Equibiaxial Deformation Research Articles

The Mullins effect in equibiaxial extension and its influence on the inflation of a balloon

It is a common practice to manually stretch a toy balloon several times prior to inflation. This preconditioning reduces the pressure required to fully inflate the balloon, and thus eases the task of inflation. The reduction in pressure required to inflate the balloon is mainly a result of the Mullins effect. The Mullins effect, also known as stress softening, refers to a change in material behavior resulting from prior deformation. The results of cyclic inflation experiments performed with latex rubber balloons are presented. Some interesting aspects of the inflation behavior are noted, and the effect of preconditioning on the inflation behavior is quantified. The balloons are modeled as incompressible, spherical membranes which undergo an equibiaxial extension during inflation. This model is used to calculate the stress-strain behavior of the balloon material in an equibiaxial extension. We generalize a constitutive equation for the Mullins effect in uniaxial extension, first proposed by Johnson and Beatty [1], to an equibiaxial extensional deformation. We are able to make certain predictions about the results of our balloon inflation experiments without specification of the two functions which comprise the constitutive equation. Our method of interpretation of experimental results from the balloon inflation tests is similar to the method in [1] for the small transverse vibration of a stretched rubber cord. Finally, we demonstrate that the equibiaxial extensional deformation of an isotropic, incompressible material is kinematically equivalent to the uniaxial compression of that material. The results of our balloon inflation experiments are used to calculate the stress softening behavior of latex rubber in uniaxial compression. The calculated behavior indicates that latex rubber does indeed stress soften in uniaxial compression. This observation confirms the early experimental findings of Mullins [2], but contradicts the analytical predictions of Lee and Williams [3].

Planar and fibre textures induced in isotactic polypropylene on equibiaxial hydrostatic deformation

Wide-angle X-ray scattering studies on equibiaxially deformed isotactic polypropylene (i-PP) have been carried out. The equibiaxial deformation is achieved by uniaxial compression below the melting point at 60 and 140°C. The study proves the equibiaxiality of the deformation with the observation of two types of crystal textures referred to as planar and fibrillar. These textures are quantified by relating the intensity distribution for a (110) reflection to the orientation distribution of the crystals. The signature of the fibre-like texture in the intensity distribution (of a given ( hkl) reflection) is obvious; the manifestation of the planar texture requires a closer analysis of the pole figure. An ‘exact method’ of formulation is used to estimate the relative fractions of the two textures. The quantitative change in the relative fraction as a function of compression ratio is explained in terms of a qualitative model based on slip systems. The mechanism of the texture developed in i-PP as a function of compression ratio is discussed in the light of crystal slip systems and the order-disorder transition during the deformation process. The latter phenomenon is shown to be a favourable route to obtaining a high chain orientation and a larger amount of the planar texture relative to the fibrillar texture.

Equibiaxial deformation of poly(4‐methyl‐1‐pentene) by a forging process

AbstractPoly(4‐methyl‐1‐pentene) (PMP) has been uniaxially compressed by a forging (equibiaxial) process. The rheology of the process has been examined for this semicrystalline polyolefin, melting point about 235°C. The yield energy, area under the compressive stress‐strain curve up to the yield point, as a function of temperature was found to consist of two linear components of different slope. These two linear relations arise from the glassy and crystalline phases of PMP. The intercept temperature (Ti) at zero yield energy for the glassy phase has been evaluated. The attainable maximum compression ratio without sample rupture (CRmax) increased steadily on increasing forging temperature above Ti, and below Tm. In this range, the crystalline relaxation temperature (Tc), evaluated from an Arrhenius plot of yield stress was 160°C. Above Tc, a CRmax of 240 was reached. This value is five times higher than that attained for isotactic polypropylene (i‐PP). However, the draw efficiency evaluated by elastic recovery in the plane direction of PMP (0.76) is lower than for i‐PP (0.97). Differential scanning calorimetry analyses showed that the melting peak became a complex doublet on increasing compression ratio ( > 100). The drawing and stress‐strain behavior of PMP are compared with i‐PP. © 1994 John Wiley & Sons, Inc.

A Theoretical Analysis of Equibiaxial Deformation Texture Under Non-prescribed Strain Path

A model is presented to calculate the rotation path of crystals under equibiaxial tension when the strain ratio is fixed (prescribed strain path) or when the strain ratio is allowed to adjust itself according to the external constraint and the current state of the plastic anisotropy of the material (nonprescribed strain path). It is found that the stability of grain orientation is related to the curvature of the strain path. There is a difference in the predicted equibiaxial deformation texture for the two types of strain paths. Grain orientations which are unstable under a linear strain path may become stable under a non-linear or varying strain path.

Strain-Hardening Characteristics of Aluminum-1050A, α-(70/30) Brass, and Austenitic Stainless Steel under Biaxial Loading

Abstract The biaxial strain-hardening behaviors of aluminum, α-brass, and austenitic stainless steel are characterized in plane and equibiaxial deformation paths using a novel low-cost biaxial device. These tests are complemented by conventional uniaxial tensile tests and by complex strain path studies consisting of uniaxial tension after biaxial pre-strain. The experimental results are analyzed and compared using two criteria of plasticity: von Mises and Hill. It is shown that different stress-strain curves obtained under different strain paths could not be correlated with the phenomenological yield criteria.

Evaluation of free and hydrostatic equibiaxial deformation of poly(ethylene terephthalate) by trirefringence measurement

Understanding the deformation behavior of an amorphous thermoplastic, e.g., poly(ethylene terephthalate) (a-PET) and one of semicrystallinity, viz., i-PP, can be is of both fundamental and practical importance. Much has been done to study the influence of temperature and strain, but not the influence of deformation conditions on the three-dimensional orientation of many thermoplastic. In this study we consider the incremental effect of hydrostatic pressure and process geometry on strain-induced deformation. a-PET has been free drawn (i.e., no hydrostatic pressure) isothermally on a tenter frame device. The hydrostatic, equibiaxial deformation was achieved by a forging process involving squeezing between two circular plates. These two processes have been carried out at a series of deformation rates, with the three-dimensional refractive index measurements having been made on the PET and i-PP films using a modified Abbe refractometer, as per Samuels. The reported trirefringence measurement provides a sensitive scale for the planar deformation.

The Mechanics of Equibiaxial Hydrostatic Deformation in Solid State: Isotactic Polypropylene

Equibiaxial, hydrostatic deformation of isotactic polypropylene (i‐PP) of an intermediate weight average molecular weight (2.9×105) has been achieved by uniaxial compression between two axially aligned circular cylinders at the desired draw temperature (TDR). Independent measurements of load (i.e., stress) and displacement (i.e., strain) are made during the course of deformation. A systematic variation in TDR (from 30–130°C) at a ram speed of 0.25 in./min. has been studied. The stress‐strain data corrected for machine compliance has been compared to a theoretical model. This model assumes a rigid‐plastic behavior with a hydrostatic pressure effect. The shear stress at the wall, caused by metal‐polymer contact, is coulombic friction. As the compressive force (and, hence the hydrostatic pressure) is increased, the frictional shear stress (in the central portion of the compressed sample) exceeds the maximum shear stress (also changing with hydrostatic pressure), causing the i‐PP to yield on the surface (referred to as “stiction”). The friction to “stiction” transition is continuous on the stress‐strain curve, but is explicitly observed as a “skin” under an optical microscope with crossed polars. The model quantifies the onset of “stiction” and gives a threshold friction coefficient (depending on material properties) below which the polymer will not shear at the wall! The static friction coefficient between metal and polymer is the only empirical parameter to fit the stress‐strain data (within 5%) up to compression ratios>700%. A quantitative measurement of the Bauschinger effect is obtained by simultaneous measurement of yield stress under compression and tension in a single experiment.

The influence of multiaxial states of stress on the hydrogen embrittlement of zirconium alloy sheet

The ductility of ZIRCALOY *-2 sheets containing 21-615 wt ppm hydrogen has been investigated at room temperature over a range of stress states from uniaxial to equibiaxial tension. Data based on locally determined fracture strains show a decrease in ductility with both increasing hydrogen content and increasing degree of biaxiality of the stress state. Metallographic and fractographic examinations indicate that the embrittlement is a consequence of void nucleation (due to hydride fracture), void growth, and void link-up. The influence of hydrogen content and stress state on each of the sequential stages of ductile fracture is determined. These results indicate that the primary cause for the influence of stress state on the hydrogen embrittlement of the ZIRCALOY sheet is that void link-up is initiated at a much lower critical void density in equibiaxial tension than in uniaxial tension. This appears to be a result of equibiaxial deformation enhancing (a) direct participation of previously unfractured hydrides in providing a fracture path linking up voids and (b) a localized shear instability process which is triggered by the nucleation of voids.

Hydrogen embrittlement of titanium sheet under multiaxial states of stress

The influence of hydrogen on the ductility of commercially pure titanium sheet has been investigated over a range of stress states from uniaxial to equibiaxial tension. The data show that hydrogen embrittlement of plastically anisotropic Ti sheet depends on stress state, being the most severe in equibiaxial tension. Quantitative metallography indicates that the effect of stress state is primarily a result of two factors: (1) plane strain and equibiaxial tensile deformation are especially effective in causing the strain-induced fracture of hydrides and consequently void formation, and (2) the void link-up process in plane strain and equibiaxial tension initiates at a comparatively low bulk void density. The results are analyzed in terms of the influence of stress state on both hydride fracture and the occurrence of shear instabilities triggered by hydride fracture/void nucleation.