The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

Heat transfer from a vertical tube bundle under natural circulation conditions

A rectangular loop (thermosyphon) was used to measure the average heat transfer coefficients for water at atmospheric pressure under natural circulation conditions. A twenty-one tube bundle with tubes 1.65 m long and 9.55 mm in diameter, and a pitch-to-diameter ratio of 1.33, was used as a test heat exchanger in one of the vertical legs of the loop. A natural circulation flow in the loop developed due to buoyancy differences of the fluid in its two vertical legs. Flow visualization experiments were performed to determine the flow regimes associated with natural circulation flow longitudinal to a tube bundle. Empirical correlations for the average Nusselt number have been developed and are reported. Grid spacers arranged on tube bundles were shown to enhance heat transfer, especially for laminar flow, without any noticeable increase in pressure drop.     

A pseudo-elastic material damage model,part I: Strain energy density criterion

A failure criterion is presented which relates the strain energy density of the material to both yielding and fracture. Cumulative material damage throughout a structural component may be monitored and the relative influence of yielding and stable crack growth assessed. The criterion is demonstrated, using finite element analysis, for center cracked panel specimens differing by material toughness values. From crack growth increment predictions using the uniaxial stress-strain behavior of the material, the criterion predicts the critical value of the strain energy density factor S_c governing crack instability.     

Analyses of steady quasistatic crack growth in plane strain tension in elastic-plastic materials with non-isotropic hardening

Steady state crack propagation problems of elastic-plastic materials in Mode I, plane strain under small scale yielding conditions were investigated with the aid of the finite element method. The elastic-perfectly plastic solution shows that elastic unloading wedges subtended by the crack tip in the plastic wake region do exist and that the stress state around the crack tip is similar to the modified Prandtl fan solution. To demonstrate the effects of a vertex on the yield surface, the small strain version of a phenomenological J₂, corner theory of plasticity (Christoffersen, J. and Hutchinson, J. W. J. Mech. Phys. Solids,27, 465 C 1979) with a power law stress strain relation was used to govern the strain hardening of the material. The results are compared with the conventional J₂ incremental plasticity solution. To take account of Bauschinger like effects caused by the stress history near the crack tip, a simple kinematic hardening rule with a bilinear stress strain relation was also studied. The results are again compared with the smooth yield surface isotropic hardening solution for the same stress strain curve. There appears to be more potential for steady state crack growth in the conventional J₂ incremental plasticity material than in the other two plasticity laws considered here if a crack opening displacement fracture criterion is used. However, a fracture criterion dependent on both stress and strain could lead to a contrary prediction.     

Flow tagging velocimetry in incompressible flow using photo-activated nonintrusive tracking of molecular motion (PHANTOMM)

We report the development of a new optical flow tagging velocimetry technique for hydrodynamic flows. The method utilizes highly water-soluble caged dye Photo-Activated Fluorophores (PAF's) which serve as fluorescent tracers, with essentially indefinite lifetime. Demonstration experiments are presented in a bench-top poiseulle flow and a 5,000 gallon water channel facility. Results of experiments designed to quantify critical optical characteristics of the caged dye PAF's are also presented, as is a comparison with other, similar, optical velocimetry approaches.The authors wish to acknowledge R. B. Miles and D. Nosenchuck for several stimulating discussions, and T. Frobose and P. Howard for providing technical support. The work was sponsored by ARPA-G. Jones, Technical Monitor, and the National Science Foundation.     

Compatibility conditions for the Cauchy-Green strain fields: Solutions for the plane case

This paper considers the issues related to uniqueness and existence of a finite deformation generated by prescribed right or left Cauchy-Green strain tensor field in the plane. First, the questions of uniqueness and existence to a pre-assigned right strain field C are discussed. It is shown that the existence condition, in the context of continuum mechanics, are naturally posed using the field corresponding to the square root of C instead of C, the latter a classical approach. Then, the corresponding questions for the left strain field are considered, which is more involved. The analysis of uniqueness gives rise to an appropriate classification of the deformation fields. The question of existence is discussed and a complete solution is presented. In both the right and left cases, we stress the techniques for obtaining the corresponding deformation fields.     

Splitting,merging and spanwise wavenumber selection of Dean vortex pairs

Splitting, merging and spanwise wavenumber selection are studied during the initial development of Dean vortex pairs in a channel with mild curvature, an aspect ratio of 40, and an inner to outer radius ratio of 0.979. Two types of splitting events, and four types of merging events are evident from flow visualizations at Dean numbers from 75 to 220. These events are described in detail along with observations that occurrances of these different events are tied to spatial and temporal variations of spanwise wavenumbers of vortex pair spacing. Also discussed are frequency spectra of different events, recurrent phenomena, and the part played by splitting and merging in laminar to turbulent transition in curved channels.This study was sponsored by the Propulsion Directorate, U.S. Army Aviation Research and Technology Activity-AVSCOM, NASA-Defense Purchase Request 030030-P. Professor C. S. Subramanian provided assistance in setting up the traversing system and data acquisition systems used for this study. Mr. R. E. Hughes assisted in obtaining some of the results presented.     

Phase volume and size effects on the terminal relaxation of ABS melts

The dynamical viscoelasticity of ABS melts with different particle size was investigated at various levels of rubbery phase contents. The effects of the rubber are more pronounced in the terminal zone: a transition from viscoelastic liquid to viscoelastic solid behavior was observed which can be interpreted as a physical gelation occurring at a critical rubbery phase content. This critical content resulted in being smaller in the case of smaller particles. A quantitative explanation of the experimental findings was proposed in terms of the average interparticle distance and overlapping of the chains grafted onto the neighboring rubber particles. The gel-like transition appeared to correspond to an approximately constant level of grafted chains overlapping.Presented in part at the Symposium Recent Developments in Structured Continua, Montreal (Canada), 26–28 May 1993.     

Rime- and glaze-ice accretion due to freezing rain falling vertically on a horizontal thermally insulated overhead line conductor

A theory of atmospheric icing due to freezing rain on an overhead line conductor (OHLC) is developed. The rain falls vertically on a horizontal OHLC that is thermally insulated. It is assumed that the collection efficiency of the accretion surface is unity and that this surface is in thermodynamic equilibrium with the environment.

For air temperature T_A 0°C and raindrop temperature T_D 0°C, the freezing rain accretes as rime ice, provided that the temperature of the ice surface T_l < 0°C. The evolution equation governing the mass transfer at the accretion surface is solved analytically, yielding the shape of the rime-ice surface. Equations governing the thermal state of the rime-ice deposit are also given. These determine the onset of wet growth or glaze accretion at the upper stagnation line during suitable environmental conditions.

For environmental conditions producing an ice surface at temperature T_l = 0°gC, the freezing accretes as glaze. Equations governing the heat and mass transfer at the surface determine the shape of the glaze surface and the downward viscous motion of the unfrozen water. For T_D < 0°C, glaze evolution equations are developed for T_A 0°C and T_A 0°C. Analytical solutions of these equations are obtained. In particular, when T_D < −T_A < 0°C, the evolution equation predicts a novel limiting growth that is triangular in shape. Further study of the mass and heat transfer conditions, in the neighborhood of this final stage of glaze accretion, shows that it is maintained in thermodynamic equilibrium with its warm air environment.