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1
Content available Mathematical foundations of limit criterion for anisotropic materials
Ostrowska-Maciejewska J., Szeptyński P., Pęcherski R. B.
Archives of Metallurgy and Materials
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2013
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Vol. 58, iss. 4
1223-1235
EN
In the paper a new proposition of limit state criteria for anisotropic solids exhibiting different strengths at tension and compression is presented. The proposition is based on the concept of energetically orthogonal decompositions of stress state introduced by Rychlewski. The concept of stress state dependent parameters describing the influence of certain stress modes on the total measure of material effort was firstly presented by Burzynski. The both concepts are reviewed in the paper. General formulation of a new limit criterion as well as its specification for certain elastic symmetries is given. It is compared with some of the other known limit criteria for anisotropic solids. General methodology of acquiring necessary data for the criterion specification is presented. The ideas of energetic and limit state orthogonality are discussed - their application in representation of the quadratic forms of energy and limit state criterion as a sum of square terms is shown.
PL
Artykuł przedstawia nową propozycję kryterium stanu granicznego dla anizotropowych ciał stałych wykazujących różną wytrzymałość przy rozciąganiu i ściskaniu. Propozycja ta opiera się na koncepcji energetycznie ortogonalnych rozkładów stanu naprężenia zaproponowanej przez Rychlewskiego. Pomysł wykorzystania zależnych od stanu naprężenia parametrów określających wpływ konkretnych form naprężenia na całkowitą miarę wytężenia materiału po raz pierwszy został przedstawiony przez Burzyńskiego. W pracy omówione są obydwie koncepcje. Przedstawione jest ogólne sformułowanie nowego warunku granicznego, jak również jego specyfikacja dla wybranych symetrii sprężystych. Kryterium to zostało porównane z niektórymi innymi spośród znanych kryteriów granicznych dla ciał anizotropowych. Przedstawiono ogólną metodologię pozyskiwania danych wymaganych do specyfikacji kryterium.
2
Content available remote Limit Condition for Anisotropic Materials with Asymmetric Elastic Range
Ostrowska-Maciejewska J., Pęcherski R. B., Szeptyński P.
Engineering Transactions
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2012
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Vol. 60, iss. 2
125-138
EN
In the paper a new proposition of an energy-based hypothesis of material effort is introduced. It is based on the concept of influence functions introduced by Burzyński and on the concept of decomposition of elastic energy density introduced by Rychlewski. A new proposition enables description of a wide class of linearly elastic materials of arbitrary symmetry exhibiting strength differential effect.
3
Content available remote Yield criterion accounting for the third invariant of stress tensor deviator. Part I. Proposition of the yield criterion based on the concept of influence functions
Nowak M., Ostrowska-Maciejewska J., Pęcherski R. B., Szeptyński P.
Engineering Transactions
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2011
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Vol. 59, iss. 4
273-281
EN
A proposition of an energy-based hypothesis of material effort for isotropic materials ex-hibiting strength-differential (SD) e?ect, pressure-sensitivity and Lode angle dependence is discussed. It is a special case of a general hypothesis proposed by the authors in [11] for anisotropic bodies, based on Burzyński’s concept of influence functions [2] and Rychlewski’s concept of elastic energy decomposition [16]. General condition of the convexity of the yield surface is introduced, and its derivation is given in the second part of the paper. Limit condition is specified for Inconel 718 alloy, referring to the experimental results published by Iyer and Lissenden [7].
4
Content available remote Review on spectral decomposition of hookes tensor for all symmetry groups of linear elastic material
Kowalczyk-Gajewska K., Ostrowska-Maciejewska J.
Engineering Transactions
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2009
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Vol. 57, iss. 3/4
145-183
EN
The spectral decomposition of elasticity tensor for all symmetry groups of a linearly elastic material is reviewed. In the paper it has been derived in non-standard way by imposing the symmetry conditions upon the orthogonal projectors instead of the stiffness tensor itself. The numbers of independent Kelvin moduli and stiffness distributors are provided. The corresponding representation of the elasticity tensor is specified.
5
Content available remote Podstawy zastosowania rachunku tensorowego (Wykład na Studiach Doktoranckich w IPPT PAN)
Ostrowska-Maciejewska J.
Prace Instytutu Podstawowych Problemów Techniki PAN
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2007
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nr 1
5-185
PL
Przedstawiony w tym opracowaniu materiał zawiera podstawy rachunku tensorowego w zakresie maksymalnie zbliżonym do potrzeb mechaniki ośrodków ciągłych. Układ materiału, jak również podane w nim informacje tworzą pewną całość i pozwalają uzyskać wiedzę z algebry i analizy tensorowe w zakresie niezbędnym do swobodnego studiowania mechaniki ośrodków ciągłych bez konieczności uzupełniania jej innymi źródłami. Zakres przedstawionego rachunku tensorowego jest ograniczony do potrzeb ze strony mechaniki ośrodków ciągłych. Przedstawiony w tym opracowaniu materiał stanowi systematyczne ujęcie wykładów z podstaw i zastosowania rachunku tensorowego, jakie od wielu lat prowadzone są przez autorkę w ramach Studium Doktoranckiego przy Instytucie Podstawowych Problemów Techniki PA>
6
Content available remote Modeling of crystallographic texture development in metals accounting for micro-shear bands
Kowalczyk-Gajewska K., Gambin W., Pęcherski R. B., Ostrowska-Maciejewska J.
Archives of Metallurgy and Materials
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2005
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Vol. 50, iss. 3
575-593
EN
The rigid-plastic model for the single grain is developed in which the velocity gradient is split into two parts connected with crystallographic slip and micro-shear bands respectively. For crystallographic slip the regularized Schmid law proposed by Gambin is used. For the micro-shear bands the framework with the function fMS that accounts for the contribution of this mechanism into the total plastic deformation described by Pecherski is applied. Different constitutive equations for the plastic spin due to two considered mechanisms of plastic deformation are used. The presented model is applied to simulate crystallographic texture evolution in the polycrystalline element.
PL
Opracowano sztywno-plastyczny model pojedynczego ziarna,w którym tensor gradientu prędkości został rozbity na dwie części związane odpowiednio z poślizgiem krystalograficznym i mikropasmami ścinania. Dla poślizgu krystalograficznego zastosowano regulryzowane prawo Schmida zaproponowane w pracy [8]. Dla mikropasm ścinania użyto formalizmu rozwiniętego w [18], gdzie uwzględnia się ich udział w przyroście deformacji plastycznej poprzez funkcje fMS. Zastosowane zostały różne równania konstytutywne dla części spinu plastycznego wywołanych rozważanymi dwoma mechanizmami deformacji plastycznej. Zaprezentowany model wykorzystano w symulacji rozwoju tekstury krystalograficznej w elemencie polikrystalicznym
7
Content available remote Energy-based limit criteria for anisotropic elastic materials with constraints
Kowalczyk-Gajewska K., Ostrowska-Maciejewska J.
Archives of Mechanics
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2005
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Vol. 57, nr 2-3
133--155
EN
The main aim of this paper is to investigate the influence of internal restrictions on the form of the energy-based limit condition. Some restrictions may be imposed in the elastic as well as in the limit states. Spectral decomposition of symmetric linear operators in a space with two different scalar products is applied. An algorithm for accounting for the considered restrictions in the limit condition is proposed. It was shown that as long as the energy scalar product is denned properly in the elastic range, the limit condition having the energy-based interpretation can be found. Examining the material with such an internal structure that there are stresses which do not cause any strain, the space with passive stresses and locked strains has to be introduced. The limit condition in this case has two parts, one connected with active part of stresses which has energy-based interpretation and the second one connected with passive stresses. The algorithm how to introduce this part of stresses to the limit condition has been proposed. As examples, the energy-based form of the Schmid law for single slip is derived and fiber-reinforced materials are analyzed.
8
Content available remote The influence of internal restrictions on the elastic properties of anisotropic materials
Kowalczyk-Gajewska K., Ostrowska-Maciejewska J.
Archives of Mechanics
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2004
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Vol. 56, nr 3
205-232
EN
The influence of internal restrictions on the elastic properties of anisotropic materials described by Hooke's law is discussed. Spectral decomposition of the stiffness tensor and the compliance tensor is applied. Possible types of restrictions imposed on the deformation modes are considered. An algorithm for accounting for these restrictions in a constitutive law that minimizes stiffening of the material is proposed. As examples, the volume-isotropic materials and fiber-reinforced materials are analyzed.
9
Content available remote An energy-based yield criterion for solids of cubic elasticity and orthotropic limit state
Kowalczyk K., Ostrowska-Maciejewska J., Pęcherski R. B.
Archives of Mechanics
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2003
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Vol. 55, nr 5-6
431-448
EN
The aim of the paper is to formulate a particular case of the J. Rychlewski yield condition for anisotropic linear elastic solids with Hooke's law and the limit tensor representing elastic range in the Mises yield condition under the assumption that different symmetry of elasticity tensors and the limit tensor appears. The elasticity tensor C is assumed to have cubic symmetry. The yield condition is based on the concept of stored elastic energy density, the theory of proper elastic states and energy orthogonal stress states developed by J. Rychlewski [1-3]. Three possible specifications of energy-based yield condition for cubic crystals are considered: the criterion based on the total distortion energy, the criterion based on the energy accumulated in the three proper states pertinent to cubic symmetry and the energy based criterion for cubic symmetry in elastic range and orthotropic symmetry in the limit state. Physical motivation, comparison with available experimental results and possible applications in mechanics of anisotropic solids as well as in nanomechanics are discussed.
10
Content available remote Energy-based limit conditions for transversally isotropic solids
Kowalczyk K., Ostrowska-Maciejewska J.
Archives of Mechanics
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2002
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Vol. 54, nr 5-6
497-523
EN
Using an example of transversal isotropy, the limit condition having an energy interpretation for anisotropic bodies proposed by J. Rychlewski [11] has been illustrated. Transversal isotropy is characterized by the highest degree of symmetry, for which the spherical tensor is not any more the eigenstate of the compliance tensor C. In the case when the spectral decomposition of the compliance tensor C is taken as a main energy-orthogonal decomposition, the limit condition representing a generalization of the Maxwell-Huber-Mises condition is obtained. For a prescribed form of the limit tensor H, the Mises condition is presented in the form of a sum of elastic energies corresponding to uniquely defined energy-orthogonal parts of stress with certain weights, representing the limiting values of those energies. The effect of Burzyński's condition on the form of anisotropy and on the limit condition is discussed. Experimental tests are proposed which could be useful in determining the physical parameters describing the transversal isotropy.
11
Energetyczne kryterium plastyczności dla monokryształów metali o sieci RSC.
Pęcherski R.B., Kowalczyk K., Ostrowska-Maciejewska J.
Rudy i Metale Nieżelazne
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2001
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R. 46, nr 12
639-644
PL
Celem pracy jest sformułowanie kryterium plastyczności dla monokryształów RSC, opartego na warunku granicznej wartości energii odkształcenia postaciowego, w połączeniu z krystalografią poślizgów plastycznych. Wyprowadzono równanie dla naprężenia zredukowanego z zastosowaniem hipotezy energii postaciowej. Porównano nowy warunek uplastycznienia z energetyczną postacią warunku kwadratowego Misesa oraz kryterium Schmida i zaproponowano testy jednoosiowego rozciągania monokryształu o różnej orientacji początkowej dla ich zweryfikowania.
EN
The aim of the paper is to formulate the yield criterion for FCC single crystals, based on the limit condition for the stored elastic energy of distortion, in relation to crystallography of plastic slip. The pertinent equation for stress intensity was derived. The new yield condition was compared with the elastic energy based formulation of the quadratic Mises criterion and Schmid condition. The appropriate tensile tests for a single crystal of different initial orientation were proposed to verify the discussed yield criteria.
12
Content available remote Generalized proper states for anisotropic elastic materials
Ostrowska-Maciejewska J., Rychlewski J.
Archives of Mechanics
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2001
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Vol. 53, nr 4-5
501-518
EN
The main aim of this paper is to determine all the unit stresses ... for which the stored elastic energy ... has the local extrema in some classes of stresses. Our consideration is restricted to two classes: K1 - uniaxial tensions and then the directions for which the Young modulus assumes its extremal value are determined, and K2 - pure shears in physical space. The problem is then reduced to the determination of the planes of minimal and maximal shear modulus. The idea of a generalized proper state for Hooke's tensor is introduced. It is shown that a mathematical treatment of the considered problem comes down to the problem of the generalized proper elastic states for the compliance tensor C. The problem has been effectively solved for cubic symmetry.
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