Principal Normal Stress Research Articles

Analysis of Matrix Cracking and Local Delamination in (0/ϑ/ − ϑ)s Graphite Epoxy Laminates Under Tensile Load

Three-dimensional element analyses of (0/theta/-theta)s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tensile load, were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and the free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized Mode I component near the free edge, within one-ply distance from the matrix crack. To examine the stress state causing the matrix cracking, the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increased through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface.

An analysis of the brittle-ductile transition in dynamic crack growth

The brittle-ductile transition in dynamic crack growth is investigated through the numerical analysis of a plane strain edge cracked specimen, subject to impulsive loading at one end. The material is characterized as an elastic-viscoplastic solid, with a temperature dependent flow strength. Thermal softening due to adiabatic heating and a model for ductile failure by void nucleation, growth and coalescence are incorporated into the constitutive relation. The ductile void growth mechanism involves two populations of void nucleating particles; discretely modelled low strength inclusions that give large voids near the crack tip at an early stage and homogeneously distributed small second phase particles that require large strains for void nucleation. Cleavage is modelled in terms of a spatially non-uniform, but temperature and strain rate independent, critical value of the maximum principal normal stress. The numerical results show a clear transition from cleavage dominated crack growth at low temperatures to purely ductile crack growth at higher temperatures. There is an accompanying large increase in the material's resistance to dynamic crack initiation and growth. The computed crack growth behaviour is a direct outcome of the material description; no ad hoc dynamic fracture criterion is employed. Effects of variations in the material model on the brittle-ductile transition are explored.

The determination of the partial molar volume of hydrogen in zirconium in a simple stress gradient using comparative microcalorimetry

In a simple stress gradient using comparative micro-calorimetry the role of stress in the diffusion of mobile atomic species in solids was established by Li, Oriani and darken. They showed that to a very good approximation the chemical potential of a mobile species in a stressed solid is given by: {mu}{sub A} = {mu}{sub 0} {minus} p{bar V}{sub A} where {mu}{sub 0} is the chemical potential at zero stress, p is the average principal stress which is positive if tensile, and {bar V}{sub A} is the partial molar volume of the mobile atom species A, and reflects the volume change per mole of species A when an atom of A enters the solid region under consideration. They also showed that for equilibrium between stressed and unstressed regions the concentration varies with respect to p in the following way: C{sup P}{sub A} = C{sup 0}{sub A} exp p{bar V}{sub A}/RT where C{sup 0}{sub A} is the concentration at zero stress and C{sup p}{sub A} that at the stress p. Consider a specimen which is at equilibrium with respect to diffusion and which contains a stress gradient. It we can measure the concentration of the species A in regions within which pmore » varies but is well-characterized, then the value of {bar V}{sub A} can be determined. We shall return to this equation later in the paper as it is key to our development. The flux of mobile species under a gradient in free energy is given by: J = {minus}Dc/kT {del}{mu} which in combination yields the flux of a mobile species in a stress gradient: J = {minus}Dc{bar V}{sub A}/kT {del}p where D is the diffusion coefficient, c is the concentration of the species, k is Boltzmann's constant and T is the absolute temperature.« less

Strength criteria of anisotropic materials, accounting for different failure mechanisms

Static strength criteria, which take into account various failure mechanisms — separation, crumpling, shear — are proposed for anisotropic materials for general cases of triaxial and biaxial stress states. The directions of critical sites of separation, crumpling, and shear do not, generally speaking, coincide with the directions of principal normal and tangential stresses and are determined analytically. A linearized modification of strength criteria, which takes into account the effect of internal Coulomb friction, is given. A comparison is made between the strength criterion obtained and experimental data.

Influence of Stress State on the Failure Behavior of Cracked Components Made of Steel

One of the decisive factors influencing the safety of components is the capacity for plastic deformation of the material employed. This depends not only on the actual material properties, such as reduction of area or notch impact energy, but also on the stress conditions prevailing in the component. With sufficiently sharp transitions of geometrical form, or at cracks, such high multiaxial stress states can arise in components, that in spite of excellent plastic deformation capability of the malterial, practically deformationless fractures are inevitable. If one generates from the principal normal stresses (σ1, σ2, σ3) the multiaxiality quotient q, which represents a characteristic quantity for the degree of multiaxiality of the stress state, the effect of the stress states on the strength and deformation behavior of a component can be estimated. With the aid of the Sandel fracture theory, which includes the von Mises yield theory as a special case, the critical q value qc, which characterises the stress conditions leading to cleavage fracture if q < qc, can be calculated. The fracture mechanics evaluation of the sharply notched specimens of dimensions similar to components shows no dependence of the effective crack initiation value on the specimen size or stress state, since at the load free crack tip, plane stress conditions generally prevail. The further failure process after crack initiation in the form of stable crack extension is very strongly controlled by the stress state. This phase could also be estimated from consideration of the pattern of the q value in the remaining cross section. The investigations have shown that the multiaxiality quotient q, which characterizes the degree of multiaxiality of the stress state, represents a characteristic quantity with which, in combination with fracture mechanics methods, the failure behavior of components may be estimated, even with respect to stable crack extension.

Melt rheology of plasticized poly(vinyl chloride)/epoxidized natural rubber miscible blends

AbstractA study of the melt rheological behavior of miscible blends of plasticized poly(vinyl chloride) (PVC) and epoxidized natural rubber (ENR) was carried out with a capillary rheometer. Melt viscosity and melt elasticity behavior was determined and surface characteristics of the extrudate was examined by using a scanning electron microscope. Melt viscosity of plasticized PVC increased with ENR content at higher processing temperatures. The melt elasticity parameters such as die swell ratio, principal normal stress difference, and recoverable shear strain at a particular shear stress increased with temperature up to a 50 wt % composition of ENR in blends. For high ENR blends the die swell ratio and recoverable shear strain decreased with temperature, and the principal normal stress difference and elastic shear modulus remained independent of temperature for all values of shear stress. It was noted that the nature of deformation in the surface layer was linear for a smooth extrudate and nonlinear for a distorted extrudate. Moreover, recoverable shear strain was found to have a correlation with the extrudate distortion of the melts.

A METHOD OF PREDICTING SOIL STRESS STATE UNDER TIRES

ABSTRACT A method was developed to predict the complete stress state at a point in the soil due to an imposed load from a tire on the soil surface. The method may be used to investigate the influence of stress distribution at the soil-tire interface on the stress state in the soil. The mean normal, octahedral shear, maximum principal, and vertical normal stress and their directions may be predicted. The complete stress state is predicted based on the Froelich equation and the modified Cerruti equation.

YIELD FUNCTION OF UNSATURATED SOIL UNDER TRIAXIAL COMPRESSION

Unsaturated soil can be simulated to elasto-plastic material. Based on the test results of suction controlled triaxial test on compacted kaolin clay, theoretical initial yield function and subsequent loading function are induced. Then the theory is examined by stress-probe test. In this paper triaxial stress state is defined by three stress components, they are, effective average principal stress, p=σm-ua, effective suction stress, f(S)=χ(ua-uw) at failure condition, and deviator stress, q=σ1-σ3, in which ua and uw are pore air and pore water pressure, respectively. Only one loading function similar to Original Cam Clay is obtained from the theory, on the other hand, results of stress-probe test indicate the presence of additional yield surface like failure surface besides one theoretically predicted.

Estimating the stressed state of soils from measurement of infrared radiation flux

1. In compacted dry and slightly moist sands and clays of different gradiation, density, and moisture content, the change in the density of the IR-radiation flux is proportional to the change in the sum of the three principal normal stresses in the specimen. 2. The thermoactivity coefficient of sand depends heavily on its initial density and moisture content, while the difference in the gradation does not affect this coefficient in our investigations. 3. For compacted sands subjected to unloading, hysteresis is virtually absent on the curve denoting the change in the density of the IR-radiation flux versus the change in the indicated invariant of the stress tensor. 4. The method of evaluating the stressed state of soil on the basis of the ΔW level makes it possible to perform noncontact and remote measurements; it can therefore be used to monitor the state of a soil subjected to variable and quasistatic loads.

Dynamic stress analysis of a coil spring of arbitrary cross-section to general transient excitations

Dynamic stresses in a coil spring of arbitrary cross-section subjected to general transient displacement with consideration of end effects are discussed. An analytical method is given for finding normal and shear stresses in the coil by use of the transfer matrix, the Laplace transform, Fourier expansion and the Fourier expansion collocation methods based on the three-dimensional theory for curved rods. For the circular cross-section coil, the stress differs along the boundary of the cross-section and has a maximum value at an interior point of the coil. The more effective coil spring having an oval cross-section is proposed. Both the principal normal and shear stresses along the surface of the proposed coil subjected to a transient excitation have been calculated. It is shown that the oval cross-section coil with an appropriate aspect ratio has various advantages as compared with the circular cross-section coil.

Melt elasticity behavior and extrudate characteristics of rigid poly(vinyl chloride)/epoxidized natural rubber miscible blends

AbstractA study on the melt elasticity behavior and extrudate characteristics of melts of rigid poly(vinyl chloride), PVC, and rigid poly(vinyl chloride)/epoxidized natural rubber (ENR) miscible blends were conducted. Extrusion studies were carried out in a capillary rheometer and examinations of the surface characteristics of the extrudate were made by taking photomicrographs in a scanning electron microscope. The anomalous behavior in the die swell ratio of rigid PVC arising from the particle agglomerates continued in its blends up to 50 wt% composition of ENR. Temperature independence for high ENR blends was noted for the principal normal stress difference and elastic shear modulus, when shear stress was held constant. Recoverable shear strain and die swell ratio behaved identically in terms of blend composition and processing temperature. Factors which control the extrudate distortion and melt fracture of the melts of rigid PVC/ENR systems were fusion of particle agglomerates and strength of melts. Diamond cavitations were typical of the extrudate surface of PVC melts as those of the fracture surface of the tensile failure of PVC. Conditions to obtain a smooth extrudate surface of rigid PVC melts in blends with ENR have been found to be the low ENR content, low shear rate, or stress and high processing temperature.

Rheological and extrusion behavior of dispersed multiphase polymeric systems

An experimental study of temperature effect and composition effect on the rheological and extrusion properties of several dispersed multiphase polymer melts were investigated, using a cone-and-plate rheometer and a capillary rheometer. The polymeric systems studied included three homopolymers (two polystyrenes and one poly(methyl methacrylate) (PMMA)), a mechanically blended copolymer of polystyrene and PMMA, two graft copolymers (rubber-modified polystyrene and PMMA), and three particulate-filled polystyrene (CaCO3, milled glass fiber, and glass flake). It was found that the principal normal stress difference plotted against shear stress gives rise to a temperature independence for all dispersed multiphase polymeric systems. Composition independent correlations, however, do not exist for the principal normal stress difference. The extrudate swell plotted against shear stress becomes independent of temperature only for the homopolymers and graft copolymers. For the mechanically blended polymers and particulate-filled polymers, the temperature independent correlation does not exist. The reduction in viscosity of the glass fiber- and glass flake-filled polystyrenes is found due to the degradation of the base polymer during mixing.

Mechanical Stresses on Closed Cusps of Porcine Bioprosthetic Valves: Correlation with Sites of Calcification

The purpose of this study was to (1) evaluate the magnitude and distribution of mechanical stresses on closed leaflets of porcine bioprosthetic valves (PBVs) by using a nonlinear, finite-element model, and (2) determine if a relationship exists between the magnitude of stresses at various sites on the leaflet and the incidence of calcification at those sites. Mechanical stresses were found to be highest near the commissures and lowest at the base of the leaflet. At a pressure of 100 mm Hg applied to the closed valve, the maximal principal normal stress was 160 kPa near the commissures, 140 kPa in the body of the leaflet, 70 kPa at the free margin, and 60 kPa near the base. Similarly, the maximal shear stress, at an applied pressure of 100 mm Hg, was 80 kPa near the commissures, 70 kPa in the body of the leaflet, 50 kPa at the free margin, and 40 kPa near the base. This distribution of mechanical stresses on the PBV leaflet coincided with the incidence of calcification of the various regions of the leaflet. Calcification was found most frequently near the commissures, less frequently in the body of the leaflet and free margin, and least frequently at the base. These observations suggest a possible causative relation between the magnitude of mechanical stresses and the site of calcification of PBV leaflets.

A comparative experimental study of the isothermal shear and uniaxial elongational rheological properties of low density, high density and linear low density polyethylenes

The rheological properties of a series of sixteen polyethylene melts with different molecular weights, molecular weight distributions and types of long chain branching have been investigated. Measurement of shear viscosity, principal normal stress difference and elongational flow response are included. The behavior of high density polyethylenes and linear low density polyethylenes are described in an equivalent way in terms of their molecular weights and molecular weight distribution. The LDPE response is different, being strongly influenced by the extent of long chain branching. This appears to elevate normal stresses, and introduce substantial “strain rate hardening” in uniaxial extension. The experimental data are interpreted in terms of the theory of second-order fluids and the convected Maxwell model. The influence of long chain branching as well as molecular weight distribution on constitutive equation parameters is discussed.

Estimation of mechanical stresses on closed cusps of porcine bioprosthetic valves: Effects of stiffening, focal calcium and focal thinning

The magnitude and distribution of mechanical stresses acting on the closed cusps of porcine bioprosthetic valves (PBVs) were estimated using a finite element model. The effects of leaflet stiffening, focal calcium and focal thinning on leaflet stresses were determined. In a normal closed PBV leaflet, stresses increased as pressure was increased. At a pressure of 80 mm Hg, the maximal normal principal stresses were 11 g/mm 2 near the center of the leaflet and increased to 19 g/mm 2 at a pressure of 160 mm Hg. These observations suggest that the closed valve in the mitral position would experience higher mechanical stresses than the closed valve in the aortic position. Tissue stiffening increased stresses throughout the leaflet and introduced a site of stress concentration near the center of the leaflet. At a pressure of 80 mm Hg, the maximal principal normal stress increased 55% when the leaflet was stiff in comparison to the normal leaflet. Focal calcium and focal thinning caused marked gradients of stress between the sites of calcium or thinning and the immediate surrounding tissue. The magnitude of these stress gradients increased with increasing pressure. These sites of mechanical stress concentration or stress gradients appear to be compatible with sites of leaflet calcification or disruption. Such stresses may contribute to spontaneous degeneration of PBVs.

High density polyethylene/polystyrene blends: Phase distribution morphology, rheological measurements, extrusion, and melt spinning behavior

AbstractAn experimental study of the development of phase morphology, rheological properties, and processing behavior of mechanical blends of a polystyrene (PS) and a high density polyethylene (PE) is presented. Phase morphologies were determined by scanning electron microscopy for (i) products prepared in a screw extruder/static mixer system, (ii) samples removed from a cone‐plate viscometer, (iii) extrudates, and (iv) melt spun fibers. Disperse phase dimensions were measured. The values varied from 1–5 μm in the products from static mixers. The dimensions of the dispersed phase in the blend products from the cone plate and capillary die were of the same order. The melt‐spun fibers exhibited disperse phase dimensions as low as 0.35 μm. Polystyrene was extracted from the blend fibers producing small diameter, PE fibrils, or minifibers. Both the initial melts and the blends were rheologically characterized. The shear viscosity and principal normal stress difference N1 exhibit maxima and minima when plotted as a function of composition. The characteristics of extrudates and melt spinning behavior of the blends were investigated. The shrinkage of extrudates of PE is much greater than PS. Additional small amounts of PE to PS greatly increase its shrinkage. Addition of PE to PS initially increases extrudate swell, though the swell shows maxima and minima when considered as a function of composition. The positions of the maxima and minima correspond to those of N1. The onset of draw resonance has been investigated in isothermal melt spinning. Wide angle X‐ray diffraction studies have been carried out on blend fibers and the orientation of the crystalline polyethylene regions has been determined as a function of process conditions. This orientation decreases rapidly with the addition of polystyrene when the melt‐spun filaments are compared at the same spinline stress or drawdown ratio.

Polypropylene/nylon 6 blends: Phase distribution morphology, rheological measurements, and structure development in melt spinning

AbstractA series of polypropylene (PP)/nylon 6 (N6) blends of composition 75/25, 50/50, and 25/75 have been prepared in a screw extruder combined with a Koch static mixer. The phase morphology was observed with a scanning electron microscope. The influence of heating in the reservoir of a rheometer followed by subsequent extrusion through a capillary on the phase morphology was investigated. Phase size growth as a function of time was observed under quiescent and mild deformation rate conditions. The discrete phase size was observed to decrease with increasing extrusion rate through dies. The shear viscosity and principal normal stress difference of the blends were measured as a function of composition. The crystalline orientation of both polypropylene and nylon 6 in blend melt spun fibers was characterized by wide angle X‐ray diffraction and interpreted in terms of Hermans–Stein orientation factors. The orientation increases with drawdown ratio. The orientation factors for the polypropylene phase vary with spinline stress in a manner independent of composition and identical to that for pure polypropylene. Extracting melt spun blend fibers with formic acid has produced small‐diameter polypropylene minifilaments with diameters of the order of microns.

The influence of particle size and surface coating of calcium carbonate on the rheological properties of its suspensions in molten polystyrene

AbstractThe rheological properties of polystyrene melts filled with 30 vol % of CaCO3 particles of varying particle size are described. The influence of surface coating the particles with stearic acid is considered. Generally, the compounds with the uncoated particles exhibit viscosities which increase at ever greater rates as the shear rates decrease. It appears that these compounds exhibit yield values. Elongational flow data also suggest the existence of yield values. Difficulties exist in measurement of normal stresses in compounds with sizeable yield values. The principal normal stress difference at fixed shear stress of the PS/CaCO3 compounds is lower than that of the PS melt. The magnitude of viscosity increases and yield values increase with decreasing particle size. Coating of particles with stearic acid results in major viscosity reductions and decreases in apparent yield values. The surface coating is most effective with the smallest particles. It presumably reduces interaction between particles and the extent of aggregation.

Comparison of the predictions of viscoelastic and plastic-viscoelastic fluid model to the rheological behaviour of polystyrene and polystyrene-carbon black compounds

The rheological properties of a polystyrene melt and its compounds with carbon black are compared with a non-linear viscoelastic fluid theory and a plastic-viscoelastic fluid model. Shear viscosities, principal normal stresses and elongational viscosities are investigated for melt and compound. The relaxation spectra for the melt was determined with an eccentric disc rheometer. The Bogue-White model gave satisfactory agreement for the melt with an “a” parameter of 0.5. For the plastic-viscoelastic fluid theory, a Bogue-White model was used to represent theH functional. Theτi and “a” parameters were taken to be the same as for the pure melt while theGi were increased by a hydrodynamic factor. A yield value was obtained from the compound data. Generally good agreement was found but some discrepancy exists for the elongational flow experiments.

A comparative study of the thermotropic mesomorphic tendencies and rheological characteristics of three cellulose derivates: Ethylene and propylene oxide ethers and an acetate butyrate ester

Samples of cellulose acetate butyrate (CAB) hydroxypropyl cellulose (HPC) and ethyl cellulose (EC) are contrasted with commercial (atactic) polystyrene (PS) and isotactic polypropylene (PP) in studies of (i) differential scanning calorimetry, (ii) quiescent polarized light microscopy (iii) optical retardation variation following an imposed stress field. It is concluced that HPC and EC are thermotropic liquid crystals, while CAB behaves in a manner similar to a vitrifying isotropic melt such as PS. Studies of the shear viscosity and dynamic viscosity indicate HPC and EC exhibit yield values while CAB shows a zero shear viscosity and Vinogradov-Malkin reduced viscosity curve identical to PS. The normal stress and extrudate swell behavior of CAB are also similar to PS. The HPC and EC exhibit substantially reduced extrudate swell. Measurement of the principal normal stress difference behavior of the HPC melt is troubled by the existence of yield values.