Numerical and Experimental Investigations of Polymer Viscoelastic Materials Obtained by 3D Printing

The aim of this research is to determine the relaxation and creep modulus of 3D printed materials, and the numerical research is based on the finite volume method. The basic material for determining these characteristics is ABS (acrylonitrile butadiene styrene) plastic as one of the most widely used polymeric materials in 3D printing. The experimental method for determining the relaxation functions involved the use of a creep test, in which a constant increase of the stress of the material was performed over time to a certain predetermined value. In addition to this test, DMA (dynamic mechanical analysis) analysis was used. Determination of unknown parameters of relaxation functions in analytical form was performed on the basis of the expression for the storage modulus in the frequency domain. The influence of temperature on the values of the relaxation modulus is considered through the determination of the shift factor. Shift factor is determined on the basis of a series of tests of the relaxation function at different constant temperatures. The shift factor is presented in the form of the WLF (Williams-Landel-Ferry) equation. After obtaining such experimentally determined viscoelastic characteristics with analytical expressions for relaxation modulus and shift factors, numerical analysis can be performed. For this numerical analysis, a mathematical model with an incremental approach was used, as developed in earlier works although with a certain modification. In the experimental analysis, the analytical expression for relaxation modulus in the form of the Prony series is used, and since it is the sum of exponential functions, this enables the derivation of a recursive algorithm for stress calculation. Numerical analysis was performed on several test cases and the results were compared with the results of the experiment and available analytical solutions. A good agreement was obtained between the results of the numerical simulation and the results of the experiment and analytical solutions.

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Characterization of Viscoelasticity of Molding Compounds in Time Domain

ASME 2009 InterPACK Conference, Volume 1 ◽

10.1115/interpack2009-89388 ◽

2009 ◽

Cited By ~ 1

Author(s):

Seung-Hyun Chae ◽

Jie-Hua Zhao ◽

Darvin R. Edwards ◽

Paul S. Ho

Keyword(s):

Time Domain ◽

Viscoelastic Properties ◽

Viscoelastic Behavior ◽

Relaxation Modulus ◽

Polymeric Materials ◽

Shift Factor ◽

Microelectronics Packaging ◽

Molding Compound ◽

Relaxation Experiments ◽

The Time Domain

Although polymer-based materials are widely used in microelectronics packaging and viscoelasticity is an intrinsic characteristic of polymers, viscoelastic properties of polymeric materials are often ignored in package stress analyses due to the difficulty of measuring this property. However, it is necessary to consider the viscoelastic behavior when an accurate stress model is required. Viscoelastic properties of materials can be characterized either in the time domain or frequency domain. In this study, stress relaxation experiments were performed on a molding compound in the time domain. Prony series expansion was used to express the material’s relaxation behavior. Thermo-rheologically simple model was assumed to deduce the master curve of relaxation modulus using the time-temperature equivalence assumption. Two methods were compared to determine the Prony pairs and shift factor.

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TO THE APPLICATION ASSESSMENT OF MASSTRANSFER ANALYTICAL CORRELATIONS TO DEFINE SORPTION CONSTANTS IN SPRM POLYMERIC MATERIALS

Perm National Research Polytechnic University Aerospace Engineering Bulletin ◽

10.15593/2224-9982/2021.66.02 ◽

2021 ◽

pp. 15-23

Author(s):

Svetlana Kulyavtseva ◽

◽

Boris Pevchenko ◽

◽

...

Keyword(s):

Analytical Solutions ◽

Numerical Experiments ◽

Structural Models ◽

Polymeric Materials ◽

Point Of View ◽

Diffusion Analysis ◽

The Difference ◽

The Right ◽

Polymeric Samples

The use of analytical solutions for Frick`s diffusion equation to define the main sorption constants leading to the necessity to solve the united problem is shown. To be more exact this is the application assessment of analytical solutions for more often used experimental results and the determination of the representative sample dimensions in the experiments which are need to construct the sorption/desorption curves. By numerical experiments it is established that the most exact values of masstransfer constants are determined for small and middle values of diffuser absorption temporary process with the help of analytical solutions. Because of the difference in real sample dimensions and structural models used for analytical solutions which as a rule are presented in the form of semi-infinite plates it is necessary to minimize the influence of side surfaces in real samples on the accuracy of masstransfer parameters determination. The numerical-analytic study according to the geometry of polymeric samples from the point of view their representation to define diffusion, solubility and swelling coefficients is conducted. Herewith it is brought out that to obtain the values of masstransfer constants to an accuracy of not more 3 %, the sample geometric features must be chosen with relative dimensions L/h >10 (L – width, h – height of sample, accordingly) – the conditions of plane omnidirectional absorption of the diffuser into the right-angle-formed plates. To obtain the diffusion, solubility and swelling coefficients to an accuracy of not more 3 % the cylinder samples with relative dimensions D/h >15 (D – diameter, h – height, accordingly) should be preferably used. The algorithm of masstransfer constants determination when jointly use the sorption curves and the numerical method of diffusion analysis – finite element method is proposed. Herewith the advantages of such approach removing the sample size and shape limits are shown in comparison with the analytical methods of diffusion analysis.

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