model crack tip. The lengths of the original and model cracks differ by the pre-fracture zone length.

Diagrams of quasi-brittle fracture of a sample under conditions of plane strain and plane stress are plotted. These diagrams consist of two curves, which divide the “crack length–stress” plane into three regions. The first region corresponds to the absence of fracture. In the second region, damages are being accumulated in the pre-fracture zone under the repeated loading. In the third region, the sample is being divided into parts under monotonic loading.

The constitutive equations of the analytical model are analyzed in detail depending on the characteristic linear size of the material structure. The authors obtained simple formulas suitable for verification calculations of the critical fracture loading and the length of the pre-fracture zone. The analysis of the parameters included in the proposed model of quasi-brittle fracture was performed. The authors propose model parameters selecting by approximation of the uniaxial tension diagram and stress intensity coefficient.

Keywords:

brittle and quasi-brittle fracture, double fracture criterion, elastoplastic material, mean diameter of a structured material grain, ultimate strain

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