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Investigation of the Strain-Rate-Dependent Mechanical Behavior of a Photopolymer Matrix Composite With Fumed Nano-Silica Filler.


Photopolymers are light-sensitive polymeric materials, which changes their chemical and physical properties when exposed to UV light. These photopolymers are very commonly used in additive manufacturing techniques such as stereolithography and fused deposition modeling. Polymers commonly exhibit weak mechanical properties, for example, low stiffness and low strength. In order to improve and expand their applications, fillers such as micro-/nano-sized silica, carbon nanotubes [1], [Al.sub.2][O.sub.3] [2], and glass are added. Polymer nanocomposites have demonstrated vast potential to significantly improve the polymers properties by the addition of nanoscale fillers [3]. In the recent past, there have been serious attempts on the development of more advanced materials by adding nanofillers on different matrices for improved mechanical and physical properties. Nanocomposites have attracted scientists, engineers, and industrialists with an aim to design and develop nanocomposites having a unique combination of materials, unlike traditional materials. Nanocomposites like traditional composites could have polymeric or ceramic matrices. Generally, polymer matrix composites yield good specific stiffness, fatigue, corrosion resistance, and specific strength than metals. Still, they exhibit weak residual strength and weak impact energy absorption [4-6]. Studies have been conducted in which nano-sized fillers with different diameters have been added into polymeric material [7], and it was reported that nano-sized filler with lower diameter has a more profound effect on mechanical properties. Recently, Asif et al. [8] reported significant improvement in mechanical properties of three-dimensional (3D) printed photopolymer with the addition of nano-sized silica filler.

An in-depth understanding of the mechanical response of polymers over a range of strain rates, temperature, and pressure is required in a wide variety of fields, for example, aerospace, automotive, and medical devices. The properties are generally governed by not only the composition and microstructure of the materials but also rely on pressure, temperature, and strain rate. Researchers have characterized the mechanical response of the polymers (specifically stress-strain relationship) over the past 40 years at strain rates between [10.sup.-4] and [10.sup.5] [s.sup.-1] [9-12]. Polymers commonly exhibit time-dependent mechanical response as shown by rate-dependent yield strength, elastic moduli, and postyield behavior. A range of strain rates and temperature can cause the polymer to change mechanical behavior from rubbery to ductile plastic to brittle [13-19].

Traditional micromechanical analytical models [20-22] commonly used for micro-sized reinforcement composites, were recently used to predict the overall stiffness of nanocomposites. These conventional theories are based on the observation that the overall mechanical response of composite materials are functions of constituent properties, volume fraction, the shape of inclusion, and dispersion, but are not dependent on size. Finite element method [23-25] and molecular mechanics [26, 27] have been recently used to study the behavior of nanocomposite systems.

There are various types of viscoelastic models which are proposed to predict the rate dependent behavior of the polymers. Green and Rivlin proposed the early models for capturing the nonlinear response of viscoelastic solids in which stress is expressed as the function of the history of the deformation gradient. For materials with fading memory, Green et al. [28] and Coleman and Noll [29] proposed constitutive models, which demonstrate the point that material response at present time is more strongly dependent on the latest deformations than the those happened in the distant past. Pipkin and Rogers [30] used the history of strain rate rather than the history of strain to express the time-dependent stress. In addition, they analyzed the likelihood that such integral expressions are also effective when the roles of stress and strain are switched. Schapery [31] analyze the nonlinear viscoelastic behavior of polymers experiencing small deformations expressed a nonlinear single integral model. In this model, he presented four nonlinear parameters related with instantaneous (elastic), loading rate, transient, and accelerated/decorated time-dependent responses. In addition, he discussed dual representations in which the roles of stress and strain are switched.

In order to capture the viscoelastic behavior of biological materials, Fung [32] proposed the quasi-linear viscoelastic (QLV) model. In the QLV model, stress relaxation function is modeled by separating it into two functions, that is, reduced (normalized) time functions and nonlinear elastic function. The nonlinear elastic function can be derived from strain energy density function [33-35]. The benefit of using the QLV model is that it has mathematical and experimental advantages as it is easy to resolve the constitutive equations and material parameter characterization. The reduced relaxation function is not special and any function that is continuous, positive, and monotonically decreasing with time is acceptable.

Muliana et al. [36] presented a modified form of QLV models in which they expressed strain as an integral of a nonlinear measure of the stress. They predicted the behavior of elastomers [37] and light-activated shape memory polymers using these models [38], The QLV model is commonly employed nowadays because it provides the simplest way to include both nonlinearity (dependence of properties of load or strain) and time dependence (viscoelasticity) in a simplified integral model. Apart from biomedical applications [39], the QLV model has also been employed to model materials such as elastomeric polymers, rubbers, and composites [37, 40].

In order to study the rate-dependent behavior of our chosen photopolymer, we have conducted tensile tests at different loading rates to characterize the rate dependency of the material. We have used fumed silica as a nanofiller to enhance the mechanical properties. Different concentration by weight has been added into the polymer and dog-bone samples have been fabricated by casting. QLV model, which combines hyperelastic and viscoelastic phenomena, has been implemented by developing a MATLAB script to capture the rate-dependent mechanical response of the polymer and of different filler concentrations. The QLV model with Yeoh strain energy density function shows remarkable agreement with the experimental results as it adequately captures the behavior of all four filler concentrations and of the polymer.


Preparation of UV Curable Resin and Casting of Samples

The photopolymer resin (UV Dome 58) used was purchased from Whitehall Technical Services Ltd, Auckland, New Zealand. It is based on an epoxy urethane that was mixed with fumed silica as the filler. Fumed silica has nanoparticles with a very large surface area and a low bulk density. Generally, it appears in the solid state in the form of a white powder. With an adequate homogenization, silica nanoparticle can be mixed with another chemical component. Silica nanoparticles have a spherical shape with a diameter ranging between 25 and 30 nm (Fig. 1). Silica nanoparticles appear to make long chains or form agglomerates.

To investigate the effect of different filler concentrations on mechanical properties, samples of different concentrations of silica filler (by weight) were mixed into the resin. In order to have the same aging, samples were prepared in the same day inside a photolithography room. A total of 100 g of the mixture was made for each concentration for instance for 4% by weight of filler, 96 g of the resin was mixed with 4.0 g of fumed silica. After a slow manual stirring for 5-10 minutes with a thin spatula, the mixture was mixed with an ultrasonic homogenizer. An ultrasonic homogenizer from Sonics and Materials, Inc. was used for 2 minutes at 20 kHz of ultrasound frequency and 130 W of intensity. Finally, in order to reduce air bubbles in the mixture, samples were degassed in a vacuum for 45 minutes at 65[degrees]C.

Samples were prepared using a mold of the Type V (ASTM D638) dog-bone specimen as shown in Fig. 2. The mixture was manually casted into a mold using a syringe and placed under a UV light box for 3 minutes. UV light box consists of the UV exposure system of 4 x 15 W (5 mW/[cm.sup.2]) having UV light source of 405 nm wavelength. Six samples for the polymer, 4%, 8%, 9%, and 10% filler concentrations were fabricated.


Uniaxial Tensile Tests at Different Strain Rates

Stress relaxation, creep, uniaxial tension, and so on are a different set of experiments normally conducted to demonstrate the material properties of the rate-dependent material. However, the uniaxial tensile test is considered to be the most common mode of deformation. Uniaxial tension tests at different strain rates could provide plausible information about the viscoelastic behavior of the rate-dependent material [41-43]. Therefore, we considered this mode to study the mechanical behavior of the photopolymer (UV Dome 58) with four different filler concentrations, for example, 4%, 8% 9%, and 10%. Tensile tests were conducted on dog-bone sample of specific dimensions (following ASTM D638 standard Type V) as shown in Fig. 3a of polymer and Fig. 3b (with silica filler) with different strain rates, for example, 1.3 X [10.sup.-2] [s.sup.-1] 1.3 x [10.sup.-3] [s.sup.-1], and 1.3 x [10.sup.-4] [s.sup.-1]. In order to capture the localized strain in gauge part of the sample, a commercial digital image correlation (DIC) open source software GOM Correlate[R] was used and a video camera was mounted in front of the tensile testing machine to record the test. Before the tests, random speckle pattern was created on the samples with the combination of white and black spray paint as shown in Fig. 3c. After the tests, recorded videos were postprocessed in GOM to obtain the strain in the gauge part of the specimen. Figure 4a-c shows the DIC images captured during localized strain measurement at gauge part of the specimen.

Figure 5a-c shows the stress-strain curves obtained for the polymer, 4%, 8%, 9%, and 10% filler concentrations with the loading rates discussed above. As most rate-dependent materials exhibit a stronger response to faster loading rate, the tensile strength of the polymer as well as of all four filler concentrations increases by increasing the strain rate. Tensile strength of polymer is significantly increased by the addition of nano-sized silica filler; tensile strength of 4% filler concentration is higher than 8%, 9% and 10% filler concentrations at all loading rates, this is because by increasing the filler concentration diameter of the nanoparticles increases and the surface area decreases resulting in a weak matrix-particle interfacial adhesion. Nanoparticles with higher surface area provide more enhanced matrix-particle interfacial adhesion. Increasing filler content increases the diameter of the filler and thereby decreasing the surface area, which results in poor matrix-particle interfacial adhesion, the particles are unable to carry any part of the externally applied load. Therefore, the strength of the composite cannot be higher than the neat polymer matrix [44], As seen in Fig. 5, 4% filler concentration has stronger mechanical properties compared to 8%, 9%, and 10%. It can be established that 4% filler content is the maximum amount of filler at which photopolymer (UV Dome 58) exhibits a stronger response. At 1.3 x [10.sup.-2] [s.sup.-1], adding filler content decreased the strain to failure of the material except for 4%. With 8% and 4% filler, the nanocomposite was found to have almost the same strain to failure as of the pure polymer exhibiting more ductile behavior than other filler concentrations. At 1.3 x [10.sup.-3] [s.sup.-1] pure polymer is found to exhibit more brittle behavior compared to all the filler concentrations used, while 4% filler showing high strain to failure demonstrating more ductile behavior. At 1.3 x [10.sup.-4] [s.sup.-1] pure polymer has low strain to failure compared to all filler concentrations used; 4% and 8% filler content exhibited almost similar strain to failure.

Nanocomposites could overcome the problems such as a uniform dispersion of nanofillers in the matrix if a suitable processing method is selected. Local stress concentration arises with in the nanocomposite structure when aggregation is formed in the nanofiller. While strength is heavily dependent on the effective stress transfer between particles and matrix, if the bond between the matrix and particle is weak, stress cannot be effectively transferred from the matrix to particles. These result in a premature failure of the polymer reducing its strength and strain to failure. To create a strong interface, a suitable nanofiller that is compatible with the polymer matrix is essential. A significant amount of research has been conducted using particulate nanocomposites and promising results have been obtained especially for the improvement of mechanical and dynamic properties [45, 46].

Application of QLV Model with Yeoh Strain Energy Density Function

Viscoelasticity is the property of the materials that exhibit both viscous and elastic characteristics when undergoing deformation where after the load is applied, there is an instantaneous elastic deformation, and the viscous part occurs with respect to time. Fung [32] first proposed the QLV model which is frequently used to study the behavior of soft biological tissues. The QLV is capable of capturing elastic nonlinearties of soft tissues. The Cauchy stress for QLV model is represented as

[sigma](t) = -pI + F(t){[S.sup.e][C(t)] + [[integral].sup.t.sub.0] [S.sup.e][C(t)[partial derivative]G(t-s)/ [partial derivative](t - s)ds} F[(t).sup.T] (1)

where [sigma](t) is the Cauchy stress tensor, F is the deformation gradient, C = [F.sup.T]F is the right Cauchy-Green tensor, p is Lagrange multiplayer, and I is identity tensor. The term [S.sup.e][C(t)] can be taken as effective (instantaneous) second Piola Kirchhoff elastic stress tensor [47].

Recently, Slesarenko and Rudykh [41] demonstrated QLV model by combining Yeoh strain energy density function and Neo Hooken strain energy density function to study the behavior of a soft rubber-like digital materials used in Polyjet multimaterial 3D printing. They reported that the QLV model with Yeoh strain energy density function successfully captures the behavior of most of the soft digital materials.

In this study, we employed a similar hyper-viscoelastic approach using QLV model with Yeoh strain energy density function to model the behavior of our chosen material under uniaxial tension. Equation 3 represents the QLV model with Yeoh strain energy density function; for the detailed theoretical background of the model, readers are recommended to read the work of Slesarenko and Rudykh [41] and references therein.

Strain energy density function for classical two-term Yeoh model [48] can be defined as

w = [mu]/2[([I.sub.1] - 3) + [alpha]/2[([I.sub.1] - 3).sup.2]] (2)

where [mu] is the instantaneous shear modulus and [alpha] is a constant.

The Cauchy stress component for QLV model with Yeoh strain energy density function can be represented as

[mathematical expression not reproducible] (3)

Stress relaxation function D(t) defines the influence of current stress state in QLV model, which is represented here by the Prony series as

[mathematical expression not reproducible] (4)

where [[gamma].sub.i] and [[tau].sub.i] represent relaxation coefficients and relaxation times, respectively.

We used five-term Prony series with relaxation times [tau] = 0.01, 0.1, 1, 10, and 100 s considering relaxation occurs at different time scales and one-term Prony series is normally insufficient to adequately define the material response different rates. The experimental stress strain curves with different strain rates have been fitted with MATLAB script using trust region reflective algorithm with nonlinear least square criterion. Figure 6a-e exhibits the fitting results of the QLV model with Yeoh strain energy density function (Eq. 3, it can be clearly seen that the model shows exceptional agreement with experimental results of polymer and filler concentrations having filler concentrations 4%, 8%, 9%, and 10%. Table 1 shows the calibrated material parameters of the QLV model with Yeoh strain energy density function for the polymer, 4%, 8%, 9%, and 10% filler concentrations. As seen in Table 1 instantaneous shear modulus [mu] increases with an increase in the filler concentration up to 8%, For 9% and 10%, it is found to be decreasing. This is because with higher filler concentration particles tend to form agglomerates, which results in weak matrix-particle interfacial adhesion. Homogenous dispersion of nanoparticles helps to decrease the agglomeration and improve the mechanical properties. However, it is very challenging to homogeneously disperse the nanofiller because of the strong tendency of nanoparticles to agglomeration [49, 50], In addition, as discussed in "Uniaxial tensile tests at different strain rates" section, adding higher filler content decreases the surface area of the particles leading to weak interfacial adhesion, which is also a major contributor to weak mechanical properties.


In this study, we have studied the rate-dependent behavior of photopolymer nanocomposite by conducting tensile tests at different strain rates. Fumed silica is used as a reinforcement and different concentrations of filler have been added to enhance the mechanical properties. We found out that the ultimate yield strength is significantly affected by the strain rate, for example, tensile strength of the photopolymer is 2.2 times higher at 1.3 x [10.sup.-2] [s.sup.-1] compared to the tensile strength at 1.3 x [10.sup.-4] [s.sup.-1]. Adding silica filler enhanced the mechanical properties of the photopolymer, for example, with 4% filler content, tensile strength is 2.25, 2.38, and 2.42 times higher than the tensile strength of the polymer at 1.3 x [10.sup.-2] [s.sup.-1], 1.3 x [10.sup.-3] [s.sup.-1], and 1.3 x [10.sup.-4] [s.sup.-1] respectively. QLV model combining hyperelastic and viscoelastic phenomena has been used to capture the rate-dependent nonlinear behavior of the material. We selected the uniaxial tension test scheme with three different strain rates to calibrate and capture the viscoelastic parameters and time-dependent response, respectively. We have successfully demonstrated the capability of the QLV model with hyper-viscoelastic phenomena to capture the behavior of the material. In this work, the QLV model with Yeoh strain energy density function bears very good agreement with the experimental results.


The authors would like to extend their appreciation to Dinesh Mathur for providing technical support in the microsystem lab.


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Muhammad Asif, (1,2) Maziar Ramezani, (1) Kamran Ahmed Khan, (3) Muhammad Ali Khan, (4) Kean Chin Aw (iD) (5)

(1) Department of Mechanical Engineering, Auckland University of Technology, Auckland, New Zealand

(2) Department of Engineering Sciences, National University of Science and Technology, Karachi, Pakistan

(3) Aerospace Engineering Department, Khalifa University, Abu Dhabi, UAE

(4) School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, UK

(5) Department of Mechanical Engineering, University of Auckland, Auckland, New Zealand

Correspondence to: K.C. Aw; e-mail:

DOI 10.1002/pen.25168

Published online in Wiley Online Library (

Caption: FIG. 1. Scanning electron microscope image of silica nanoparticles. [Color figure can be viewed at]

Caption: FIG. 2. Mold of Type V (ASTM D638) dog-bone specimen. [Color figure can be viewed at]

Caption: FIG. 3. Dog-bone specimen of (a) polymer, (b) with silica filler, (c) with random speckle pattern. [Color figure can be viewed at]

Caption: FIG. 4. Strain measurement using GOM correlate at gauge part: (a) 1.3 x [10.sup.-2] [s.sup.-1], (b) 1.3 x [10.sup.-3] [s.sup.-1] and (c) 1.3 x [10.sup.-4] [s.sup.-1]. [Color figure can be viewed at]

Caption: FIG. 5. Stress-strain curves of polymer, 4%, 8%, 9%, and 10% filler concentration at strain rate: (a) 1.3 x [10.sup.-2] [s.sup.-1], (b) 1.3 x [10.sup.-3] [s.sup.-1], and (c) 1.3 x [10.sup.-4] [s.sup.-1]. [Color figure can be viewed at]

Caption: FIG. 6. Fitting of experimental results with QLV model with Yeoh strain energy density function: (a) polymer, (b) 4% filler concentration, (c) 8% filler concentration, (d) 9% filler concentration, and (e) 10% filler concentration. [Color figure can be viewed at]
TABLE 1. Material parameters for QLV model
with Yeoh strain energy density function.

Calibrated parameters of QLV model with
Yeoh strain energy density function

Material   [mu] (MPa)   [alpha]   [[gamma].sub.1]   [[gamma].sub.2]

Polymer      142.90     -1.069         0.999             0.601
4%           172.89     -0.9416       0.1025             0.999
8%          245.322     -0.1105       0.7305             0.999
9%           231.45     -0.5989       0.5902             0.999
10%          168.97     -0.9679          0               0.999

Material   [[gamma].sub.3]   [[gamma].sub.4]   [[gamma].sub.5]

Polymer           0                 0               0.742
4%             0.3334               0                 0
8%             0.3744               0              0.6860
9%             0.0343               0                 0
10%            0.3768            0.0295             0.999
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Author:Asif, Muhammad; Ramezani, Maziar; Khan, Kamran Ahmed; Khan, Muhammad Ali; Aw, Kean Chin
Publication:Polymer Engineering and Science
Article Type:Report
Geographic Code:7UNIT
Date:Aug 1, 2019
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