Overstress Theory Research Articles

Tensile properties and stress relaxation of polypropylene at elevated temperatures

AbstractSamples of isotactic polypropylene(PP) were subjected to stress‐relaxation experiments after simple tensile tests at four strain rates and at different levels of temperature. The relaxation moduli were determined in the range of temperature between 20 and 80°C with a relaxation period of 1200s duration. The activation energy value of the shift factor was determined using the time‐temperature superposition principle. The calculated stress‐strain curves and stress‐relaxation curves were obtained from constitutive equations based on an overstress theory in which the temperature dependence of viscosity and the activation energy were considered. The temperature dependence of viscosity was amenable to an Arrhenius type equation. The quasi‐equilibrium stress depends on both the current strain and the temperature. The calculated results were obtained by the proposed constitutive equation and compared with the data. The proposed constitutive equations based on the overstress model explain well the viscoelastic‐plastic behavior of PP samples.

Viscoelastic‐plastic deformation behavior of polypropylene after cyclic preloadings

AbstractStress‐relaxation behavior is studied in polypropylene samples subjected to different cyclic preloadings and to simple tension. The relaxation tests are performed under different sets of strain amplitude, number of cycles, and strain rate, using a closed‐loop, electrohydraulic, servocontrolled testing machine. The calculated stress‐strain curves are determined from a constitutive equation based on an overstress theory in which an equilibrium stress and a viscosity function are treated. The calculated results agree well with the experimental ones. It is concluded that the overstress theory explains the nonlinear viscoelastic‐plastic behavior of polypropylene.

Strain Hardening of Annealed 304 Stainless Steel by Creep

Combined axial-torsional experiments have been conducted at room temperature on thin-walled tubes to investigate the strain hardening behavior of annealed 304 stainless steel due to creep. The constant strain-rate dynamic loading (or SCISR) surfaces representing the state of material before and after creep have benn determined. It has been found that transient creep essentially causes the loading surface to undergo kinematic hardening with insignificant amount of isotropic hardening for this material. A conclusion is drawn that the loading surface hardened by transient creep is the same as that hardened by plastic deformation. This is true both for specimens with pure tension and pure torsion loading paths. The results confirm assumptions of the overstress theory of viscoplasticity.

新開発の引張・ねじり２軸ひずみ計による高分子材料の応力‐ひずみ曲線

In order to investigate a constitutive law for various materials, many combined tension-torsion tests have been performed at complex strain paths. During these tests, it is more difficult to measure the axial and the shear strain simultaneously than to obtain the load and the torque. Although some instruments to measure both strains have been deviced, these are considerably large in comparison with the specimen dimensions, and therefore, it may be difficult to attach them briefly to the cylindrical specimen. In this paper, a small-sized biaxial strain meter was newly developed to measure the axial and shear strains. The stress-strain curves were measured for solid polymers by use of the new meter and were compared with the numerical computation of an overstress theory.

Viscoelastic-Plastic Deformation Characteristics of Polypropylene after Cyclic Preloadings.

Stress-relaxation behavior is studied in polypropylene samples subjected to different cyclic preloadings and to simple tension. The relaxation tests are performed under different sets of strain amplitude, number of cycles, and strain rate using a closed-loop, electrohydraulic, servocontrolled testing machine. The calculated stress-relaxation curves are determined from the constitutive equation based on an overstress theory, in which an equilibrium stress and a viscosity function are treated. The calculated results agree well with the experimental ones. It is concluded that the overstress theory explains the nonlinear viscoelastic-plastic behavior of polypropylene.

Stress-strain curve in polyester filament yarn for tensile deformation at high rates.

An impact tensile testing apparatus with cantilever type load cell was developed for obtaining stress-strain curves of polyester multi-filament yarn at various strain rates. The experimental results were compared with the numerical results derived from an over-stress theory. By using this apparatus, tensile tests of yarn at wide range of strain rate from 10-3 to 102s-1 could be performed in the same measuring system. The over-stress theory gave satisfactory interpretation of the stress-strain curves of polyester multi-filament yarn up to breaking point at low strain rate, and up to yielding point at high strain rate. The difference between the calcurated curve and experimental results at high strain rate seemed due to the temperature rise of yarn during extension.

Rate‐dependent nonlinear constitutive equation of polypropylene

AbstractIn order to investigate the viscoelastic‐plastic properties of polymer solids and construct a constitutive equation for them, torsional tests were performed on polypropylene (PP) hollow cylinders. Testing was conducted under constant strain rate, abrupt change of strain rate, stress relaxation, creep, and cyclic loading conditions. The experimental data were compared with the numerical results derived from an overstress model. It is shown that the overstress theory explains the viscoelastic‐plastic properties of PP well, provided that the current strain is not below the maximum previous strain.

ポリエチレン材の応力・ひずみ曲線

The linear theory of viscoelasticity has been well formulated and successfully used in the past. In comparison, however, nonlinear viscoelastic plastic behavior at finite strains is less understood because of several complexities characteristic of polymer solids. In order to construct a visco-elastic-plastic constitutive equation in polymer solids, systematic experiments should be planned to demonstrate the effects of time, temperature and pressure on their material properties. In this paper, compressive and torsional tests were performed using polyethylene (PE) specimens under the conditions of constant strain rate, abrupt change in strain rate, stress relaxation and creep to provide some experimental facts on the time dependence of stress-strain curves. The experimental results were compared with the numerical results based on a over-stress theory. It is shown that the over-stress theory well explains the stress-strain curves of PE in the case where the current strain is not below the previous strain and the theory may become a valid model to infer the nonlinear behavior not only at a uniaxial stress state, but also at a biaxial one.

Constitutive Behavior and Testing of Structural Adhesives

Material characterization of structural adhesives in the bulk and bonded forms is discussed. Constitutive relations used for describing stress–strain data are reviewed. The difficulties associated with adhesive characterization in the bonded form are cited. Common testing procedures for adhesive characterization in the bulk and bonded forms are reviewed. In presenting the constitutive relations used in material characterization of structural adhesives, deformation theories introduced by Hencky are reviewed first. The modifications made in this theory to render it rate dependent and bilinear are discussed and applications to adhesive characterization are cited. Application of linear viscoelasticity, mechanical model characterization, and its use in describing the dependence of adhesive and cohesive strengths on rate, temperature, and bond thickness are presented. The time–temperature superposition principle and three-dimensional stress–strain relations in integral and differential operator forms are reviewed. Frequent assumptions for dilatation and distortion operations are presented. Procedures for describing nonlinear viscoelastic behavior are reviewed. It is pointed out that the extent of nonlinearity is dependent on both the stress level and the time scale. The use of nonlinear spring and dashpot elements, nonlinear differential operators, and perturbation of elastic and viscous coefficients are cited. Prandtl’s incremental theory of plasticity and its extension in the form of over-stress theory is presented. The incorporation of this over-stress idea into the viscoelastic mechanical model characterization is discussed. The modified Bingham model and the Chase–Goldsmith model developed in this fashion and their application to adhesive material characterization are presented. The use of empirical relations for the description of creep behavior is discussed. Prediction of shear behavior based on bulk tensile data is demonstrated. It is suggested that characterization of adhesive behavior in the bonded form should include the application of stress analysis, fracture mechanics, polymer chemistry and surface analysis techniques. In testing bonded samples the use of thick adherend symmetric single lap geometry or napkin ring test geometry is advised and it is suggested that the specimens should be prepared with the same surface preparation and cure techniques.