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1

Testing metals in tension and relaxation at elevated temperatures

Darrieulat M., Aoufi A., Desrayaud CH.

Archives of Mechanics

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2023

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Vol. 75, nr 1-2

75--106

EN

This article describes an apparatus for testing viscoplastic metallic alloys in tension at temperatures up to 400ºC. Its distinctive feature is a two-shelled furnace which encompasses the test-piece. The extensometer is attached to the shoulders of the specimen and remains outside the oven, so that it works at room temperature. The strain εrs in the reduced section inside the tight fitting oven is calculated with the help of a finite element software from the strain εext given by the extensometer. In the elastic range, the set-up was used for the measurement of Young’s moduli. In the plastic and viscoplastic ranges, it was used to draw work-hardening curves and to perform relaxation tests representative of in-service conditions. In this later case, a method to derive the strain rate sensitivity from the decrease with time of the registered stress is presented. The furnace can be easily machined in a mechanical workshop for all shapes and dimensions of test-pieces, so that it can be adapted to various studies of the workability of metallic alloys, especially those which necessitate a rapid rise and precise maintenance in temperature.

2

Microstructure of warm worked Zircalloy-4

Paul H., Darrieulat M., Vanderesse N., Lityńska L., Miszczyk M.

Archives of Metallurgy and Materials

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2010

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Vol. 55, iss. 4

1007-1019

EN

The microstructure of commercial purity Zircalloy-4 (Zry-4) compressed at temperatures 650°C and 750°C up to strains of 0.8 was characterized over a wide range of scales, using optical metallography, scanning (SEM) and transmission (TEM) electron microscopy. The typical microstructure after warm deformation consisted of the α-phase matrix and the second phase particles (SPP) enriched in Fe and Cr. Two kinds of these particles were observed. The large isolated SPP were situated along boundaries of lamellae of α-phase, whereas very fine intermetallic particles were nearly homogeneously distributed inside the lamellae. The intensity of recrystallization was main factor deciding on microstructure development in this material. The efficiency of that process increased quite rapidly with temperature or decreasing strain rate. The appearance of twins was the second important feature of the "warm deformed" structure with the prevailing {1102} - type system of twins. They were occasionally observed in all samples after the deformation at 650°C and 750°C temperatures.

PL

W pracy dokonano wieloskalowej charakterystyki mikrostruktury stopu Zircalloy-4 przerabianego plastycznie w zakresie pośrednich temperatur, tj. 650°C-750°C, w zakresie odkształceń logarytmicznych do 0.8, z wykorzystaniem technik mikroskopii optycznej oraz skaningowej i transmisyjnej mikroskopii elektronowej. W obrazie mikrostruktury obserwowano płytki fazy α oraz wydzielenia cząstek drugiej fazy wzbogaconoej w Fe oraz Cr. Obserwowano dwa typy wydzieleń. Duże izolowane cząstki usytuowane były wzdłuż granic płytek fazy α, podczas gdy wydzielenia dyspersyjne rozmieszczone były równomiernie w strukturze stopu. Głównym parametrem który decydował o zróżnicowaniu w strukturze stopu była intensywność zachodzenia procesu rekrystalizacji, która silnie uzależniona była od temperatury i prędkości odkształcenia. Drugim istotnym zjawiskiem obserwowanym po odkształceniu w obydwu temperaturach było pojawienie się obszarów zbliźniaczonych, przy czym dominował system zbliźniaczenia na płaszczyźnie {1102}.

3

Quantiative Analysis of Heterogeneties of Deformation with the Grid Method

Molimard J., Darrieulat M.

Archives of Metallurgy and Materials

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2009

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Vol. 54, iss. 1

7-17

EN

The article deals with the measurement of heterogeneous deformations during the plastic flow of metals. To encode de surface of the test-pieces, transferable carbon grids were used. They proved a reliable technique in the conditions of the experiments (channel-die, step of 100μm), even for highly localized deformations. To calculate the displacement field, the grid method was chosen. Up to now it has been developed for elastic structures. It is extended here to large displacement situations. Results are analysed from a metrological point of view and the resolution is kept at 1/100th fringe, the final spatial resolution being at two fringes. The mean deformation is 15% between each loading step. Displacement maps, or better, principle shear strain maps, derived from the previous ones, show the presence of a preferential direction even at low deformation levels. They put forward the decisive role played in the development of heterogeneities by the corners of the test-piece, sensitive in channel-die compression because two of their faces are submitted to friction while the third is free. This first attempt of using the grid method for large displacements will be optimized in the future by automating the iterative procedure and reducing the calculation time.

PL

Praca dotyczy pomiarów niejednorodnych odkształceń podczas plastycznego płynięcia metali. Na powierzchnie próbek naniesiono siatki weglowe; stwierdzono ich dobrą przyczepność w warunkach prowadzonego eksperymentu (nieswobodne ściskanie w kanaliku – channel die, krok równy 100μm) również dla silnie zlokalizowanych odkształceń. Metoda siatek została wybrana celem wyliczenia pola przemieszczen. Dotychczas ta metoda uzywana była tylko w przypadku struktur sprężystych. W pracy rozszerzono zastosowanie metody do przypadku dużych przemieszczeń. Rezultaty są analizowane z metrologicznego punktu widzenia a rozdzielczość metody utrzymuje się na poziomie 0,01 oczka, końcowa przestrzenna rozdzielczość osiąga dwa oczka. Średnie odkształcenie wynosi 15% między każdym krokiem obciążenia. Mapa przemieszczeń, albo inaczej, mapa głównych odkształceń postaciowych, wyznaczona z tej pierwszej, pokazuje obecność uprzywilejowanych kierunków również na poziomie małych odkształceń. Mapy wskazują na decydującą role naroży próbki w rozwoju niejednorodnosci, które są wrażliwe podczas nieswobodnego ściskania (channeldie), ponieważ dwie z trzech ścian próbki są poddane tarciu, a trzecia ściana jest swobodna. To pierwsze osiągniecie przy zastosowaniu metody siatek do dużych odkształceń zostanie zoptymalizowane w przyszłości dzięki zautomatyzowaniu procedury iteryzacji i zredukowaniu czasu obliczeń.

4

Biaxial extension of a plane single crystal

Merabet K., Chenaoui A., Sidoroff F., Darrieulat M.

Archives of Mechanics

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2008

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Vol. 60, nr 5

363-384

EN

This paper concerns the rigid-plastic modelisation of a f.c.c. single crystal, deforming by crystallographic slip, under large strain. Adopting the plane single crystal model, which corresponds to a true two-dimensional evolution of a real three-dimensional crystal, the activity of slip systems and the plastic indetermination, due to multiplicity of solutions, are studied according to the rate-independent Schmid law or the rate-dependent Bingham law. To promote a more general situation of potential multiple slip and therefore of potential indeterminacy, the biaxial loading is investigated. Based on this model and the Bingham slip law, the indeterminacy problem is surmounted, by adopting the geometrical analysis in the strain rate space and it is proved that the linear viscoplastic analysis is a new way of solving the indeterminacy problem.

5

Homogeneity and heterogeneity of single crystalsin channel-die compression; representation of the yield locus

Darrieulat M., Desrayaud Ch.

Archives of Metallurgy and Materials

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2005

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Vol. 50, iss. 1

101-109

EN

A polynomial approximation of the flow surface of single crystals deforming plastically on various slip systems is considered. Because it involves an exponent n, it is known as ‘the power law’. It is shown that, by introducing deviations from the Schmid law (but deviations not discernible by measurement), an extension of the normality rule can be proposed: not only the flow direction, but also the rate of rotation due to the glide on the slip systems are obtained in a single algebraic formula. The validity of all this is assessed by comparing its predictions with the results of the compression of single crystals in channel-die. The lateral reactions and the lattice rotations have been measured in typical rolling orientations and found in good agreement with the calculations.

PL

Przedmiotem pracy jest wielomianowa aproksymacja powierzchni płynięcia monokryształów odkształcanych plastycznie na różnych systemach poślizgu, która ze względu na występujący wykładnik n nazywana jest ‘prawem wykładniczym’. Pokazano, że wprowadzając mierzalne odchylenia od prawa Schmidta, można zaproponować pewne rozszerzenie reguły normalizacji: nie tylko kierunek płynięcia, ale także prędkość rotacji spowodowanej poślizgiem w danym systemie są uzyskane w pojedynczej formule algebraicznej. Zasadność tych spostrzeżeń oceniono poprzez porównanie odpowiednich wartości oczekiwanych z wynikami ściskania monokryształów w kanale kątowym.

6

Bifurcation into shear bands on the Bishop and Hill polyhedron. Part 3, Case of the edges of dimension one

Darrieulat M., Damamme G.

Archives of Mechanics

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2005

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Vol. 57, nr 5

387--404

EN

The present paper ends a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It presents the results on the edges of dimension 1 (encompassing the states of the deviatoric stress applied between two vertices of the Bishop and Mill polyhedron). They show that bifurcation is possible with a relatively small number of active slip systems, in conditions of strain hardening which are of the same order of magnitude as those at the vertices. An application is given to the case of the C {112} (111) oriented single crystal compressed in a channel die. The characteristic experimental feature: appearance of two successive sets of bands (111) [112] and (i 11) [112] is explained in terms of the most favoured bifurcation planes and the local rotation of the crystal. Though convincing to predict the onset of shear bands, the above calculations do not provide a description of their intergranular development, especially crossing of the grain boundaries, since at this stage the material has been too much affected by the intense shearing to be treated by a method of bifurcation.

7

Bifurcation into shear bands on the Bishop and Hill polyhedron. Pt. 1, General analysis

Darrieulat M., Chenaoui A.

Archives of Mechanics

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2004

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Vol. 56, nr 2

137-156

EN

Existence and uniqueness for the reflection-transmission process originated in a viscoelastic solid layer are investigated. Wave propagation is framed within the Fourier-transform domain and the oblique incidence is modelled by a factor involving a transverse wave vector. The backward-forward propagation in the axial direction is ascertained through the sign of an energy flux. Next, a connection is established between the energy flux and an Hermitian matrix whose eigenvalues are half positive and half negative. The proof is given that if the matrix has two diagonal blocks, one of which is positive definite and the other is negative definite, the solution to the reflection-transmission problem exists and is unique. The condition on the blocks is found to hold, e.g., for obliquely propagating homogeneous waves in anisotropic elasticity or normally propagating waves in isotropic viscoelasticity.

8

Bifurcation into shear bands on the Bishop and Hill polyhedron. Part 2, Case of the vertices

Darrieulat M., Chapelle D.

Archives of Mechanics

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2004

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Vol. 56, nr 6

465-484

EN

The present paper is the second of a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It focuses on the deformation at the vertices of the Bishop and Hill polyhedron, which are important because most of the shear bands originate at the grain boundaries where many slip systems are active. The conditions of bifurcation are analysed on the scale of the slip systems by crystallographic class of vertices. An application is given in the case of channel-die compression and it shows that the texture components are unequally liable to shear banding, the Copper one, for example, being more sensitive than Goss, as known experimentally. There is also a good agreement of the predictions with the geometry of the bands, especially the characteristic feature of the inclination at 35o with respect to the rolling axis. Considerations follow on the actual implementation, by micro-structural phenomena, of the localization whose mechanical possibility has been discussed in the article.

9

The plane single crystal under off-axis uniaxial tension

Chenaoui A., Sidoroff F., Darrieulat M., Hihi A.

Archives of Mechanics

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2002

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Vol. 54, nr 3

223-244

EN

The tensile behaviour of a rigid-plastic single crystal obeying Schmid's law with isotropic hardening is investigated for an off-axis tensile test in one of its symmetry planes (plane single crystal). Identification of the active slip systems allows the determination of the plastic spin and the resulting evolution of the crystallographic directions. This results in the description of the tensile behaviour-stress and strain response, onset of instability - depending upon the initial orientation of the crystal and the hardening law.