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Rheology of PIM Feedstocks SPECIAL FEATURE Metal Powder Report Volume 72, Number 1 January/February 2017 metal-powder.net Rheology of PIM feedstocks SPECIAL FEATURE Christian Kukla, Ivica Duretek, Joamin Gonzalez-Gutierrez and Clemens Holzer Introduction constant viscosity is called zero-viscosity h0 (Fig. 1). After a certain > g Powder injection molding (PIM) is a cost effective technique for shear rate ( ˙1), viscosity starts to decrease rapidly as a function of producing complex and precise metal or ceramic components in shear rate, this is known as shear thinning or pseudoplastic behav- mass production [1]. The used raw material, referred as feedstock, ior. For highly filled compounds like PIM feedstocks a yield stress consists of metal or ceramic powder and a polymeric binder can be observed. Thus the viscosity increases dramatically when mainly composed of thermoplastics. The thermoplastic binder decreasing the shear stress and the zero shear viscosity is hard to composition gives plasticity to the feedstock during the molding measure and thus shear thinning is observed even at very low shear g process and holds together the powder grains before sintering. rates. Around a certain higher shear rate ˙2 a second Newtonian > g Most binder systems are made of multi-component systems plateau can be observed and at very high shear rates ( ˙3) the with a range of modifiers which fulfill the above mentioned plateau can change to an increasing viscosity curve due to formation requirements. The flow behavior of the feedstock is the result of of particle agglomerates that can restrict the flow of the binder complex interactions between its constituents. The viscosity of the system. In various industrial processes the shear rate usually ranges À3 7 À1 feedstock and its reproducibility batch by batch is the base for a between 10 and 10 s . The very high shear rates occur, e.g. in the production of high quality green parts with low scrap rates. Thus molding of thin walled parts [3–5]. rheology is a key factor for the production of high quality PIM Additional importance has the temperature dependence of the parts, the characterization of feedstocks themselves and for reli- viscosity. It can be described according to the Arrhenius equation able results of numerical simulation of the PIM process. especially for semi-crystalline polymers, whereas the WLF (Wil- From the rheological point of view the PIM-feedstocks are liam, Landel, Ferry) equation is used for amorphous plastics. For highly-filled polymeric suspensions. The flow behavior is further thin walled parts the temperature dependency of the viscosity is complicated by particle–particle interactions, which cause their more important; due to the narrow flow channels the shear rate is redistribution and reorientation in the binder, and thereby influ- very high which causes a high temperature rise. The temperature ence the bulk rheological behavior [2]. Due to these interactions PIM feedstocks, compared to thermoplastics, have their own spe- cific rheological behavior. Furthermore effects such as yield stress, wall slip, phase separation, and pre-shearing can have a significant effect on the flow behavior, the accuracy of the measurement and thus on related results of injection molding simulation. In general, the flow properties of feedstocks depend on the temperature, binder composition, powder content and powder characteristics (particle size distribution and shape of particles). The viscosity curve describes the dependence of the viscosity on the shear rate. At very low shear rates, for thermoplastics the viscosity curve usually changes to a horizontal viscosity line. The viscosity value at very low shear rates is more or less constant or independent from the shear rate (Newtonian behavior). This FIGURE 1 Viscosity of one suspension. E-mail address: [email protected]. 0026-0657/ ß 2016 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mprp.2016.03.003 39 SPECIAL FEATURE Metal Powder Report Volume 72, Number 1 January/February 2017 TABLE 1 Different types of rheometers. Measuring instrument Measurement Measurement Measured material data tools range À4 2 À1 Rotational rheometer Plate & plate 10 –10 s - Zero viscosity, viscosity curves – complex viscosity 0 00 (rotational & oscillating mode) Cone & plate - Storage- and loss modulus, G , G - Normal force À normal stress differences À3 3 À1 Rotational rheometer Cup & bob 10 –10 s - Low viscosities 1 5 À1 High pressure capillary rheometer Capillary 10 –10 s - Viscosity curves – slip velocity curves – critical shear stresses Slit dies SPECIAL FEATURE 1 7 À1 Injection molding machine rheometer [7] Slit dies 10 –10 s - Pre-shearing flow correction – viscosity curves – slip velocity curves – critical shear stresses Rotational rheometry Principle The most important rheological property is viscosity, which repre- sents the resistance to flow. Fluid deformation under steady shear flow can be appropriately described by considering the parallel-plate model. This model helps to define shear stress and shear rate and it is schematically shown in Fig. 3-left. The upper plate, with area A, is moved by a shear force F and the velocity vmax is measured. The lower plate remains stationary (v = 0). Between the plates there is a gap y where the liquid sample is sheared. The rheological parameters can be measured when two conditions are satisfied: (i) samples must adhere to the plate surface, assuming the no-slip condition at the solid boundary; and (ii) the flow is a laminar flow. FIGURE 2 The rotational rheometer with parallel plate fixtures (Fig. 3- Types of rheometers used for different ranges of the shear rate. right) is widely used to measure the viscosity, viscoelastic proper- ties and the normal stress functions as functions of shear rate and À1 rise decreases the viscosity. Above 100 s the increase in temper- temperature at a low shear rate range. The measured geometry is ature due to shear dissipation has to be taken into account for determined by the radius R and the gap height H. In contrast to the viscosity measurements [6]. parallel-plate model (Fig. 3-left) the moved surface performs a Generally viscosity curves of polymers cannot be measured in rotational movement. For the analysis of the measurements, the À3 7 À1 the large range of shear rates between 10 and 10 s with one maximum shear rate on the edge is used. In addition to viscosity, À1 type of rheometer (Fig. 2). For the shear rate range between 10 this rheometer can perform other rheological tests, such as stress À1 and 1 s , the rotational rheometer is used under steady-state relaxation, creep, oscillatory and ramp tests. shearing conditions. In the transition range between 5 and Rotational rheometers with parallel plates are suitable to mea- À1 100 s it is used under oscillating shear conditions. In the shear sure feedstocks. However, the particle size dp or size of agglomer- 2 4 À1 rate range between 10 and 10 s the high pressure capillary ates should be considered; the minimum gap height H should be at rheometer is utilized. For even higher shear rates the injection least 5cd_ p [5]. molding machine rheometer can be used [7]. Table 1 gives a good In a Newtonian fluid, the viscosity is constant and independent overview of the use of the different types of rheometers. of shear rate and shear stress is proportional to the applied strain. In this paper we present the two most common methods of However, most PIM-feedstocks are pseudoplastic fluids and the obtaining viscosity curves for feedstock materials: rotational rheo- shear stress correlates to the shear strain by, e.g. a power law metry and high pressure capillary rheometry. equation. FIGURE 3 Flow behavior between two parallels plates [4] (left); parallel-plate rheometer (right). 40 Metal Powder Report Volume 72, Number 1 January/February 2017 SPECIAL FEATURE FIGURE 4 Smooth plate (a), plate with slits (b), serrated plate (c), plate with glued sand paper (d). The no-slip condition between fluid and solid boundary in plates (Fig. 4). The investigation of the effect of surface roughness contact with the fluid is one of the most classical assumptions on wall-slip formation during rheological measurements of bronze in continuum fluid mechanics. For Newtonian fluids, the assump- (CuSn8) PIM-feedstock was of particular interest [13]. tion of no-slip condition leads to good agreement with experi- SPECIAL FEATURE mental observations. Measurement procedure For two-phase (or multi-phase) systems, slip at the wall of the Dynamic rheological tests (i.e. frequency sweeps) must be done in measuring geometry could originate from steric, hydrodynamic, linear viscoelastic region (LVR) to prevent overstrain of the sample viscoelastic, chemical and gravitational forces acting on the dis- and not to destroy its elastic structure. The LVR can be measured persed particles immediately adjacent to the walls. As a result of using a strain sweep test. In a strain sweep test, the frequency of the these forces, a low viscosity depleted layer forms between the wall test is fixed and the amplitude is incrementally increased. To and the bulk fluid, which then acts as a lubricant to produce slip determine the linear viscoelastic region, the storage modulus effects. Factors that could lead to slip effects include large dispersed should be plotted against the amplitude. A good rule for defining (or flocculated) particles, concentrated solutions, low flow rate, the end of the linear region is to find the amplitude at which the electrically charged particles or walls, and smooth measuring value of the storage modulus changes by 5% with respect to the geometries. Therefore, performing measurements of PIM-feed- value at the lowest measured amplitude. stocks on rheometers with smooth measuring geometries could Fig. 5 shows a comparison of storage modulus versus strain for lead to wall-slip effects [8,9]. CuSn8 feedstock and silicon oil using the smooth plate-plate The problem of slip can be eliminated by using serrated, rough- system.
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