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　　外文翻译

　　专业机械设计制造及其自动化

　　学生姓名陈艳

　　班级 BD机制04 2

　　学号 0420110213

　　指导教师刘道标

　　外文资料名称：Cooling behaviour of particle filled polypropylene during injection moulding process

　　外文资料出处： department of mechanical

　　Engineering , National Central University

　　附件： 1.外文资料翻译译文

　　2.外文原文

　　指导教师评语：签名：年月日

　　注塑成型中颗粒填充物聚丙烯的冷却情况

　　何敏嘉，费尔布

　　陈艳译

　　摘要：聚丙烯复合材料的冷却情况被用于在同一注塑成型过程中，对影响散热性能的各种填料（磁铁矿，重晶石，铜，滑石，玻璃纤维和锶铁氧体）于不同比例下的调查。注塑成型期间，分别对室温和高温时热电偶在型腔模具表面的测量记录和对斜坡冷却曲线的热扩散分析中发现：该注射成型的工艺和该模具的填充材料使冷却曲线显示出不同的合并路段。所以说热扩散系数是个暂时性的系数。热扩散表明，最高值为30％的滑石粉填充聚丙烯，在最短的冷却时间可以发现35％铜填充聚丙烯。系统性变化的具有热传递性能的复合材料，在不同的填充材料和填充比例中使注塑过程优化，并以此来定制热流性能。此外，滑石粉填充聚丙烯使设计的复合材料与预定的最高热流相附，是热传递的首选方向。

　　关键词：聚丙烯 ;热性能;注塑成型;微粒填料

　　1 .导言

　　常用的塑料，如聚丙烯和聚酰胺都有一个低导热系数。不过在汽车行业，如传感器或执行器，需要新的材料或具有高导热性。通过增加合适的填料，比如塑料，其热行为聚合物是可以改变的。系统的热扩散大于1.2/秒，从0.2/秒多为补聚丙烯。这种填充聚合物具有较高的热导率，由于广泛的应用在电子封装上而成为一个越来越重要的研究领域。较高的热导率可以通过使用一个合适的填料达到，如铝，碳纤维和石墨，铝氮化物或磁铁矿颗粒。此外，在注塑机上模具的冷却反应，是受聚合物填料的热性能影响。然而，填充材料比较能体现出热导率的价值观。大幅比较不同的材料，是很困难的，甚至可以说是不可能的。因此，聚丙烯样品不同的填充剂（四氧化三铁，硫酸钡，铜，玻璃纤维，滑石粉）的挤出和注射成型用各种体积分数（ 0-50 ％）来表示。

　　磁铁矿重晶石一般是用来增加重量的聚丙烯，如：为一瓶措施，锶铁氧体是用聚合物粘结磁铁，玻璃纤维是用于加固新材料，滑石粉是一种反阻断剂。然而，铜被选为额外灌装机，因为它具有高度的热导率相对于其他材料。热性能，这些注射成型样品和注塑成型行为人调查和相关的金额和种填充材料。

　　2 .理论思考

　　傅立叶法的热量传递，在一维给出

　　与温度T ，时间t ，位置x和热扩散在一个均质体，热扩散率A和热导率L是相互关联的，由具体密度r 和具体的热容量Cp根据

　　假设一名注射成型工艺与恒温灌浆期为聚合物的温度TP和相对恒定的温度Tm及作为温度独立的热扩散，解析解决式（ 1 ）结果

　　在式（ 3 ） ,S是指壁厚注射模压部分和T的温度zai 时间t后注射。忽略高阶计算，式（ 3 ）可以减少为

　　式（ 4 ）给出的关系冷却速度和热扩散率，在注射成型过程中，凡高热扩散导致更高的冷却速度和短周期的过程。

　　3 .实验

　　3.1 材料

　　试验材料供应合作编写RTP的有限公司（法国）几种聚丙烯（ PP ）化合物与各种填料（四氧化三铁，硫酸钡，铜，玻璃纤维，滑石粉）在挤出过程中讲到的类似在式 [ 2 ] 。填充物材料是常用材料在工业产品。填料粒子不具备表面涂层可以影响热性能。一些选定的性能灌装材料列在表1

　　图1.模具注塑成型实验。

　　图 2 .模具与腔准备测试样本，在一个注塑机。立场与热电偶温度测量标志是一个箭头。

　　3.2 热扩散率测量

　　热扩散的高分子材料，是衡量一个瞬态法，与雷射闪光实验有密切的关系。温度信号由热电偶转移到上侧的抽样检验和注册,被转让温度信号启动一个热平衡过程该标本，记录由热电偶作为区别样品的背面和恒定温度，用来为评价的热扩散率。最小二乘算法是用来确定热扩散率，而变系统地热扩散值在一个特别设计差分计划。精确的测量多于总量的3 ％。为热扩散率测量，小缸10毫米直径5-6毫米的身高，剪下的注射成型棒（参见图1 ）。

　　3.3 注塑成型

　　与注塑机标准样品测量拉伸性能连同一棒热测量10毫米直径和130毫米的长度分别准备在一模（参见图1 ）。在腔的拉伸试验棒铬（ K型）热电偶中的应用。在注塑成型实验温度记录每0.5秒一个数字万用表和储存在一台个人电脑。热电偶s大约0.2毫米成空腔。因此，一个良好的热之间的接触聚合物和热电偶，甚至后缩的成型，是为了保证录得更好的温度时间。用过的注射液成型参数列于表2 。由此时代特征的注塑成型周期提交见表3 。

　　4 结果与讨论

　　图 3 比较冷却曲线填补聚丙烯与聚丙烯复合材料的各种填料组分的四氧化三铁。

　　在图 3 中，聚丙烯的冷却过程在一个时间在温度测量所热电偶达到最高值约。随着越来越多的时间观测到温度下降。经过在模具打开，冷却行为记录与热电偶变化，因为它是无较长的接触与注射成型的材料。由于以大直径的棒，这个时间（），直到模具是打开及注射成型零件跳伞选择相对较高，以确保该部分肯定凝固。可以看出，在图 3斜率曲线变化显着后，这对应于时间那里后，压力是拆除。此外，图。三指出这种复合材料在腔降温快随着越来越多的磁铁矿分。要达到的温度条-温度远远低于凝固的采样聚丙烯需求，在描述实验的时候，，而冷却时间聚丙烯的Fe3O4减至（参看表四）。减少冷却时间，是在好的协议所增加的热扩散的磁铁矿填充复合材料由于高的热扩散粒子（参见附表一），其中的线索，就式（ 4 ），以一个增加冷却速度。温度时间依赖性图。 3条不遵循一个简单的线性行为预期温度-时间曲线由式（ 4 ）在对数计。只为填补聚丙烯实测值可安装一个单一的直线之间大约15 和第54秒的这条路线通往一个扩散（参见式（ 4 ））。其他测量冷却曲线的聚丙烯复合材料的磁铁矿装有在每个个案，两直线，为高温第和低温的地区。热扩散估计从斜坡上的回归直线

　　计算热扩散系数的的温度较高部分的冷却曲线有一点点低于扩散系数测量暂态技术，而计算热扩散酶的温度越低，部分地区的冷却曲线满足实测值扩散图 3 比较冷却曲线填补聚丙烯与聚丙烯复合材料的各种填料组分的四氧化三铁。该符号字里行间都回归直线（参见文）。

　　图 4显示测得的热扩散率数据的调查样本中可以看出，该热扩散的磁铁矿-聚丙烯复合材料是由为填补聚丙烯截至增加磁铁矿负荷。因此，冷却时间变短为高磁铁矿填料馏分（图三）。原因之一，为改变在边坡的冷却曲线显示图3是改变热扩散率随温度的，其中就表现在是图 5 磁铁矿和重晶石聚丙烯复合材料随着温度的升高热扩散率降低。因此，价值观来自模实验应小于测值的复合材料在室温。热扩散的PP基体中，主要是所造成的声子，是关系到等于无害速度v和平均自由程长度L声据上述凝固温度的影响PP基体（约条，测量的DSC ），热扩散的基质减少，以致降低了体积弹性模量k ，因而减少了声子速度，并降低平均自由程的长短。此外，上述凝固温度日Ts无晶在聚丙烯矩阵是在低于Ts结晶下在聚丙烯基体中出现的。存在或缺乏微晶影响体积弹性模量K和声子自由的道路。其原因是不同实验都是非等压条件在注塑成型过程和非等温条件样品的厚度的冷静过程，磁铁矿，重晶石，玻璃纤维，滑石，永磁铁氧体和铜填料比较空聚丙烯图 6 冷却的过程与铜填充聚丙烯存在差异。

　　图 4 在室温下热扩散价值观注射成型聚丙烯样品中不同填料和各种填料的比重来衡量暂态技术（参见文）

　　图 5 温度依赖性的热扩散的磁铁矿和重晶石填充聚丙烯的填料含量

　　图 6聚丙烯复合材料的填料在30vol%后

　　铜填充复合降温速度远远超过其他调查材料。该温度的影响剩余聚丙烯是，在整个注射液成型工艺高于气温其他调查材料。冷静的过程与其他复合材料没有显示有较大的差别。该气温的磁铁矿装聚丙烯是一种比温度低一点的重晶石填充聚丙烯。气温的锶铁氧体聚丙烯复合材料，再次是低于那些该磁铁矿填充聚合物。而测得的热扩散率的滑石粉填充聚丙烯是远高于热扩散其他调查材料，甚至远高于这对铜填充聚丙烯，冷却行为滑石粉是较小较其他调查材料。魏登费勒等人研究出该滑石粉沿着自己的方向填充复合一个对齐的滑石粉。测量的热扩散率是平行于这个主轴的最高热导率，而温度测量在注塑成型过程中揭示扩散垂直流方向发展。这意味着，该滑石粉填充聚丙烯样品中有强烈各向异性最高并在流动方向低垂直于水流。尽管出现了高导热的铜（参看表1 ）相对于其他用于填充材料，冷静是相对的测气温的。结果表明：这是一个相对的措施，一个最理想的互联网络的高导电粒子在聚丙烯基体，低于1 ％和极差相比，互联磁铁矿55 ％或互联的重晶石46 ％。作者还讨论了影响颗粒大小和形状的聚丙烯矩阵[ 2,3 ] 。

　　图 7 各种聚丙烯复合材料的冷却时间（从200下降到60度）

　　冷却时间是线性依赖于填料量分数在聚丙烯基体中，数据计算回归系列于表6 。它可以清楚看出，铜填充聚丙烯降温下降速度，远远超过其他调查材料。冷却的情况，聚丙烯重晶石，锶氧体和磁铁矿是相似的，而磁铁矿降温一点点速度比所有其他材料。

　　5 结论

　　冷静的过程中聚丙烯在注塑成型工艺可以减少所使用的磁铁矿重晶石，锶铁氧体，玻璃纤维，滑石粉和铜填料。冷却过程中，由于的依赖了传热和潜热凝固温度，所以不能完全解释由简单指数律来自傅立叶的法热传导。此外，在注射成型周期，的注射液成型周期和热扩散的聚丙烯矩阵周期，冷却曲线显示不同的合并路段。此外，各向异性的热传导性，例如：为滑石粉填充物，或低互联的粒子影响冷却行为，如铜。为使用的材料和在调查范围填料冷却时间冷却下来注射成型复合材料，从温度200 降至60是线性依赖于填料。铜在聚丙烯基体中的冷却时间可缩短从50.5 至20，9秒。在这个过程循环中，具有较高热传递性能的一些复合材料，可以用来优化模具进程提高冷却速度。

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QQ 29467473

内容简介：: ofstryacceptedAbstractTherefore, polypropylene samples with different com-Composites: Part A 36The effects of thermal properties of various fillers (magnetite, barite, copper, talc, glass fibres and strontium ferrite) in various proportionson the cooling behaviour of polypropylene matrix composites are investigated in an injection moulding process. A thermocouple in the cavityof the mould records the temperatures at the surface of the composite during injection moulding. From the slope of the cooling curves thethermal diffusivities of the composites are estimated and compared with thermal diffusivities at room temperature and elevated temperaturesmeasured with a transient technique. The cooling curves show different merging sections affected by the after pressure, the diffusivity of thecomposite and the diffusivity of polypropylene matrix. The cooling behaviour depends on the anisotropic thermal diffusivity of the usedcomposite, which is caused by the alignment of filler material due to the injection moulding process and the interconnectivity of the fillerparticles. The thermal diffusivity shows the highest value for 30 vol% talc filled polypropylene, whereas the shortest cooling time was foundfor 35 vol% copper filled polypropylene. The knowledge of the systematic variation of thermal transport properties of composites due todifferent filler material and filler proportions allows to optimize the mould process and to customize the heat flow properties. Furthermore, thestrongly anisotropic thermal transport properties of talc filled polypropylene allow the design of composites with a predefined maximum heatflow capability to transport heat in a preferred direction.Keywords: A. Polymermatrix composites (PMCs); B. Thermal properties; E. Injection moulding; Particulate filler1. IntroductionCommonly used plastics, such as polypropylene andpolyamide, have a low thermal conductivity. However, newapplications, mainly in automotive industries, e.g. forsensors or actuators, require new materials with anenhanced or high thermal conductivity 1. By the additionof suitable fillers to plastics, the thermal behaviour ofpolymers can be changed systematically up to significanthigher thermal diffusivity of O1.2 mm2/s from 0.2 mm2/sfor unfilled polypropylene 2,3. Such filled polymers withhigher thermal conductivities than unfilled ones becomemore and more an important area of study because ofthe wide range of applications, e.g. in electronic packaging46. The higher thermal conductivity can be achieved bythe use of a suitable filler such as aluminium 1, carbonfibres and graphite 7, aluminium nitrides 6,8 ormagnetite particles 2. Also, the cooling behaviour in themould of the injection moulding machine is influenced bythe thermal properties of the polymer-filler composite.However, published values of thermal conductivities of thesame filler materials in different polymer matrices varydrastically and a comparison of different materials isdifficult or at least impossible 2.Cooling behaviour of particleinjection mouldingBernd Weidenfellera,*, MichaelaInstitute of Polymer Science and Plastics Processing, Technical UniversitybGeoForschungsZentrum Potsdam, Section 4.1 Experimental GeochemiReceived 25 June 2004;filled polypropylene duringprocessHoferb, Frank R. SchillingbClausthal, Agricolastrasse 6, D-38678 Clausthal-Zellerfeld, Germanyand Mineral Physics, Telegrafenberg, D-14473 Potsdam, Germany4 July 2004(2005) 345351talc and SrFe12O19) were prepared by extrusion and injectionmoulding using various volume fractions (050%). Magne-tite and barite are generally used to increase the weight ofKoch-Str. 42, D-38678 Clausthal-Zellerfeld, Germany. Tel.: C49-5323-723708; fax: C49-5323-723148.E-mail address: bernd.weidenfellertu-clausthal.de (B. Weidenfeller).* Corresponding author. Present address: Institute of Metallurgy, Robert-mercially available fillers (Fe3O4, BaSO4, Cu, glass fibres,nts3. ExperimentalTalc, Mg3Si4O10OH2Strontiumferrite,SrFe12O19Copper,CuGlassfibresl11:1.76G0.00,l33:10.69G1.35,a:2.97,a:3.00G0.10,a:6.10G0.90l11:401 l:1.21.513 14 152.0 1.5 15 11Platelet Irregular Irregular Fibre2.78 5.11 8.94 2.58aretes: Part A 36 (2005) 3453512. Theoretical considerationsThe Fourier law of heat transport in one dimension isgiven byvTvtZ av2Tvx2(1)with temperature T, time t, position x and thermal diffusivity a.In an homogeneous body, thermal diffusivity a andthermal conductivity l are interrelated by specific density rpolypropylene, e.g. for bottle closures (cosmetics industry,cf. Ref. 10), strontium ferrite is used in polymer bondedmagnets, glass fibres are used for the reinforcement ofmaterials, and talc is an anti-blocking agent. However,copper was chosen as additional filler because of its highthermal conductivity compared to the other materials.The thermal properties of these injection mouldedsamples and the injection moulding behaviour wereinvestigated and correlated to the amount and the kind offiller material.Table 1Selected properties of filler materialsMagnetite, Fe3O4Barite, BaSO4Thermal conduc-tivity (W/(m K)a:4.61G0.42,a:5.10,l11:9.7l11:2.07G0.02,l33:2.92G0.07,a:1.72G0.04Reference 13 13Mean particle diam-eter (mm)9 1.5Particle shape Irregular IrregularDensity (g/cm3) 5.1 4.48a denotes measurements on monomineralic aggregates. Directions of anisotropyand l33are parallel to the crystallographic axes a, b and c, respectively.B. Weidenfeller et al. / Composi346and specific heat capacity cpaccording tol Z cpra (2)Assuming an injection moulding process with anisothermal filling stage for a polymer with a temperatureTPand a constant temperature of the mould TMas well as atemperature independent thermal diffusivity a, an analyticalsolution of Eq. (1) results in 9T ZTMC4pTPKTM!XNnZ012nC1exp Ka2nC12p2ts2C26C27sin2nC1pxsC18C19(3)In Eq. (3), s denotes the wall thickness of the injectionmoulded part and T the temperature of the moulding after3.1. MaterialsTest materials were supplied by Minelco B.V. (TheNetherlands). Minelco B.V. prepared in cooperation withRTP s.a.r.l (France) several polypropylene (PP) compoundswith various fillers (Fe3O4, BaSO4, Cu, glass fibres, talc andSrFe12O19) in an extrusion process similar to that describedin Ref. 2. The filler materials are commonly used materialsin industrial products. The filler particles do not have atime t after injection. Neglecting higher order terms, Eq. (3)can be reduced for the position xZs/2 toT ZTMC4pTPKTM expKap2ts2C18C19C26C27(4)Eq. (4) gives a relation between cooling rate and thermaldiffusivity in an injection moulding process, where highthermal diffusivities result in a higher cooling rate andshorter process cycles.specified by the thermal conductivity tensor (l11, l22, l33), where l11, l22surface coating which can affect thermal properties. Someselected properties of the filler materials are listed inTable 1.Fig. 1. Photograph of the used mould for the injection mouldingexperiments. The mould consists of a standard tensile test sample and atest bar for the measurement of thermal diffusivity.ntstime curves the same injection moulding parameters for allcomposite materials were chosen. The used injectionmachine. The position of the thermocouple for temperature measurements isPart A 36 (2005) 345351 3473.2. Thermal diffusivity measurementsThe thermal diffusivity of the polymers is measured by atransient method 12, closely related to laser-flash experi-ments 11. The used transient technique is especiallyoptimized for measurements of polyphase aggregates. Atemperature signal is transferred to the upper side of thesample and registered by a thermocouple. The transferredtemperature signal starts a thermal equilibration process inthe specimen, which is recorded by a thermocouple as thedifference between samples rear surface and a constanttemperature in a furnace and which is used for theevaluation of thermal diffusivity. A least squares algorithmis used to determine the thermal diffusivity, while varyingsystematically the thermal diffusivity value in an especiallyFig. 2. Mold with cavity for preparing test samples in an injection mouldingmarked by an arrow.B. Weidenfeller et al. / Composites:designed finite-difference scheme. A detailed description ofthe apparatus is given by Schilling 12. The accuracy of themeasurements of the polyphase aggregates is 3%.For thermal diffusivity measurements, small cylinders of10 mm diameter and 56 mm height were cut out of theinjection-moulded rods (cf. Fig. 1).3.3. Injection mouldingWith an injection moulding machine (Allrounder 320C600-250, Arburg, Germany) standard samples for measuringtensile properties together with a rod for thermal measure-ments of 10 mm diameter and 130 mm length were preparedin one mould (cf. Fig. 1). In the cavity of the tensile test bar achromel alumel (Type K) thermocouple was applied.During injection moulding experiments the temperaturewas recorded every 0.5 s by a digital multimeter and storedin a personal computer. The position of the thermocouple atthe sample surface and its position in the cavity of theejector are shown in Figs. 1 and 2, respectively.The thermocouple submerges approximately 0.2 mm intomoulding parameters are listed in Table 2. The resultantcharacteristic times of the injection moulding cycle aretabled in Table 3.4. Results and discussionIn Fig. 3, the cooling behaviour of polypropylene withoutand with various fractions of magnetite filler are presented.the cavity. Therefore, a good thermal contact betweenpolymer and thermocouple even after shrinkage 10 of themoulding is ensured.For a better comparison of the recorded temperatureTable 3Characteristic times in one injection moulding cycle starting with theinjection of the polymer into the cavity at time tiZK8.5 s until the ejectionof the mould at tfZ68 sInjection time (s) K8.52Dwell time (s) 29Cooling time (s) 954Open/close time ejection time (s) 5468Total cycle time (s) 76.5These times define the time axis (abscissa) of Figs. 3 and 6.Table 2Injection moulding parameters during preparation of sample rods formeasurements of thermal diffusivity by transient techniqueMass (polymer) temperature (8C) 200Mould temperature (8C) 20Cycle time (s) 76.5Injection time (s) 10.5Dosing time (s) 12.4Holding pressure time (s) 7.0Injection pressure (Pa) 6!107ntsylene composites with various filler fractions of Fe3O4. The symbols are measuredtes: Part A 36 (2005) 345351At a time t0Z0 s the temperature measured by thethermocouple reaches a maximum value around 200 8C.With increasing time the observed temperature decreases.After tZ54 s the mould opens and the cooling behaviourrecorded with the thermocouple changes because it is nolonger in contact with the injection moulded material. Dueto the large diameter of the rod, the time (54 s) until themould is opened and the injection moulded parts are ejectedis chosen relatively high to ensure that the parts are surelysolidified.It can be seen in Fig. 3 that the slope of the curve changessignificantly after tz9 s, which corresponds to the timeFig. 3. Comparison of cooling curves of unfilled polypropylene with polypropvalues; the lines are regression lines (cf. text).B. Weidenfeller et al. / Composi348where the after pressure is removed. Additionally, Fig. 3points out that the composite in the cavity cools down fasterwith increasing magnetite fraction. To reach a temperature ofTZ60 8Ca temperature far below the solidification of thesamplethe polypropylene needs in the described exper-iment a time of tZ50.5 s, whereas cooling time ofpolypropylene with 50 vol% Fe3O4is reduced to tZ30.9 s(cf. Table 4). The reduced cooling time is in good agreementwith the increased thermal diffusivity of magnetitefilled composites due to the high thermal diffusivity ofthe particles (cf. Table 1) which leads, regarding Eq. (4), to anincreased cooling rate. The temperature time dependence inFig. 3 does not follow a simple linear behaviour expected fortemperaturetime curves by Eq. (4) in a logarithmic plot.Only for the unfilled polypropylene the measured values canbe fitted with a single straight line between approximately 15and 54 s. The slope of this line leads to a diffusivity ofaz0.21 mm2/s (cf. Eq. (4). The other measured coolingcurves of the polypropylene-magnetite composites are fittedin each case with two straight lines, for the high temperature(a1) and low temperature (a2) region. The thermal diffusiv-ities estimated from the slopes of the regression linesare a1(15 s!t!40 s)z0.24 mm2/s and a2(41 s!t!54 s)z0.19 mm2/s for PP with 15 vol% Fe3O4, a1(12 s!t!33 s)z0.29 mm2/s and a2(34 s!t!54 s)z0.19 mm2/sfor PP with 30 vol% Fe3O4,anda1(9 s!t!22 s)z0.33 mm2/s and a2(28 s!t!54 s)z0.16 mm2/s forPP with 50 vol% Fe3O4(cf. Table 5).It is remarkable that the calculated thermal diffusivitiesa1of the higher temperature parts of the cooling curvesare a little bit lower than the diffusivities measured withthe transient technique, while the calculated thermaldiffusivities a2of the lower temperature parts of thecooling curves meet the measured diffusivity valuesTable 4Time t to cool down a polypropylene-filler composite from a mass(polymer) temperature of TMZ200 down to 60 8CComposite Filler fraction(vol%)t (from 200 to 60 8C)(s)PP 0 50.5PPCFe3O415 46.4PPCFe3O430 40.5PPCFe3O445 34.6PPCFe3O450 34.9PPCBaSO415 44.3PPCBaSO430 40.7PPCBaSO445 35.6PPCCu 15 40.5PPCCu 30 33.8PPCCu 35 29.0PPCglass fibres 15 46.0PPCglass fibres 30 41.8PPCglass fibres 35 40.8PPCtalc 15 45.7PPCtalc 30 42.5PPCSrFe12O1930 40.9The cooling is measured in situ within a cavity of the mould by a K-typethermocouple.ntsof unfilled polypropylene quite well (cf. Table 5 andFig. 4).Fig. 4 shows the measured thermal diffusivity data of theinvestigated samples at ambient conditions. It can be seenthat the thermal diffusivity of the magnetite-polypropyleneAbove the solidification temperature of the PP matrix(around 110 8C, DSC measurements) the thermaldiffusivity of the matrix is reduced due to the loweredbulk modulus K which results in a reduced phonon velocity(vz(K/r)0.5) and reduced mean free path length of phononsin a liquid (Einstein approximation). Furthermore, aboveTable 5Thermal diffusivity estimated from the cooling behaviour of injection moulded polypropylene-filler composites using the slope of the regression lines (a1, a2)(cf. Fig. 3) compared to thermal diffusivity values measured by the transient method (a)Composite Regression lines Transient methoda1(mm2/s) a2(mm2/s) a (mm2/s)PP 0.21 (12055 8C) 0.19 (26 8C)PPC15 vol% Fe3O40.24 (12067 8C) 0.19 (6751 8C) 0.27 (26 8C)PPC30 vol% Fe3O40.29 (12068 8C) 0.19 (6845 8C) 0.35 (26 8C)PPC50 vol% Fe3O40.33 (12577 8C) 0.16 (6745 8C) 0.48 (26 8C)The temperature values in parenthesis give the temperature region of the regression lines and the ambient temperature during the measurement with thetransient technique.B. Weidenfeller et al. / Composites: Part A 36 (2005) 345351 349composite is increased from aZ0.19 for unfilled poly-propylene up to aZ0.48 (PPC50 vol% Fe3O4) withincreasing magnetite loading. Therefore, the cooling timebecomes shorter for higher magnetite filler fractions(Fig. 3).One reason for the change in the slope of the coolingcurves shown in Fig. 3 is a change of the thermaldiffusivity with temperature which is shown in Fig. 5 formagnetite and barite polypropylene composites with45 vol% filler fraction. With increasing temperaturethermal diffusivity decreases. Therefore, the valuesderived from mould experiments should be smaller thanthe measured values of the composites at room tempera-tures. Thermal diffusivity of the PP matrix is mainlycaused by phonons and is related to the mean soundvelocity v and mean free path length l of phononsaccording toa Z13vl (5)Fig. 4. Thermal diffusivity values of injection moulded polypropylenesamples with different fillers and various filler proportions measured by atransient technique at room temperature (cf. text). Solid lines are plotted toguide eyes.solidification temperature TSno crystallites in the poly-propylene matrix are present, but below TSa crystallizationin the polypropylene matrix appears, and the degree ofcrystallization as well as the bulk modulus of the compositeis dependent on the amount of filler 16. The presence orabsence of crystallites affects the bulk modulus K and thephonon free path. Other reasons for the discrepancybetween diffusivity values of the different experimentsare the non-isobaric conditions in the injection mouldingprocess and the non-isothermal conditions along thesamples thickness.The cooling behaviour of magnetite, barite, glass fibre,talc, hard ferrite and copper fillers in comparison withthe unfilled polypropylene are plotted in Fig. 6. Only thecooling behaviour of the unfilled and the copper filledpolypropylene show significant differences to the othercomposites.Fig. 5. Temperature dependence of thermal diffusivity of magnetite andbarite filled polypropylene with a filler content of 45 vol%. The symbolsrepresent measured values, the lines are deduced by linear regression.ntstes: Part A 36 (2005) 345351The copper filled composite cools down much faster thanthe other investigated composites. The temperature of theunfilled polypropylene is during the whole injectionmoulding process higher than the temperature of the otherinvestigated materials. The cooling behaviour of the othercomposite materials does not show large differences. Thetemperatures of the magnetite loaded PP is a little bit lowerthan the temperatures of the barite filled PP at the samecooling time. The temperatures of the strontium ferritepolypropylene composite again are a little bit lower thanthose of the magnetite filled polymers.While the measured thermal diffusivity of the talc filledFig. 6. Comparison of the cooling behaviour of polypropylene matrix compositesmachine.B. Weidenfeller et al. / Composi350polypropylene is much higher than the thermal diffusivi

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