Advances in Materials Science and Engineering

Volume 2019, Article ID 7201215, 10 pages

https://doi.org/10.1155/2019/7201215

## Effect of Process Parameters on Short Fiber Orientation along the Melt Flow Direction in Water-Assisted Injection Molded Part

^{1}School of Mechanical and Electrical Engineering, Nanchang University, Nanchang 330031, China^{2}Jiangxi Province Key Laboratory of Polymer Micro/Nano Manufacturing and Devices, East China University of Technology, Nanchang 330013, China^{3}School of Mechanical and Electrical Engineering, East China Jiaotong University, Nanchang 330013, China

Correspondence should be addressed to Hesheng Liu; moc.361.piv@uilsh

Received 21 February 2019; Revised 8 July 2019; Accepted 22 July 2019; Published 19 August 2019

Academic Editor: Francisco Chinesta

Copyright © 2019 Haiying Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The short fiber orientation (SFO) distribution in the water-assisted injection molding (WAIM) is more complicated than that in traditional injection molding due to the new process parameters. In this work, an improved fiber orientation tensor method was used to simulate the SFO in WAIM. The result was compared with the scanning electron micrograph, which was consistent with the experiments. The effect of six process parameters, including filling time, melt temperature, mold temperature, delay time, water pressure, and water temperature, on the SFO along the melt flow direction were studied through orthogonal experimental design, range analysis, and variance analysis. An artificial neural network was used to establish the nonlinear agent model between the process parameters and *A*_{11} representing the fiber orientation in melt flow direction. Results show that water pressure, melt temperature, and water temperature have significant effects on SFO. The three-dimensional (3D) response surfaces and contour plots show that the values of *A*_{11} decrease with the increase in water pressure and melt temperature and increase as the water temperature rises.

#### 1. Introduction

With the development of advanced, economical, and environmentally friendly society, higher requirements are placed on the performance of plastic products. The short-fiber-reinforced polymer composite (SFRPC) is a material with a polymer as a matrix and short fibers as a dispersed phase. Its characteristics are lightweight, high specific strength and specific modulus, stable chemical properties, heat resistance, and good wear resistance [1]. In recent years, SFRPCs have gradually replaced metal materials in some fields, making them widely used in aviation, automotive, shipping, and medicine [2, 3].

Fluid-assisted injection molding is an emerging process that includes gas-assisted injection molding (GAIM) and water-assisted injection molding (WAIM) [4, 5]. The fluids used in GAIM and WAIM are nitrogen and water, respectively. Due to incompressibility, high heat capacity, and good thermal conductivity of water, the advantages of WAIM over GAIM are high product efficiency, more uniform and thinner residual wall thickness (RWT) [6]. Based on whether or not the cavity is completely filled with melt, WAIM can be categorized into two types: short-shot WAIM and overflow WAIM. In short-shot WAIM, the mold cavity is partially filled with melt, followed by the injection of water into the core of melt. In overflow WAIM, the mold cavity is completely filled with melt, followed by the injection of water that pushes the melt into the overflow cavity to form a part with a hollow cross section. Compared with the standard injection molding, WAIM offers significant advantages in the preparation of shaped hollow plastic parts with uniform RWT. However, due to the difficulty in controlling the water injection pressure and the turbulence characteristics of the injection water, the quality of the products is not stable [7, 8]. Present researches on WAIM focus on the distribution of RWT [9], the length of water column penetration [10, 11], and the defects of molded parts [12, 13].

The RWT of water-assisted injection molded parts is thin, and the mechanical properties of the parts can be greatly improved by using SFRPC as a raw material. Many studies reported that the distribution of short fiber orientation (SFO) determined the mechanical and physical properties of the plastic parts, while fiber orientation was affected by mold structure, molding process parameters, flow field distribution, initial state of fibers, fiber properties, and matrix properties [14–16]. The molding process parameters influence temperature, velocity distribution, melt viscosity gradient, and flow field, which ultimately determine the fiber orientation. Liu et al. [7, 12] found that the short fibers mostly aligned along the melt flow direction in WAIM. Huang et al. [17] suggested that high-pressure water penetration significantly affected fiber orientation in WAIM, and increasing melt temperature decreased fiber orientation. Systematic studies on the influence of process parameters on the SFO help understand the fiber orientation mechanism, optimize the SFO distribution, and improve the overall performance of the parts in WAIM.

WAIM, including the melt and high-pressure water filling stages, is more complicated than the standard injection molding process. Due to the difficultly in accurately controlling all the process parameters simultaneously, the research of SFO in laboratory is performed for qualitative analysis. With the development of computer technology, the three-dimensional numerical simulation technology developed rapidly, enabling simulating complex injection molding. The process parameters can be accurately controlled in simulation, but the reliability of SFO simulation depends on the accuracy of the mathematical model. The fiber orientation distribution in injection molding is very complicated microscopically. In the past three decades, theoretical studies on fibers suspension rheology have achieved a great success. Based on the classic fiber orientation models, including Jeffery hydrodynamics model, Folgar–Tucker model [18], and ARD-RSC model [19], Tseng et al. recently proposed an improved iARD-RPR model [20, 21], which can provide good simulation results of SFO in standard injection molding.

In this work, based on the iARD-RPR model, the SFO in WAIM was simulated, and the results were compared with the scanning electron micrographs (SEMs) to verify the applicability of this model for WAIM. The influences of process parameters on the fiber orientation along the melt flow direction were studied through the methods of orthogonal experimental design, range analysis, and variance analysis. The nonlinear proxy model between process parameters and fiber orientation along the melt flow direction was constructed by artificial neural network (ANN), and the interaction effect of significant process parameters was investigated using 3D response surfaces and contour plots.

#### 2. Methods

##### 2.1. Fluid Mechanics Governing Equations

The movement of short fibers in injection molding is a transient, non-Newtonian, and nonisothermal process. In numerical simulations, the melt is considered to be incompressible and laminar, and the inertial term is ignored. The governing equations for transient and nonisothermal fluid motion in WAIM processes are as follows:where is the velocity vector, is the shear viscosity, is the pressure, *ρ* is the melt density, is the total stress tensor, is the gravity, is the specific heat capacity, *T* is the temperature, *k* is the thermal conductivity, *t* is the time, and is the shear rate.

##### 2.2. Rheological Model

The Cross-WLF rheological model with seven parameters was used in the simulation, which can describe complex viscosity behaviors, including the viscosity varying with shear rate and the zero-shear-rate viscosity, depending on temperature and pressure [20].where *η* is the viscosity of the melt, is the zero shear viscosity, is the shear rate, is the material constant, *n* is the power law index in the shear rate, *T* is the melt temperature, is the glass transition temperature, and , , , , and are the constants associated with the selected material.

##### 2.3. Fiber Orientation Model

The fiber orientation is often described by two methods including orientation probability density distribution function and orientation tensor. The orientation probability density distribution function is used to calculate the ratio of short fibers to the total number of fibers in a certain orientation direction. It is intuitive and easy to understand, but its wide application is limited due to the large amount of calculation. In this work, the numerical simulation of SFO in WAIM is based on the fiber orientation tensor evolution equation. To succinctly represent the orientation of a large number of fibers, a second-order orientation tensor is defined as follows [18]:where is the probability density distribution function of the whole orientation space, is the fiber’s unit vector, is a symmetric matrix, and when = /3, it represents the orientation state isotropic, where represents an identity matrix. The three components A_{11}, A_{22}, and A_{33} on the diagonal represent the fiber orientation in the melt flow direction, the cross-flow direction, and the thickness direction, respectively.

Tseng recently proposed a new fiber orientation prediction model (iARD-RPR) [21] as below:where is a Jeffery hydrodynamic model, is an improved anisotropic rotational diffusion model with two effective parameters: fiber-fiber interaction factor and fiber-matrix interaction influence factor , and is the retarding principal rate model that contains the parameter *α* (0 < *α* < 1), which is mean to slow the response rate of fiber orientation. The orientation tensor will be influenced by the parameters, and the default parameters ( = 0.005, = 0.1, and *α* = 0.7) of iARD-RPR model for short fibers were used in the simulations:where is the vortex tensor, is the deformation rate tensor, is the particle shape factor, and the fourth-order orientation tensor A_{4} can be estimated from *A* by using the eigenvalue-based optimal fitting (EBOF) closure [22] or the invariant-based optimal fitting (IBOF) closure [23]. EBOF was chosen in this paper.where is a material derivative of a diagonal tensor and its superscript is the intrinsic orientation kinetic (IOK) assumption, is the *i*-th diagonal component of , is a rotation matrix, is the eigenvalue of matrix and .

In the simulation, the melt flow problem was solved firstly, and then the resulting velocity field was applied to compute the short fiber orientation.

##### 2.4. Geometric Model

The geometric model is shown in Figure 1. The length of the functional hollow duct is 245 mm, and the diameter is 20 mm. The overflow cavity was used to accommodate the melt pushed out by the high-pressure water. The connecting pipe between the duct and the overflow cavity had a diameter of 10 mm. The 3D model was created using Pro/E software. Moldex3D, developed by CoreTech System Co. Ltd., was used to simulate the melt filling and high-pressure water penetration process of WAIM. The combined model, imported into the Moldex3D R15.0, was meshed with Boundary Layer Mesh format. In the simulation, a short-fiber-reinforced PP (Fiberfil J-68/30/E with a short grass fiber mass fraction of 30% and an aspect ratio of 20) was selected as material, and its properties were available in the data bank of Moldex3D. The simulation of overflow WAIM process was carried out. First, the melt was injected into the mold cavity of the functional plastic part. Second, after a short delay time, the high-pressure water was injected into the core of the melt and penetrated along the core position with the least flow resistance and pushed the core melt into the overflow cavity to form a plastic part with a hollow cross section.