Determination of plastic stress-strain behavior by digital-image-processing techniques

This work explores the application of digitalimage-processing techniques to the measurement of large plastic strains. Two sample problems have been selected, namely the uniform tensile deformation of aluminum-sheet metal strips and the post-necking deformation of copper circular rods. Images of these gridded metallic test pleces were captured, digitized and analyzed in a fully computerized way to evaluate strain distributions, anisotropic parameters and plastic stress-strain flow curves. For post-necked test pieces, Bridgman stress correction has been easily applied by defining the neck profile contour from the automated processing of digitized images. Results compare satisfactorily with those based on displacements measured by conventional microscopy. The presented technique, with added improvements, can consititute a viable one for accurate and fully computerized measurement of large deformations.     

General stress-strain relations in non-linear theory of viscoelasticity for large deformations

Conclusion General phenomenoligical stress-strain relations in non-linear theory of visco-elasticity for large deformations have been presented.In the first place, according to V. V. Novozhilov 1 we express the generalized equilibrium equation for large deformations in the Lagrange representation, and we apply the generalized Hamilton's principle to the equation of energy conservation, which denotes that the sum of the elastic energy and the dissipative energy is equal to the work done by the body force and the surface on the substance; so that we obtain the required general stress-strain relations in comparison with the above two equations.On the condition that the elastic potential is a function only of the strain, and the dissipation function is a function of the rate of strain and of strain; such a substance is reduced to the Voigt material necessarily, and the stresses which act on the substance are given by the sum of elastic- and viscous stresses, and the stress-strain relations are reduced to the so-called Lagrangian form.If elongations, shears and angles of rotation are small and also the strains and rates of strain are sufficiently small, the stress-strain relations are expressed by a linear Voigt model constituting a Hookian spring in parallel with a Newtonian dashpot.Non-linearity in the theory is classified into two groups i. e. the geometrical non-linearity and the physical non-linearity. The former is introduced into the theory through the definition of the generalized strain and of the generalized stress and through the equilibrium equation for large deformation, and the latter through the general stress-strain relations.The main result of this paper is that the general stress-strain relations in viscoelasticity are deduced necessarily from the physically appropriate assumptions.     

Fracture data and stress-strain behavior of rocks in triaxial compression

Test results are reported for a recently completed experimental research program on rocks subjected to triaxial compression. Sandstone, marble, granite and shale specimens were tested at confining pressures as high as 90,000 psi corresponding to mean stresses of up to 143,000 psi. Recognizing that the largest potential experimental error in such tests results from making strain and load measurements external to the vessel, special load and strain-measuring devices were designed and fabricated for use inside the pressure vessel. The specimens were carefully machined cylinders with length-to-diameter ratios of two and with diameters ranging from 4/16 in. to 1 in. The confining pressure was held constant during each run, but varied from 0 to 90,000 psi over the tests. Results are reported in the form of:

1. Stress-strain curves for individual specimens
2. Maximum shear stress at fracture vs. mean-stress curves for each rock type tested
3. Tabulation of results for 59 specimens

A number of tests were run on granite specimens which had been previously fractured. Results from these tests showed good agreement with tests on intact granite, providing the confining pressure was above 30,000 psi.     

Liquid–crystalline nematic polymers revisited

A new model for nematic polymers is proposed, based on the probability ψ(u,u,t) for a macromolecule to be oriented along direction u while embedded in a u environment created by its neighbours. The potential of the internal forces is written Φ(u,u) accordingly. The free energy contains a contribution ν Φ + k_BT ln ψ where the brackets mean an average over the probability distribution, while ν is the (uniform) polymer number density. An equation is derived for the time-evolution of the order parameter S = uu − I/3, together with an expression for the stress tensor. These two results offer a generalization of the Doi Model in so far as they include a distortional energy, analogue to the Frank elastic energy for low molecular mass nematics. Extending the Maier–Saupe variational procedure, we specify the way that the internal potential Φ(u,u) must be written for it to favour non-zero values of the order parameter, while giving a penalty to situations with gradients of the order parameter. The result is quite different from the potential proposed a decade ago by Marrucci and Greco (their Φ depends on u only), while it has a clear connection with the so-called Landau-de Gennes (LdG) tensor models, which are based on a free-energy depending on the order parameter and its gradients.     

Dynamic rheology of the immiscible blends of liquid crystalline polymers and flexible chain polymers

Immiscible blends containing liquid crystalline polymers (LCP) as dispersed phases show different dynamic rheological properties than those composed of flexible polymers. The widely used Palierne’s model was shown by many authors to be insufficient to describe the frequency dependence of dynamic modulus of such blends. A new model was presented to describe the dynamic rheology of the immiscible blend containing LCP as a dispersed phase. The flexible chain polymer matrix was assumed to be a linear viscoelastic material under small amplitude oscillatory shear flow, and the LCP was assumed to be an Ericksen’s transversely isotropic fluid. The Rapini-Papoular equation of anisotropic interfacial energy was used to account for the effect of nematic orientation on the interfacial tension. It was found that the orientation of the director and the anchoring energy greatly influenced the storage modulus at the “shoulder” regime. The overall dynamic modulus of the blend can be well described by the model with suitable choice of the orientation of the director and anchoring energy of LCP.     

A constitutive equation of elastic-visco-plasticity for polymers

The rheological behavior and a constitutive relationship of elastic-visco-plasticity for polymers are investigated in this paper. Several sets of experiments have been carried out to determine the material constants and to test the validity of constitutive formulation. It is shown that the theoretical profiles are in good agreement with experimental results. The rheological characteristic and the strain-rate effect of model are analyzed by computer simulation.The project is supported by the National Natural Science Foundation of China     

Characterization of hysteretic stress-strain behavior using the integrated Preisach density

In this paper, we introduce the concept of Integrated Preisach-Mayergoyz (IPM) density to analyze static uniaxial compression tests at values well below the critical strength, and to characterize the elasticity of materials with hysteresis in their stress-strain relationship. The IPM density can be deduced from a particular force protocol following basic data treatment. The advantage of the IPM density over prior approaches is that no second order differentiation of the data is required which reduces the errors and uncertainties typical for past practice in the specific context of rock elasticity using scanning curves and PM density analysis. The characterization of the elasticity of the material is established in terms of a non-hysteretic strain contribution in the form of a non-linear but reversible equation of state, and a hysteretic contribution represented by the IPM density. The IPM inversion procedure is tested for simulated stress-strain data subjected to additive noise, and the results are compared to the traditional methodology. In addition, we analyze the hysteretic and non-hysteretic characteristics of five natural building stones, and show evidence for a classification based on the inferred properties.     

Molecular orientation in channel flows of main-chain thermotropic liquid crystalline polymers

 In situ wide angle X-ray scattering is employed for quantitative measurements of flow-induced molecular orientation in channel flows of thermotropic hydroxypropyl-cellulose (HPC). An extrusion die, constructed to allow X-ray access, generates slit flow, slit flow with superimposed contractions and expansions in cross-section, and slit flow past an obstruction. In slit flow, weak molecular orientation develops slowly with downstream position. Superimposed extension associated with contraction flows leads to a strong enhancement in orientation, which persists with distance further downstream of the contraction. Conversely, transverse extension present in expansion flows generates a bimodal orientation state and substantial reductions in average molecular orientation. These results are compared to earlier measurements on a commercial fully aromatic thermotrope. HPC is found to respond more strongly to superimposed extension, and more weakly to the prevailing inhomogeneous shear flow than the commercial material. Received: 22 October 1999/Accepted: 13 January 2000     

Mechanical behavior of amorphous polymers in shear

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “ viscous dissipation induced“ anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G‘ Sell et al. , thus the validity of the proposed model is verified.     

Pressure-driven startup flows of liquid crystalline polymers through slit cells

A wavy texture occurs in the flows of liquid crystalline polymers through a slit cell. In the present paper the development of the wavy texture is examined in pressure-driven startup flows for four types of slit cells, using a liquid crystalline solution of 50 wt% hydroxypropylcellulose (HPC). There exists a comparatively long induction period until the wavy texture appears after the startup of the flow, and the induction time decreases with increasing apparent shear rate. However, it is found that the apparent shear strain at which the wavy texture emerges is independent of the apparent shear rate though the value of the apparent shear strain slightly varies with the type of flow cell. Furthermore, the light scattering experiments are carried out to examine the structure of wavy texture. After the startup of the flow, a homogeneous pattern of the light scattering quickly shrink in size and a spike pattern perpendicular to the flow direction is emphasized. While the wavy texture is seen, the ellipsoidal pattern of light scattering oscillates with the same frequency as the passage of the wavy texture. A structure of scattering objects in the wavy texture is proposed, based on the observation of change in the light scattering pattern with time.     

The strain-rate behavior of ductile polymers

The stress-strain-strain-rate behavior of polycarbonate is presented. It is demonstrated that the material does not exhibit a double-yield-point phenomenon, as others have reported, if true stress is plotted against actual strain. Also, the behavior of polycarbonate is presented under constant strain rate and relaxation conditions. The observed behavior of the material is discussed in relation to elements of recent theories of viscoelasto-plasticity due to Nagdi and Murch and Crochet. Simple mechanical models of the Bingham type are presented and are discussed with respect to the constitutive equation characterization of polycarbonte. The advantages and disadvantages of more general models are mentioned. Finally, the strain-rate behavior of PMMA (Polymethylmethacrylate) and a poylester given by others is presented and discussed, relative to polycarbonate and the characterization procedures used.     

Orientation dynamics in commercial thermotropic liquid crystalline polymers in transient shear flows

In situ X-ray scattering measurements of molecular orientation under shear are reported for two commercial thermotropic liquid crystalline polymers (TLCPs), Vectra A950® and Vectra B950®. Transient shear flow protocols (reversals, step changes, and flow cessation) are used to investigate the underlying director dynamics. Synchrotron X-ray scattering in conjunction with a high-speed area detector provides sufficient time resolution to limit the total time spent in the melt during testing, whereas a redesigned X-ray capable shear cell provides a more robust platform for working with TLCP melts at high temperatures. The transient orientation response upon flow inception or flow reversal does not provide definitive signatures of either tumbling or shear alignment. However, the observation of clear transient responses to step increases or step decreases in shear rate contrasts with expectations and experience with shear-aligning nematics and suggests that these polymers are of the tumbling class. Finally, these two polymers show opposite trends in orientation following flow cessation, which appears to correlate with the evolution of dynamic modulus during relaxation. Specifically, Vectra B shows an increase in orientation upon flow cessation, an observation that can only be rationalized by the assumption of tumbling dynamics in shear. Together with prior observations of commercial LCP melts in channel flows, these results suggest that this class of materials, as a rule, exhibits director tumbling.     

Orthogonal and parallel superposition measurements on lyotropic liquid crystalline polymers

 Mechanical spectroscopy is used to probe the structure of lyotropic liquid crystalline polymers during flow and after the cessation of flow. The oscillatory flow is either parallel or perpendicular to the steady-state flow. The resulting moduli provide information about the time- and shear-dependent microstructure, including anisotropy. Two different concentrations of poly(benzylglutamate) (PBG) in m-cresol and a concentrated hydroxypropylcellulose (HPC) solution, also in m-cresol, are investigated. In all cases, the orthogonal superposition moduli evolve differently from the parallel ones. The former are less sensitive to the flow-induced changes in structure than the latter ones. Together with the lack of sensitivity of the superposition moduli to texture refinement during flow, this suggests a strong relation between director orientation and superposition moduli. After the cessation of flow the parallel moduli decrease for the PBG solutions, whereas the opposite is observed in the HPC solutions. A comparison with the orthogonal moduli provides a direct measure of anisotropy. At rest, the PBG solutions tend toward a higher degree of anisotropy while the HPC solutions become more isotropic. In the latter systems, all moduli are much larger, reflecting a larger contribution from the texture. Received: 8 July 1999/Accepted: 1 October 1999     

Microstructure constitutive equation for discotic nematic liquid crystalline materials –

The rheological material functions predicted by a previously selected constitutive equation (CE) for discotic mesophases are presented. The predicted relations among rheological properties, shear-induced microstructure, processing conditions and material parameters of discotic mesophases are characterized and discussed. The first and second normal stress differences corresponding to planar (i.e., 2-D orientation) microstructure mode of discotic nematics are found to be qualitatively similar to those for rod-like nematics despite the existing differences in flow-orientation characteristics. The first (second) normal stress difference for discotic mesophases corresponding to non-planar (i.e., 3-D orientation) microstructure mode is always positive (positive or negative depending on viscous effects) and is found to be due to flow-induced biaxiality. The effect of change in nematic potential (or temperature) on rheological properties of discotic mesophases is also presented. The apparent shear viscosities for various microstructure modes and material properties are also presented and shown to agree qualitatively with the available experimental data. Though only restricted validation of the predicted results with the actual experimental data of discotics is possible, the present study provides essential theoretical feedback to the on-going experimental work being pursued in understanding the processing behavior of mesophase pitches. Received: 24 February 1998 Accepted: 15 May 1998     

2D编织陶瓷基复合材料应力-应变行为的试验研究和模拟

本文对2D编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟。将2D编织结构简化为：正交铺层结构和纤维束波动结构。基于基体随机开裂、纤维随机断裂的统计分布理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分分割为若干子单元;由于纤维束的波动使各子单元材料方向与加载方向不一致,因此考虑了各子单元的线性行为和非线性行为对材料响应的影响,同时引入强度分析模型,得到纤维束波动部分的应力-应变关系。结合正交铺层部分和纤维束波动部分的应力-应变关系,得到2D编织结构的应力-应变行为,理论与试验吻合较好。     

An evaluation of the Larson-Doi model for liquid crystalline polymers using recoil

The mesoscopic models for the rheological properties of liquid crystalline polymers proposed by Larson and Doi in 1991 and Kawaguchi and Denn in 1999 are based on phenomenological expressions that describe the evolution of the defect density and the contribution of the “texture” to the stress. In the present work, we attempt to assess some of these assumptions by monitoring how the energy stored in the texture of liquid crystalline materials evolves during shear flows. For that purpose, strain recovery is measured as a function of the applied strain for flow reversal and intermittent flow. Solutions of poly-benzylglutamate in m-cresol, hydroxypropylcellulose in water and a nematic surfactant solution are used as model systems. Although the behaviour is described qualitatively by the model, discrepancies between the predictions and the experiments are observed, especially when the shear history includes rest periods. Received: 14 July 1999 /Accepted: 30 August 1999     

Impact of texture on stress growth in thermotropic liquid crystalline polymers subjected to step-shear

The Landau-de Gennes tensor order parameter equations of nemato-dynamics are formulated, solved and used to find the impact of textural transformation on stress growth in thermotropic liquid crystalline polymers subjected to shear start-up flow. The simulated textural transformations include nucleation and annihilation of twist inversion walls. Coarsening processes include wall-wall annihilation, wall pinching and wall-bounding surface reactions. In the absence of defect-related effects, the stress growth is characterized by an early stress plateau, intermediate power law growth, and a late stage stress plateau. As the Deborah number (De) increases, flow-induced textural transformations affect the late stage and then the intermediate stress growth stage. Defects are found to be stress sinks, and so removal of defects increases stress. At lower Deborah numbers, few defects arise and coarsening rates are low, so the main texture effect in this regime is in the late stage plateau region, causing localized step increases. At Deborah numbers close to one, nucleation and coarsening rates increase, and textural effects appear closer and closer to the intermediate stress growth regime. As De increases further, coarsening by pinching processes overcomes nucleation, and all defects disappear in the intermediate stress growth regime, causing the stress growth to exhibit a smooth staircase shape. Strain and amplitude scaling is not observed. Simulated textural transformations show that smooth staircase stress growth is the result of defect annihilation processes. The non-monotonic stress growth is consistent with experimental observations. Simulated textures provide specific knowledge important to the eventual understanding of the rheologies of textured liquid crystal polymers.