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  • 1965-1969  (10)
  • 1
    Electronic Resource
    Electronic Resource
    Higher spectra approximations derived from multistep loading (1967)
    Springer
    Colloid & polymer science 215 (1967), S. 149-157 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Zusammenfassung Ein Programm, bei dem ein vernetztes Polymeres mit diskontinuierlichen Sprüngen von gleichem zeitlichem Abstand und konstanter Amplitude in bezug auf Dehnung oder Spannung belastet wird, kann höhere Näherungen für Retardations- und Relaxationsspektra mit einem ausreichenden Grad an Genauigkeit liefern, vorausgesetzt, daß dasBoltzmannsche Superpositionsprinzip nicht verletzt wird. Im Falle der Retardationsspektren ist die Mehrstufenbelastung ersetzbar durch eine anfängliche Kriechbelastung, gefolgt durch Stufen der Entlastung mit gleichen Amplituden und gleichen Zeitabständen. In dem Fall, daß eine exakte Master-Kurve für das Material durch Anwendung des Prinzips der reduzierten Variablen erlangbar ist, gewährt diese Kurve genügend Information für die Ermittlung des Retardationsoder Relaxationsspektrum mit ausreichender Näherung. Beispiele werden für die Gewinnung von Retardations- und Relaxationsspektren bis zu ihrer dritten Näherung für ein Epoxidharz und für ein Polyurethan-Elastomeres unter Verwendung der Mehrstufenmethode gegeben. Drei Näherungen der Relaxationsspektren für N.B.S., Polyisobutylen und Polymethylmethacrylat werden aus den Master-Kurven abgelcitct.
    Notes: Summary A multistep loading programme for a cross-linked polymer with equidistant discontinuities jumping with constant amplitudes of stress or strain may yield higher approximations of the retardation or relaxation spectra to any degree of accuracy provided that theBoltzmann superposition principle is not violated. In the case of retardation spectra the multistep loading programme can be replaced by an initial creep loading followed by steps of recovery of equal amplitudes and time. In the case when an accurate composite curve of the material is available by application of the principle of reduced variables, this curve yields sufficient information for the tracing of retardation or relaxation spectra to any degree of approximation. Examples are given for the tracing of retardation and relaxation spectra up to their third approximation for an epoxy polymer and a polyurethane elastomer by using the multistep method. Three approximations of relaxation spectra for N.B.S. Polyisobutylene and Polymethylmethacrylate are also derived from their composite curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01520396
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  • 2
    Electronic Resource
    Electronic Resource
    Time dependence of creep recovery in cross-linked polymers (1967)
    Springer
    Rheologica acta 6 (1967), S. 246-251 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Summary Transient creep recovery tests in simple tension were performed in a series of cross-linked high polymers in pure and plasticized states. A loading cycle was adopted according to which each specimen was loaded in creep for a time period of 16′ followed by recovery for the same time period. This loading cycle was repeated for various steps of temperature from ambient temperature up to a temperature corresponding to the rubbery region of each polymer. It was shown that, while the 15″ measurements of deformation after loading or unloading were approximately equal, recovery individual curves were always lagging in time the corresponding creep curves. Composite curves of creep or recovery deformation in semi-log time scale reduced to a temperature of 30 °C were plotted by applying the method of reduced variables. The creepdeformation composite curve was always advancing in time relatively to the respective recovery composite curve. This phenomenon was an accumulation of the partial difference of the corresponding individual curves. Time-shift factor versus temperature curves for creep and recovery were plotted and compared. It was established that the remaining deformation after 16 minutes of a 16′ creep recovery normalized to the initial deformation at the beginning of recovery, if plotted versus temperature, presented the same shape of curves for all types of materials tested. The maxima of these curves were diminishing with addition of plasticizer according to a straight line.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01976441
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  • 3
    Electronic Resource
    Electronic Resource
    Phenomenical analysis of linear viscoelastic media (1966)
    Springer
    Colloid & polymer science 209 (1966), S. 34-43 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Zusammenfassung Einfache Typen von Grund-Gleichungen, die das Verhalten von viskoelastischem Material im linearen Bereich auszudrücken gestatten, werden aus Näherungsbeziehungen abgeleitet, die die charakteristischen Funktionen zur Beschreibung mechanischen Fließens rheologisch einfacher Substanzen wiedergeben. Es wurde früher experimentell gezeigt, daß das Paar von Differential- oder Integral-Operatoren, erforderlich zur Definition des viskoelastischen Verhaltens linearen Materials für das Gesamtspektrum, mit einer guten Näherung zu einer einzigen Operatorbeziehung und einem Anfangswert reduziert werden kann. Es wird eine indirekte Methode eingeführt, welche die oberen und unteren Grenzen für die weniger empfindlichen charakteristischen Funktionen, die die Kompressibilität und das Querkontraktionsverhältnis beschreiben, liefern. Die Gleichungen für die Bulk-Compliance und den Bulk-Modul, sowie für die komplementäre Querkontraktion für Kriechen und Relaxation sind durch einfache Produkt-Korrektionsformeln ausgedrückt, wobei die Werte dieser Funktionen in demn-Subintervall der Zeit in Termen der entsprechenden Anfangswerte des Glas- oder Gummizustandes definiert sind, multipliziert mit den Verhältnissen der aufeinanderfolgenden Werte des entsprechenden Dehnungsmoduls bzw. Dehnungscompliance. Die Ergebnisse wurden ausführlich an verschiedenen Typen von linearem Material geprüft, wie auch mit den Werten aus anderen charakteristischen Funktionen berechnet und verglichen.
    Notes: Summary Simple types of constitutive equations appropriate to materials exhibiting linear viscoelasticity are derived from approximate relationships interconnecting the characteristic functions which describe the transient mechanical properties of rheologically simple substances. It has been previously shown experimentally that the pair of differential or integral operators necessary to define the viscoelastic behaviour of a linear material along the whole viscoelastic spectrum may be reduced, to a high degree of approximation, to one operator relationship and an initial value. An indirect method is introduced which yields upper and lower bounds for the less sensitive characteristic functions expressing the bulk and the lateral contraction ratio variation. The constitutive equations for the bulk compliance and modulus, as well as the complementary lateral contraction ratio functions for creep and relaxation are expressed by simple product correction formulas, where the values of these functions at then-subinternal of time are defined in terms of their corresponding initial values at the glassy or rubbery state multiplied by the ratios of the consecutive values of the corresponding extension compliance or modulus. The results checked well with extensive experimental evidence on various types of linear materials, as well as with the values calculated from the corresponding values of the other characteristic functions related to them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01500044
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  • 4
    Electronic Resource
    Electronic Resource
    Interrelation between dynamic moduli and compliances in polymers (1969)
    Springer
    Colloid & polymer science 235 (1969), S. 1182-1188 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Based on the fact that, for a large number of polymers, the lateral deformation in tension is a contraction and the volume dilatation must be positive, bounds were established for the values of the lateral contraction ratio functions in creep and relaxation. These bounds are thatv *=(v′ -i v″) must be positive and smaller than 0.5. It was shown in the paper that in the case whenv* is positive, the loss tangents for various modes of deformation in relaxation or creep follow the relations: a) For relaxation: tanδ G 〉 tanδ E 〉 tanδ m 〉 tanδ K 〉 tanδ vr b) For creep: tanδ j 〉 tanδ D 〉 tan δM 〉 tanδ B 〉 tanδ vc where the indicesG andJ correspond to a shear mode of deformation in relaxation or creep, the indicesE andD to extension, the indexM to longitudinal bulk, the indicesK andB to bulk deformation andv r andv c to the LCR functions in relaxation or creep. Extensive experimental evidence with various types of polymers submitted to different modes of loading corroborates with the results of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01542525
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  • 5
    Electronic Resource
    Electronic Resource
    Transient lateral contraction ratio of polymers in creep and relaxation (1965)
    Springer
    Colloid & polymer science 202 (1965), S. 133-139 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Zusammenfassung Gleichzeitige Messungen von Längsdehnung und Querkontraktion wurden an reinen Epoxydharzen durchgeführt, indem die Differential-Moiré-Methode angewendet wird, die Kriechverhalten und Relaxations-Master-Kurven über das ganze viskoelastische Spektrum des Materials liefert. Darüber hinaus ergibt sich das Querkontraktionsverhältnis für Kriechen und Relaxation. Beide Kurvenpaare bestimmen vollkommen das viskoelastische Verhalten polymerer Substanzen. Es lä\t sich zeigen, da\ die Querkontraktions-funktionen monoton wachsende Funktionen mit Zeit und Temperatur sind und da\ die Kriechfunktion hinsichtlich der entsprechenden Relaxationsfunktion verzögert verläuft.
    Notes: Summary Simultaneous measurements of the longitudinal extension and the lateral contraction strains in tension specimens made from a pure epoxy polymer by using the differential moiré method yielded the extension creep compliance and relaxation modulus master curves along the whole viscoelastic spectrum of the material. Moreover, they provided the lateral contraction ratio curves in creep and relaxation. Both pairs of curves determine completely the viscoelastic behavior of the polymeric substances. It was shown that the transient lateral contraction ratio functions are monotonically increasing functions with time and temperature and the creep function is lagging in time with respect to the corresponding relaxation function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01497100
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  • 6
    Electronic Resource
    Electronic Resource
    The formation of necking in polycrystalline steel (1967)
    Springer
    Acta mechanica 3 (1967), S. 103-122 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Zur Ermittlung der Spannungs- und Verzerrungsverteilung in der Umgebung der Einschnürung bei dünnen, polykristallinen Stahlproben wurden Zugversuche bis knapp an die Grenze der Zugfestigkeit durchgeführt. Die experimentelle Untersuchung beschränkte sich auf das erste Stadium eines zähen Bruches, d. h. auf die Betrachtung der Instabilität in der Wechselwirkung zwischen geometrischen Faktoren und solchen der Verfestigung in der Nähe der maximalen Zugbelastung und der daraus folgenden Ausbildung der Einschnürung. Der Vergleich eines auf die Probe kopierten Gitterrasters mit einem Bezugsraster ergab die Verschiebungskomponenten entlang der Hauptrichtungen der Probe im Bereich plastischer Deformation. Ein schräg auf die Probe projiziertes Linienraster ermöglichte die Berechnung der Dickenänderung nahe der Einschnürung. Die Kombination dieser beiden Methoden ergab den Deformationszustand über einen weitgespannten Meßbereich bei verschiedenen infinitesimalen Belastungsschritten vor und nach der maximalen Zugbeanspruchung und erwies sich als sehr empfindlich gegenüber Verzerrungsänderungen. Die Untersuchung ergab wesentliche Charakteristika hinsichtlich der Instabilität der Spannungen und Verzerrungen vor Beginn der Einschnürung und der darauf folgenden Ausbildung und Stabilisierung der Lage und Größe des Einschnürungsbereiches.
    Notes: Summary Tensile tests of thin-flat specimens of polycrystalline steel were carried out at the vicinity of their ultimate tensile strength to determine the strain- and stress-distribution at the neighborhood of the neck. The experimental analysis was restricted to the study of the first stage of a ductile fracture i. e. the study of the instability in balance between geometric and strain-hardening factors at the vicinity of the maximum tensile load with the subsequent initiation and formation of the neck. Mechanical interference of crossed gratings photoprinted on the surface of thinflat specimens, and similar reference gratings yielded the components of displacements along the principal directions of the specimens at the plastic domain of deformation. Interference of a line grating superimposed on the specimen and obliquely illuminated and viewed, and its shadow on the matt reflective surface of the specimen allowed the evaluation of the thickness variation at the neighborhood of the neck. The combination of these two methods gave the state of deformation over a large gage area at various infinitesimal loading steps before and after the maximum tensile load and it proved to be very sensitive to strain-variation. The experimental study revealed important features of the phenomenon of instability of stresses and strains preceding the initiation of neck, as well as the subsequent appearance, evolution and stabilization of the position and size of the necked area.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01453710
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  • 7
    Electronic Resource
    Electronic Resource
    Surface topography by multisource moiré patterns (1968)
    Springer
    Experimental mechanics 8 (1968), S. 82-87 
    Details
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Moiré patterns produced by interference of a series of periodically arranged linear light sources with a line-specimen grating of similar pitch are located at a plane parallel to the sources and the specimen grating and at some distance away from these planes. A transparent or reflecting specimen located at a distance from the specimen grating distorts the image of the multisource projected on the specimen grating due to its surface irregularities and forms a moiré pattern. This pattern yields the partial-slope contours of the topography of the specimen along a direction normal to the lines of the grating. Two such contour patterns taken at mutually perpendicular directions are sufficient to yield the complete topographic picture of the surface. The method was used for determining gradients of thickness variations in two-dimensional specimens due to lateral contraction. The technique is highly accurate in determining the values of thickness in such cases, since the integration of the slope of thickness variation along any traverse of the specimen is a steady and accurate process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02326131
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  • 8
    Electronic Resource
    Electronic Resource
    The moiré method of zonal and line gratings (1965)
    Springer
    Experimental mechanics 5 (1965), S. 267-272 
    Details
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The theory of moiré fringes produced by zonal gratings interfering with line gratings of equal or slightly different pitch was developed. Differential equations relating the pitches of the two gratings to the interfringe spacing of the moiré pattern produced were established. It was shown that the moiré fringes produced belong to families of confocal ellipses, parabolas or hyperbolas in the cases where the zonal-grating pitch (p m ) is greater than, equal to, or smaller than the line reference-grating pitch (p r ). These patterns yielded all the displacement components of a two-dimensional strain field. Therefore, they are sufficient for the complete determination of the strain and stress distribution in any elastic or plastic plane-stress problem. As an illustration, the method has been applied to the determination of the lateral-contraction-ratio function of a polymeric substance (cold-setting pure epoxy resin) in creep at various steps of temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02327151
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  • 9
    Electronic Resource
    Electronic Resource
    The moiré method for the study of explosions (1967)
    Springer
    Experimental mechanics 7 (1967), S. 202-210 
    Details
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Explosives have been used to produce weak shock waves in central cavities of Plexiglas spheres. Shock pressures engendered were less than the so-called stable shock threshold and they resulted in a decomposition of the shock wave into an elastic precursor preceding the so-called plastic shock wave. The differential moiré method has been used to measure simultaneously the precursor and shock-wave velocities, as well as the velocity of the cavity interface. Moreover, the displacement field given by the moiré pattern yields the components of strains and the particle velocity behind each shock.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02326511
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  • 10
    Electronic Resource
    Electronic Resource
    Relaxation response of polyurethane elastomers (1965)
    New York : Wiley-Blackwell
    Journal of Polymer Science Part A: General Papers 3 (1965), S. 2619-2635 
    Details
    ISSN: 0449-2951
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The transient extension relaxation modulus E(t) and the lateral contraction ratio vr(t) for a polyurethane elastomer have been simultaneously measured in the transition region from the glassy to the rubbery consistencies of the material. The differential moiré method was used in these measurements and yielded simultaneous values of the longitudinal extension and the lateral contraction principal strains of the tension specimen. Composite curves of E(t) and vr(t) reduced to a standard temperature were obtained by applying the method of reduced variables. The time factors KT in both curves were coincident and they followed the WLF equation. The shear and bulk modulus characteristic functions were determined from the extension modulus and lateral contraction ratio functions. The values of the lateral contraction ratio in relaxation were determined by using data of the extension relaxation modulus along the whole viscoelastic range and the initial value of the lateral contraction ratio at the rubbery state and applying an indirect method. The results obtained by the indirect method coincided with the experimental values. The shear modulus function was evaluated from the extension relaxation modulus and the lateral contraction ratio functions and compared with the shear dynamic compliance determined by Landel. The experimental data indicated that a linear relationship holds between the lateral contraction ratio in relaxation and the bulk modulus along the whole response spectrum. The same relationship was previously shown to hold for a series of various polymeric substances.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/pol.1965.100030718
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