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1

A dislocation density-based model for the work hardening and softening behaviors upon stress reversal

Lisiecka-Graca Paulina, Bzowski Krzysztof, Majta Janusz, Muszka Krzysztof

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 2

721--731

EN

The mechanical behaviours of microalloyed and low-carbon steels under strain reversal were modelled based on the average dislocation density taking into account its allocation between the cell walls and cell interiors. The proposed model reflects the effects of the dislocations displacement, generation of new dislocations and their annihilation during the metal-forming processes. The back stress is assumed as one of the internal variables. The value of the initial dislocation density was calculated using two different computational methods, i.e. the first one based on the dislocation density tensor and the second one based on the strain gradient model. The proposed methods of calculating the dislocation density were subjected to a comparative analysis. For the microstructural analysis, the high-resolution electron backscatter diffraction (EBSD) microscopy was utilized. The calculation results were compared with the results of forward/reverse torsion tests. As a result, good effectiveness of the applied computational methodology was demonstrated. Finally, the analysis of dislocation distributions as an effect of the strain path change was performed.

2

A minimal gradient-enhancement of the classical continuum theory of crystal plasticity. Part I: The hardening law

Petryk H., Stupkiewicz S.

Archives of Mechanics

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2016

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Vol. 68, nr 6

459--485

EN

A simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip is proposed for incorporating size effects in a manner consistent with phenomenological laws established in materials science. Despite considerable efforts in developing gradient theories, there is no consensus regarding the minimal set of physically based assumptions needed to capture the slip-gradient effects in metal single crystals and to provide a benchmark for more refined approaches. In order to make a step towards such a reference model, the concept of the tensorial density of geometrically necessary dislocations generated by slip-rate gradients is combined with a generalized form of the classical Taylor formula for the flow stress. In the governing equations in the rate form, the derived internal length scale is expressed through the current flow stress and standard parameters so that no further assumption is needed to define a characteristic length. It is shown that this internal length scale is directly related to the mean free path of dislocations and possesses physical interpretation which is frequently missing in other gradient-plasticity models.

3

A minimal gradient-enhancement of the classical continuum theory of crystal plasticity. Part II: Size effects

Stupkiewicz S., Petryk H.

Archives of Mechanics

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2016

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Vol. 68, nr 6

487--513

EN

In our previous paper, a simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip has been proposed for incorporating size effects. A single internal length scale has been derived as an explicit function of the flow stress defined as the isotropic part of critical resolved shear stresses. The present work is focused on verification whether the simplifications involved are not too severe and allow satisfactory predictions of size effects. The model has been implemented in a finite element code and applied to three-dimensional simulations of fcc single crystals. We have found that the experimentally observed indentation size effect in a Cu single crystal is captured correctly in spite of the absence of any adjustable length-scale parameter. The finite element treatment relies on introducing non-local slip rates that average and smoothen on an element scale the corresponding local quantities. Convergence of the finite element solution to the analytical one is also verified for the one-dimensional problem of a boundary layer formed at a constrained interface.

4

Components of energy storage rate during plastic deformation and their identification

Oliferuk W., Maj M.

Rudy i Metale Nieżelazne

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2009

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R. 54, nr 11

732-735

EN

The subject of the present paper is decomposition of energy storage rate into terms related to different mode of deformation. The stored energy is the change in internal energy due to plastic deformation determined after specimen unloading. Hence, this energy describes the state of the cold-worked material. Whereas, the ratio of the stored energy increment to the appropriate increment of plastic work is the measure of energy conversion process. This ratio is called the energy storage rate. Experimental results show that the energy storage rate is dependent on plastic strain. This dependence is influenced by different microscopic deformation mechanisms. It has been shown that the energy storage rate can be presented as a sum of particular components. Each of them is related to the separate internal microscopic mechanism. Two of the components are identified. One of them is the storage rate of statistically stored dislocation energy related to uniform deformation. Another one is connected with non-uniform deformation at the grain level. It is the storage rate of the long range stresses energy and geometrically necessary dislocation energy.

PL

Artykuł jest poświęcony rozkładowi zdolności magazynowania energii na składniki odpowiadające poszczególnym mechanizmom deformacji. Energia zmagazynowana stanowi przyrost energii wewnętrznej podczas odkształcenia plastycznego badanej próbki. Zatem opisuje on stan odkształconego materiału, podczas gdy stosunek przyrostu tej energii do odpowiadającego mu przyrostu pracy plastycznej jest miarą przemiany energii w procesie deformacji. Ów stosunek nazwano zdolnością magazynowania energii. Wykazano eksperymentalnie, że zdolność magazynowania energii jest funkcją odkształcenia plastycznego. Charakter tej funkcji określają mikroskopowe mechanizmy deformacji. W artykule pokazano, że zdolność magazynowania energii można przedstawić w postaci sumy poszczególnych jej składników. Każdy z nich odpowiada określonemu mikroskopowemu mechanizmowi lub określonemu modowi deformacji. Dwa tego typu składniki zidentyfikowano eksperymentalnie. Pierwszy z nich jest związany z generowaniem dyslokacji statystycznie zmagazynowanych i odpowiada odkształceniu jednorodnemu w skali ziarna, drugi - odkształceniu niejednorodnemu w tej skali i jest zdolnością magazynowania energii pola naprężeń dalekiego zasięgu i energii dyslokacji geometrycznie niezbędnych.