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"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality." Albert Einstein (1879-1955)

On the surface, this may appear a strange way to begin a discussion about a predictive capability that relies heavily on mathematics for its success. However the perspective it brings captures the essence of modeling such a complex physical behavior. In cases, such as the modeling of shrinkage, the general theory accurately captures the basic behavior and trends. However, the results are more useful if they can be made far more specific.

CRIMS (Corrected Residual In-Mold Stress) is a hybrid modeling technique that augments the mathematical theory used to predict shrinkage in injection molded parts. It works by comparing this general model to real molded samples and creating a function to minimize the difference. This function and its coefficients then become part of the predictive model when used for real applications.

The benefits of using CRIMS are too compelling to ignore. Moldflow analyzed nearly 20,000 moldings, each with varied process conditions, thickness, or material. The purpose was to compare the accuracy of predictions based on mathematical theory alone and those based on CRIMS. Greater than 85 percent of the predictions based on CRIMS were within 20 percent of the experimental result, whereas for the prediction based on mathematical theory alone, less than 15 percent of achieved this result.

Shrinkage background

As a brief introduction, Moldflow's approach to modeling shrinkage starts from the basic drivers for the phenomena. A model based on mathematical theory is used to simulate those drivers, which in turn is compared to the result of experimental observation and corrected to ensure that the model predicts what really occurs.

When shrinkage occurs in an unconstrained and undeformed material, the material attempts to shrink equally in all directions (isotropically) as shown in Figure 1. The shrinkage itself is caused by the change in state of the material from a molten, high pressure/high temperature state, as exists inside a mold, to a solid, low pressure/low temperature state, as exists at atmospheric conditions. For semi-crystalline materials, this change in state includes the crystallization process.

Inside the mold, the mold and its features resist this shrinkage, which in realistic moldings constrains all shrinkage to the dimensions of the mold with the exception of shrinkage across the thickness, where the material is free to move (Figure 2). Therefore, if the change of state requires that a certain volumetric change occur yet that change is resisted, a stress is built up in the material, which in turn begins to be relieved while the part cools in the mold.

When the part is ejected from the mold, the constraint is removed and the remaining stresses cause a change of shape in the part that we know as shrinkage. Subsequent cooling will also cause thermal contraction and more shrinkage.

There are other issues such as variations in crystallinity and the stresses due to the orientation of molecules and fibers that I will not address here. For further information, please see the references at the end of this article.

The steps to solve this are:

This is a general model called the residual stress model. The steps are straightforward to describe. However, this is an example of where the direct implementation of the mathematical model will result in a model that predicts the trends but does not describe reality with sufficient precision.

In order to calculate residual stress, a viscoelastic model with suitable material data over the range of conditions encountered in injection molding is required. In view of the temperature range in injection molding, such a model must be valid in the melt state, during the phase change, and in the solid state. At this time no suitable theoretical models are available. In order to make progress in simulation, some simplification is required. This simplification introduces errors that can make predictions from the simplified theoretical model too inaccurate for use.

The solution to this problem is the CRIMS model. This is a hybrid model that utilizes measured shrinkage data to improve the prediction of shrinkage and warpage from theoretical models such as previously described. By comparing theoretical model predictions to experimentally measured shrinkages on molded samples, the CRIMS technique creates a function to minimize the error. The coefficients of this function are the "CRIMS coefficients" and are stored in the Moldflow Material Database. When users perform perform shrinkage and warpage predictions on their parts, these coefficients are used to correct the calculated residual stresses and so minimize the error introduced by using a simplified model.

The CRIMS method may be used for filled and unfilled materials and also performs well for polymer blends. It allows us to overcome the inaccuracy inherent in simplified models while retaining the ability of these models to follow trends. It also enables predictions using conditions outside the range of measurement of the samples used to obtain the coefficients.

The instrumented experimental mold is shown in Figure 3. Shrinkage values are measured both along and across the direction of flow under a variety of thicknesses and molding conditions. Figure 4 shows the measured results obtained for an unfilled polypropylene. The anisotropy in shrinkage between the flow and cross-flow directions is evident. Figures 5 and 6 each show experimental results, the mathematical theory result, and the CRIMS result for shrinkage in the flow and cross-flow directions, respectively. The improvement in the prediction is dramatic.

Moldflow supplies its mathematical model in both a CRIMS form and in a form that does not use measured values. The latter is useful for showing trends, for example, how a change in processing conditions would affect shrinkage, and allows predictions using the over 7000 grades of thermoplastics in the Moldflow Material Database.

For more information we recommend the articles and books listed below among the references.

For information on the Moldflow Material Database, CRIMS shrinkage modeling, or comprehensive material testing services, contact Moldflow Plastics Labs at mpl@moldflow.com.

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References:

[1] Santhanam, N. and Wang, K.K., A Theoretical and Experimental Investigation of Warpage in Injection Molding, Soc. Plastics Engineers, ANTEC 90. 270-273, (1991).

[2] Kabanemi, K.K. and Crochet, M.J., Thermoviscoelastic Calculation of Residual Stresses and Residual Shapes of Injection Moulded Parts, Inter. J. Polym. Process., 7, 60-70, (1992).

[3] Lee, E.H., Rogers, T.G. and Woo, T.C., Residual Stresses in a Glass Plate Cooled Symmetrically from Both Surfaces, J. American Ceramic Soc., 48, No. 9, 480-487, (1965).

[4] Baaijens, F.P.T., Calculation of Residual Stress in Injection Moulded Products, Rheol. Acta, 30, 82-89, (1991).

[5] SWIS (Shrinkage Warpage Interface to Stress) Manual, Moldflow Pty. Ltd., Melbourne, 1990.

[6] Walsh, S.F., Shrinkage and Warpage Prediction for Injection Molded Components, J. Reinforced Plas. Compos., 12, 769-777, (1993).

[7] Rezayat, M. and Stafford, R.O., A Thermoviscoelastic Model for Residual Stress in Injection Moulded Thermoplastics, Polym. Eng. Sci., 31, 393-398, (1991).

[8] Zuidema, H., Flow Induced Crystallization of Polymers, Application to Injection Molding, Ph.D. Thesis, Eindhoven University of technology, 2000.

[9] G. Eder and H. Janeschitz-Kriegl and S. Liedauer, Crystallization Processes in Quiescent and Moving Polymer Melts Under Heat Transfer Conditions, Prog. Polym. Sci., 15, 629-714, (1990).

[10] Zheng, R. and Kennedy, P., Numerical Simulation of Crystallization in Injection Molding, Proc. 6th World Congress of Chemical Engineering, Melbourne, September 2001.

[11] Doufas, A.K., Dairanieh, I.S. and McHugh, A.J., A Continuum Model for Flow-Induced Crystallization of Polymer Melts, J. Rheology, 43, 85-109, (1999).

[12] T. Huang and M.R. Kamal, Morphological Modeling of Polymer Solidification, Polymer Eng. Sci. 40, No. 8, 1796-1808, (2000).

[13] R. Zheng, P. Kennedy, N. Phan-Thien and X.J. Fan, Thermoviscoelastic Simulation of Thermally and Pressure Induced Stresses in Injection Moulding for the Prediction of Shrinkage and Warpage for Fibre-reinforced Thermoplastics, J. Non-Newtonian Fluid Mech., 84, 159-190, (1999).