Equal Biaxial Tension Research Articles

Plastic Stress Concentration at a Circular Hole in a Finite-Sheet Subjected to Equal Biaxial Tension

二軸応力下における破壊の問題はその重要性にもかかわらず,実験方法の難しさなどのためまだ十分に検討されておらず,ほとんど明らかにされていない現状である.そこで本研究はこのような二軸応力の影響について明らかにするため,等二軸応力場における円孔縁近傍の塑性応力集中係数を光弾性法により求め,それをもとに塑性ひずみ集中係数を算出し理論値と比較検討した結果ほぼ一致することを明らかにした.

The initiation of necking in rectangular elastic/plastic specimens under uniaxial and biaxial tension

N ecking in a rectangular parallelepiped of incompressible elastic/plastic material under uniaxia tension is studied as a bifurcation problem. Approximate upper-bound bifurcation stresses are found which show that bifurcation can occur immediately after the load on the specimen reaches a maximum if the length of the specimen is sufficiently great compared to the width and thickness. A simple formula applicable to sufficiently thin specimens is obtained for the approximate bifurcation stress. Sufficient conditions for uniqueness are found for elastic/plastic solids subjected to a general homogeneous stress-field. The particular case of the rectangular specimen under equal biaxial tension is investigated further, and the magnitude of the bifurcation stress is found to be very sensitive to the particular boundary conditions imposed.

Stresses in the Plastic Range Around a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial Tension

AbstractThe stresses in the plastic range around a circular hole in an infinite sheet of strain‐hardening material subjected to equal biaxial tension are found analytically on the basis of the simple deformation theory of plasticity. The stress concentration factor is given by 2Es (Sc · p)/Es(p) where Es(Sc · p) and Es(p) are the secant moduli at points around a circular hole and far removed from the hole.Der Spannungskonzentrationsfaktor wird durch 2Es(Sc · p)/Es(p) gegeben, wobei Es(Sc · p) und Es(p) die Sekanten‐module an Punkten um eine kreisförmige Öffnung und weit entfernt von der Öffnung sind.

Viscoelastic Properties of a Rubber Vulcanizate Under Large Deformations in Equal Biaxial Tension, Pure Shear, and Simple Tension

Stress-strain data were determined on an unfilled styrene-butadiene rubber vulcanizate in equal biaxial tension (EBT) at deformations up to rupture. Tests were made at temperatures from −43° to 90°C and at extension rates from 0.15 to 4 min−1. The data are represented in terms of a time- and temperature-independent function, Ω(χ), the reduced modulus, T0F(t/aT)/T, and the maximum extensibility, λm(t/aT), the latter two quantities being functions of the temperature-reduced time, t/aT. The function Ω(χ) gives the stress-strain relationship for the material in a reference state for which the modulus is unity and λm=λm0, the equilibrium value. The maximum extensibility equals the extension ratio at which the slope of a stress-strain curve from isochronal data becomes infinite; it cannot be measured directly because rupture always occurs at an extension less than λm. Data from extensive tests in simple tension (ST) have been reported previously, as well as data in pure shear (constrained biaxial tension, CBT) at 1<λ<2.5, where λ is the extension ratio. The three Ω(χ) functions, which represent stress-strain behavior in ST, CBT, and EBT, were considered in terms of the Valanis-Landel theory of finite elasticity, which is based on the assumed validity of the strain-energy function W=ω(λ1)+ω(λ2)+ω(λ3). In this way, the characteristic function λω′(λ)/F was evaluated over the range 0.028<λ<7.5. From this function along with the modulus, the stress-strain behavior in any pure homogeneous deformations can be calculated readily over extended ranges of temperature and extension rate. Because λm(t/aT) depends somewhat on the type of deformation (λm0 in ST is at least 30% greater than in EBT), data at very large deformations under an arbitrary pure homogeneous deformation can be derived only if λm is known as a function of both t/aT and the type of deformation.

Fracture of polymers in biaxial and triaxial tension

AbstractMacroscopic fracture is preceded by localized deformation and rupture processes that depend on the state of combined stress (i.e., on the stress state) and other test conditions as well as on polymer structure and morphology. To illustrate the effect of stress state on the mode of fracture initiation and crack growth, data obtained on elastomers in triaxial tension are reviewed along with those for an unfilled styrenebutadiene rubber vulcanizate in simple tension, equal biaxial tension, and under the biaxial tensile conditions that give a pure shear deformation. The behavior of plastics, including the dependence of the strength of a notched specimen on its thickness, is briefly considered.

Viscoelastic Tests Under Finite Strain and Variable Strain Rate

In this paper we present the results of uniaxial, equal biaxial, and unequal homogeneous biaxial tension of viscoelastic materials under isothermal conditions and compare them with predictions based on the approximate constitutive equations of Refs. 1 and 2. Theoretical expressions for uniaxial and equal biaxial constant and logarithmic stretch-rates and for unequal homogeneous biaxial single-step and double-step relaxation and constant stretch-rate are developed and compared with experimental results for a styrene-butadiene rubber (SBR); agreement is found to be satisfactory. The uniaxial and equal biaxial constant stretch results for very short ramp times are used to predict the behavior of actual single-step relaxation tests and to study the effects of fast motion on the constitutive equations of Refs. 1 and 2.

Ultimate tensile properties of elastomers. VI. Strength and extensibility of a styrene–butadiene rubber vulcanizate in equal biaxial tension

AbstractThe ultimate properties of an unfilled styrene‐butadiene rubber vulcanizate in equal biaxial tension were determined by inflating a circular membrane into a bubble. Tests were made at several extension rates (evaluated at the pole) from about 0.15 to 4 min−1 and at temperatures from −43 to 90°C. The stress in the vicinity of the pole when rupture occurred was evaluated from the pressure, the radius of curvature, and the extension ratio λ, the latter two quantities being obtained from photographic data. Below 70°C, the ultimate extension ratio λb is approximately 5.2 and is essentially independent of extension rate and temperature, in striking contrast to the behavior in simple and constrained biaxial tension (pure shear). Likewise, the rupture stress is manyfold greater than in either simple or constrained biaxial tension. From the extremum points of failure envelopes, the maximum extension ratio (λb)max in equal biaxial tension is 5.7 and in simple tension is 7.2. An examination of ruptured membranes showed that, except at 70 and 90°C, rupture began away from the pole in a region where the stress state is unequal biaxial tension. Hence, values of the ultimate properties in truly equal biaxial tension are no doubt somewhat greater than those obtained from the membrane tests. However, it is shown that (λb)max in truly equal biaxial tension must be lower than that in simple tension by at least 10%. A consideration of rupture data in simple, constrained biaxial, and equal biaxial tension leads to the conclusion that no simple failure criterion is applicable for interrelating data obtained under the several states of combined stress. The rupture patterns and factors that affect the site of rupture initiation and the mode of crack growth are also discussed.

Plastic Stress Concentration at a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial Tension

With the use of J2 deformation theory, the stress-concentration factor at a circular hole in an infinite sheet of strain-hardening material subjected to equal biaxial tension at infinity is found for a variety of representative materials. The analysis exploits a transformation which permits the calculation of the stress-concentration factor without determining the stress distribution in the sheet. Subsequent calculations reveal that, for a monotonically increasing applied stress, the stress history at all points in the sheet is nearly radial.