Small Strain Deformation Research Articles

Effects of particle sizes on dynamic and static small strain deformation properties

Effects of particle sizes on dynamic and static small strain deformation properties

Calibration of Testing Equipment for Reliable Small-Strain Deformation Measurements Using Synthetic Specimens

Abstract For reliable deformation measurements at small strains, calibration of the entire testing system in addition to routine transducer calibrations are very important. Seven synthetic specimens of varying stiffness (4.3 to 1500 MPa) were constructed and tested to measure the compliance of testing equipment and to improve the measurement setups. Testing equipment used in this study included resonant column device (RC), torsional shear device (TS), free-free resonant column device (FF-RC), cyclic resilient modulus testing device (MR) and the static compression testing device. Moduli of synthetic specimens determined by various testing equipment after improvement were almost identical if considered the effect of loading frequency, indicating that all of the testing devices were well calibrated over a wide stiffness range. To verify the effectiveness of calibration on soil testing, two subgrade soils were tested, and moduli determined by various tests compared well. Use of synthetic calibration specimens shows potential for calibrating testing equipment and determining its capability and limitation of small-strain deformation measurements.

A mixed finite volume formulation for determining the small strain deformation of incompressible materials

A mixed finite volume formulation for determining the small strain deformation of incompressible materials

On the general structure of small on large problems for elastic deformations of Varga materials II: Axially symmetric deformations

In Part I of this article, we have formulated the general structure of the equations governing small plane strain deformations which are superimposed upon a known large plane strain deformation for the perfectly elastic incompressible 'modified' Varga material, and assuming only that the initial large plane deformation is a known solution of one of three first integrals previously derived by the authors. For axially summetric deformations there are only two such first integrals, one of which applies only to the single term Varga strain-energy function, and we give here the corresponding general equations for small superimposed deformations. As an illustration, a partial analysis for the case of small deformations superimposed upon the eversion of a thick spherical shell is examined. The Varga strain-energy functions are known to apply to both natural and synthetic rubber, provided the magnitude of the deformation is restricted. Their behaviour in both simple tension and equibiaxial tension, and in comparison to experimental data, is shown graphically in Part I of this paper [1].

Small strain deformation characteristics of two chalks subjected to varying stress conditions

Abstract The paper presents an attempt to consider the small strain characteristics of two high-porosity chalks from the northern Negev desert in Israel. Special attention was given to anisotropy, nonlinearity and stress regime; compression or tension. A theoretical and experimental framework for considering these aspects is presented and employed. The experimental programme included testing of air-dried hollow cylinder specimens under conditions of uniaxial compression, radial compression and radial tension. Results of the laboratory testing indicate that the chalks tested display a high degree of anisotropy in the modulus of deformation measured parallel and perpendicular to the direction of sedimentation. The stiffness of the chalks was found to be significantly higher perpendicular to the direction of sedimentation, despite the apparent massive uniform appearance of the intact rock. The chalks displayed significant non-linear stress-strain behaviour, with a strong tendency for the stiffness to decrease as deviator stress is increased. The ratio between material stiffness when subjected to compressive deviatoric stresses in comparison to tensile deviatoric stress was found to be very close to unity.

Atom-Based Modeling of Elastic Constants in Amorphous Polystyrene

Molecular mechanics and molecular dynamics simulations have been used to predict the mechanical properties of amorphous polystyrene as a function of the chain tacticity. Relaxed and equilibrated microstructures were generated and the cohesive energy density and the solubility parameter calculated. The amorphous state disorder was analyzed in terms of the pair correlation functions and the Voronoi polyhedra. Two separate methods, the static structure deformation and the stepwise loading molecular dynamics were used to apply small strain deformations to generated microstructures to obtain the elastic constants. The resulting values for moduli are compared, and the performance of the methods is discussed

Modelling the linear viscoelasticity of unfilled and carbon black loaded elastomers

Cyclic small strain deformation of unfilled and carbon black loaded vulcanised elastomers was investigated over a range of strain amplitudes, frequencies, and temperatures in order to determine and model the response of these materials. The elastomer used was a butadiene-acrylonitrile base polymer, KRYNAC 806. The carbon black filler was SRF N774 at a loading of 50 phr (parts per hundred by weight). Experiments were conducted in oscillatory shear using a Weissenberg rheogoniometer. Complex modulus data were obtained for a range of oscillatory shear strain amplitudes not exceeding 0.03 rads, for frequencies in the range 5 Hz–60 Hz and at temperatures between −20°C and 20°C. Time-temperature superposition was obtained for data above −10°C, with the same shifts applicable to both unfilled and carbon black loaded materials. Shifts were represented using the WLF equation. It was found that reduced data over a range of ten decades of log frequency were well represented by a Huet model. Varying the Huet model parameters thus, in principle, affords a means of modelling linear deformations of elastomers containing different loadings of carbon black filler.

Deformation calorimetry of polyurethane block-copolymers

A thermodynamic analysis of the uniaxial stretching of polyurethanes of various compositions and mechanical histories was carried out by using deformation calorimetry. The initial small strain deformations were found to result from the volume elasticity of the hard phase. The intramolecular energy contributions of the soft blocks were estimated. The hard block contributions were shown to depend on their content and on the degree of sample stretching. The predominant role of the soft component is proved to be manifested only in softened samples with a hard block content not exceeding 30%. The thermodynamics of the softening and hysteresis phenomena were studied. The dependence of the deformation mechanism on the hard block content and mechanical history is discussed.

Elastic-Plastic Deformation in Surface-Cracked Plates: Experiment and Numerical Analysis

Detailed three-dimensional nonlinear finite element (FE) analyses and experimental moire studies are performed on a plate containing a moderately deep part-through surface crack to establish limits of HRR-dominance. The plate is subjected to predominantly far-field tensile loading. The material under investigation is ASTM A710 steel, which was constitutively modeled by large deformation J2 flow theory of plasticity. The FE mesh was carefully constructed to resolve both crack front fields (such as J-integral and CTOD) and global fields (such as surface displacements, strains). By comparing the J-integral and CTOD results with an earlier HRR-dominance study using (small strain) deformation theory of plasticity, we found little effect of the different formulations on the crack front fields. The global deformation fields from the numerical simulation are in good agreement with our experimental results. The eventual loss of HRR-dominance is intimately related to the interaction of the global plastic flow fields with those of the crack front.

Rheology of the Earth's mantle and geodynamical processes

A non‐linear integral rheological model consistent with general creep theory and laboratory studies of rock creep is proposed to describe the rheology of the Earth's mantle. This model is universal, i.e., relevant to all strains, stresses and timescales. For constant stresses the model behaves like a power law non‐Newtonian fluid. However, the model differs significantly if stresses change with time, because it has a memory, in contrast with the power law fluid model. A linear anisotropic integral rheological law that relates stress perturbation to strain perturbation is obtained for small‐strain flows superimposed on a basic steady large‐strain convective flow in the mantle. The rheological parameter in this law depends on the basic flow. The small‐strain deformations associated with seismic waves and postglacial rebound are considered. In a pure power law fluid the effective viscosity associated with the convective flow is equal to the effective viscosity associated with postglacial rebound, whereas in the proposed model, the effective convective viscosity is about three orders of magnitude larger than the effective postglacial viscosity, at least for the lower mantle.

Elastoplastic Buckling of Annular Plates in Pure Shear

A linear buckling analysis is presented for annular elastoplastic plates under shear loads. The standard plate buckling equations are used in conjunction with the small strain J2 flow and deformation theories of plasticity. The main numerical finding is that deformation theory predicts critical loads which are considerably below the predictions obtained with the flow theory. Furthermore, comparison with experimental data for different metals shows a good agreement with the deformation theory results over a wide range of geometries. The limiting buckling problem of a long narrow panel under shear stresses is treated separately. This problem admits an exact solution and it is shown that the critical loads for the panel are approached asymtotically by the annular plate results. Contact is made with earlier studies on the buckling of elastic-orthotropic and elastoplastic shear panels.

Modeling Internal Stresses in the Nonelastic Deformation of Metals

The roles of short range and long range internal stresses during nonelastic deformation have been postulated and explored using the MATMOD-4V deformation model. New microstructural variables have been introduced in MATMOD-4V which represent the effects of internal stresses upon deformation. Simulations for aluminum have been performed to demonstrate improved capability to represent small strain deformation behavior and dynamic recovery. Comparisons are made between experimental data and computer predictions of microplastic straining and cyclic deformation.

Cavity expansion in cohesive frictional soils

Closed form solutions are presented for the expansion of cylindrical and spherical cavities in an ideal, cohesive frictional soil. An explicit solution for the pressure-expansion relationship can be obtained for infinitesimal (small strain) deformations. For finite deformations it is necessary to adopt a numerical approach to obtain the complete pressure-expansion relationship and it is found that the cavity pressure approaches a limiting value for infinite deformation. It is, perhaps surprisingly, possible to determine the precise value of this limiting pressure analytically. It is suggested that the small strain solution for a cylindrical cavity is applicable to the interpretation of pressuremeter tests in sand, and that the solutions for limit pressures have application to the problem of pile installation and the end bearing pressure of deep foundations. L'article présente des solutions de forme fermée pour l'expansion de cavités cylindriques et sphériques dans un sol idéal cohérent à frottement. On peut obtenir une solution explicite pour le rapport entre la pression et l'expansion dans le cas des déformations infinitésimales (contraintes faibles). Pour les déformations finies il faut adopter une méthode numérique pour obtenir le rapport complet entre la pression et l'expansion et on trouve que la pression de cavité atteint une valeur limite à peu près pour la déformation infinie. Il est peut-être surprenant que la valeur précise de cette pression limite puisse être déterminée de façon analytique. On en tire la conclusion que la solution à faible contrainte pour une cavité cylindrique peut s'appliquer à l'interprétation des essais pressiomètriques dans le sable et que les solutions pour les pressions limites trouvent une application au problème de l'installation des pieux et à celui de la résistance limite des fondations profondes.

Small strain deformations of elastic beams and rods including large deflections

A consistent theory for linear elastic behavior in which the strains are small but the displacements and rotations can be large is applied to the bending and twisting of a rod or beam by end loads and by its own weight. The theory provides solutions for geometries and loadings between those for which the infinitesimal theory applies and those for which structural theories, such as Kirchhoff s theory for rods, can be used. The results confirm the validity of Kirchhoff's rod theory within the range of small-strain, linear elastic behavior.

Thermodynamics of the deformation of segmented polyurethanes with various percentages of hard block I. The initial deformation

The thermodynamic analysis of the uniaxial stretching of the polybutadiene polyurethanes of various compositions and mechanical history was carried out using deformation calorimetry. The initial small strain deformation was found to result from the volume elasticity of the hard phase. Samples containing up to 50% of the hard block behave like typical thermoelastoplastics, which are characterized by the “plastic-to-rubber” transition and large reversible deformations. More rigid samples behave similar to typical solid crystalline polymers aboveTg.

Thermodynamic behavior of solid polymers in uniaxial deformation

AbstractThe heat and work of uniaxial deformation were measured for two commercial polyurethane elastomers and a low density polyethylene using a new deformation calorimeter. Internal energy changes in the materials resulting from deformation were calculated from the difference between the heat and work according to the first law of thermodynamics. The elastomers were found to exhibit complete reversibility for small and large strain deformation cycles as determined from the absence of a permanent internal energy change, even though one of these undergoes strain‐induced crystallization and melting. The low density polyethylene behaves irreversibly even at small strains, and will store 30 percent of the deformation work as internal energy during drawing at room temperature.

The Penny-Shaped Crack and the Plane Strain Crack in an Infinite Body of Power-Law Material

A study is carried out of the problem of a penny-shaped crack in an infinite body of power-law material subject to general remote axisymmetric stressing conditions. The plane strain version of the problem is also examined. The material is incompressible and is characterized by small strain deformation theory with a pure power relation between stress and strain. The solutions presented also apply to power-law creeping materials and to a class of strain-rate sensitive hardening materials. Both numerical and analytical procedures are employed to obtain the main results. A perturbation solution obtained by expanding about the trivial state in which the stress is everywhere parallel to the crack leads to simple formulas which are highly accurate even when the remote stress is perpendicular to the crack.