Monotonic Paths Research Articles

変形経路変化下の加工硬化挙動と破断予測

The work-hardening behavior under strain path changes for dual phase (DP) steel has been investigated by using simple shear sequences, in comparison with that for interstitial free (IF) steel. The results show that a strong hardening followed by softening in an orthogonal path change, which is normally seen in IF steel, is not significant in DP steel. Based on these results, analytical approaches to predict forming limit strain and stress in monotonic and orthogonal paths by using Hill criterion have been conducted. It is known that stress based forming limit curves are path independent, while strain based forming limit curves are strongly path dependent. For IF steel, the localized necking is started just after the second loading in orthogonal sequence, which thus shows that even stress based forming limits are path dependent in IF steel. On the other hand, DP steel exhibits localized necking at the same amount of total strain both for monotonic and orthogonal paths and thus the stress based forming limits are path independent, which reflects differences in work-hardening under strain path changes in DP and IF steels. It might be pointed out that these differences are originated in the microstructural evolution of both steels.

Challenges to modelling heave in expansive soils

There are challenges associated with the numerical modelling of unsaturated expansive soils. The challenges are primarily related to the quantification of the void ratio constitutive surface, the characterization of the void ratio constitutive surface at low stresses and (or) suction, and the solution of coupled equations with several nonlinear unsaturated soil property functions. This study suggests that the void ratio constitutive surface of an expansive soil subject to a monotonic wetting path can be estimated from volume change indices obtained from conventional laboratory tests. The constitutive surfaces for both the soil structure and the water phase can be described using mathematical equations that allow net normal stress and suction to be reduced to zero. The solutions for two typical volume change problems are presented using both a coupled approach and an uncoupled approach. The first example problem simulates water leakage from a pipe under a flexible cover. The second example problem simulates the infiltration of water at ground surface. The results of the analyses are in accordance with anticipated behaviour. The results also show that the answers from an uncoupled analysis compared well with those from a coupled analysis. It is suggested that an uncoupled analysis may be adequate for most prediction of heave problems involving unsaturated expansive soils.Key words: heave prediction, numerical modelling, expansive soil, constitutive surface, uncoupled analysis, matric suction.

Population Monotonic Paths Schemes for Simple Games

A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player's payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. We show that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. Extensions of these results to other probabilistic values are discussed.

Prediction of crystallographic texture evolution and anisotropic stress–strain curves during large plastic strains in high purity α-titanium using a Taylor-type crystal plasticity model

A new Taylor-type polycrystalline model has been developed to simulate the evolution of crystallographic texture and the anisotropic stress–strain response during large plastic deformation of high purity α-titanium at room temperature. Crystallographic slip, deformation twinning and slip inside twinned regions were all considered as contributing mechanisms for the plastic strain in the model. This was accomplished by treating the dominant twin systems in a given crystal as independent grains once the total twin volume fraction in that crystal reached a predetermined saturation value. The newly formed grains were allowed to independently undergo further slip and the concomitant lattice rotation, but further twinning was prohibited. New descriptions have been established for slip and twin hardening and the complex coupling between them. Good predictions were obtained for the overall anisotropic stress–strain response and texture evolution in three different monotonic deformation paths on annealed, initially textured samples of high purity α-titanium.

Monotonic robust optimal control policies for the time-quality trade-offs in concurrent new product development (NPD)

Recent research suggests that new product specifications evolve during its realization. In this paper, we introduce a nonstationary Markovian model that supports the dynamic achievement of the new product definition without precedence constraints, taking into account both market and technological uncertainty. We use lattice programming techniques to prove the existence of a nondecreasing monotonic optimal policy. Thus, we enable a more efficient computation of optimal policies of the Markov decision process. We also prove that the monotonic optimal paths are robust to the variation of key-parameters as the solving rate of the design activities and the safety margin for achieving the new product at the deadline.

On the Transition from Instantaneous to Time-Lagged Capital Accumulation: The Case of Leontief-Type Production Functions

We formulate an optimal control capital accumulation model with a Leontief-type production function and an exogenously given time-lag between investment and the accumulation of the capital stock, to analyze the qualitative and quantitative influence of time-lags on the system dynamics. As known from the time-to-build literature, optimal investment paths for positive and finite time-lags are in general cyclical, in contrast to the monotonic optimal paths for instantaneous capital accumulation. We show that the transition between instantaneous and time-lagged capital accumulation is continuous, in the sense that the greater is the time-lag between investment and capital accumulation, the more likely and more pronounced becomes cyclical behavior of the optimal paths.

Application of a substructure-based hardening model to copper under loading path changes

In addition to texture, plastic anisotropy of a polycrystalline fcc metal stems from the directional nature of the dislocation substructure within individual grains. This produces the marked work hardening or softening observed immediately following load path changes. Following the framework of Peeters et al., in bcc steel, we develop a dislocation substructure evolution-based stage III hardening model for copper, capable of capturing the constitutive response under load path changes. The present model accounts for the more complicated substructure geometry in fcc metals than in bcc. Using an optimization algorithm, the parameters governing substructure evolution in the model are fit to experimental stress-strain curves obtained during compression along the three orthogonal directions in samples previously rolled to various reductions. These experiments approximate monotonic, reverse, and cross-load paths. With parameters suitably chosen, the substructure model, embedded into a self-consistent polycrystal plasticity model, is able to reproduce the measured flow stress response of copper during load path change experiments. The sensitivity of the parameters to the assumed substructure geometry and their uniqueness are also discussed.

FLAG UPNESS and its application for mapping seasonally wet to waterlogged soils

The UPNESS index derived from the Fuzzy Landscape Analysis Geographic information system (FLAG) model was calculated for the Wagga Wagga and Kyeamba Creek Catchments in NSW, Australia. The model uses digital elevation data only to derive UPNESS and several other indices of relative height in the landscape. UPNESS is an index of surface and subsurface water accumulation calculated as the set of cells above any given point in a raster grid that are connected by a continuous monotonic uphill path. Accumulation of groundwater causes increased secondary weathering, solubilisation of rock and soil minerals, and soil pedogenic development. In this paper the UPNESS index is compared with depth to a shallow water table and groundwater electrical conductivity (EC). Reasonable relationships with r2 = 0.71 and 0.74 were found between the UPNESS index and depth to watertable and groundwater EC, respectively, in the Wagga Wagga study area.UPNESS was then used to predict spatial extents of waterlogged to seasonally waterlogged, saline, and sodic soil landscapes within the Kyeamba Catchment, a larger catchment, with soil landscape mapping at a scale of 1:100 000. Most differences between UPNESS and soil landscape mapping occurred in broad valleys where deeply incised channels have caused UPNESS calculations to be more restricted to the stream lines than mapped boundaries. In valley-filled areas with little incision, the UPNESS index derived similar areas but with substantially more detail than the soil landscape mapping. The UPNESS index provides an efficient method to help differentiate seasonally and fully waterlogged, saline, or sodic soils from the drier soils in a catchment. This may aid in objectively establishing initial soil landscape boundaries with detail that would otherwise be too costly to obtain.

Optimization of the design ingenerating of composite plates under compression with analytic and experimental study

The aerospace structural components are inevitably subjected to high compression loads, which lead at most of times to the instability problems, by mean of buckling phenomenon. Thus, their buckling response studies must be given by renewed attention because of the intrinsic property obtained by a large number of parameters as well as the mechanical properties and geometrical one. The interaction/between non linearity of the material and of the geometry can lead in most of the times at a failure of the structure under compressive loads. In this survey we are dealing with the analytic resolution of the problem of plate bifurcation in submissive composites to a loading of simple or combined compression. In a first objective we go tried to give an evaluation of the critical bifurcation load of the considered plates. For sake of simplicity this survey is restrained to the case of the simply supported- four edge plates. In a second objective, an experimental study is used to validate the analytic one. We have analyzed the effect of variation in aspect ratio with a monotonic loading path, and the Bifurcation Load Factor, labeled is studied. Laminated plates of 200 mm width are used for this purpose under uni-axial compression. The comparative study of analytic and experimental results show a good agreement in many cases and a number of concluding remarks was obtained.

A modified Beremin model to simulate the warm pre-stress effect

Starting from the pioneering work of Beremin (Met. Trans. A 14A (1983) 2277), a modified Beremin model is proposed. As a result of temperature effect on mechanical fields heterogeneity at the micromechanical scale, an apparent temperature dependence of the macroscopic cleavage stress is first introduced to fit correctly the brittle to ductile transition. Then, the classical Beremin–Weibull fracture probability expression is extended to take account of non monotonic thermomechanical loadings. The modified Beremin model is applied to warm pre-stress (WPS) tests performed on low alloy ferritic steel compact tension specimens (see IAEA Specialists’ meeting, Rockville (2000)). Apart from ‘load–unload–cool–fracture’ (LUCF) cycles, for which additional investigations are needed, these simulations are in good agreement with experiments provided that an additional microcrack propagation condition is introduced, namely, necessary slip activity. This additional condition is consistent with the classical Beremin model restricted to monotonic loading paths.

A sand model with state-dapendent dilatancy

A comprehensive bounding surface sand model has been formulated within a critical-state framework. This model differs from some existing models in that it incorporates the concept of state-dependent dilatancy in its formulation. The concept of state-dependent dilatancy states that the dilatancy of a granular soil depends not only on the stress ratio η = q/p, where q and p are the deviatoric and mean effective normal stresses respectively, but also on the current material internal state in reference to the critical state in e–p–η space, where e is the void ratio. By adopting such a state-dependent dilatancy, the present model simulates, with a single set of model constants, both the contractive and the dilative responses of granular soils over a wide range of variations in stress and material internal states. The model is formulated in general three-dimensional stress-strain space, and works for both monotonic and cyclic loading paths, and under either drained or undrained conditions. The formulations and the underlying concepts are presented in this paper.

A sand model with state-dependent dilatancy

A comprehensive bounding surface sand model has been formulated within a critical-state framework. This model differs from some existing models in that it incorporates the concept of state-dependent dilatancy in its formulation. The concept of state-dependent dilatancy states that the dilatancy of a granular soil depends not only on the stress ratio η = q/p, where q and p are the deviatoric and mean effective normal stresses respectively, but also on the current material internal state in reference to the critical state in e–p–η space, where e is the void ratio. By adopting such a state-dependent dilatancy, the present model simulates, with a single set of model constants, both the contractive and the dilative responses of granular soils over a wide range of variations in stress and material internal states. The model is formulated in general three-dimensional stress-strain space, and works for both monotonic and cyclic loading paths, and under either drained or undrained conditions. The formulations and the underlying concepts are presented in this paper.

Overall softening and anisotropy related with the formation and evolution of dislocation cell structures

In this work, a model, based on a representation of the dislocation cell microstructures by a non-local two-phase material with evolving microstructures, is proposed for the elastic–plastic behavior of metals under monotonic and sequential loading. The first phase represents the cell interior and the second one, the cell walls. The evolution of the microstructure is taken into account considering the cell-wall interfaces as free boundaries. Finally, the accumulation within walls of dislocations crossing the cells defines a non-local hardening process. Assuming a piecewise uniform plastic strain field and assuming ellipsoidal cells, the free energy of the system is calculated. The driving and critical forces associated with the plastic flow of the two-phases and the morphology of the cells are established. In a third part, numerical results are presented for monotonic and sequential loading. The results show an overall softening related to the destabilization of the dislocation microstructures which occurs in sequential as well as monotonic paths.

Mesostructural approach of localization

In polycrystals, heterogeneities of plastic deformation have a strong impact on technological forming processes resulting in global softening, specific deformation texture and recrystallization. An experimental work was performed in a scanning electron microscope at the scale of the grain, focused on the formation of bands of localization during monotonic and sequential loadings in steel polycrystals. For monotonic loading, such experiments pointed out, an early localization of the strain field in parallel mesobands, few micrometers width, crossing grain boundaries. For sequential loading path, instabilities led to some macrobands composed of a set of mesobands. A crystalline model using a finite element code is proposed. This model gives a description of the microstructure evolution which mainly depends on the nature of the activated slip systems and on their interactions by a hardening matrix expressed in terms of dislocation densities. Due to the particular discretization of the sample based on an actual set of grains, the interactions between adjoining grains were emphasized. The strain localization predicted by this model, during monotonic and sequential loading paths, fits with the experimental observations. These results are compared to those obtained by a mechanical model based on the Asaro's criteria of bifurcation and a discussion on the weight of the different physical parameters acting on localization bands is conducted.

Stability of the market equilibrium in Romer's model of endogenous technological change: A complete characterization

Despite much interest in the dynamic behavior of endogenous growth models, the dynamics of probably the most influential endogenous growth model, Romer's celebrated model of Endogenous Technological Change, has not yet been fully analyzed. This gap in the literature is filled by the present paper. It is shown that a unique and monotonic growth path converges to the steady state. No indeterminacies can arise, as already shown by Benhabib, Perli and Xie. Instability and cyclical behavior are likewise ruled out—the equilibrium growth path is “well-behaved.”

Thermal and mechanical characterisation of films from Nylon 6/EVOH blends

Blown films from blends of dispersed ethylene-co-vinyl alcohol copolymer in a Nylon 6 matrix were characterised thermally and mechanically in humid laboratory conditions. Preliminary evaluations in terms of tensile tests revealed a non-equilibrium state for all the prepared Nylon 6/EVOH ratio based systems. Dynamic mechanical tests on films from blends appeared to indicate the occurrence of a single glass transition temperature ( T g) located between the T g of the two homopolymers. However the T g composition trend did not follow a monotonic path showing a maximum for EVOH contents close to 25% by weight. At this composition, the highest environmental ageing and the minimum of static tensile properties of blown films were also evident. Thermogravimetric analysis of all the investigated samples revealed an equilibrium water up-take close to 2% by weight with a maximum of 2.6% by weight for pure polyamide films.

Modeling temperature and strain rate history effects in OFHC Cu

Abstract In this paper, we report the modeling of a series of large strain deformation experiments on initially annealed OFHC Cu involving sequences of temperature, and strain rate (varying from quasi-static to dynamic). It is shown that equations-of-state with parameters determined using constant strain rate data from monotonic loading paths, although they employ instantaneous temperature and strain rate dependence, are insufficient to describe mechanical behavior. Macroscale internal state variable (ISV) viscoplasticity models, such as the Mechanical Threshold Stress (Follansbee, P.S., Kocks, U.F., 1988. A constitutive description of the deformation of copper based on the use of the mechanical threshold as an internal state variable. Acta Metall. 36, 81.) and BCJ–SNL (Bammann, D., Chiesa, M.L., Johnson, G.C., 1990a. A strain rate dependent flow surface model of plasticity. Sandia National Laboratory Report, SAND90-8227, Livermore, CA.) models, representative of a broad class of such models, are fit to the quasistatic isothermal and high strain rate (approximately adiabatic) data for compression and then predictions are compared to the experimental results for path sequence experiments. Implications for the representation of path history effects through the hardening, static and dynamic recovery functions are considered. A mesoscale polycrystal plasticity model with one and two slip system hardening variables is also examined in the context of sequence experiments.

Modeling of complex cyclic inelasticity in heterogeneous polycrystalline microstructure

Based on the crystallographic slip theory, a micromechanical model for polycrystal elasto–inelasticity is proposed and applied to describe the mechanical behavior of a such structure under monotonic and cyclic loading paths. Small strain theory and isotropic elasticity are assumed. Biaxial cyclic loading is of particular interest in proposed work. The kinematic hardening of the polycrystal is naturally obtained from the averaging scheme. In this scheme, we use a self-consistent interaction law. The proposed modeling effort is tested for a FCC metal under different loading situations in order to elucidate its capability. The obtained results show that this model reproduces appropriately the principle cyclic features such as Bauschinger effect, strain memory effect, ratcheting and additional hardening and other effects.

Principles of Three Phase Capillary Pressures

Abstract In porous media, there are a variety of configurations in which three immiscible fluids can be distributed within a single body. For example, the fluids may be distributed as concentric rings. Alternatively, two fluids may be dispersed as separate blobs within the third fluid. The configuration governs the mobility of each fluid, and under equilibrium conditions is dictated by the three phase capillary pressure of the system. If the capillary pressure is altered, the configuration will change. Capillary pressure can be altered by flow of any phase through the pore body. However, in a three phase system flow cannot be described as simply "drainage" or "imbibition." Rather, flow must be described as "drainage/drainage," "drainage/imbibition: or "imbibition/imbibition" to account for the change in saturation of all three phases. This paper elaborates on the issues governing three phase capillary pressures and presents some first experimental results on oil/water/gas capillary pressures in a drainage/drainage mode. Literature Review Three phase capillary pressure data were first presented in a ternary plot format by Leverett(1). Details of how the data were obtained were not discussed. Another effort to present quantitative information on three phase capillary pressure systems was recently initiated in the field of hydrology. Lenhard and Parker(2) developed an experimental apparatus to directly measure monotonic capillary pressure curves for water/oil/air systems in unconsolidated media. Treated ceramic disks were used to create semi-permeable membranes for the free flow of water and oil from different ports. Direct measurements of water and total liquid saturations in three phase systems as functions of oil/water and air/oil capillary heads, respectively, were compared to saturation-pressure measurements in two-phase air/oil and oil/water systems for monotonic drainage saturation paths. Excellent agreement was observed between total liquid saturations in an air/oil/water system and oil saturations in an air/oil system as functions of air/oil capillary head. Excellent agreement was also found between water saturations in air/oil/water and oil/water fluid systems versus oil/water capillary head. The concept of three phase capillary pressures in enhanced oil recovery was recently revisited by Kantzas et al.(3,4) and Chatzis et al.(5) Three phase interactions (water/oil/gas) were evaluated in the course of investigating gravity assisted immiscible gas injection (GAIGI). Three phase capillary interactions were studied visually in regular geometry pores, but were not quantified. This was done by Kalaydjian(6) who performed both drainage and imbibition capillary pressure measurements using a multi porous membrane apparatus. Clashach sandstone cores were used. Measurements showed that both drainage and imbibition curves are dependent on the three saturations. This conclusion contradicts the results of Leverett as well as the hydrology models presented earlier. Kalaydjian(6) and Kalaydjian and Tixier(7) demonstrated the effect of the spreading coefficient on drainage capillary pressures (gas/oil) in the presence of connate water. It was found that the residual oil saturation was lower in the case of positive spreading coefficient than in the case of a negative one. Except for the low saturation values, the capillary pressure was higher in the case of a positive spreading coefficient than in the case of a negative one.

Plastic Model for Concrete in Plane Stress State. II: Numerical Validation

A constitutive model for plain concrete proposed in Part I of this paper is comprehensively verified by a comparison of the model prediction obtained numerically with available experimental data for the plane stress state. At first, calibration of some model parameters is briefly discussed. Next, the model validation is made at the material point level for monotonic proportional load paths in the stress space covering all possible stress combinations, i.e., the compression-compression, compression-tension, and tension-tension regions. In the following, the postcritical behavior in uniaxial compression and tension is thoroughly studied. Next, the model prediction for cycling loadings is compared with experimental data, mostly for uniaxial compression and tension. Finally, two examples of structural computations of reinforced concrete (RC) deep beams for model implementation into an FEM code are presented. A good agreement with experimental data is found at the material point level. Also, the FEM computations render satisfactorily the actual behavior of RC deep beams.