Elsevier

Additive Manufacturing

Volume 11, July 2016, Pages 40-48
Additive Manufacturing

Hyperelastic strain measurements and constitutive parameters identification of 3D printed soft polymers by image processing

https://doi.org/10.1016/j.addma.2016.03.005Get rights and content

Abstract

To realize the full potential of 3D Printing technology in the design of materials and structures, it is indispensable to characterize and predict the mechanical response of 3D Printing materials to external stimuli. This study is focused on hyperelastic strain measurements and constitutive parameters identification of 3D printed soft polymers undergoing uniaxial deformation. A simple method using an optical camera in conjunction with an image processing tool is proposed to accurately measure the average strain experienced by rubbery polymers during a tensile test. The potential of the method is demonstrated through tensile tests of 3D printed soft polymer by accurately determining the stress–strain response and the Poisson's ratio without using extensometers. Influence of printing direction on the anisotropic behavior of 3D printed polymer is investigated by applying the proposed test method to specimens printed in two different directions. The Neo-Hookean constitutive parameters of the soft polymer are determined from the experimentally obtained stress–strain data. The method is validated and a technique to conveniently determine associated error-margins is presented. Moreover, finite element analysis (FEA) of the soft polymer is performed to show that the constitutive parameters determined can predict the mechanical response of the tested polymer accurately if used in commercial FEA packages.

Introduction

Engineering analysis and design of materials and structural components rely on appropriate constitutive models and material properties in order to predict their structural and functional response. For highly deformable materials (e.g. rubber, gel, foam), such constitutive models are often non-linear, and several material properties may be required to predict their mechanical behavior [1].

With the advent of 3D Printing technology, the ability to readily fabricate complex 3D geometries has been made possible for customized prototypes. In recent times researchers showcased novel application of the 3D Printing technique by introducing new methods and materials to the industry [2]. Furthermore, the potential use of 3D Printing technology has recently been demonstrated in several fields including electronics [3], [4], sensors [5], detectors [6], optics [7], batteries [8], composites [9], [10], tissue engineering [11], prototyped organs and implants [12], [13], pharmaceutical tablets [14], cancer cell migration [15] and even in the field of sustainable development [16]. Emergence of novel techniques and materials in the field of 3D Printing has revolutionized the industry from being a mere prototyping technique to increasingly become a full-scale manufacturing solution, called additive manufacturing [17], [18]. To realize the full potential of the 3D Printing technology, it is indispensable to characterize and understand the response of 3D Printing materials to external stimuli. While electrical, thermal, optical and magnetic properties may all be necessary for certain applications, mechanical behavior of 3D printed soft materials is investigated in this study. An Objet Connex 260 3D Printer is used to additively manufacture specimens using TangoPlus FullCure® 930 (TP) photopolymer through jetting of ink droplets via print-head nozzles. Polymer droplets get cured by UV light. In order to determine the complete set of constitutive parameters, multiple experiments such as tension, compression, shear and volumetric tests need to be conducted. The macroscopic force–displacement data recorded during these tests can be subsequently used to estimate various material properties of hyperelastic constitutive models through curve fitting [19]. Nevertheless the primary focus of this study is on the constitutive response of TP under tension. The tensile test is performed by stretching the test specimen uniaxially. With recorded force-displacement data and known geometric parameters of the specimen, the stress–strain relationship is obtained and the constitutive parameters are estimated. Significant error in strain can creep in during tensile tests of materials exhibiting large deformation, due to the conventional dog bone-shape of test samples. While the shape is crucial for preventing premature fracture and to provide desired boundary conditions for the test region, it inhibits the test machine to measure the strain accurately, without the use of extensometers.

There are several types of both mechanical and optical extensometers that are commercially available. For soft and rubbery materials, advanced mechanical extensometers are required to reduce the influence caused by the physical contact between the specimen and the extensometer. Optical extensometers can also be used as these have no physical contact with the test specimens, but these together with other optical solutions such as Digital Image Correlation (DIC) are relatively expensive. A few investigators have adopted optical strain approaches using a stretch measure between two finite gage points. Using deformed images captured during tensile testing, they have demonstrated the use of image processing and correlated the force and strain through time synchronization. For instance, Derwin et al. [20] proposed a new optical method for the determination of strains and demonstrated excellent performance in calibration and experimental tests. A similar approach was used by Coimbra et al. [21] to characterize the tensile properties of microscale ceramic fibers using video extensometry. Wolverton et al. [22] have developed the noncontact video multiextensometry technique for shape memory alloy wires of circular cross-section at high temperature. Recently, Islam [23] has used similar approach for strain measurement by video extensometry for polymers using LabVIEW. Aforementioned studies use an optical method to measure infinitesimal strain correlating the force and strain through time synchronization. In this study we propose an optical method to accurately capture the average strain of the test region during tensile test of a hyperelastic soft material through image processing, by capturing the force measurements within the recorded images themselves. With an image series containing both length and force measurements a stress–strain curve can be generated directly without the need for correlating strain from images with force readings from the test machine. This eliminates the necessity to import force data from the test machine and properly correlate them with the strain measurements, which may also introduce an uncertainty if the equipment and the image recordings were not started at the same time. This method has both length and force measurements saved in the captured images, thus they can readily be converted into stress–strain curves without correlating data from several sources. Therefore, in this study an inexpensive method for measuring the finite length strains in a conventional load frame tensile test for isotropic hyperelastic materials using specimen markings in conjunction with an optical camera is proposed and the constitutive parameters of incompressible version of the Neo-Hookean model are obtained. It utilizes the Image Processing Toolbox in Matlab to post-process images captured at frequent intervals during tensile test, thus working under DIC principles [24]. Error margins associated with the method and camera setup are also investigated and a secondary test-method to quantify them is described. The test-method for determining the error margins is non-destructive and can be employed before the actual tensile test is performed.

Section snippets

Materials and specimens

Objet Connex family of 3D printers can print multiple materials forming an integral prototype from two basic polymeric materials ensuring perfect bonding between different constituents. One of the two basic materials is a rigid polymer called VeroWhite FullCure® 830 (VW), and the other polymer is TP (rubbery). The Connex family of 3D printers are capable of combining these two basic polymers in different proportions to obtain a range of materials with different properties, called digital

Issues in tensile testing of soft materials

In this section, issues encountered while performing tensile tests of dog bone-shaped specimens in the absence of an extensometer are discussed. The crux here is inaccurate estimation of change in length of the test-region by the tensile test machine. The machine uses the change in grip-separation as the change in test-length, which in reality also includes the deformation of the region of the specimen that lies outside the gage length between grips. To accurately obtain strain measures in the

Methodology – image processing (IP)

The method utilizes a camera and the Image Processing Toolbox in Matlab. Explanation on capturing the strain and the force is presented in Sections 4.1 Image processing – capturing the strain, 4.2 Image processing – capturing the force, respectively. Advantages, uncertainties and validation of the methodology are described in Sections 4.3 Image processing – merits, 4.4 Image processing – uncertainties and errors, 4.5 Image processing – validation, respectively. In this method, instantaneous

Results and discussion: constitutive parameters

The results from the tensile tests of TP are presented in this section. Specimens were 3D printed with the dimensions given in Fig. 1 in both longitudinal and transverse printing directions, as illustrated in Fig. 2. The tests were recorded and one frame per second was extracted and processed. The specimens were stretched at 10 mm/min. Fig. 15 shows the engineering stress–strain curves for TP obtained through the IP-method and FEA, discussed later in this section. The plotted IP stress–strain

Conclusion

An image processing (IP) method for accurately measuring the finite length strains in a conventional load frame tensile test for 3D Printed isotropic hyperelastic materials (TP) using specimen markings in conjunction with an optical camera is presented. Neo-Hookean constitutive parameters of TP are determined using stress–strain data obtained by the IP-method for both longitudinally and transversely printed specimens. It was found that the stress–strain curves for the two orientations have

Acknowledgements

This research was sponsored by the MIT & Masdar Institute Cooperative Program (Project Code: 12MAMA1). Authors would like to acknowledge the financial support received from Masdar Institute of Science and Technology for this research work.

References (29)

  • K. Sun et al.

    3D printing of interdigitated Li-ion microbattery architectures

    Adv. Mater.

    (2013)
  • B.G. Compton et al.

    3D-printing of lightweight cellular composites

    Adv. Mater.

    (2014)
  • J. Liljenhjerte et al.

    Pull-out performance of 3D printed composites with embedded fins on the fiber

  • Y. Tan et al.

    3D printing facilitated scaffold-free tissue unit fabrication

    Biofabrication

    (2014)
  • Cited by (35)

    • Parametric visco-hyperelastic constitutive modeling of functionally graded 3D printed polymers

      2022, International Journal of Mechanical Sciences
      Citation Excerpt :

      Furthermore, as they often show strongly rate-dependent behavior, visco-hyperelastic constitutive models should be used to capture their time-dependent behavior. Such visco-hyperelastic material models have already been formulated for inkjet-printed photopolymers in [57,58], for FFF-printed thermoplastic elastomer (TPE) in [59], and for digital light synthesis (DLS) technology in [60]. Furthermore, a linear elastoplastic constitutive model for polymers fabricated via stereolithography was developed and characterized in [61].

    • Additive manufacturing enabled, microarchitected, hierarchically porous polylactic-acid/lithium iron phosphate/carbon nanotube nanocomposite electrodes for high performance Li-Ion batteries

      2021, Journal of Power Sources
      Citation Excerpt :

      Additive manufacturing (AM) (aka 3D printing) has become a widespread technology due to its ability to realize complex 3D architectures across different length scales, ease of processing and a relatively lower cost than traditional manufacturing [1–4,58,61,62].

    View all citing articles on Scopus
    View full text