Staff

Abstract:
Intrinsic features (eigenproperties) of the Cauchy stress tensor are discussed. Novelty notions of isotropy and skewness mode angles are introduced for the improved parametric description of spherical (isotropic) and deviatoric (anisotropic) components of stress tensor. The skewness angle is defined with pure shear employed as a comparison reference mode upon observing that pure shear states can be interpreted as elementary (atomic) blocks of any macroscopic deviatoric stress state. An original statistical-physical interpretation of the stress tensor orthogonal invariants is provided. A micromechanical explanation for observed decrease of the stress tensor anisotropy factor values, measured in terms of the tensor orbit diameter, with stress deviator diverging from pure shear mode, is proposed. Explicit reasons explaining why biaxial experimental layouts (simple shear and/or planar shear) are insufficient for the comprehensive characterization of materials properties submitted to complex stress states loadings are presented. New explicit formulas for the triaxiality factor valid for biaxial stress states are delivered.

Keywords:
cauchy stress, oriented geometrical object, isotropy angle, skewness angle, isomorphic cylindrical coordinates, pure shear, comparison reference state, anisotropy factor, biaxial tests, simple shear, planar shear, triaxiality factor

Abstract:
Through an analysis of TAWS/FMS data collected and registered during the last minute of TU-154M aircraft flight fromWarsaw to Smolensk, we show the value and existence of space for undertaking research works on enhancing standard functionality of TAWS/FMS systems to enable their effective use in examination of the course and causes of air accidents. The flight ended up in the total destruction of the aircraft and the death of all passengers and crew on board. The TAWS/FMS flight altitudes and spatio-temporal data, i.e. geographical location and speed of the aircraft motion, were inspected for their internal and external consistency with the data from the ATM QAR service recorder. Using the data from ATM QAR, records from the cockpit voice recorder (CVR), jointly with data from the TAWS/FMS systems, it was possible to reconstruct the most probable horizontal and vertical trajectory of the TU-154M aircraft during the last minute of flight before its complete destruction, as well as the likely scenario of accompanying events. The data available from recorders enabled the authors to gain information on the preliminary stage of the course of accident, and the first phase of the aircraft’s destruction, resulting in serious damage of the left wing of the aircraft. Enhanced standard functionality of TAWS/FMS systems, incorporating use of their data in the post-accident situations examination, would have improved results and simplified the present analysis considerably.

Keywords:
TAWS system, aircraft accident examination, Polish TU-154M, Smolensk, abductive analysis, aircraft safety engineering, Q codes altitudes corrective formulas, ICAO atmosphere

Abstract:
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.

Keywords:
SMA, NiTi alloys, adaptive composite, macroscopic free energy functions, Gibbs energy, micromechanics, coherence energy, stored coherency energy, ultimate phase transformation eigenstrains, self-equilibrated eigenstrains influence moduli, SEIM, effective property estimates, martensitic phase transformation

Abstract:
The case study is analyzed of the catastrophe of Polish Air Force One, TU-154M aircraft on 10th of April 2010, near Smolensk North airfield, Russia. The catastrophe ended up in total destruction of the aircraft and death of all the passengers and crew on board. The results of the official investigations of the Russian Federation executed by the Interstate Aviation Committee and Poland executed by the Committee for Investigation of State Aviation Accidents are recalled, which found that the crash resulted due to pilot's errors. The evidence is presented showing faults in official examination proceedings and thus existence of grounds for possibility of drawing false conclusions. An academic investigation effort is undertaken to reconstruct the course of events during the last few seconds of flight of the TU-154M aircraft. The publicly available data, photographic evidence, and circumstantial information have been analyzed, which allowed pointing out a number of observations, which were not reliably explained by official reports scenarios. In view of that, execution of a new fully fledged repair investigation is recommended.

Keywords:
Air Force One, Polish TU-154M, Smolensk, aircraft crash, catastrophe, academic investigation, repair examination, abductive analysis, metallic fragments, airframe wreckage, blast, explosive damage, TAWS, aircraft safety engineering

Abstract:
In response to engineering needs of measuring moderate or large strains in metallic structures’ progress in resistance strain gages, technology resulted in widening the measurement range of this type of sensors to a range of 10–15%. For precision strain measurement applications, especially when a considerable number of measurement points are involved, single strain gage sensors are commonly used in quarter Wheatstone bridge configurations. Extension of measurement range to moderate strains requires taking into account inherent nonlinearities in signal transfer functions of the elements present in measurement chain. This work discusses in detail the most important ones, that is resistive gage sensor and quarter bridge measurement configuration nonlinearities to indicate that they are of the same order for moderate strains. Quite straightforward, shunt calibration procedure, taking into account these nonlinearities, is delivered or proposed enabling elimination of systematic errors. Thus, optimum accuracy of strain measurements matching the characteristics of components of strain measurement system can be conveniently achieved upon following simple steps. Inverse hyperbolic tangent—ϵLn =tanh−1(2 ∙e0/Eex)—linking scalar logarithmic strain and bridge reduced output voltage is shown to be a transfer function of strain measurement system with gage sensor in quarter bridge configuration for moderate or large strains.

Keywords:
Experimental Data Acquisition, Data Processing, Nonlinear Transfer Functions, Nonlinear Signal Conditioning, Experimental Strain/Stress Analysis, Accurate Finite Strain Measurements, Resistance Strain Gages, Nonlinear Sensors, Small/Technical Strain, Logarithmic/Natural Strain, Moderate Strains, Quarter Bridge Configuration, Wheatstone Bridge Circuits, Shunt Calibration, Scaling Amplifier Gain

Abstract:
Phenomenon of finite-disturbance buckling (FDB) is commonly attributed to thin elastic cylindrical and spherical shells and it has been rarely associated with columns. Ziolkowski and Imielowski's, Experimental Mechanics 51(8), (2011) 1335–1345, recent experimental study, revealing appearance of FDB in aluminum columns with slenderness remaining within specific range only, raises questions about its physical sources and mechanism. The main objective of the presented work is to provide a theoretical explanation and quantitative evaluation on the phenomenon of finite-disturbance buckling of columns undergoing elasto-plastic deformation and expressing itself in the form of critical load drop. Elucidation of the issue may have some implications to the hitherto design procedures. The paper presents a coherent analytical model of the phenomenon supported by comprehensive finite element results, compared with experimental data.

Keywords:
Column, Finite-disturbance buckling, Critical load drop, Inelastic buckling, Return point memory, Shanley's theory, Snap down

Abstract:
Differential Scanning Calorimetry (DSC) is discussed as a tool for characterization of Shape Memory Alloy (SMA) materials with the example of Ni51at%-Ti polycrystalline material. Some inconsistencies connected with the DSC analysis results present in the contemporary literature are indicated, for example large discrepancies in the registered heats of phase transition (PT.) or differences in registered heats of forward and reverse PT, especially in the case of multi-stage PT sequences. An attempt is undertaken to explain some of the discrepancies. The overall conclusion from the present work is that forward and reverse sensible heats of PT are equal, and discrepancies reported in the literature are artefacts. It is recommended that as a standard practice of DSC analysis of SMA materials not only characteristic temperatures but also sensible heat of PT should be reported, which can be done at practically no additional cost.

Keywords:
Nonequilibrium and irreversible thermodynamics, martensitic transformations, thermal analysis, Heat capacities and heats of phase transitions, Shape-memory effect, yield stress, superelasticity

Abstract:
The buckling and post-buckling behaviour of prismatic aluminium columns from stocky to very slender shapes is investigated. The unconventional, in terms of buckling tests, displacement control of compressive load and a series of loadings provided an enhanced insight into the buckling process. A phenomenon of buckling load drop has been detected in columns of intermediate slenderness, reaching over 20% of the load early critical value. This newly observed occurrence resembles finite disturbance instability, which until recently was commonly believed to only appear in cases of thin walled cylindrical shells, but not columns. The observation is in contradiction to predicted results from the elasto-plastic buckling models of Engesser or Shanley, with constant or growing values of load during the post-buckling process. Further tests on columns of intermediate slenderness, with strain gauges glued at node and anti-node locations of the buckled profiles, revealed that even minute buckling results in fields of highly non-symmetric residual microplastic strain. The results of the present study indicate that running column buckling tests under displacement control is worthy of being adopted as common practice. The envelope of column post-buckling states can be conveniently determined. This information will in turn allow for the quick and reliable estimation of the safety of a column, which has undergone accidental or deliberate damage in the form of limited buckling when under operational load.

Keywords:
Aluminium column instability, Finite disturbance buckling, Buckling load drop, Post-buckling, Micro plastic strains, Non-symmetric residual stresses, Column design criteria

Abstract:
The buckling phenomenon of prismatic column is experimentally investigated in this work, being major structural design concern. A number of tests were performed on aluminum made prismatic columns with slenderness index λ_ef remaining within range of 15 to 460 submitted to programs of multiple in time compressive loads – force and displacement controlled. The experimental evidence obtained here for stocky and slender columns confirm already well known information that column failure results from structural material plastic flow deformation or lateral buckling, respectively. A new, interesting observation has been made for intermediate slenderness columns that “drop” of buckling load takes place (reaching in some cases over 20% of early critical force value) after the very initiation of elasto-plastic buckling process. The observation is in contradiction to adopted in elasto-plastic buckling models assumption of constant (Engesser model) or growing (Shanley model) buckling load during buckling process. The obtained experimental evidence indicates that mysterious scatter in buckling loads for apparently identical columns with intermediate slenderness index can be attributed to minute residual stresses, which easily and in hardly controlled manner can be introduced during industrial production processes.

Abstract:
Presuming that the incremental free energy is invariant under a change of the Lagrangean finite strain measure and/or the reference configuration Hill’s transformation rules for the basic quantities occurring in mechanics of elastic–plastic solids are recasted in general 3D situation. On this background the invariant incremental plastic work is defined. The basic connections between Hill–Rice theoretical framework and Eckart–Mandel approach, involving the mobile stress-free configuration, are discussed both in generalized coordinates and in the tensorial notation. To this end the selected fundamentals of solid mechanics including the work-conjugacy are recalled. The structure of the updated Lagrangean plastic increment of the total strain is exhibited accounting for the deformation and stress effects due to possible damage and pressure sensitivity of a solid. Special simple approximate relations are derived for the situations when non-dilatational elastic strains are small. The merits of using the logarithmic elastic strain as a state variable are also discussed.

Abstract:
The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate d−e are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate d−in, describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.

Keywords:
Shape memory alloys, NiTi, Pseudoelasticity, Thermoelastic martensitic transformation, Thermodynamic SMA constitutive model, Finite deformations, Hyperelastic–hypoelastic equivalence, Bridging equation, Coupled thermomechanics

Abstract:
Taking for granted that the free energy function is invariant under a change of a finite strain measure and/or the reference configuration, Hill's transformation rules for selected fundamental constitutive quantities (such as tangent elastic modulus, plastic increments of total strain and work conjugate stress, the work of work-conjugate stress, the work expended in the plastic part of incremental strain etc.) are derived in a manner different from that of Hill. On this background distinguished by Hill [6] subtle aspects of invariance in mechanics of elastic plastic solids are discussed. It is shown that the plastic part of the increment of elastic strain energy (when taken with reverse sign) defines the true invariant incremental plastic work which in general is not equal to the work expended in the plastic part of the strain increment. It plays the role of a potential for the plastic part of the increment of work-conjugate stress. This fundamental fact has not found proper account in the literature. The analytical interrelations between two apparently different theoretical frameworks, Hill-Rice (fixed reference configuration) and Eckart-Mandel (mobile unloaded configuration) are discussed showing their equivalence. Since the transformation rules are complex in the general 3D case, the first part of the paper illustrates instructively the discussed aspects in a 1D situation (simple tension or simple extension).

Abstract:
The present work is directed at evaluation of the simple shear test for identification of constitutive behaviour of materials submitted to large deformations. For that purpose, actual experimental conditions together with theoretical background of the test are analyzed on the example of two hyperelastic material models. Advantages and disadvantages of various strain and stress measures used for presentation of simple shear test (SST) results are analyzed. The most often presented as the only result of „standard” SST proof chart, i.e. shear nominal stress -- shear nominal strain, characterizes the material energetically in the sense that it reveals its capacity for elastic energy storage. However, it characterizes the constitutive behaviour of the material only partially, since it is equivalent to shear II Piola Krichoff stress -- shear Green- Lagrange strain chart, within the large deformations context. This data alone does not even allow to reconstruct the shear Cauchy stress -- shear spatial Hencky strain chart for the tested material. In order to take full advantage of the constitutive information available from simple shear test, it is highly recommended to extend the experimental methodology of „standard” SST proof in such a way as to determine simultaneously two components (shear and normal) of nominal stress tensor in the same SST proof. Such experimental information allows for subsequent recalculation of non-symmetric nominal stress tensor components into Cauchy stress components.

Keywords:
simple shear, large deformations, hyperelasticity, identification of constitutive behaviour

Abstract:
W pracy wprowadzono podstawowe zależności teoretyczne umożliwiające poprawne opracowanie danych uzyskiwanych na drodze doświadczalnej w próbie prostego ścinania dla materiałów poddawanych dużym odkształceniom. Przedyskutowano uwarunkowania teoretyczno-doświadczalne próby, jak również wskazano pożądany kierunek dalszego jej udoskonalania.

Keywords:
proste ścinanie, duże odkształcenia, doświadczalne wyznaczanie własności materiałowych

Abstract:
W pracy podano ogólne za sady, metodologię, sposoby i narzędzia prowadzenia badań nieszczęśliwych zdarzeń. Wskazano rozbieżności pomiędzy dobrymi praktykami postępowania i faktycznie podjętymi/wykonanymi czynnościami śledczymi w przypadku badania katastrofy samolotu TU-154M w Smoleńsku. Uwagę skupiono na metalowych elementach wraku samolotu. Na podstawie publicznie dostępnych informacji sformułowano Hipotezę 1, że pierwotną techniczną przyczyną katastrofy TU-154M w Smoleńsku był wybuchy na pokładzie samolotu, gdy znajdował się on w powietrzu. Podano i zilustrowano graficznie cechy charakterystyczne elementów metalowych, które w sposób jednoznaczny pozwalają stwierdzić, że dany element uległ zniszczeniu na skutek wybuchu. Dokonano wstępnego przeglądu dostępnej dokumentacji zdjęciowej wraku samolotu TU-154M pod kątem występowania ww. cech charakterystycznych. Wskazano na kilka przypadków metalowych elementów wraku samolotu TU-154M ze zniekształceniami odpowiadającymi wzorcom zaklasyfikowanym jako typowe dla zniszczenia na skutek eksplozji/wybuchu. Dostarcza to przesłanek/dowodów przemawiających za prawdziwością Hipotezy 1.

Keywords:
Katastrofa Smoleńska badania eksperckie, metalowe elementy, wrak TU-154M, cechy charakterystyczne zniszczenia na skutek wybuchu