Stress-strain Dependence Research Articles

Determination of the strain characteristics of interblock contacts using rock specimen testing results

A technique for interpreting rock specimen compression testing data is proposed. It consists of mathematical modeling of the loading of a specimen containing the sliding line L, on which the stresses are continuous and the displacements are discontinuous. At each step of loading the values of a jump of displacements on L are found from the experimentally known stress-strain dependences. The empirical relations describing the strain process on the sliding line are found using these results. Based on Stavrogin's experimental data, we estimate the parameters of the dependence of the peak strength of the interblock contact on the shift from the normal stress.

High-temperature deformation of commercial-purity aluminum

The stress-strain behavior of aluminum 99.5 pct (2–9) purity deformed under hot-working conditions has been found to be satisfactorily described by combining the exponential saturation equation earlier proposed by Voce and a latter model advanced by Kocks. Voce’s equation describes the strain dependence of the flow stress, whereas the temperature and strain rate dependencies of both the initial flow stress and the saturation or steady-state stress are introduced by means of Kocks’ model, which leads to the definition of a different temperature-compensated strain rate parameter. The basic principles of the dynamic materials model (DMM) advanced by Gegel and co-workers has been reassessed, leading to a different proposition in relation to the calculation of both the power dissipator co-content (J) and the power dissipation efficiency (η), which makes use of the constitutive equation previously developed. Such concepts are later applied to the analysis of a typical industrial hot-rolling process conducted on commercial-purity aluminum. From the microstructural point of view, hot rolling of commercial-purity aluminum has been found to be conducted under conditions of relatively low power dissipation efficiency (η ≈ 0.20 to 0.25), which is likely to be associated with the predominance of dynamic recovery as the main dislocation rearrangement mechanism.

Effects of the time-dependent behavior on strain softening of diatomaceous soft rock

This paper is concerned with a new concept of modeling the strain softening behavior of diatomaceous soft rocks based on the laboratory investigation. An approximate solution was described for a stress-strain-time relation taking into account strain softening phenomenon. The treatment of the post-peak behavior in the calculation is discussed and comparisons of the experimental observations of normally consolidated specimens with results of numerically simulated undrained triaxial tests are given. The strain rate effect and strain softening behaviors are controlled by the time dependent stress strain relation.

Response analysis of the Higashi-Kobe Bridge and surrounding soil in the 1995 Hyogoken-Nanbu Earthquake

This paper presents results of observation and analysis of the response of one of the longest cable-stayed bridges in the world to the Hyogoken–Nanbu (Kobe) Earthquake of 17 January 1995. It is determined that interaction of the foundations of the bridge towers with the supporting soil plays a decisive role in the overall structural behaviour. The key factor governing the changes of the soil properties at this site is pore-water pressure buildup, which results in liquefaction of the saturated surface soil layers under large dynamic loads. Models of the soil and structure are created and initially validated by accurately simulating the system response to a small earthquake. Soil parameters reflecting the pore-water pressure buildup in the strong earthquake are determined by an advanced non-linear effective stress analysis, combining the Ramberg–Osgood model of stress–strain dependence with a pore pressure model based on shear work concept. They are utilized to investigate and simulate the interaction of the foundation and the supporting soil using the program SASSI with the flexible volume substructuring approach. The results show a good agreement with the observations and have useful implications to the scientific and engineering practice. © 1998 John Wiley & Sons, Ltd.

Modelling Soft Tissue Using Biphasic Theory — A Word of Caution

In recent years the biphasic approach initiated by Mow and coworkers, has been very popular in modelling soft, hydrated, cartilage tissues as well as other soft tissues, such as the brain. This work points out that due to the inherent inability of biphasic models in their present form to account for stress-strain rate dependence resulting from the viscoelasticity of the solid phase, the applicability of these models is limited to the loading conditions producing large relative velocities of phases.

Stress concentrations in multiple fibre model composites

Abstract The finite element method is used to examine the load transfer in the fibre–matrix interface and between broken and neighbouring unbroken fibres. Three different models for the stress–strain dependence of the matrix were chosen for modelling the stress transfer: linear elastic, linear elastic–ideal plastic and hypoelastic. The hypoelastic behaviour is similar to the time independent viscoelastic behaviour of the polymer matrix. The hypoelastic model of the stress–strain behaviour can describe the mechanical properties of different matrix materials taken from simple tensile tests. The values of the stress intensity factors were used to discuss the different material models. The hypoelastic matrix behaviour results in realistic stress concentration factors K caused by a single fibre break.

Nonlinear shear behavior of poly(vinyl acetate) material

Because of the strong environmental sensitivity of poly(vinyl acetate), PVAc, especially with respect to moisture, and the fact that shear deformation is essentially equivoluminal up to moderate strain levels, little has been reported in the literature on the nonlinear mechanical creep behavior of this polymeric material loaded in shear. This paper presents the results of torsional tests which establish the shear response through the linear zone and well into the nonlinear region. Test specimens were thin-walled cylinders giving an approximately uniform deformation field. Because of carefully chosen wall thickness to length ratio, it is considered that these measurements represent some of the most accurate nonlinear shear results to date in the strain range above 1%. Measurements of stress, strain and creep compliance were made at temperatures near the glass transition temperature and somewhat below it. Isochronal shear stress-strain dependence into the nonlinear range was used to establish limits of viscoelastic linearity during creep. As temperature is increased toward the glass transition, the limit shows a greater dependence on stress than on strain. The stored distortional strain energy at the limit of linearity was not a constant but varied with temperature and load. Thus, these results appear not to support the concept of stored energy as a material property defining the threshold for nonlinear viscoelastic behavior. Strain during the short-time load-up period gives evidence that PVAc is also subject to nonlinear elasticity in the glassy response region.

Constitutive modelling of brain tissue: Experiment and theory

Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.

Response of beams of non-linear viscoelastic materials exhibiting strain-dependent stress relaxation

A constitutive equation for non-linear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The non-linearity arises from a reduced time variable which causes stress relaxation to occur faster as strain increases. This constitutive equation has almost exclusively been used to study the response of materials subjected to homogeneous strains, and has been shown to account for the occurrence of ‘yield’ in homogeneous constant strain rate tests. Here, it is used in a study of the pure bending of beams. The classical assumptions of beam theory are made, i.e. plane sections remain plane so that, at each fixed time, the strains vary linearly through the depth of the beam. The interaction of this spatial variation of strain with the non-linear dependence of the reduced time on strain leads to a response which significantly differs from that determined using linear viscoelasticity theory. This interaction is explored by numerical simulation of the response of beams under conditions of curvature control and of bending moment control. The curvature and bending moment histories are: step change, constant rate, and constant rate increase and decrease to zero. The bending moment and curvature response histories, stress distributions, cross-section shape and other factors which relate to beam design are discussed.

Functionality dependence for molecular nonaffine deformation of polymer networks

The dependence of the stress—strain behaviour of polymer networks on functionality is investigated. The network is described in terms of a gas of simple units of arbitrary functionality f. The macroscopic deformation is taken into account by constraints, which allow molecular nonaffine deformations. For Gaussian network strands the model leads to the same stress—strain dependence as in the well known model, but shows a modified dependence of the modulus on functionality.

Photocured polymer networks based on multifunctional ?-ketoesters and acrylates

The objects of this study are highly crosslinked networks. The base-catalyzed Michael reaction of β-ketoesters with vinyl groups of the pentaerythritol tetra-acrylate (PETA) was used for a step grow formation of the crosslinked polymer in dark. The nonreacted vinyl groups and vinyl monomer were built up to the network structure by photopolymerization in the second step of synthesis. An analysis of crosslinked polymers shows that the long spacer between β-ketoester groups in propylenglycol-425-diacetoacetate (PGDAA) favors an extent of reaction compared to pentaerythritol tetrakis (acetoacetate) (PETAA). The excess of vinyl monomers added to polymerization batch functions in the first step of the synthesis as a reactive solvent [triethylene glycol dimethacrylate (TEGDMA); PETA]. The dissolution of reactants has a positive effect on homogeneity, conversion, and crosslink density of prepared networks. The consumption of reactive groups in a course of the network formation, the crosslink density, and dynamic mechanical properties of the prepared networks were determined from Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), sol-gel analysis, dynamic testing, and stress-strain dependencies. The dynamic testing indicates that the networks synthesized in two steps from batches containing an excess of vinyl monomer consist from two highly crosslinked phases interpenetrating each other. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 165–178, 1997

Transient flow-induced crystallization of a polyethylene melt

Extensional, flow-induced crystallization (FIC) of a high-density polyethylene (HDPE) melt has been studied using a four-roll mill flow cell. Simultaneous measurement of the birefringence and scattering dichroism are used to quantify the crystallization process during and following transient flow deformation in planar extensional flow. Suspension of the HDPE phase as a droplet in a linear low-density polyethylene carrier phase prevents die blockage on crystallization and allows measurement of the flow kinematics. Initial crystallization rates following a transient flow deformation show a stress-strain dependence. Crystallization induction times during flow correlate with the extension rate during the transient flow deformation. Measurement of the HDPE melt steady and oscillatory flow rheological properties, along with measurements of time constants following step-shear and extensional strains, allow determination of the viscoelastic properties which enhance FIC. Parameters obtained from these experiments are used in a phenomenological model for FIC which allows qualitative and semiquantitative analysis of the data trends, particularly the relaxation behavior of the birefringence during flow cessation/crystallization. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2165–2176, 1997

Magnetization and magnetostriction processes in Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0)

The present analysis provides Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) magnetization and magnetostriction states during applied magnetic field and stress processes by minimizing the total magnetic free energy in the presence of a parameter selected inverse exponential magnetic free energy distribution. A comparison between experimental and model results shows that the model provides a qualitatively accurate description of the magnetostriction and magnetization in Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) during applied magnetic field processes for a range of constant uniaxial applied stresses. Therefore, the model appears to be a useful tool for the analysis of Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) applications with constant stress or strain dependent stress states. Furthermore, the good qualitative agreement between model and experiment supports the contention that the magnetostriction and magnetization response of Tb(0.27−0.30)Dy(0.73−0.70)Fe(1.9−2.0) is influenced by a defect induced defocusing of local magnetization direction about the average magnetization direction.

On the mechanical behavior of commercial-purity aluminum deformed under axisymmetric compression conditions

Abstract The stress-strain behavior of commercial-purity aluminum deformed under axisymmetric compression conditions in the temperature range of 293–673 K is analyzed on a rational basis. The strain dependence of the flow stress at every temperature and strain rate is satisfactorily described by means of the exponential-saturation equation earlier proposed by Voce (1948, 1955). The temperature and strain rate dependence of both the initial flow stress and the saturation or steady- state stress is analyzed in terms of two different models. First, the hyperbolic-sine model advanced by Sellars and Tegart (1972) in terms of the Zener-Hollomon parameter, assuming that the activation energy for deformation of this material remains constant and equal to 156 KJmol−1 in the whole temperature interval. Second, the model proposed by Kocks (1976) in terms of a power-law considering that the stress sensitivity exponent of the strain rate is significantly temperature-dependent. This model leads to the introduction of a temperature-compensated strain rate parameter similar to the MacGregor-Fisher parameter. Under the consideration that the initial strain hardening rate should be independent of temperature and strain rate it is determined that the relaxation strain parameter involved in the Voce equation can be calculated as a linear function of the saturation stress. It is concluded that although both models describe the experimental data with similar accuracy, according to the statistical parameters calculated for every approach, Kocks model allows a somewhat better correlation with the present experimental data. The description of the stress parameters by means of the hyperbolic-sine relationship suggests a decrease in the activation energy for deformation with temperature below 473 K. Significant deviations in the computation of the stress-strain curves and in the description of the work hardening behavior of the material under some deformation conditions are still observed independently of the model employed. However, it is believed to be due to two severe requirements imposed simultaneously to the model: the description of experimental data determined under a wide spectrum of deformation conditions while maintaining a minimum of material parameters in the constitutive functions developed.

The strain dependence of flow stress in an aged Cu-1.5wt% Ti alloy

The flow stress-grain size relationship of a number of metals and alloys can be expressed by a modified Hall-Petch equation. The authors have recently established the Hall-Petch relationship for several Cu-Ti alloys (containing 1.5, 2.7, 4.5 and 5.4 wt% Ti), in the solution treated condition. The present investigation has been taken up to study the flow stress-grain size relationship in the peak aged Cu-1.5wt%Ti alloy and to confirm the earlier observation that precipitation rather than composition variation, is the cause for {sigma}{sub {omicron}{var_epsilon}} and hence {sigma}{sub {var_epsilon}}, the flow stress to vary with strain, i.e. {var_epsilon}{sup 3/2}.

Elastic, plastic and cracking indentation behavior of silicon crystals

The ambient temperature indentation hardness properties of silicon crystals have been studied over the full range of their nanoscale elastic/plastic and microscale elastic/plastic/cracking behaviors. The material properties are interpreted on the basis of applied force versus residual indentation size or crack size measurements and, also, on the basis of computed hardness stress-strain dependencies. Cracking, when it occurs, is attributed to sessile dislocation reactions that are initiated at microslip system intersections. Significant hardening was revealed in nanoindentation tests of carbon-ion implanted material, particularly, for crack-free plastic deformation obtained when silicon carbide was formed in the crystal surface layer by high temperature implantation. Otherwise, continuous force vs. displacement curves were employed to track the occurrence of cracking during indenter loading and crack growth on unloading, as facilitated in the latter case by the residual plastic deformation produced during the loading part of the hardness cycle.

The grain size and strain dependence of the flow stress of polycrystalline iron

Abstract The effect of grain size and strain on the flow stress of polycrystals has long been studied. However, the effect especially for polycrystalline iron, still cannot be fully explained by most of the models. In this paper, a unified equation based on a one-parameter approach has been proposed to predict the relation between flow stress and grain size at various strains. The predictions are found to be consistent with the published experimental data.

Deformation behavior of a alpha brass in plane stress/plane strain

Generally a simple power law ~ = K E (where K and n are empirical constants called the strength coefficient and the work hardening coefficient respectively) is used to describe plastic stress-strain dependence of deformable metals (1,2). This equation was employed by Low (3) to describe the uniaxial tensile behavior of an annealed 70/30 brass. The slope of the corresponding double logarithmic true stress-true strain plot gives a single value of n. However, this fit is not always adequate. Geil and Carwile (4) reported a deviation in the linearity of the double logarithmic plot for steel. Two sets of K and n values were used to describe the stress-strain relationship in a spheroidized hypo-eutectoid steel by Wilson and Konnan (5). Various reasons, such as grain size effects, cementite particle distribution, cell formation, stacking fault energy, etc. were proposed to rationalize the double-n behavior (6-9). Ollilainen reported a triple-n behavior for a decarburized steel (10).

Shock waves in dynamic compacting powders and porous bodies. II. Propagation of shock waves in porous materials with a reinforcing frame

The main special feature of dynamic compacting of powders in rigid dies is the formation of shock waves and the associated piecewise-constant distribution of the axial component of speed and density If]. This is the largest difference between dynamic and quasistatic compacting. The results show [i, 2] that these phenomena are closely linked with the nature of the stress-strain or pressure-density dependence.

Strain Gradient Influence on Brittle Failure of Ice

Eccentric and concentric unconfined compression tests are conducted to examine the influence of strain gradients on the brittle failure of ice. Fresh-water columnar-grained ice specimens are tested at a temperature of -10°C and average strain rates of approximately 10\u–\u4 s\u–¹. Considering the strain varies linearly across a specimen, the stress distribution is determined from conditions of equilibrium of forces and moments. At failure, the average stresses for eccentrically loaded specimens are usually less than those for concentrically loaded ones. In the case of eccentrically loaded specimens, however, local stresses at some point along the specimen’s width (usually one of the sides) reach a maximum value exceeding the average stress for a concentrically loaded specimen. Measured failure stresses show some scatter, which is commonly observed for brittle failure. Nonetheless, the maximum local stress reached in a specimen appears to increase with increasing strain (or stress) gradient. The maximum stress-strain gradient dependence provides an explanation of the apparent size effect on ice failure stresses.