# ASTM D4092-07 (Reapproved 2013)

Designation: D4092 − 07 (Reapproved 2013)Standard Terminology forPlastics: Dynamic Mechanical Properties1This standard is issued under the fixed designation D4092; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the Department of Defense.1. Scope1.1 This terminology is a compilation of definitions anddescriptions of technical terms used in dynamic mechanicalproperty measurements on polymeric materials, includingsolutions, melts, and solids. Terms that are generally under-stood or defined adequately in other readily available sourcesare either not included or sources identified.1.2 A definition is a single sentence with additional infor-mation included in notes. It is reviewed every five years andthe year of the last review or revision is appended.1.3 Definitions identical to those published by anotherstandards organization or ASTM committee are identified withthe abbreviation of the name of the organization or the ASTMcommittee.1.4 Descriptions of terms specific to dynamic mechanicalmeasurements are identified with an italicized introductoryphrase.NOTE 1—This terminology standard is similar to ISO 6721–1 however,the ISO document cites fewer terms.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD883 Terminology Relating to PlasticsD2231 Practice for Rubber Properties in Forced Vibration(Withdrawn 1998)3E6 Terminology Relating to Methods of Mechanical Testing2.2 ISO Standards:4ISO 472: 1988 (E/F) DefinitionsISO 6721–1 1994 (E) Plastics-Determination of DynamicMechanical Properties, Part 1, General Principles3. Terminology Definitions and Descriptionsalpha (α) loss peak (in dynamic mechanical measurement)—the first peak in the damping curve below the melt, in orderof decreasing temperature or increasing frequency. (1981)beta (β) loss peak (in dynamic mechanical measurement)—thesecond peak in the damping curve below the melt, in orderof decreasing temperature or increasing frequency. (1981)complex modulus, E*, K*, or G*—the ratio of the stress tostrain where each is a vector that may be represented by acomplex number.E*=E + iE“G *=G +iG“K *=K +iK“where:E* = complex modulus, measured in tension or flexure,E = storage modulus, measured in tension or flexure,E9 = loss modulus, measured in tension or flexure,G* = complex modulus, measured in shear,G = storage modulus, measured in shear,G9 = loss modulus, measured in shear,K* = complex modulus, measured in compression,K = storage modulus, measured in compressionK9 = loss modulus, measured in compression, andi 5œ21 , measured in compression.DISCUSSION—The complex modulus may be measured in tension(E*), compression (K*), flexure (E*), or in shear (G*). (1981)complex shear compliance, J *—the reciprocal of complexshear modulus. (1981)J* 51G*1This terminology is under the jurisdiction ofASTM Committee D20 on Plasticsand is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.Current edition approved May 1, 2013. Published May 2013. Originallyapproved in 1982. Last previous edition approved in 2007 as D4092 - 07. DOI:10.1520/D4092-07R13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1complex tensile compliance, D*—the reciprocal of complextensile modulus. (1981)D* 51E*critical damping (in dynamic mechanical measurement)—thatdamping required for the borderline condition betweenoscillatory and nonoscillatory behavior. (1983).damping—the loss in energy, dissipated as heat, that resultswhen a material or material system is subjected to anoscillatory load or displacement. (1981)damping ratio, µ —the ratio of actual damping to criticaldamping. (1983).DISCUSSION—Damping ratio is a function of the logarithmic decre-ment (∆):µ 5∆/2π=11~∆/2π!25 sin arctan~∆/2π!For small values of ∆,itis:µ=∆/2πdissipation factor— see tan delta.dynamic mechanical measurement—a technique in whicheither the modulus or damping, or both, of a substance underoscillatory load or displacement is measured as a function oftemperature, frequency, or time, or combination thereof.(1981)dynamic modulus—see complex modulus.elasticity—that property of materials that causes them to returnto their original form or condition after the applied force isremoved. (1981)elastic modulus—see complex modulus and storage modu-lus.energy loss—the energy per unit volume that is lost in eachdeformation cycle. (ISO) (1983)DISCUSSION—Energy loss is the hysteresis loop area, calculated withreference to coordinate scales.free vibration (in dynamic mechanical measurement)—a tech-nique for performing dynamic mechanical measurements inwhich the sample is deformed, released, and allowed tooscillate freely at the system’s natural resonant frequency.DISCUSSION—Elastic modulus is calculated from the measured reso-nant frequency, and damping is calculated from the rate at which theamplitude of the oscillation decays. (1981)frequency profile , n—a plot of the dynamic properties of amaterial, at a constant temperature, as a function of testfrequency. (1981)gamma (γ) loss peak , n—the third peak in the damping curvebelow the melt, in the order of decreasing temperature orincreasing frequency. (1981)glass transition—the reversible change in amorphouspolymer, or in amorphous regions of a partially crystallinepolymer, from (or to) a viscous or rubbery condition to (orfrom) a hard and relatively brittle one.DISCUSSION—The glass transition generally occurs over a relativelynarrow temperature region and is similar to the solidification of a liquidto a glassy state; it is not a phase transition. Not only do hardness andbrittleness undergo rapid changes in this temperature region, but otherproperties, such as coefficient of thermal expansion and specific heat,also change rapidly. This phenomenon has been called second-ordertransition, rubber transition, and rubbery transition. The word transfor-mation has also been used instead of transition. When more than oneamorphous transition occurs in a polymer, the one associated withsegmental motions of the polymer backbone chain, or accompanied bythe largest change in properties, is usually considered to be the glasstransition. (D20) (1981)glass transition temperature, Tg—the approximate midpointof the temperature range over which the glass transitiontakes place.DISCUSSION—The glass transition temperature can be determinedreadily only by observing the temperature at which a significant changetakes place in a specific electrical, mechanical, or other physicalproperty. Moreover, the observed temperature can vary significantly,depending on the specific property chosen for observation and ondetails of the experimental technique (for example, rate of heating,frequency). Therefore, the observed Tgshould be considered only anestimate. The most reliable estimates are normally obtained from theloss peak observed in dynamic mechanical tests or from dilatometricdata. (D20) (1981)hysteresis loop (in dynamic mechanical measurement)—theclosed curve representing successive stress-strain status ofthe material during a cyclic deformation. (ISO) (1983)DISCUSSION—Hysteresis loops may be centered around the origin ofcoordinates or, more frequently, displaced to various levels of strain orstress; in this case, the shape of the loop becomes variouslyasymmetrical, but this fact is frequently disregarded.logarithmic decrement, ∆ (in dynamic mechanicalmeasurement)—the natural logarithm of the ratio of any two(or more) successive amplitudes of like sign, in the decay ofsingle frequency oscillation:∆ 51klnAnAn1kwhere: Anand An+kare amplitudes (in radians of rotation)of two oscillations, and k is the number of oscillations sepa-rating the two amplitude measurements. (1981)loss angle, δ— see phase angle.loss factor—see tan δ.loss modulus—M“(Pa)—[loss compliance O“ (Pa−1)]: theimaginary part of the complex modulus (compliance).DISCUSSION—It is a measure of the energy lost (dissipated during aloading cycle). (See also complex modulus and complex compliance.)(See ISO 6721–1.)loss tangent—see tan delta.mean modulus—the ratio of mean stress to mean strain. (ISO)(1983)mean strain—the average value of strain during a singlecomplete hysteresis loop of cyclic deformation. (ISO) (1983)mean stress—the average value of the stress during a singlecomplete hysteresis loop of cyclic deformation. (ISO) (1983)modulus, complex—see complex modulus.modulus, elastic—see complex modulus and storage modu-lus.modulus, loss—see complex modulus and loss modulus.D4092 − 07 (2013)2modulus, storage—see complex modulus and storage modu-lus.modulus of elasticity— see complex modulus and storagemodulus.nonresonant forced and vibration technique , n—a tech-nique for performing dynamic mechanical measurements, inwhich the sample is oscillated mechanically at a fixedfrequency.DISCUSSION—Storage modulus and damping are calculated from theapplied strain and the resultant stress and shift in phase angle. (1981)normal stress, s—the stress component perpendicular to aplane on which the forces act. (E28) (1981)phase angle, δ—the angle between a sinusoidally appliedstrain and the resultant sinusoidal stress. (1981)Poisson’s ratio, ν—the absolute value of the ratio of transversestrain to the corresponding axial strain resulting from uni-formly distributed axial stress below the proportional limitof the material.DISCUSSION—Poisson’s ratio will have more than one value if thematerial is anisotropic. (E-28) (1981)power loss—the power, per unit volume, that is transformedinto heat through hysteresis. (ISO) (1983)DISCUSSION—Power loss is the product of energy loss and frequency.quality factor, Q—the ratio of elastic modulus to lossmodulus, measured in tension, compression, flexure, orshear.DISCUSSION—The quality factor is a nondimensional term. Thequality factor is the reciprocal of tan delta. (1981)relative rigidity (in dynamic mechanical measurement)—theratio of modulus at any temperature, frequency, or time tothe modulus at a reference temperature, frequency, or time.(1981)resonant forced vibration technique (in dynamic mechanicalmeasurement)—a technique for performing dynamic me-chanical measurements, in which the sample is oscillatedmechanically at the system’s natural resonant frequency.DISCUSSION—The amplitude of oscillation is maintained constantthrough the addition of makeup energy. Elastic modulus is calculatedfrom the measured frequency. Damping is calculated from the addi-tional energy required to maintain constant amplitude. (1981)root–mean–square strain—the square root of the mean valueof the square of the strain, averaged over one cycle ofdeformation. (ISO) (1983).DISCUSSION—For a symmetrical sinusoidal strain, the root-mean-square strain equals the strain amplitude divided by = 2.root–mean–square stress—the square root of the mean valueof the square of the stress, averaged over one cycle ofdeformation. (ISO) (1983)DISCUSSION—For a symmetrical sinusoidal stress, the root-mean-square stress equals the stress amplitude divided by = 2.shear—an action or stress, resulting from applied forces,which causes (or tends to cause) two contiguous parts of abody to slide, relative to each other, in a direction parallel totheir plane of contact. (1981)shear modulus, G (Pa) —the quotient of shear stress and shearstrain. (See ISO 537.)G 5σγshear rate, γ—the time rate of change of shear strain. For aone-dimensional shear flow, it is the velocity gradient.(1981)shear strain, γ—the tangent of the angular change, due toforce, between two lines originally perpendicular to eachother through a point in a body. (E-28) (1981)shear stress, τ—the stress component tangential to the planeon which forces act. (E-28) (1981)storage compliance, C (Pa−1)—the quotient of strain andstress.C 5εσ51Mwhere: D is the tensile compliance; J is the shear compli-ance; C is the storage compliance; and M is the storagemodulus.storage modulus—M (Pa), [storage compliance C (Pa−1)]—the real part of the complex modulus (complex compliance).DISCUSSION—It is a measure of the energy stored and retained duringa loading cycle. (See also complex modulus and complex compli-ance.) (See ISO 6721–1.)strain, ε—the unit change, due to force, in the size or shape ofa body referred to its original size or shape.DISCUSSION—Strain at a point is defined by six components of strain:three normal components and three shear components, referred to a setof coordinate axes. With appropriate rotation of coordinate axis, thestrain may be fully described by three normal components alone. (E-28)(1981)strain amplitude—the ratio of the maximum deformation,measured from the mean deformation, to the free length ofthe unstrained test specimen. (ISO) (1983)DISCUSSION—Strain amplitude is measured zero to peak on one sideonly.stress, σ—the intensity at a point in a body of the internalforces or components of force that act on a given planethrough the point. (E-28) (1981)stress amplitude—the ratio of the maximum applied force,measured from the mean force, to the cross-sectional area ofthe unstressed test specimen. (ISO) (1983)tan delta, tan δ—the ratio of the loss modulus to the storagemodulus, measured in compression, tension, flexure, orshear. (1981)Tan δ 5K“K 5E“E 5G“G time profile—a plot of the modulus or damping, or both of amaterial versus time. (1981)torsional pendulum—a device for performing dynamic me-chanical analysis, in which the sample is deformed torsion-ally and allowed to oscillate in free vibration.D4092 − 07 (2013)3DISCUSSION—Modulus is determined by the frequency of the resultantoscillation, and damping is determined by the decreasing amplitude ofthe oscillation. (1981)torsional stress—the shear stress on a transverse cross section,resulting from a twisting action. (E-28) (1981)viscosity, η—the property of resistance to steady flow exhib-ited within the body of the material.DISCUSSION—In determining the ratio of the shearing stress to the rateof shear of a fluid, viscosity is usually taken to mean “NewtonianViscosity”, in which case the ratio of shearing stress to the rate ofshearing strain is constant. In non-Newtonian behavior, which is theusual case with plastic materials, the ratio