Modeling of Ultrasonic ProcessingMargaret Roylance, John Player, Walter Zukas,* David Roylance†Foster-Miller Inc., Waltham, MassachusettsReceived 11 November 2003; accepted 21 December 2003DOI 10.1002/app.20595Published online in Wiley InterScience (www.interscience.wiley.com).ABSTRACT: Curing of fiber-reinforced thermoset poly-mer composites requires an elevated temperature to accel-erate the crosslinking reaction and also hydrostatic pressureto consolidate the part and suppress the formation of voids.These processing conditions can be provided by autoclavesof appropriate size, but these are expensive and sometimesdifficult to schedule. Ultrasonic debulking followed by ovencure is an attractive alternative to autoclave cure. In thistechnique a movable “horn” driven at ultrasonic frequencyis applied to the surface of the uncured part. This generatespressure and at the same time produces heating by vis-coelastic dissipation. The part can be debulked to net shapeand staged through the action of the ultrasound. There are alarge enough number of experimental parameters in ultra-sonic debulking and staging to make purely empirical pro-cess optimization difficult, and this paper outlines numericalsimulation methods useful in understanding and develop-ing the process.© 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93:1609–1615, 2004Key words: composites; computer modeling; curing of poly-mers; differential scanning calorimetry (DSC); viscoelasticpropertiesINTRODUCTIONUltrasonic tape lamination (UTL) is a technique thatuses high-frequency loading to achieve heating andconsolidation of fiber-reinforced composite materialsvia viscoelastic energy dissipation.1In conjunctionwith E-Beam curing or a variety of thermal techniques,such as solid state cure, UTL provides an avenue forout-of-autoclave curing of high-quality, large-scale fi-ber placed composite structures. This approach offersthe possibility of out-of-autoclave processing withoutthe development and qualification of new resin for-mulations.Although the use of ultrasonic welding of metalsand unreinforced polymeric materials is an importantindustrial process, process innovations have only re-cently made the use of ultrasound for the consolida-tion of polymer matrix composites containing morethan 35 to 40% by volume of reinforcing fiber possible.Among other process parameters, experiments havedemonstrated that the angle at which insonificationoccurs is a critical process variable. Figure 1 shows theUTL head mounted on a filament winder. To induceconsolidation without damaging a fiber-reinforcedcomposite, a horn angle of less than 90ois required.Changing the horn angle changes the stress state inthe material during insonification and thus changesthe relative amount of energy dissipated by vis-coelastic heating of the matrix compared to fiberdisruption.Experiments have shown UTL to be effective bothfor consolidation of thermoplastic matrix compositematerials and debulking of B-staged thermosetprepreg.2In both processes the ultrasonic loadingmust generate sufficient heat to induce flow and pro-vide sufficient support for consolidation, but oneadded complication of UTL of thermosets is the po-tential for thermally induced curing. An ability tomodel and control this chemical reaction is essential tothe use of UTL as part of an out-of-autoclave process-ing scheme. This paper will describe some of the de-velopment required for such a model, and some ex-amples of the results that can be obtained from it.To clarify the relative importance of frictional andviscoelastic heating, the effects of pressure and ampli-tude on UTL-induced heating have been measured.3The data showed that increasing the static pressurehas no observable effect on the heat generation in thematerial during UTL, suggesting that the viscoelasticheating is dominating the UTL heat generation. Thisconclusion is in agreement with the results of Tolunayet al.,4which showed, for soft polymers, the interfacedid not have a significant effect on the amount of heatdissipated during ultrasonic welding of unreinforcedmaterials. They observed that in this case the heatingoccurs over the whole volume.Correspondence to: D. Roylance ([email protected]).*Permanent address: W. Zukas, U.S Army Soldier andBiological Chemical Command, Natick, MA.†Permanent address: Department of Materials Science andEngineering, Massachusetts Institute of Technology, Cam-bridge, MA 02139.Journal of Applied Polymer Science, Vol. 93, 1609 –1615 (2004)© 2004 Wiley Periodicals, Inc.Further, they observed that intensive heating of thematerial began only after a certain temperature wasreached. This temperature most probably correspondsto the glass transition temperature, since, as Tgisapproached, the level of viscoelastic energy dissipa-tion as measured by loss modulus increases markedly.As the material continues to heat above Tg, the lossmodulus drops again, and Tolunay et al.4observedthat the heating rate also generally drops until thetemperature remains constant. Based on these results,the UTL process model described here focuses onviscoelastic energy dissipation and reaction exothermas volumetric heat sources rather than frictional heat-ing at the interfaces.VISCOELASTIC DISSIPATION OFUNCURED RESINA first step in developing a process model for ultra-sonic consolidation is estimating the amount of ther-mal energy dissipated during a loading cycle. This canbe written in terms of the material’s “loss” modulus E⬙in the theory of linear viscoelasticity.5The material’scomplex modulus E* ⫽ E⬘⫹iE⬙ is a function of bothtemperature and frequency, and a convenient modelfor this dependency is the “Wiechert” viscoelastic ex-pressionE⬘ ⫽ k0⫹冘j⫽1Nkj共␻␶j兲21 ⫹ 共␻␶j兲2, E⬙ ⫽冘j⫽1Nkj共␻␶j兲1 ⫹ 共␻␶j兲2(1)where the k’s and␶’s are adjustable constants and␻⫽ 2␲f is the frequency (rad/s). The Wiechert modelcan be represented by a spring-dashpot analogy, withthe k’s being spring stiffnesses and the␶’s being asso-ciated relaxation times. The temperature dependenceis introduced by making the␶’s an Arrhenius expres-sion of the form␶j⫽␶0jexp冉E⬘RgT冊(2)where the␶0jare preexponential constants and E␶is anactivation energy for viscoelasticity. Each␶jis giventhe same activation energy, which renders the model“thermorheologically simple” and amenable to time–temperature shifting methodology.Numerical