Influence of material models on quality of results of plastic parts ’ mechanical analyses

Nowadays, more and more elements originally made of metal are replaced with plastic parts. This is due to the low density of polymer materials, their high relative strength, as well as the ease of forming (complicated elements can be produced in one operation). The disadvantages of plastics are low rigidity and very non-linear material properties. To increase rigidity, a glass fiber filler is used above all. Its addition to the polymer allows to increase the rigidity from four to six times (depending on the type and amount of fiber added, in the case of carbon fiber, it is possible to achieve up to 10-fold improvement in rigidity), due to which the manufactured elements have less deformability with a slight increase in basis weight [1, 2]. The disadvantage of using glass fibers is to reduce the maximum elongation of details and their impact strength. In addition, the introduction of glass fibers into the polymer matrix results in the anisotropy of the material depending on the orientation of the fiber, which in turn depends on the method of filling the cavity forming the mold. In addition, it complicates the mathematical description of the phenomenon of deformation under the influence of applied loads.

The influence of simplified and expanded material model on stress and strain in plastic parts was presented.Because of nonlinear properties the prediction of the behavior of plastic parts is difficult.In this work it was shown what simplifications should be used with linear material model for fiber-filled plastics.

KEYWORDS: plastics, postmoulding properties, Ramberg-Osgood model
Nowadays, more and more elements originally made of metal are replaced with plastic parts.This is due to the low density of polymer materials, their high relative strength, as well as the ease of forming (complicated elements can be produced in one operation).
The disadvantages of plastics are low rigidity and very non-linear material properties.To increase rigidity, a glass fiber filler is used above all.Its addition to the polymer allows to increase the rigidity from four to six times (depending on the type and amount of fiber added, in the case of carbon fiber, it is possible to achieve up to 10-fold improvement in rigidity), due to which the manufactured elements have less deformability with a slight increase in basis weight [1,2].The disadvantage of using glass fibers is to reduce the maximum elongation of details and their impact strength.In addition, the introduction of glass fibers into the polymer matrix results in the anisotropy of the material depending on the orientation of the fiber, which in turn depends on the method of filling the cavity forming the mold.In addition, it complicates the mathematical description of the phenomenon of deformation under the influence of applied loads.
The relationship between stress and strain for plastics is well described by the Ramberg-Osgood (RO) model.It is expressed as follows [4]: where:   -stress,   -yield point, n -exponent of power law,   -modulus of warp stiffness,    ,   equivalent strain -respectively -elastic and plastic.
This non-linear model was created in 1943 to describe materials, in which plastic deformation occurs with a smooth transition between elastic and plastic deformation [5].For this reason, it is often used for polymeric materials.

Description of experiment
Autodesk Nastran In-CAD 2018.1 was used in conjunction with Autodesk Helius PFA 2018.1 to predict the behavior of plastic moldings under load.The first software is a tool for mechanical analysis, the second allows to extend the capabilities of the former to include the repetitive properties of plastics along with their nonlinearity.
In order to take into account the impact of processing on mechanical properties, injection molding was first performed in Autodesk Moldflow Insight Standard 2018.1.The results have been coupled with a mechanical analysis program via a module found in Autodesk Helius (called the Advanced Material Exchange).It allows transferring information about fiber orientation, deformation of the compact, strength of the connection line and conditions of destruction of the compact to the structural analysis program [6].
Two examples were used -a material test rig in accordance with ASTM D638-10 and a brake pedal.In both cases, the same type of material was used -Tenacc polyol T14066 and T14067 (with 25 and 35 percent glass fiber contentreferred to as: POM25 and POM35) to show the sensitivity of the results to the reinforcing fiber.Material characteristics are presented in fig. 1 and fig. 2.
Strength analyses were carried out in two variants of both models.In the linear model, different values of rigidity modulus and Poisson's coefficient were used (each material had two values given in the first and second main directions): maximum (H1), minimum (H2) and average (Hśr).Autodesk Helius PFA software was used to transfer linear material properties.The second example (P2) was the brake pedal.The analysis was carried out with one injection point placed at one end.If the appropriate material data are available, it is possible to automatically determine the strength of individual lines.For the purposes of the analysis, the possibility of movement of the part on the shafts and in its lower part was blocked as well as all degrees of freedom on the chamfered part were received.Perpendicular force of 500 N was applied to the surface of the pedal.

Results
Fig. 4 presents the results -the first two strain maps show a clear difference in the magnitude of strain (4a-b).In the case of the RO model, a greater deformation in the central part and less deformation in the wider areas were observed.This is important, because the displacement was applied to the upper and lower extremities of the sample.The stresses calculated according to Hooke's law had a distribution as for RO, but the minimum and maximum values were different.On the last paddle (fig.4d), it can be seen a significant reduction in the rigidity of the element in the central part at the end of stretching, which cannot be predicted with the use of Hooke's law.The list of tested parameters for various material models for P1 is presented in the Table I.In the first part of the Table I, the results obtained from the RO model and Hooke's law were included.The results coincide with the data presented in fig. 1 and fig. 2. With the increase of fiber content, the maximum deterioration of the rigidity of the element in the central part decreases.For deformation of the sample according to fig. 2, similar maximum displacements Δl of both materials were observed.Based on the comparison of results with the Hooke's law, the stress value for the maximum Δlmax displacement and the boundary conditions, was determined.In the case of Δlmax, the best accuracy was obtained after linearization using the Autodesk Helius software (Elin) and after applying the averaged value of the Eav rigidity modulus (but only with the parallel arrangement of the fibers).For the maximum displacement, more than twice the stresses were obtained than in the RO model, which were admissible values from the point of view of displacements (the sample length was 176.72 mm, thus a displacement of 5 mm occurs with uniform strain of the sample at 0.028).For this reason, without a simulation showing the distribution of the deformation of the sample and taking into account its destruction, predicting the correct behavior of the elements filled with fiber is very difficult.
In the case of P2, slight differences in the stresses between the materials were observed (fig.5, Table II)the bottom rib and the chamfered shaft were analyzed.On the other hand, the plastic type had a very pronounced effect on the rigidity and maximum displacement of the loaded compact.In the case under consideration, the results obtained on the basis of the Autodesk Helius data linearization are characterized by good accuracy -too large values were obtained in the case of a rib.The disadvantage of this solution was practically twice as large displacement compared to the RO model.
In the assumption of a linear material consistent with Hooke's law, the stress value for the rib had a very good convergence, but in the case of shear within the shaft, the program predicted much higher stresses.The best deformation mapping was observed when the rigidity modulus conforming to the first main direction was usedthe deformations were not much smaller than for the RO.Fig. 6 shows the changes in the tangent rigidity modulus, where along with the increase in the reinforcing fiber content, the value of rigidity in the area of the chamfered roller and the rib has increased.However, it was observed that the minimum rigidity value was similar in both cases.
The use of RO model also allows to predict the amount of plastic deformation.In the P2 model, plastic deformations amounted to approximately 0.009, which means that for the assumed load, the compact should be redesigned to prevent permanent deformation.

Conclusions
The linear model (Hooke's law) allowed good representation of the deformation of the element when the applied force was the load.The highest accuracy was obtained using a rigidity module determined parallel to the direction of the EH1 fiber orientation.The displacement was slightly less than the displacement obtained for the RO model.The use of the average rigidity modulus Eav gave much less accurate results than EH1.In the case studied, the application of Hooke's law allowed for a good reproduction of stresses due to compression and deformation in the direction of the fiber orientation.On the other hand, it was definitely less accurate in the case of shearing and stretching.
The application of the Autodesk Helius linear deformation module allowed for a much better stress pattern in the case of stretching and shearing (greater discrepancy was observed in compression).On the other hand, when bending, the module indicated a twice larger displacement than obtained for the non-linear model and gave worse results than the application of Hooke's law.

Fig. 1 .
Fig. 1.Material characteristics of POM25 [7].Experimentexperimental curve; fit -curve tailored to the RO model, used in simulations; E H -dependence according to Hooke's law; 0º, 45º, 90º -angles at which samples were cut in relation to the orientation of the fibers Eksperyment -Experiment Dopasowanie -Fit

Fig. 2 .Fig. 3 .
Fig.2.Material characteristics of POM35[7].Experimentexperimental curve; fit -curve tailored to the RO model, used in simulations, E H -dependence according to Hooke's law; 0º, 45º, 90º -angles at which samples were cut in relation to the orientation of the fibersThe first example (P1) was a piece of a plate used to test the mechanical properties of fiber-filled plastics.A dray cut in the perpendicular direction (⊥) and parallel to the direction of fiber orientation (∥) was used for the simulation.The distribution of the fiber orientation in the plate to be injected and the cut holes are shown in fig.3.The element was subjected to uniaxial stretching, where the sample elongation was 5 mm.

Fig. 4 .
Fig. 4. Deformation according to Hooke's law ε H1 (a); deformation according to the RO ε R0 model (b); stresses   in MPa (c); tangent rigidity modulus E T in MPa before destruction of the P1 specimen oriented along the fibers (from the left) for POM25 (d)

Fig. 5 .
Fig. 5. Stresses   in MPa for: a) POM25 and b) POM35 according to the RO model