C-MOLD CAE software comprises a set of computer programs for plastics molding simulation. The analyses require accurate material-property data to generate the best predictions. Obtaining quality data is critical; simulation results can be only as good as the material-property data used. This chapter serves as a reference for material-property data producers, providing essential information about the generation of this data for C-MOLD analyses. This chapter also contains other useful information, such as polymer nomenclature and unit conversion charts specific to such applications. Much of the material presented in this chapter is based on the document Characterizing Polymers for C-MOLD Simulations, Third Edition (PL-E3-0994), available separately from AC Technology Polymer Laboratories.
Why Use Standard Test Methods
Standards are nationally and internationally defined test procedures used to characterize a particular property of a material. A standard test method ensures that data is produced to internationally accepted norms. Such data can be verified or tested anywhere else in the world, using comparable equipment, to yield results within the stated accuracy of the method. Standard test methods go through an extensive review by experts in the field, resulting in robust and well-defined techniques. Round-robin tests are conducted to provide a sound level of confidence in the standard test methods. Widely recognized standards-setting organizations for the plastics industry include the ASTM (USA), DIN (Germany), JIS (Japan), and the international ISO. Models Used in C-MOLD
To use a computer simulation of any engineering process, it is important to provide accurate information about material behavior under the conditions encountered during processing, such as temperature, shear rate, pressure, or cooling rate. Standard procedures can be provided to measure these properties under some ideal conditions. It is impractical (and, fortunately, unnecessary) to perform the measurements under all circumstances. Instead, it is more reasonable to find a good model that describes the material behavior under the conditions of interest. Such models can be derived from scientific principles or from semi-empirical rules. The model constants can be determined from limited experiments, then used to describe material behavior under other conditions.
The models described below have been selected after intensive review. These are believed to be the most valid to represent the behavior of the material. C-MOLD accepts several other models; however, their use is not recommended.
To incorporate the dependence of melt viscosity on shear rate, temperature, and pressure, the following 5-constant (n,
*, B, Tb, 
), Cross-exp model is adequate for simulating the filling stage in injection molding:(2.1)
with
(2.2)
The Cross-exp model treats polymer viscosity as a function of temperature, T, and shear rate,
. It handles both the Newtonian and the shear-thinning flow regions found in polymer rheology. Unlike many other models in present use, the constants of the Cross-exp model do have a physical significance. The transition between the two regimes is characterized by *, the shear stress at which shear thinning behavior begins to manifest itself. The slope of the shear-thinning curve is characterized by (1 - n). Depending on the material, it might not be possible to generate the complete curve. However, the best rheology data spans both of these regions. If there are insufficient points in the shear-thinning region, the value of n might be erroneous. Similarly, if the data set lies almost entirely in the power-law region, the values of the zero-shear viscosity, 
o and *, will tend to be ill-defined, even though the product, on x (*)1-n, will be well-defined, corresponding to the multiplicative factor in the power-law region.The remaining three constants of the Cross-exp model are used to model the zero-shear-rate viscosity. Concerning Tb, which characterizes the temperature sensitivity of
o, note that this quantity tends to depend on temperature, especially in the vicinity of the glass transition. As such, this modeling is adequate for the filling stage, where the bulk of the polymer is in the vicinity of the processing temperature, usually more than 100 °C away from the glass transition, where Tb is relatively constant (see Figure 2-1). A more sophisticated model (described on pages 2-7 through 2-8) is adopted for post-filling simulations.
, which characterizes the pressure dependence of o, note that this quantity tends to be more difficult to determine experimentally. It is not necessary to determine this constant if the analysis is used only for design purposes, such that = 0. Since most of the viscosity measurement is performed in the processing pressure range (near 50 MPa), the measured data already includes the pressure effect. If the analysis is used for research purposes, a more elaborate procedure could be included to determine the value of [2-6]. There does tend to be a correlation between the pressure and the temperature sensitivity of o.
.o, note that o at a fixed temperature and pressure strongly depends on the molecular weight, Mw, being approximately proportional to Mw raised to the 3.4 power.
(2.4)
To extend the modeling into the post-filling stage, it is more appropriate to employ the following 7-constant (n, *, D1, D2, D3, A1, 
), Cross-WLF model, which still represents the shear-thinning behavior according to Equation 2.1, but replaces Equation 2.2 with a more extensive model based on the WLF [7] functional form:
(2.5)
Thermal and Mechanical Properties
In addition to the shear viscosity, the simulation of polymer flow dynamics during the filling and post-filling stages requires other properties: mass density, 
, or specific volume, 
1/; specific heat, Cp; thermal conductivity, k; and transition temperature, Ttrans. To complete warpage analysis, mechanical properties are also required.
denotes the volume fraction of filler, and subscript f refers to property values of the filler; and
denotes the weight fraction of filler.
and , it follows:
can be determined from , or vice versa.
.
Specific Volume (pvT Diagram)
This data is used to obtain information about the compressibility and volumetric expansion of polymeric materials. If the data are obtained under equilibrium, they are fundamental thermodynamic properties of the material. The data are seen to reflect transitions as the material moves from one physical state to another.-T curve, b2m and b2s, denote the bulk thermal-expansion coefficients in the liquid and solid phases, respectively. On the other hand, a schematic diagram for the pvT behavior of a semi-crystalline material under atmospheric pressure is shown in Figure 2-2(b). The abrupt transition in the -T curve is associated with the crystallization temperature, which is also a function of pressure.
.
Specific Heat, Cp
A schematic specific-heat diagram for amorphous polymers is shown in Figure 2-3(a). The inflection point corresponds to the glass-transition temperature, Tg. Typically, the variation in the specific-heat of amorphous materials can be about 50-70% between the processing temperature and room temperature.
Commonly available specific heat data are measured under a heating scan. The polymer, however, undergoes high cooling rate (quenching) during the injection molding process. While this will not affect the transitions of amorphous polymers significantly, the transition shifts for semi-crystalline materials can be dramatic. Accordingly, specific heat data measured under a high cooling rate is desirable for C-MOLD analyses.
Thermal Conductivity, k
Thermal conductivity is one of the most important properties that influence the injection molding pressure prediction. Similar to specific heat, thermal conductivity also exhibits variations from room temperature to processing temperature. Shown in Figure 2-4(a) is a schematic thermal conductivity diagram for amorphous polymers. It consists of two regions in a piece-wise linear manner. Thermal conductivity remains constant when temperature is above Tg and decreases linearly when temperature is below Tg. The slope of the line below Tg is about 0.04 W/m - K per 100 °C and is reasonably universal to all pure, amorphous polymers.
Thermal conductivity for semi-crystalline polymers, however, shows an abrupt increase when temperature drops below the crystallization temperature, Tc. This is because of the appearance of the crystalline phase, which creates regions of high thermal conductivity. Figure 2-4(b) gives a schematic thermal conductivity diagram for semi-crystalline polymers.
(b) Schematic thermal conductivity diagram for crystalline polymers. Transition Temperature, Ttrans
The transition temperature is used by C-MOLD analyses as the polymer freeze temperature. This temperature corresponds to the glass-transition temperature, Tg, for amorphous polymers and to the crystallization temperature, Tc, for crystalline polymers. In theory, the transition points determined from pvT, specific heat, thermal conductivity, and viscosity measurements should be identical. However, typical data for these transition points are not so close, due to the limitations of today's measurement techniques. Particularly for semi-crystalline materials, rate dependence tends to create a significant spread in the transitions measured by the various instruments. At this moment, the best way to determine transition temperature is by a DSC cooling scan.
A single transition temperature is easy to determine from the DSC cooling scan for homopolymers. Multiple transitions can be found in polymer blends, and it is difficult to determine which transition is to be used in the simulation. A classic case is the Xenoy resin, where the polymer flows below the crystallization temperature of the PBT component. An additional test for Vicat temperature is typically required. The closest DSC cooling scan transition below the Vicat temperature is the one to use. It is very helpful if you know the composition of the blend before the test.
Mechanical Properties
In warpage analysis, additional properties, such as the thermal expansion coefficient and mechanical properties, are required. The following models can be used, based on different degrees of complexity:
1, and in the transverse direction, 2.
12, and in the transverse-to-thickness direction, 23.
, can be obtained from the data sheet provided by resin suppliers.
, can be obtained from the data sheet provided by resin suppliers.
(2.20)
The equipment used for these tests is fairly common in modern plastics testing facilities. This section therefore assumes familiarity with such test equipment. No attempt is made to describe the operation or use of the instruments. Refer to instrument manuals or contact the manufacturer if such details are desired.
To ensure traceability of data, all transducers and measurement devices must be calibrated to a national standard such as NIST. We also recommend that regular verifications be carried out to ensure that the instruments maintain calibration. Round-robins are an excellent method for determining precision and bias of the laboratory instruments.
For measurements of mechanical properties, the specimens should be taken from injection-molded plaques molded at normal processing conditions. High injection speeds are specified to maximize any anisotropic effects that may occur. The plaques must be nominally five inches (125 mm) square and one-eighth inch (3 mm) thick. Specimens must be cut from regions of the plaque where the flow direction is clearly defined, to characterize the effect of the anisotropy adequately (see Figure 2-5). Specimens should not be taken close to gate areas. Specimens should not be conditioned, annealed, irradiated, or subjected to any other treatment that will change their properties as molded.
Rheology
Melt Viscosity
Method
ASTM D3835, Rheological Properties of Thermoplastics with a Capillary Rheometer. Description of Method
Viscosity is measured using a capillary rheometer (see Figure 2-6). The rheometer piston pushes the material specimen at a constant temperature and flow rate, Q, through a cylindrical die of known length, L, and diameter, D. The apparent shear rate is defined as:
(2.21)
p, across the die, the wall-shear stress, w, is calculated as:
a, is given by:
Test Specification
Specimen form: pellets
Shear rates: 3 per decade, 10-10,000 /s (see Table 2-3)
General Guidelines
Use the maximum L/D that still produces measurements in the desired shear-rate range. The selection of capillary die might vary due to the limitations of the instrument and the viscosity of the polymers.
.
Thermal Properties
Solid Density
Method
ASTM D792, Specific Gravity (Relative Density) and Density of Plastics by Displacement, Method A. Description of Method
Solid density is measured using a hydrostatic balance apparatus. The specimen is weighed in air, then immersed in a liquid, and its weight loss upon immersion is determined. Test Specification
Specimen form: molded plaques Melt Density
Method
Extrusion flow-rate measurement. Description of Method
Melt density is measured using a capillary rheometer. The rheometer piston pushes the melt at processing temperature, at constant rate and temperature, through a die of known length and diameter. The mass of a sample of extrudate from a measured time interval is determined. The polymer melt pressure is recorded. Test Specification
Specimen form: pellets Procedure
A capillary rheometer can be used to measure single-point melt density. The measurement provides reasonable accuracy for CAE simulations and is done in the following manner. The sample at the desired melt temperature is extruded from the die at a reasonable speed, so that a clean string of extrudate begins to form. Using scissors and stop watch, a segment of the extrudate is collected for a reasonable time period, t. Knowing the speed of the rheometer piston, , the diameter of the rheometer barrel, D, and the mass, m, of the extrudate collected, the melt density m can be determined by:
pvT
Method
High-pressure dilatometry. Description of Method
This test method covers measurement of the affect of temperature and pressure on the specific volume (pvT) of polymers. The specimen is heated in an enclosed cell and the change in its volume when subjected to a range of pressures is measured. Measurement techniques differ, mainly in the method used to apply the pressure. Both the direct method (piston and cylinder as shown in Figure 2-7) and the indirect method (high-pressure dilatometer, as shown in Figure 2-8) are found to yield pvT data of sufficient accuracy for the simulation programs.
Apparatus
Method A, also called the direct method, applies the pressure directly to the specimen, using a piston and cylinder set-up. Piston deflections are used to measure volume change. Since the volume of the cell is known, the absolute specific volume can be measured by this technique. Test Specimens
Specimens may be in the form of polymer pellets or may be cut from molded plaques. Since polymer pellets often contain voids within them, it is recommended that the specimens be cut from injection- or compression-molded samples. The quantity of specimen should not exceed 1-3 gms.
Conditioning
Specimens should be well dried prior to testing. A minimum of eight hours at 50 °C in a dessicant drier is recommended. Procedure
The specific specimen loading procedures depend on the apparatus, and the manufacturer-recommended procedures should be used. In addition, the high-pressure dilatometry technique, being a relative method, requires the acquisition of a series of isothermal measurements as described below, at close to the ambient conditions, to which the reference specific volume will be mapped. The reference specific volume is determined by displacement methods following ASTM D792. Specific Heat
Method
ASTM E1269, Determination of Specific Heat Capacity by Differential Scanning Calorimeter. Description of Method
A temperature scan is performed using empty pans in both chambers to establish a baseline. A specimen of mass, m, is then loaded into one of the pans, and the scan is repeated. The specific heat, Cp, is calculated from the difference in heat flow, Q, between the baseline and the specimen needed to change the temperature by an amount, T:
Test Specification
Specimen form: pellets or plaques
General Guidelines
Specimens, sample pans and covers must not be touched by hand. Contamination can lead to spurious peaks. Moist specimens may show a peak at 100 °C. Thermal Conductivity
Method
Transient Line-Source Technique. Description of Method
A probe is inserted into a molten specimen at its processing temperature. The probe contains a line-source heater running the length of the probe, and a temperature sensor in the middle of the probe. When thermal equilibrium is attained, a known amount of heat, Q, is supplied to the line-source heater, and the temperature rise in the sensor is recorded over a period of time. The thermal conductivity, k, is calculated from the following equation:
Test Specification
Specimen form: pellets Apparatus
The K-System II from AC Technology is recommended to make measurements of thermal conductivity. This technique requires a very short measurement time and can significantly reduce the risk of thermal degradation.
Procedure
Load the specimen quickly, tamping frequently to eliminate entrapped air. Alternatively, use a molded rod of the resin. Transition Temperature
Method
ASTM D3418, Transition Temperatures of Polymers by Thermal Analysis. Description of Method
The cooling mode is to be used for these measurements. The transition temperatures are determined from the extrapolated onset, Tf, for crystalline transitions and from the glass transition temperature, Tg, as defined by the midpoint temperature, Tm, for amorphous materials. Test Specification
Specimen form: pellets or plaques General Guidelines
For semi-crystalline materials, the transition temperature depends on direction and cooling rate. A significant hysteresis may be observed between the melting and crystallization transitions; additionally, the faster the cooling rate, the lower the transition temperature. To approximate the actual molding conditions, the DSC cooling rate should be as fast as possible, at a minimum of 20 °C/min. The transition temperature is determined from the onset of the curve, as shown below for amorphous and crystalline polymers.
Mechanical Properties
Modulus of Elasticity
Method
ASTM D638, Tensile Properties of Plastics. Description of Method
Elastic modulus, E, is defined as the ratio of stress, 
, to strain in the direction of load, 
L, within the elastic range of the material. Specimens are placed in the self-aligning jaws of a tensile testing machine equipped with an extensometer (see Figure 2-12), and load is applied. Take care to ensure that all data used for these measurements are taken in the elastic region of the stress-strain curves.
Test Specification
Specimen form: molded plaques Poisson's Ratio
Method
ASTM E 132, Poisson's Ratio at Room Temperature Description of Method
Poisson's ratio, , is defined as the ratio of the lateral contraction strain to the longitudinal strain.12 is the ratio of the strain in the transverse direction, T, to the strain in the longitudinal direction, L, when the load is applied in the flow direction.
23 is the ratio of the strain in the thickness direction, Th, to the strain in the transverse direction, T, when the load is applied transverse to the direction of flow. For weakly reinforced plastics, 23 is approximately equal to matrix, which is the Poisson's ratio for the unfilled material.
23) of the specimen. Test Specification
Specimen form: molded plaques
In-Plane Shear Modulus
Method
Rail Shear Test. Description of Method
This technique uses a test fixture mounted in a basic lever loading frame (see Figure 2-15). Specimens are machined from the specimen and notched to fit the fixture, with round end profiles designed to minimize end effects and produce a homogeneous stress field. The specimen is mounted in the test fixture and bolted in position between the rails. An extensometer is placed on the specimen between the rails, with needle-point arms at 45° to the direction of loading. Load is applied to the specimen and shear strain is monitored by the extensometer. This is repeated in each of four positions (front right and left, back right and left) on the specimen. Shear modulus, G, is calculated from the data for each position as:
(2.29)
= P/2, 
= 245°, P = load, A = area of one web, and 45° = 45° strain. The results from each position are averaged. Test Specification
Specimen form: molded plaques
Thermal Expansion Coefficients
Method
ASTM D 696, Coefficient of Linear Thermal Expansion of Plastics. Description of Method
A quartz tube dilatometer (see Figure 2-16) is used. A specimen is prepared and placed at the bottom of the outer dilatometer tube with the inner one resting on the specimen. The dial gauge, firmly attached to the outer tube, is placed in contact with the top of the inner tube so as to measure variations in the length of the specimen with changes in temperature. Temperature changes are brought about by immersing the outer tube in a liquid bath at the desired temperature. If the temperature of a specimen of initial length, L, is changed by T, and the specimen undergoes a change in length, L, the thermal expansion coefficient, , is given by:
Test Specification
Specimen form: molded plaques
References
