# Impact behavior and modeling of engineering polymers.

INTRODUCTIONEngineering polymers have increasingly been applied in applications such as housings for electronic appliances, lenses, goggles, and windows, which have to sustain accidental impact without showing signs of damage. In these applications, it is important that the impact behavior and the safe operating limits of the polymeric structures are known. Currently, the evaluation of impact design failure of polymeric structures has to be experimentally performed on molding prototypes. The experimental trial-and-error method significantly retards design progress and optimization and wastes a lot of time, money, and effort. To decrease these disadvantages, a computer aided design method based on finite element analysis is proposed to simulate the mechanical behavior of polymeric structures under impact loading.

During the past two decades, considerable progress has been made with respect to the computer simulation of multiaxial impact behavior of polymers based on finite element analysis (1-3). Number (1) created a finite element analysis model to simulate a fixed velocity puncture test of Bisphenol A-polycarbonate disk where a constant bilinear stress-strain curve was used to approximate the material behavior. Good agreement was achieved between model prediction and experimental load vs. deflection data for deflections up to four times the thickness of the test disk. Billon and Haudin (2) numerically explored the effects of specimen thickness, friction between striker and specimen disk, and quality of the clamping device during multiaxial impact test of polypropylene, a semicrystalline polymer. They indicated that the material response during impact requires complicated analysis since the deformation is neither homogeneous nor isothermal. Schang et al. (3) developed a finite element analysis model to simulate the m ultiaxial impact test of a semicrystalline polymer polyamide 12. Model predictions were compared with experimental data over the history of impact load. Although good agreement at the beginning was achieved, the maximum impact load was largely overestimated. There are few reports found in open literature dealing with finite element analysis of multiaxial impact behavior of polymers as a function of impact velocity and temperature.

In this paper, the impact behavior of a glassy polymer acrylonitrile-butadiene-styrene (ABS) and a semicrystalline polymer alloy of polycarbonate and polybutylene-terephthalates (PBT) are obtained as a function of impact velocity and temperature from the standard ASTM D3763 multiaxial impact test. Finite element analysis (FEA) and ABAQUS/Explicit are used to simulate the impact behavior of the two polymers ABS and PBT involved in the standard ASTM D3763 multiaxial impact test. The generalized DSGZ constitutive model, previously developed by the authors to uniformly describe the entire range of deformation behavior of glassy and semicrystalline polymers for any monotonic loading modes, is applied. The phenomenon of thermomechanical coupling during high strain rate plastic deformation is modeled and a failure criterion based on maximum plastic strain is proposed. The generalized DSGZ model, the thermomechanical coupling model and the failure criterion are integrated into the ABAQUS/Explicit through a user mater ial subroutine. Impact load vs. displacement curves and the impact energy vs. displacement curves from computer simulation are compared with multiaxial impact test data.

MECHANICAL TESTS

This work focused on two representative polymers: a glassy polymer acrylonitrile-butadiene-styrene (ABS) with the trade name of Cycolac GPM5500 and a semicrystalline polymer alloy of polycarbonate and polybutylene-terephthalates (PBT) with the trade name of Valox 357U. Both of the polymers are products of GE Plastics (4).

Standard multiaxial impact tests must be conducted to obtain the multiaxial impact behavior of polymers at various temperatures and impact velocities. There are several types of standard multiaxial impact tests for polymers. among which the ISO 6603-2 and ASTM D3763 are the most often used. Both of the standard tests are designed to provide impact load vs. striker displacement and impact energy vs. striker displacement response of polymers in the form of flat test specimens under essentially multiaxial deformation conditions. In this research, the impact behavior of ABS and PBT polymers are obtained as a function of impact velocity and temperature from the ASTM D3763 multiaxial impact test. The equipment used in ASTM D3763 multiaxial impact test is GRC Dynatup Model # 8200--Series 930-v1.21. The striker, consisting of a 12.7 mm diameter steel rod with a hemispherical end and a mass of 22.7 kg, is dropped at a given initial impact velocity in the center of a clamped polymer disk. The clamp assembly consists of two circular parallel plates with a 76 mm diameter opening in the center. Sufficient pressure is applied to prevent slippage of the polymer disk from the clamp assembly during impact. The injection molding polymer specimen disk, with a dimension of thickness 3.2 mm and diameter 102 mm, is conditioned at the required testing temperature for a minimum of 6 hours, then removed from the conditioning chamber and impacted within 5 seconds. During impact, the striker moves down, polymer specimen disk is penetrated. and the history of impact load, impact energy. striker displacement and striker velocity are recorded.

Four sets of multiaxial impact tests, at a testing temperature of 296 K and impact velocities of 1 m/s, 2 m/s, 3 m/s and 4.2 m/s. were conducted to explore the effect of impact velocity on the impact behavior of ABS and PBT polymers. It was observed that the impact load vs. displacement curves and the impact energy vs. displacement curves are consistent over the entire range of displacement for each set of the tests. Although the failure displacement showed consistent for PBT. it scattered broadly for ABS. The scatter of failure displacement indicates that ABS polymer is brittle at room temperature. With an increase of impact velocity, the impact load generally increases over the entire range of displacement. It was also observed that impact velocity had almost no effect on the failure mode in the range of 1 m/s to 4.2 m/s.

Three sets of multiaxial impact tests, at an impact velocity of 4.2 m/s and testing temperatures of 296 K, 273 K, 253 K, were carried out to investigate the effect of temperature on the impact behavior of ABS and PBT polymers. It was observed that the impact load vs. displacement curves and the impact energy vs. displacement curves are consistent over the entire range of displacement for each sets of the tests. With a decrease of temperature, the impact load generally increases over the entire range of displacement. Temperature significantly affects failure modes of the two polymers. Figure 1 shows the failure modes of ABS polymer specimen disks at various testing temperatures. At room temperature (296 K), it appears that a radial crack initiates under the striker and rapidly propagates through the specimen disk. With the decrease of temperature, it seems that the fracture failure occurred along a circumferential edge and became localized. Figure 2 shows failure modes of the PBT polymer alloy specimen disks a t various testing temperatures. At room temperature, the specimen disks failed in ductile mode and a regular shaped ductile hole was created. The PBT polymer disk scattered when the temperature dropped to 253 K. With lower and lower temperature, the PBT specimen disks became more and more brittle.

Glass transition temperature (Tg) is a significant factor that affects the mechanical behavior of poLymers. The Tg is around 378 K for the ABS polymer and around 253 K for the PBT polymer alloy. The ABS polymer was in glassy state for all the tests conducted at 296 K, 273 K and 253 K. Therefore, the ABS polymer specimen disks broke in brittle manner and the failure displacements scattered broadly. However, the PBT polymer alloy was in rubbery state for the impact tests conducted at 296 K and 273 K. The PBT polymer specimen disks broke in ductile manner at 296 K and a regular shape ductile hole was created, as shown in Fig. 2a, and the failure displacements show consistent. At 253 K, the PET polymer alloy starts to become glassy and therefore shows brittle failure.

Uniaxial tensile and compression tests are widely used to calibrate fundamental mechanical properties of materials because the deformation fields are homogeneous and the strain rate are easier to control in these two types of tests. These characteristics simplify the task of interpreting material response from mechanical tests. However, the load-elongation data are usually transformed into engineering stress-strain curves in uniaxial tensile tests via dividing load by the initial cross section and elongation by initial length. These engineering stress-strain curves do not provide a correct description of the mechanical behavior of material subject to large deformation because of the appearance of necking that lead to strain localization. A uniaxial compression test is a better choice to obtain true stress-strain data at large strain since it can be globally homogeneous for the full range of deformation.

To explore the effect of temperature and strain rate on the stress-strain behavior of the two polymers, a series of low strain rate ([10.sup.-3] ~ [10.sup.-2]/s) and high strain rate ([10.sup.2] ~ [10.sup.3]/s) uniaxial mechanical tests were conducted at temperature of 243 K, 253 K, 273 K and 296 K, respectively. Low strain rate uniaxial compression tests were carried out on an Instron servo-hydraulic testing machine, which was connected to a personal computer for test control and load vs. displacement data acquisition. A chamber with automatic temperature control was used to control the testing temperature. The cylindrical testing specimens were punched from the injection molding polymer specimen disks used in multiaxial impact test, with a dimension of thickness 3.2 mm and diameter 6.4 mm. During testing, the cylindrical specimen faces were placed in contact with flat platens on the actuator and axially aligned with it. The displacement was monitored using the actuator and the corresponding load was recorde d. High strain rate uniaxial compression tests were carried out on Split Hopkinson Pressure Bar (SHPB). The high strain rate uniaxial tensile tests were conducted on a special designed equipment.

CONSTITUTIVE MODELING

Stress-strain constitutive model is the foundation of computer simulation. Over the past four decades, much effort has been devoted to modeling stress-strain constitutive relationships for engineering polymers (5-18). Using concepts from the Johnson-Cook model, G'Sell-Jonas model. Brooks model, and Matsuoka model, the authors (19) developed a phenomenological constitutive model (DSGZ model) to uniformly describe the entire range of deformation behavior of both glassy and semicrystalhine polymers under compressive loading. Using hydrostatic pressure effect, the DSGZ model is generalized to describe the stress-strain constitutive relationship of polymers under any monotonic loading. and is given by

[sigma] ([epsilon], [epsilon], T, p) =

K{f([epsilon]) + [[epsilon] * e(1 - [epsilon]/[C.sub.3] * h([epsilon], T))/[C.sub.3] * h([epsilon], T) - f([epsilon])]

* [e.sup.[ln(g([epsilon], T)) - [C.sub.4]]*[epsilon]]} * h([epsilon], T) - [gamma]p (1)

where, f([epsilon]) = ([e.sup.-[C.sub.1]*[epsilon]] + [[epsilon].sup.[C.sub.2]]) (1 - [e.sup.-[alpha]*[epsilon]) and h([epsilon], T) = [[epsilon].sup.m][e.sup.a/T]. The equivalent stress [sigma] is defined by [sigma] = [square root of (3/2([s.sub.ij] * [s.sub.ij]))], the hydrostatic stress p is defined as 1/3[[sigma].sub.ii] and the equivalent strain [epsilon] is defined as [epsilon] = [square root of (2/3([e.sub.ij] * [e.sub.ij]))]. The equivalent strain rate [epsilon] is the derivative of the equivalent strain [epsilon] with respect to time t, [epsilon] = d[epsilon]/dt. The [gamma], called hydrostatic pressure sensitivity coefficient, is a material coefficient accounting for the effect of loading mode. The other eight material coefficients in the generalized DSGZ model are K (Pa*[s.sup.m]), [C.sub.1], [C.sub.2], [C.sub.3] ([s.sup.m]), [C.sub.4], and (K), m and [alpha].

In the generalized DSGZ model for a uniaxial compression test, the compressive stress [[sigma].sub.c] can be written in the form

[[sigma].sub.c]([epsilon], [epsilon], T) =

(K/1 - [gamma]/3){f([epsilon]) + [[epsilon] * e(1-[epsilon]/[C.sub.3] * h([epsilon], T))/[C.sub.3] * h([epsilon], T) - f([epsilon])]

* [e.sup.[ln(g([epsilon], T))-[C.sub.4]]*[epsilon]]} * h([epsilon], T) (2)

For a uniaxial tensile test, the tensile stress [[sigma].sub.t] can be written as

[[sigma].sub.t]([epsilon], [epsilon], T) =

(K/1 + [gamma]/3) {f([epsilon]) + [[epsilon] * e(1 - [epsilon]/[C.sub.3] * h([epsilon], T))/[C.sub.3] * h([epsilon], T) - f([epsilon])]

* [e.sup.[ln(g([epsilon], T))-[C.sub.4]]*[epsilon]]} * h([epsilon], T) (3)

The value of [gamma] can be calculated by combining Eqs 2 and 3. For a given strain [epsilon], strain rate [epsilon] and temperature T, [gamma] has the form

[gamma] = 3 [[sigma].sub.c]([epsilon], [epsilon], T) - [[sigma].sub.t]([epsilon], [epsilon], T)/[[sigma].sub.c]([epsilon], [epsilon], T) + [[sigma].sub.t]([epsilon], [epsilon], T) (4)

It can be seen from Eq 4 that [gamma] is a function of strain [epsilon], strain rate [epsilon] and temperature T over the entire range of deformation. Because of failure of polymers during uniaxial tensile tests at low strains in comparison to the large strains obtained in compression tests, the [gamma] can not be calculated over a large strain range. Therefore [gamma] is calculated at the yield stress and assumed to be constant in the form

[gamma] = 3 [[sigma].sub.cy] - [[sigma].sub.ty]/[[sigma].sub.cy] + [[sigma].sub.ty] (5)

where [[sigma].sub.cy] is the yielding stress in uniaxial compression test and [[sigma].sub.ty] is the yielding stress in uniaxial tensile test. The values of the two yielding stresses can be obtained experimentally. The other eight material coefficients in the generalized DSGZ model can be deduced from uniaxial compression stress-strain curves following the procedures given in reference (19).

THERMOMECHANICAL COUPLING AND FAILURE CRITERION

It is well established that the mechanical work in plastic deformation process transforms partly into heat. Since the mechanical properties of polymers are sensitive to temperature, an accurate estimate of the temperature rise during plastic deformation is important. Arruda et al. (10) did a series of uniaxial compression tests in which the specimen surface temperatures were monitored using an infrared detector to investigate the relationship between strain rate and temperature rise for the glassy polymer polymethylmethacrylate (PMMA). It was found that the specimen was nearly isothermal up to a true strain of 0.8 at a strain rate of 0.001/s, but significant temperature rise (around 30[degrees]C) were observed up to the same true strain at strain rates of 0.01/s and 0.1/s. The rise of temperature has a dramatic effect on the stress-strain curves. Rittel (20) embedded a small thermocouple in polycarbonate specimen disks to record the transient temperature during impact tests with strain rates ranging from 5000 /s to 8000/s. Within a time order of [10.sup.-4] s, a true strain of 0.45 was obtained and the recorded temperature increased by nearly 25[degrees]C. The temperature rose significantly in the softening region of the corresponding stress-strain curve. Using a fast response infrared radiometer to monitor the surface temperature of epoxy specimens in a Split Hopkinson Pressure Bar (SHPB) impact test, Trojanowski et al. (21) observed that there was an increase of approximately 50[degrees]C. These experimental results indicate that, for polymers, the temperature rise is significant during high strain rate large plastic deformation.

It has been shown that the highest strain rates encountered in multiaxial impact simulations are of the order of [10.sup.2] ~ [10.sup.3]/s (22). For such an order of strain rates it is reasonable to assume that the deformation process is essentially adiabatic. The governing equation for the increase of temperature [DELTA]T at each increment of plastic strain is

[DELTA]T = [beta] ([[sigma].sup.old] + [[sigma].sup.new])[DELTA][[epsilon].sup.pl]/2[rho]c (6)

where [rho] is material density, c is specific heat, [beta] is the fraction of dissipated plastic energy which converts into thermal energy, [[sigma].sup.old] is the equivalent stress at the beginning of a strain increment, [[sigma].sup.new] is the equivalent stress at the end of the strain increment and [DELTA][[epsilon].sup.pl] is the increment of equivalent plastic strain. At each increment of plastic strain, the local temperature of the plastic deformation zone will increase by an amount governed by Eq 6. The increase in temperature decreases the equivalent stress [sigma] through the generalized DSGZ model given by Eq 1. This gives a framework to account for the thermomechanical coupling during high strain rate plastic deformation. The issue is how to decide the value of [beta] in Eq 6 for each increment of strain. Rittel (20) found that [beta] is dependent on strain and strain rate during plastic deformation of polymers. The behavior is similar to that exhibited by metals (23). Since there is a lack of a vailable experimental data for [beta] vs. strain [epsilon] and strain rate [epsilon] for the ABS and PBT polymers, a constant value of 0.9 is used for the numerical simulations. Macdougall and Harding (24) used a similar approximation in their numerical modeling of the high strain rate torsion tests on Ti-6Al-4V bars.

The failure of a polymer in multiaxial impact test can be understood as the sudden significant reduction of its load-carrying capability. A failure criterion has to be combined together with constitutive model in order to simulate impact failure. There are a variety of proposed material failure criteria such as maximum tensile stress, maximum principal stress, maximum shear strain, and maximum strain energy density (25). The maximum plastic strain failure criterion is used in this paper. A failure indicator [psi] is created and defined as,

[psi] = [SIGMA][DELTA][[epsilon].sup.pl]/[[epsilon].sub.max.sup.pl] (7)

where, [[epsilon].sub.max.sup.pl] is a prescribed maximum equivalent plastic strain, and [DELTA][[epsilon].sup.pl] is the increment of equivalent plastic strain. When the sum of the equivalent plastic strain increment at a material point is equal to or greater than the prescribed value of [[epsilon].sub.max.sup.pl], i.e. when [psi] [greater than or equal to] 1, the material point fails and is permanently removed from future calculations.

FINITE ELEMENT ANALYSIS MODEL AND IMPLEMENTATION

Figure 3 shows a FEA model of the ASTM D3763 multiaxial impact test created using ABAQUS/Explicit. Nine hundred eight-noded linear brick, reduced integration C3D8R elements with a total of 1519 nodes are used to mesh the polymer disk. An analytical rigid surface is used to model the geometry of the steel striker. The rigid surface is associated with a rigid body reference node that defines the mass (22.7 kg) and the motion of the striker. The boundary conditions are set as fixed support around the outer edge of the disk and the six degrees of freedom of those nodes located on the circular edge are set to zero. The striker can only move along the vertical axis, all the other five degrees of freedom of the rigid body reference node are set to zero. The finite-sliding contact model of ABAQUS/Explicit (26) is used, and the friction coefficient [mu] between the striker and the polymer disk is assumed to be a constant value of 0.3 for ABS and 0.4 for PBT.

An algorithm of elastic prediction-plastic correction is applied to update the stress tensor of each material point where the first predicted stress tensor is based on generalized Hooke's law and inputted values of elastic modulus and Poisson's ratio. The elastic modulus used is 2.0 GPa for ABS and 2.2 GPa for PBT, the Poisson's ratio is 0.25 for both the polymers, and are assumed to be constant. At the end of each strain increment, the predicted stress tensor is [[[sigma].sup.new]]corrected using the generalized DSGZ model. Equation 6 is then applied to calculate the increase of the local temperature of polymers. The failure indicator [psi] is updated through Eq 7 and when [psi] [greater than or equal to] 1 the material point fails and is permanently removed from future calculations. Based on this framework of calculation, an Abaqus/ Explicit user material subroutine was encoded using Fortran 77 and applied in the FEA simulations to implement the generalized DSGZ model, the thermomechanical coupling model an d the failure criterion.

RESULTS AND DISCUSSION

The material coefficient [gamma] in the generalized DSGZ model is calculated from Eq 5 using yielding stresses in uniaxial tensile test and uniaxial compression test. The other eight material coefficients in the generalized DSGZ model are calculated from the true stress-strain curves of uniaxial compression tests following the procedures given in reference (19). Table 1 shows the calculated material coefficients for the two polymers ABS and PBT, respectively. The value of [gamma] for PBT is zero as PBT is a semicrystalline polymer, and the effect of hydrostatic pressure is not significant for semicrystalline polymers. The uniaxial tensile tests we conducted on the two polymers only provide data in a strain range of 0 to 0.08. However, uniaxial compression tests provide data in a much larger range of strain of 0 to 0.90. Figures 4 and 5 show comparisons of the constitutive model prediction from Eq 2 with uniaxial compression test data for the two polymers ABS and PBT, respectively. It can be seen that at a giv en strain rate the stress over the entire range of strain generally increases with the decrease of temperature. However, at a given temperature the stress over the entire range of strain decreases with the decrease of strain rate. The stress-strain behavior at high strain rate is significantly different from that at low strain rate for both the polymers. The stress-strain behavior of polymers is sensitive to strain rate and temperature. These two factors have to be considered in modeling stress-strain constitutive behavior of polymers. From Figs. 4 and 5. we can see that model predictions agree well with the low strain rate uniaxial compression test data for both of the polymers. However, a wide disparity exists between model predictions and the SHPB test data (with a nominal true strain rate of 1000/s) in a strain range of around 0 to 0.2 though at larger strains model predictions and the SHPB test data are in good agreement. The disparity is partly due to the nature of the SHPB compression tests in which th e strain rates change rapidly and are much higher than the nominal 1000/s at a true strain of around 0.035, as shown in Fig. 6.

Figure 7 shows comparison of FEA simulation result with the experimental data for ABS at 296 K and 2 m/s where Test 1 and Test 2 are replicates performed under the same test conditions. Figure 8 shows comparison of FEA simulation result with the experimental data for PBT at 296 K and 2 m/s. The results of other FEA simulations (with a temperature of 296 K and impact velocities of 1 m/s, 3 m/s and 4.2 m/s, and with an impact velocity of 4.2 m/s and temperatures of 273 K, 253 K) are similar. It can be seen that the FEA model predictions. with [beta] = 0.9 and [gamma] appropriately taken from Table 1, agree well with the multiaxial impact test data of both the polymers up to the maximum impact loading (failure). From the experimental impact load vs. striker displacement. curves, it was observed that the impact load oscillates during the initial impact stage for both the ABS and the PBT polymers. This phenomenon is the result of vibration occurring during the elastic deformation stage of the polymer specimen disks.

As previously stated, a constant value of 0.9 is used for [beta] in Eq 6 in the simulations of the multiaxial impact test for both ABS and PBT. In order to estimate the importance of thermomechanical coupling, simulations were performed where the effect of the thermomechanical coupling was ignored by setting [beta] = 0. For the test with a temperature of 296 K and an impact velocity of 2 m/s. Fig. 9 shows the effect of thermomechanical coupling on the computer simulation results for ABS. Similar results are obtained for PBT. It is observed that not accounting for [beta] in the simulation model tends to overestimate the impact load, especially at large displacements. It is found that the lack of thermomechanical coupling accounts for overestimates of around 5% for the maximum impact load of ABS and around 2% for the maximum impact load of PBT. It can be seen from these simulation results that the effect of thermomechanical coupling can be neglected for both these materials at room temperature and an impact velocity of 2 m/s.

To evaluate the effect of hydrostatic pressure on the impact behavior of ABS polymer, a simulation was done in which the constitutive model was calibrated using uniaxial compression test data with the parameter [gamma] set to zero. For the test with a temperature of 296 K and impact velocity of 2 m/s, Fig. 10 shows the effect of hydrostatic pressure on the simulation results for ABS polymer. It is observed that not accounting for hydrostatic pressure effect in the simulation model tends to overestimate the impact load, especially at large displacements. It is found that the lack of hydrostatic pressure effect accounts for overestimates of around 24% for the maximum impact load of ABS. The effect of hydrostatic pressure is very important. The simulation result indicates that for materials that exhibit different behavior in uniaxial tension and uniaxial compression, the effect of hydrostatic pressure has to be included. If the difference is large, neglecting the hydrostatic pressure effect will lead to a much g reater error for the simulations of the multiaxial impact tests. Uniaxial compression or tensile tests taken individually are not representative of the general deformation behavior of polymers. In the application of the generalized DSGZ constitutive model, it is important to experimentally calibrate the parameter [gamma].

As previously mentioned, the finite-sliding contact model of ABAQUS/Explicit is used and the friction coefficient [mu] between the striker and the polymer disk is set to a constant value of 0.3 for ABS and 0.4 for PBT in the simulations. In order to study the effect of the assumed value of friction coefficient, additional simulations of the impact behavior were performed using [mu] = 0. Figure 11 shows the effect of friction between the striker and polymer disk on the simulated impact load vs. displacement curves of PBT. Similar results are obtained for ABS. It can be seen that if one neglects friction, the impact loads decrease significantly at large displacements. Similar experimental observations have been reported for the friction effect in literature (2). It is found from simulation results that the lack of friction effect accounts for underestimates of around 17% for the maximum impact load of PBT and around 11% for the maximum impact load of ABS. The friction effect is an important factor in computer simulation.

CONCLUSIONS

The standard ASTM D3763 multiaxial impact tests on a glassy polymer ABS and a semicrystaline polymer alloy PBT were conducted at various temperatures and impact velocities. Finite element analysis and Abaqus/Explicit were used to simulate the impact behavior of the two polymers ABS and PBT involved in the standard ASTM D3763 multiaxial impact test. The impact load vs. displacement curves and the impact energy vs. displacement curves from computer simulation were compared with test data. They agree well up to the maximum impact load. From the simulation results, we find the computer simulation based on finite element analysis can work well to eliminate the disadvantages associated with experimental trial and error in product design process.

In the application of the generalized DSGZ model, it is important to experimentally calibrate the material coefficient [gamma]. In addition, in general the thermomechanical coupling and friction are also important factors in computer simulation. It is shown that not accounting for the different behavior of the polymer in uniaxial tensile and compression tests ([gamma]) tends to overestimate the impact load, especially at large plastic deformations. If one neglects the friction between the striker and polymer disk, the simulated impact loads decrease significantly at large deformations.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 11 OMITTED]

Table 1 Material Coefficients in Generalized DSGZ Model for ABS and PBT. Polymers [C.sub.1] [C.sub.2] m a(K) K(MPa * [s.sup.m]) ABS 1.83 0.20 0.044 306 17.85 PBT 0.32 0.12 0.058 140 24.5 Polymers [C.sub.3]([s.sup.m]) [C.sub.4] [alpha] [gamma] ABS 0.06 5 50 0.4 PBT 0.1 6 200 0

ACKNOWLEDGMENT

The support of Lucent Technologies during this research is gratefully acknowledged.

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A. Saigal *

* Corresponding author. Email: anil.saigal@tufts.edu.

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Author: | Duan, Y.; Saigal, A.; Greif, R.; Zimmerman, M.A. |
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Publication: | Polymer Engineering and Science |

Date: | Jan 1, 2003 |

Words: | 5169 |

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