Some observations of the permanent set of cross-linked natural rubber samples after heating in a state of pure shear

Experimental evidence is presented to show that when cross-linked natural rubber samples are heated in air whilst subject to a pure shear strain and subsequently freed of all forces the new force-free or set state is not related to the original force-free state by a pure shear. During a pure shear linear elements along one of the principal directions of strain remain unchanged in length; it is shown that these elements undergo an increase in length as a result of the recovery after heating. The results are compared with the predictions of the two-network theory of permanent set propounded by previous workers.

---

Zusammenfassung Vernetzte Naturkautschuk-Proben, in Luft erhitzt, zeigen bei gleicher Beanspruchung mit reiner Scherung und anschließender Entlastung einen neuen spannungsfreien (oder gesetzten) Zustand, der mit dem ursprünglichen spannungsfreien Zustand nicht durch eine reine Scherung in Beziehung steht. Durch eine solche bleiben lineare Elemente entlang einer der Hauptachsen der Spannung in ihrer Länge unverändert; es. wird gezeigt, daß diese Elemente an Länge bei der Erholung nach dem Aufheizen zunehmen. Die Resultate werden mit den Voraussagen der Zweinetzwerk-Theorie des permanent set der Autoren verglichen.

     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

---

Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

---

---

The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

Experimental and theoretical determination of frequencies of elastic toroids

Experiments are described which determine natural frequencies of five toroidal models whose major diameters are of 10 in. and whose minor diameters vary from 0.25 to 2 in. The experimentally determined frequencies are compared with the theoretical frequencies derived using the elementary theories for the in-plane and out-of-plane vibrations of circular rings of R. Hoppe and J. H. Michell, as well as the method of internal constraints. The comparative results for the frequencies are presented in tabular form.     

Dual-beam holographic deflection measurement

Deflection is recorded at different sensilivities over a limited portion of the holographic range by introducing equal but opposite phase changes into the holograms created by a dual-beam illumination. The technique does not require a partially reflecting mirror, patterns can be optically filtered for better fringe contrast and in-plane displacement can be recorded without making any modifications in the experimental setup. Results obtained from two-and three-dimensional surfaces agree well with theory and verify analytical arguments presented throughout the paper.     

Thermographic detection of adhesive-bond and interlaminar flaws in composites

This paper reports the development of a liquid-crystal passive thermographic technique for the detection of adhesive-bond-line and interlaminar flaws in composite materials. The technique was successfully used for the detection of flaws in three composite systems: E-glass/epoxy, graphite/epoxy and HMC. Thermographic results are compared to ultrasonic C-scan results to assess the relative effectiveness of the new technique. A photomicrographic study was also used to verify the detected flaws and to characterize the type and extent of the actual damage.     

Equivalent linearization for systems subjected to non-stationary random excitation

The method of eauivalent linearization is applied to the general problem of the response of non-linear discrete systems to non-stationary random excitation. Conditions for minimum equation difference are determined which do not depend explicitly on lime but only on the instantaneous statistics of the response process. Using the equivalent linear parameters, a deterministic non-linear ordinary differential equation for the covariance matrix is derived. An example is given of a damped Duffing oscillator subjected to modulated white noise.     

An extension of Reiner's “Deborah Number” concept to a Wide field of rheological investigations

Summary Reiner defined a numeric, which he called theDeborah Number to represent the ratio of a relaxation time to a natural (observation) time. This implies aMaxwell model but is readily extended to complete relaxation spectra. Similar Numbers are proposed for retardation times and also for some conditions of coagulation thixotropy and for data from certain psychophysical experiments.     

Influence of molecular weight upon drag reduction by polymers

Summary Drag reduction measurements have been made with samples of polyethyleneoxide and polyacrylamide with relatively narrow molecular weight distributions obtained by fractionation of commercial polymers. Relationships between the polymer molecular weight and the concentration required to give the same drag reduction have been determined. The influence of polymer degradation upon these relationships has been investigated.Molecular weight distributions of commercial polymers have been determined and their influence upon the drag-reducing properties is noted.The influence of wall shear stress has been investigated over the range 1.0 × 10² - 4.5 × 10³ dyn/cm². The results with unfractionated polymers were found to be consistent with other results in the literature.     

Modeling and simulation of martensitic phase transitions with a triple point

A framework for modeling complex global energy landscapes in a piecewise manner is presented. Specifically, a class of strain-dependent energy functions is derived for the triple point of Zirconia (ZrO₂), where tetragonal, orthorhombic (orthoI) and monoclinic phases are stable. A simple two-dimensional framework is presented to deal with this symmetry breaking. An explicit energy is then fitted to the available elastic moduli of Zirconia in this two-dimensional setting. First, we use the orbit space method to deal with symmetry constraints in an easy way. Second, we introduce a modular (piecewise) approach to reproduce or model elastic moduli, energy barriers and other characteristics independently of each other in a sequence of local steps. This allows for more general results than the classical Landau theory (understood in the sense that the energy is a polynomial of invariant polynomials). The class of functions considered here is strictly larger. Finite-element simulations for the energy constructed here demonstrate the pattern formation in Zirconia at the triple point.