Some comments on the effect of biaxial stress on fatigue crack growth and fracture

The influence of biaxial loading on plastic zone size and crack opening displacement has been examined. Loading parallel to the crack plane was accounted for in satisfying the yield criteria, proposed by Von Mises, along the crack plane. Comparing plastic zone sizes for biaxial and uniaxial loading, when the applied stress normal to the crack plane is the same in both cases, shows a reduction of up to 65 per cent in plastic zone size for the biaxial loading case. The crack opening displacement is also reduced up to 33 per cent for biaxial loading. Based on critical crack opening displacement, fatigue crack propagation rates would be lower than for uniaxial loading, and an apparent increase in fracture toughness would also occur. The theoretical predictions are supported by a limited amount of experimental data.     

Non-linear viscoelasticity and viscoplasticity of isotactic polypropylene

Observations are reported in tensile tests with constant cross-head speeds (ranging from 5 to 200 mm/min), relaxation tests (at strains from 0.02 to 0.08), creep tests (at stresses from 15.0 to 25.0 MPa) and recovery tests (after straining up to the maximal strains ranging from 0.04 to 0.12 and subsequent retraction) on isotactic polypropylene at room temperature. A constitutive model is derived for the time- and rate-dependent responses of a semicrystalline polymer at isothermal deformation with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical cross-links and lamellar blocks). The network is thought of as an ensemble of meso-regions linked with each other. The viscoelastic behavior of the ensemble reflects thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). To describe the viscoplastic response, the entire plastic deformation is split into the sum of two components: one of them is associated with sliding of junctions in the non-affine network of chains, while the other accounts for coarse slip and fragmentation of lamellar blocks. Stress–strain relations and kinetic equations for the plastic strains are developed by using the laws of thermodynamics. The constitutive equations involve five material constants that are found by fitting the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.     

Value-at-risk and data envelopment analysis: comments on Wu and Olson (2010)

In this note, we identify three major errors contained in Wu and Olson [Wu, D.D. and Olson, D., 2010. Enterprise risk management: a DEA VaR approach in vendor selection. International Journal of Production Research, 48 (16), 4919–4932]. It is shown that the ‘DEA VaR’ model named by the authors is not truly a Value-at-risk (VaR) minimisation problem. It is also pointed out that the authors confused two concepts of stochastic efficiency. Finally, it is revealed that the linearisation technique proposed by the authors is questionable under some conditions and a correction is suggested.     

A theory of viscoplasticity based on infinitesimal total strain

Summary A viscoplasticity theory based upon a nonlinear viscoelastic solid, linear in the rates of the strain and stress tensors but nonlinear in the stress tensor and the infinitesimal strain tensor, is being investigated for isothermal, homogeneous motions. A general anisotropic form and a specific isotropic formulation are proposed. A yield condition is not part of the theory and the transition from linear (elastic) to nonlinear (inelastic) behavior is continuous. Only total strains are used and the constant volume hypothesis is not employed. In this paper Poisson's ratio is assumed to be constant. The proposed equation can represent: initial linear elastic behavior; initial elastic response in torsion (tension) after arbitrary prestrain (prestress) in tension (torsion); linear elastic behavior for pure hydrostatic loading; initial elastic slope upon large instantaneous changes in strain rate; stress (strain)-rate sensitivity; creep and relaxation; defined behavior in the limit of very slow and very fast loading. Stress-strain curves obtained at different loading rates will ultimately have the same slope and their spacing is nonlinearly related to the loading rate.The above properties of the equation are obtained by qualitative arguments based on the characteristics of the solutions of the resulting nonlinear first-order differential equations. In some instances numerical examples are given.For metals and isotropy we propose a simple equation whose coefficient functions can be determined from a tensile test [Eqs. (31), (35), (37), (38)]. Specializations suitable for materials other than metals are possible.The paper shows that this nonlinear viscoelastic model can represent essential features of metal deformation behavior and reaffirms our previous assertion that metal deformation is basically rate-dependent and can be represented by piecewise nonlinear viscoelasticity. For cyclic loading the proposed model must be modified to account for history dependence in the sense of plasticity.

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Eine viskoplastische Theorie für infinitesimale totale Verzerrungen

Zusammenfassung Eine viskoplastische Theorie für nichtlineare viskoelastische Festkörper, linear in den Geschwindigkeiten des Verzerrungs- und Spannungstensors jedoch nichtlinear im Spannungstensor und dem infinitesimalen Verzerrungstensor, wird für isotherme, homogene Bewegungen betrachtet. Eine allgemeine, anisotrope Form und eine spezifisch isotrope Formulierung werden vorgeschlagen. Eine Fließbedingung ist in der Theorie nicht enthalten und der Übergang von linearem (elastischem) zu nichtlinearem (inelastischem) Verhalten ist kontinuierlich. Nur totale Verzerrungen werden verwendet; die Hypothese der Volumenkonstanz wird nicht herangezogen. Die Poisson-Zahl wird als konstant vorausgesetzt. Die vorgeschlagene Gleichung kann repräsentieren: Anfänglich linear elastisches Verhalten; anfänglich elastisches Verhalten für Torsion (Zug) nach beliebiger Vorverzerrung (Vorspannung) durch Zug (Torsion); linear elastisches Verhalten für rein hydrostatische Belastung; anfänglich elastischer Anstieg nach sprunghaften Wechseln in der Verzerrungsgeschwindigkeit; Spannungs- (Verzerrungs-) Geschwindigkeitsempfindlichkeit; Kriechen und Relaxation; definiertes Verhalten im Grenzbereich von sehr langsamer und sehr schneller Belastung. Spannungs-Verzerrungskurven zufolge unterschiedlicher Belastungsgeschwindigkeiten erreichen denselben Anstieg und ihr Abstand hängt nichtlinear von der Belastungsgeschwindigkeit ab.Die obigen Eigenschaften der Gleichungen werden durch qualitative Argumente für die Charakteristiken der Lösungen von nichtlinearen Differentialgleichungen erster Ordnung erhalten. In einigen Fällen werden numerische Beispiele angegeben.Für isotrope, metallische Werkstoffe wird eine einfache Gleichung vorgeschlagen, deren Koeffizientenfunktionen aus einem Zugversuch bestimmt werden können. [Gln. (31), (35), (37), (38)]. Spezialisierungen für andere Materialien sind möglich.Die Arbeit zeigt, daß dieses nichtlineare viskoelastische Modell wesentliche Merkmale des Metalldeformationsverhaltens beschreiben kann und unterstreicht die frühere Behauptung, daß die Metalldeformation im wesentlichen geschwindigkeitsabhängig ist und durch abschnittsweise nichtlineare Viskoelastizität dargestellt werden kann. Für zyklische Belastung muß das vorgeschlagene Modell modifiziert werden, um die history dependence in the sense of plasticity wiedergeben zu können.

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With 5 Figures     

Phase equilibrium,microstructure and properties of some magnesite-chromite refractories

The effect of phase equilibrium and microstructure of magnesite-chromite batches containing from 0 to 100% Egyptian chrome ore, with intervals of 10%, on their physical properties was studied. The phase equilibrium data were calculated using the phase relationships within the system M-M₂S-CMS-MR (M=MgO, S=SiO₂, C=CaO, R=R₂O₃). A computerized electron-probe microanalyser was applied to study the microstructure as well as microchemistry of the fired magnesite-chromite co-clinkers. Some physical and technological properties of the co-clinkered briquettes were also investigated by determining densification parameters, spalling resistance and load-bearing capacity.It is concluded that dense, spalling resistant and refractory magnesite, magnesite-chrome and chrome-magnesite refractories could be produced by co-clinkering of magnesite-chromite batches of 1000, 7030 and 3070 weight ratios, respectively, at 1600 °C. The prepared co-clinkers were subsequently graded, moulded and refired up to 1700 °C in order to obtain direct-bonded bricks. Meanwhile, dense chromite refractories with lower refractory quality could be processed by firing the Egyptian chrome ore up to 1600 °C.     

Discussing some basic critique on Journal Impact Factors: revision of earlier comments

In this study the issue of the validity of the argument against the applied length of citation windows in Journal Impact Factors calculations is critically re-analyzed. While previous studies argued against the relatively short citation window of 1–2 years, this study shows that the relative short term citation impact measured in the window underlying the Journal Impact Factor is a good predictor of the citation impact of the journals in the next years to come. Possible exceptions to this observation relate to journals with relatively low numbers of publications, and the citation impact related to publications in the year of publication. The study focuses on five Journal Subject Categories from the science and social sciences, on normal articles published in these journals, in the 2 years 2000 and 2004.     

A total ALE FE formulation for axisymmetric and torsional problems (including viscoplasticity,thermodynamic coupling and dynamics)

This paper—first—extends a recent ‘assumed enhanced deformation gradient’ finite ring(segment) element (Int. J. Numer. Methods Eng. 2001; 50 :899–918.) to Arbitary Lagrange Euler (ALE) computations, by setting up the assumed tensor on the computational configuration, and—second—shows an elegant way of incorporating dynamics into real ALE computations (no splitting into purely—Lagrange steps and then—remeshing steps), by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of annealing on viscoplasticity of polymer blends: Experiments and modeling

Observations are reported on polypropylene/polyethylene blends with various concentrations of components in uniaxial tensile tests at ambient temperature. Three types of blends are analyzed: (i) non-annealed, (ii) annealed below the melting temperature of polyethylene, and (iii) subjected to thermal treatment above this temperature. A constitutive model is developed for the viscoplastic behavior of polymer blends that treats a semicrystalline polymer as a two-phase composite medium. The stress–strain relations involve four adjustable parameters that are found by fitting the observations. The model is applied to examine the effect of annealing on elastic moduli of amorphous and crystalline phases.     

Some comments on the Arcan mixed-mode (I/II) test specimen

Although the Arcan specimen has been used frequently for mixed-mode crack growth testing using single-axis servohydraulic test equipment, the specimen and its commonly-used fixturing have features and behaviors that have implications to the proper understanding of results garnered from their use. These implications extend to hardware issues as well, as the Arcan specimen (when mounted at off-axis angles) can generate significant and even potentially damaging side loads on the load frame actuator. This paper discusses a number of the issues associated with the Arcan specimen and Arcan testing.     

A stability analysis of the uniaxial viscoplasticity theory based on overstress

In the development of a viscoplasticity theory without a yield surface and without a loading and unloading condition, the properties of a uniaxial constitutive model consisting of two coupled nonlinear differential equations are examined. The critical points of the system of differential equations are evaluated for monotonic loading, creep and relaxation conditions and are shown to be stable. The conditions necessary for the elimination of stable but oscillatory solutions are given. Also given are the asymptotic solutions valid near the critical points. The analytical predictions are confirmed by numerical results.     

Adsorption of Pb(II) and Pb(II)-citric acid on sawdust activated carbon: Kinetic and equilibrium isotherm studies

The removal of Pb(II) and Pb(II)-citric acid (Pb(II)-CA) from aqueous solutions by sawdust activated carbon (SDAC) was investigated. The higher adsorptive removal of Pb(II) from aqueous solutions containing Pb(II)-CA than Pb(II) only was observed due to the presence of CA in the former system. The mechanism of adsorption process was studied by conducting pH as well as kinetic studies. Batch adsorption experiments were conducted to study the effect of adsorbent dose, initial concentration and temperature for the removal of Pb(II) from Pb(II) only and Pb(II)-CA aqueous systems. The adsorption was maximum for the initial pH in the range of 6.5-8.0 and 2.0-5.0 for Pb(II) and Pb(II)-CA, respectively. The solution pH, zero point charge (pH(zpc)) and species distribution of Pb(II) and Pb(II)-CA were found to play an important role in the adsorption of Pb(II) and Pb(II)-CA onto SDAC from water and wastewaters. SDAC exhibited very high adsorption potential for Pb(II) ions in presence of CA than when Pb(II) ions alone were present. The kinetic and equilibrium adsorption data were well modeled using pseudo-first-order kinetics and Langmuir isotherm model, respectively.     

软丁腈橡胶(N41)新型平衡硫化体系研究

通过对配合体系的探究,构建以硫载体二硫化二己内酰胺(DTDC)、硫化促进剂、硅烷偶联剂及硫磺为主体的新型平衡硫化体系;软丁腈橡胶(N41)应用这种新型的平衡硫化体系,拉伸强度最好可达29MPa,断裂伸长率超过500%,通过改变促进剂、硫磺和DTDC用量,分析各项物理机械性能,比较不同硫化体系下的动态性能,探究这种平衡硫化体系在软丁腈橡胶中的应用。