Determination of deformation of a highly oriented polymer under three-point bending using finite element analysis

1 Introduction

The main method for manufacturing highly oriented polymer involves the die drawing of thermoplastic without the addition of any other materials, followed by cooling to change its molecular chain fibrous structure in a manner that causes all of the molecular chains to point in the same direction, increasing its strength (1), (2), (3). In previous studies that have involved the die drawing of thermoplastic, a highly oriented polymer is typically made by inducing a uniaxial molecular chain arrangement, improving the properties of the material in the drawing direction, but such a method slightly worsens the properties of the material perpendicular to the drawing direction, making the product highly vulnerable to bending (4), (5), (6), (7), (8). The die drawing of a mold can be performed using a rotating mandrel assembly system to produce a polymer with a biaxial molecular chain arrangement. This method improves the properties of the material perpendicular to the die drawing direction, solving the problem of high vulnerability to bending (9). However, this technique is effective only in making tube-shaped material. Mohanraj used the finite element analysis (FEA) software Abaqus to simulate the manufacture of highly oriented polyoxymethylene rods by die drawing. If the die drawing of the material is faster at the die outlet than elsewhere, then the material will ultimately fracture. Therefore, the strain and strain rate of the polyoxymethylene rods in the forming (axial) direction must be controlled, and the strain rate of the die at the outlet must be minimized (10). In the authors’ laboratory, polymer with a biaxial molecular chain arrangement has been used to manufacture I-beams.

With respect to the use of die drawing in the manufacture of highly oriented polymers, many problems are yet to be solved. These include the problem of residual stress distribution and insufficient shear strength, both of which prevent the use of highly oriented polymers in drilling or its use as a structural material. Therefore, in this study, FEA is used to determine the deformation and damage of highly oriented polymers upon the application of a force, and the problems of residual stress distribution and insufficient shear strength are then solved. The results in this research serve as a reference for the design and development of die drawing molds.

Based on the principles of the mechanics of materials, and using FEA, this study investigates the relationships among the size, tensile stress and shear stress of a highly oriented polyethylene I-beam (11). The tension failure and shear failure that are predicted by FEA can be used as references in setting parameters for the manufacture of orthotropic material. The results of the simulation of the polyethylene I-beam can be utilized in the manufacture of vehicle bumpers and gratings. As a polyethylene I-beam is light and strong, it can replace steel, aluminum alloy, fiberglass-reinforced plastic and wood. The most recent literature on the subject concerns the use of finite element analysis to study the effect of different process parameters on the die drawing. However, neither the deformation of nor the damage to highly oriented polymer has been discussed and most finite element analysis of deformation and failure has involved homogeneous or composite materials (12), (13), (14), (15).

2 Experimental details

The I-beam of interest is taken from the product catalog of the Strongwell Corporation (Bristol, VA, USA) (16). Solid models of I-beams are constructed, with five length-to-height ratios, yielding aspect ratios of 1:4, 1:8, 1:12, 1:16 and 1:20. Figure 1 shows the 2D geometries of I-beams.

Figure 1:

Two-dimensional geometries of I-beams.

The solid models of I-beams are made from a highly oriented orthotropic material that is manufactured by die drawing. Data on the material from which the solid models of I-beams are made are taken from the relevant literature (17). The material parameters of interest are Young’s modulus, Poisson’s ratio and the shear modulus (Table 1).

The tensile strength of the I-beams in this study is 482.63 MPa (70,000 psi). Based on the shear strengths of the products in the catalog of Strongwell Corporation, samples A, B and C, were ordered by shear strength, as presented in Table 2.

Under the boundary conditions in the three-point bending test, the I-beams of the six degrees of freedom of the constraint support-point are all zero (U1=U2=U3=UR1=UR2=UR3=0). With respect to the loading conditions, the loading-point round rod is displaced downward until the I-beams are destroyed.

This investigation concerns three-point bending and deformation as part of an engineering problem that involves contact deformation or bending deformation. Therefore, in the FEA software, non-conforming elements (C3D8I) are used in the finite element model. Each element is hexahedral, and its size is 1.5875 mm (Figure 2).

Figure 2:

Finite element model of three-point bending.

The “static, general” module in the Abaqus software is used to solve the engineering problem that involves the three-point bending load. As the module in Abaqus/Standard imposes no limit on the time increment of the simulation, if the time increment is less than the commonly used setting, then the simulation can be completed. Herein, analytical results are generated every 0.025 s. Based on the results of the three-point bending load analysis, the tension failure and shear failure of highly oriented polyethylene are elucidated. When the tensile stress and shear stress of the material exceeds its tensile strength and shear strength, respectively, the material undergoes tension failure and shear failure, respectively; these phenomena will be discussed further.

3 Results and discussion

As revealed by the FEA results, when the aspect ratio is 1:4, tension failure occurs below the middle of the upper edge of the I-beam (Figure 3). When the aspect ratio is between 1:8 and 1:20, tension failure occurs below the middle of the lower edge of the I-beam (Figure 4). In the figure, the white block indicates the position of tension failure.

Figure 3:

Location of tension failure when aspect ratio is 1:4.

Figure 4:

Location of tension failure when aspect ratio is 1:8.

As revealed by the FEA results, when the aspect ratio is between 1:4 and 1:20, shear failure occurs above the left and right sides of the lower edge of the I-beam (Figure 5). In the figure, the white block (positive value) and the black block (negative value) indicate the locations of shear failure. Shear failure is initiated at the lower edges close to the two sides of the I-beam, and then tension failure occurs in the central part of the I-beam, and more specifically at the upper edge of the center.

Figure 5:

Location of shear failure when aspect ratio is 1:4.

Based on the FEA-generated information concerning the tensile force, shear stress, and displacement of material A, the orders of occurrence of the tension failure and the shear failure of I-beams with different aspect ratios are examined. As revealed by the FEA results, when the aspect ratio is between 1:4 and 1:20, shear failure occurs first in material A (Figure 6). As the tensile strength of material A is extremely low and shear failure occurs easily, material A cannot be used in industry.

Figure 6:

Order of tension failure and shear failure of material A.

Based on the FEA results concerning tensile stress, shear stress, and displacement for material B, the orders of occurrence of tension failure and shear failure of I-beams with various aspect ratios are examined. As shown in the FEA results, when the aspect ratio is 1:4, 1:8 or 1:12, shear failure occurs first. When the aspect ratio is 1:16 or 1:20, tension failure occurs first (Figure 7). Therefore, when the aspect ratio is greater than 1:16, the destruction of the far end of the I-beam by the shear force is avoided. Therefor, manufacturing using material B is recommended to involve an aspect ratio of greater than 1:16.

Figure 7:

Order of tension failure and shear failure of material B.

Based on the FEA results concerning the tensile stress, shear stress, and displacement for material C, the orders of occurrence of tension failure and shear failure of I-beams with various aspect ratios are obtained. When the aspect ratio is 1:4 or 1:8, shear failure occurs first. When the aspect ratio is 1:12, 1:16 or 1:20, tension failure occurs first (Figure 8). Therefore, when the aspect ratio of material C exceeds 1:12, shear failure at the far end of I-beam does not occur. Manufacturing using material C is recommended to involve with an aspect ratio of greater than 1:12. The FEA results herein show the order of occurrence of tension failure and shear failure, based on which the feasibility of the manufacturing of I-beams can be determined. As revealed by the simulation results, material A is not useful for manufacturing because its shear strength is too low; material B is suitable if it has an aspect ratio of greater than 1:16, and material C is suitable if it has an aspect ratio of greater than 1:12.

Figure 8:

Order of tension failure and shear failure of material C.

It can be seen from Figure 9 that five polyethylene (PE) materials with aspect ratios of 1:4, 1:8, 1:12, 1:16 and 1:20 are taken for FEA simulation, intending to acquire the failure mode which occurred to PE material. Results in Figure 9 show that tensile failure occurs first in the PE material. But when aspect ratios are 1:4 and 1:8, shear failure even occurs in addition to tensile failure. As to PE materials with aspect ratios of 1:12, 1:16 and 1:20, only tensile failure occurs. Taking the aspect ratio of 1:4, for example, the time required for the occurrence of tensile failure is 0.475 s, with the deformed amount of material being 6.65 mm; and the time required for shear failure which subsequently occurred is 0.775 s, with the deformed amount of material being 10.85 mm.

Figure 9:

Order of tension failure and shear failure of PE.

Figure 10 shows the tensile and shear failure regions under different conditions of shear strength and aspect ratio of highly oriented polymer. The results in Figure 10 provide materials of different shear strengths with the applicable aspect ratios for the occurrence of tensile failure. As is seen in Figure 10, when shear strength of material is greater, the aspect ratio required for the occurrence of tensile failure first is smaller. Therefore, if the shear strength of material increases, the I-beam of highly oriented polymers can be manufactured under the condition of a lower aspect ratio.

Figure 10:

Failure region under different conditions of shear strength and aspect ratio for highly oriented polymer.

4 Conclusions

FEA and the three-point bending tests are carried out herein to examine materials with five aspect ratios and three shear strengths. The locations of tension failure and shear failure and the order of their occurrence are examined. The FEA results show the order of occurrence of tension failure and shear failure of each material, which can be used to determine the feasibility of the manufacture of I-beams. The following conclusions are drawn from the FEA results.

1. FEA was used to simulate the cracking of I-beams. Their stress intensity factors can be acquired. The direction of growth and the lengths of cracks are obtained, and further relevant studies are being performed.

2. The FEA results in this investigation reveal the order of tension failure and shear failure, from which the feasibility of manufacturing of highly oriented polymers can be evaluated. As the shear strength of material A is extremely low, material A is not suitable for use in industry. Manufacturing using material B should be performed only with an aspect ratio of greater than 1.16, and manufacturing using material C should be carried out only using an aspect ratio of greater than 1.12.

3. As revealed by the predictions made using FEA, if the tensile strength of a material is increased above 6000 psi, then tension failure occurs sooner as the aspect ratio is reduced, so shear failure at the far end of the I-beam can be prevented.