1
Time dependent crashworthiness of polyurethane foam Munshi Mahbubul Basit1,*,Seong Sik Cheon2
Abstract Time-dependent stress strain relationship as well as crashworthiness of Polyurethane foam was investigated under constant impact energy with different velocities, considering inertia and strain rate effects simultaneously during the impact testing. Even though the impact energies were same, the percentage in increase in densification strain due to higher impact velocities was found, which yielded the wider plateau region, i.e. growth in crashworthiness. This phenomenon is analyzed by microstructure of Polyurethane foam obtained from scanning electron microscope. The equations, coupled with the SherwoodFrost model and the Impulse-Momentum theory, were employed to build the constitutive equation of the Polyurethane foam and calculate energy absorption capacity of the foam. The nominal stress-strain curves obtained from the constitutive equation were compared with results from impact tests and were found to be in good agreement. This study is dedicated to guide designer use Polyurethane foam in crashworthiness structures such as automotive bumper system by providing crashworthiness data, determining crush mode, and mathematical model of crashworthiness. Keywords Impact; Crashworthiness; Constitutive model; Microstructure; Polyurethane (PU) foam 1 Introduction Polyurethane (PU) foam is universally applied in automotive manufacturing; for instance, it is used inside motor vehicles to protect the passengers during the traffic accidents. Due to its combination of lightweight, higher compressive strength, and lower cost, it is considered as a popular smart material that can be widely applied in producing various automotive parts. Again, PU foam can be modeled in complex parts of automobile because it allows great design flexibility. Moreover, PU foam is commonly used in shock absorption applications such as packaging and cushioning because of their effectiveness in absorbing impact energy and mitigating collision damage while limiting force levels. Of particular interest to this study is to guide designer use PU foam in crashworthiness structures such as automotive bumper system by providing crashworthiness data, determining crush mode, and mathematical model of crashworthiness. Key design parameters such as impactor’s velocity, mass, impact energy have been considered in this study. In the recent years’ mechanical properties and energy absorption of foams have been extensively studied by some researchers (Zhang et al. 2014; Taher et al. 2009; Serban et al. 2016; Pellegrino et al. 2015). Espadas-Escalante and Avilés (2015) obtained a very strong property-structure relationship between the anisotropic microstructure of the foam’s unit cell and the resulting anisotropic mechanical properties of the macroscopic foam. Some other researchers (Song et al. 2009; Mukai et al. 2006; Chao et al. 2012; Kumar et al. 2016; Wu et al. 2007) investigated compressive behavior of foam over a wide range of strain rates. Constitutive modeling of PU foam considering strain rate sensitivity has been studied before (Jeong et al. 2012; Jeong 2016), whereas Pawlikowski (2014) presented the non-linear constitutive modelling of PU nanocomposite. The simulation and modeling approach to study crashworthiness property of PU foam was proposed at extreme ranges of temperature by Beheshti and Lankarani (2010). Foam recovery for different densities of the polyurethane foams were analyzed by Apostol and Constantinescu (2013) as a function of direction of testing, temperature, and speed of testing.
M.M. Basit
[email protected] S.S. Cheon
[email protected] *
Corresponding Author Department of Mechanical Engineering, Georgia Southern University, USA 2 Division of Mechanical and Automotive Engineering, Kongju National University, Chungnam, Korea 1
2 Effects of density and filler particle size on mechanical behavior of PU foam, were examined by Michel et al. (2006). Marsavina et al. (2008) determine the dynamic fracture toughness of PU foam and study the effect of impregnation on the fracture toughness. A new method based on the split Hopkinson pressure bar was developed by Lin et al. (2014) to test the dynamic friction under impact loading. They studied rigid PU foam samples with different densities and thicknesses subjected to high-velocity impact loadings in both normal and oblique cases with different projectile nose shapes. Sherwood and Frost (1992) modified the shape function of constitutive model for the compressive behavior of the PU foam. Vehicles undergo load varying due to the different number of passengers, weight as well as speeds during accidents. However, no data are available in the literature under the condition of constant impact energy by varying impactor masses and velocities. Therefore, the aim of the current work is to understand the crashworthy behavior of PU foams with different masses and velocities of the striker under the constant impact energy. This allows a rigorous investigation on the time sensitive crashworthy properties of PU foam considering inertia and strain-rate effects simultaneously. In this study, quasi-static and impact tests were performed with cylindrical PU foam specimens. Also, the model of Sherwood-Frost (1992) and Impulsemomentum theory (Beer and Johnston 1981) were coupled to characterize the compressive behavior of PU foams in terms of the nominal stress-strain curves. The iterative method for solving the coupled equations was employed. 2 Experimental Typical engineering stress-strain curve of PU foam is divided into three main regions, i.e. elastic, plateau and densification. In the elastic region, stress proportionally rises with strain. Plateau region represents fairly constant stress due to localised plastics collapse propagated from one cell wall to another. Trend of plateau stress remains fairly constant with or without oscillation with respect to deviation of cell size as well as wall thickness. In the densification region, cell walls are totally compressed and the stress rises rapidly along with the strain. Plateau region has major role in crashworthiness of the structures since the effective crushing of the foam cell is indispensable to absorb kinetic energy. The energy absorbing PU foam in the current study is widely used as automotive bumper cores. The closed-cell type cylindrical PU foam (Fig. 1, Supplied by Lacomtech, co. ltd., Republic of Korea) with densities of 67 and 89 kg/m 3 were tested at room temperature. Dimensions of the specimen were carefully chosen to aim at the one-dimensional deformation during crush. Fig. 1 Specimen of the PU foam.
42
40
2.1 Quasi-static test The quasi-static tests were carried out in a MTS 810 machine (Maximum load capacity: 100 kN) at room temperature to determine the material constants in Sherwood-Frost model (1992). It was equipped with the displacement measuring device and force transducers. Several commands were given to operate the machine by software that the specimen would be loaded and unloaded hydraulically. The test was terminated when the compressive deformation would reach the 90% of the total height of the specimen for the sake of safety. 0.001 s-1 and 0.1 s-1 strain rates were applied to the foam specimen of lower density and higher density, i.e. 64 kg/m3 and 89 kg/m3, respectively. Density irregularity exists within 5% for 64 and 12% for 89 kg/m 3. Fig. 2 shows the nominal stress-strain curves of each specimen for the quasi-static loading. It was obvious from our previous study (Jeong et al. 2012) that the PU foam was strain-rate sensitive; however, it was impossible to analyse the strain-rate and inertia effects based only on quasi-static test results.
3 5
Nominal stress (MPa)
Nominal stress (MPa)
5 4 10-1 S-1
3 2 1
-3
10 S
-1
0
10-1 S-1
4 3 2
-3
1
10 S
-1
0 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
Strain
0.6
0.8
1
Strain
(a)
(b)
Fig. 2 Stress-strain curves of PU foam under quasi-static test: (a) Density: 64 kg/m3 and (b) 89 kg/m3. 2.2 Impact test A drop tower type impact testing machine (Instron Dynatup 9250 HV) was employed in impact testing on the inertia and strain-rate effects. The machine can raise a discretely changeable weight to a specific height and drop it to the specimen either using gravitation or accelerating springs. Impact tests were performed under two different initial impact energies of 100 J and 200 J with moderate variation of each case. Three types of masses were used, i.e. 7 kg, 16.5 kg and 26.5 kg. For 100 J, the corresponding impact velocities of the striker for those masses were set to be 2.75 m/s, 3.50 m/s and 5.35 m/s in turns to produce constant impact energy. Also, the corresponding initial velocities of the striker were set to be 3.85 m/s, 5.00 m/s and 7.60 m/s in turns for 200 J. The masses and velocities of the striker and the absorbed energy results were listed in Table 1. In the Table 1, initial triple digit in specimen ID implies impact energy (J), letter does lower (L) or higher (H) density, and last number is impact velocity level. Absorbed energy was calculated using the data of the stress-strain curve. The area under the stress-strain curve up to the densification strain (d) was calculated as an absorbed energy. It indicated that there was growth of absorbed energy while the impact velocity was increased under constant impact energy. The absorbed energy for lower density specimen was gradually changed from 27.78 J to 31.12 J which is about 12% increase by the higher impact velocity when impact energy was 100 J. Table 1 Impact crush test results Impact energy (J)
Absorbed energy (J)
Densification strain (d)
For 100 J of impact impact energy 100L1 2.75 26.50 67 100L2 3.52 16.50 63 100L3 5.40 7.00 61 100H1 2.73 26.50 97 100H2 3.52 16.50 84 100H3 5.60 7.00 93
100.20 102.22 102.06 98.80 102.22 109.76
27.78 29.37 31.12 34.39 37.24 45.36
0.60 0.65 0.71 0.45 0.57 0.64
For 200 J of impact impact energy 200L1 3.88 26.50 67 200L2 4.98 16.50 64 200L3 7.73 7.00 60 200H1 3.86 26.50 88 200H2 5.00 16.50 94 200H3 7.71 7.00 78
199.47 204.60 209.14 197.42 206.25 208.05
31.09 32.48 33.12 41.61 44.22 45.90
0.62 0.66 0.72 0.55 0.59 0.64
Specimen ID
Impact velocity (m/s)
Striker mass (kg)
Specimen density (kg/m3)
4 5
100L2 100L3
3 2
100H3
2 1
0
0 0.2
100H2
3
1
0
100H1
4 Stress (MPa)
4 Stress (MPa)
5
100L1
0.4
0.6
0.8
1
0
0.2
0.4
Strain
5
200L2
0.8
1
200H1 200H2
4 Stress (MPa)
Stress (MPa)
1
(b)
200L1
4
0.8
Strain
(a)
5
0.6
200L3 3 2 1
200H3 3 2 1
0
0 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
Strain
(c)
0.6
Strain
(d)
Fig. 3 Stress-strain curves of impact tests: (a) Impact energy: 100 J, specimen density: low (b) 100 J, high, (c) 200 J, low and (d) 200 J, high. Fig. 3 showed the stress-strain curves of impact tests. It indicated that there were insignificant changes in plateau stress with respect to the initial impact velocities under constant impact energy, however, the higher impact velocities caused the bigger increase in densification strain for all cases, which yielded the wider plateau region, i.e. growth in crashworthiness. The higher density specimens underwent the larger oscillation especially in the plateau region as well as yield point. While the equation proposed by Gibson and Ashby (1998) to determine the onset of densification in term of relative density, it was found that the densification strain was affected both by the relative density and strain rate especially for the polymeric foams in the current study. Tan et al. (2005) suggested the method for determining densification strain of the metallic foams using the efficiency of the energy. However, it did not match well with the PU foam specimen. Therefore, the intersection of tangent method, described by Paul and Ramamurty (2000) and followed by Lopatnikov et al. (2007) was used to determine the onset of densification in this study. In Fig. 4, the densification strain range was plotted since tangent lines could be chosen subjectively from the different point of view. The average of the lowest and the highest values in the range was selected as the onset of densification strain of each curve. After evaluating the densification strain, the results were plotted in Fig. 5. It was found that the onset of densification strain of low density specimen changed from 60% to 71% and 62% to 72%, as the striker velocity increased under 100 J and 200 J impact impact energies respectively. On the other hand, for higher density specimen it varied from 45% to 64% and 55% to 64%.
5
Stress
Fig. 4 Determination of densification strain.
Densification strain (d) range
Plateau Densification
Strain
Impact energy 100 J
0.7
0.6
low density specimen
0.5
Impact energy 200 J
0.8
Densification strain
Densification strain
0.8
0.7
0.6
low density speciment
0.5
high density specimen 0.4
high density specimen 0.4
0
2
4 6 8 Impact velocity (m/s)
(a)
10
0
2
4 6 8 Impact velocity (m/s)
10
(b)
Fig. 5 Variation of the onset of densification strain with respect to the initial impact velocity of the striker: (a) impact energy =100 J and (b) 200 J. Fig. 6 shows microscopic structures of the uncrushed and crushed PU foam, captured by a scanning electron microscope (SEM, Phillips W type 535M). PU sample was cut at one time with a sharp knife and gilt to promote its conductivity. The micrographs were analyzed to quantify void ratio of the arbitrary cross-section of the PU foam. Microstructures of uncrushed low and high density PU foams are shown in Figs. 6(a) and (b). From the uncrushed images it was found that most of the cells were basically isolated with thin membrane, i.e. closed cell morphology. The main difference between low and high density specimens was the cell size. Cell size of high density foam is comparatively smaller than low density foam. It is believed that smaller cell sizes are less prone to buckling which translates to higher peak stress Saha et al. (2005). Moreover, the low density specimen had comparatively minor standard deviation in the geometry of the cell. Morphological defects such as missing of cells are prominent in the images of high density PU foam. Therefore, in the stress strain curve, higher peak stress as well as frequent oscillation was found for high density specimen. Microstructures of crushed PU foam by lower velocities are shown in Figs. 6(c), and (d). Also, Figs. 6(e) and (f) shows micrographs of crushed PU foam by higher velocities. Those images of specimen crushed by higher impact velocities illustrated that the collapse became general with severe wall contact while comparatively lower wall contact and some voids were observed in the images of specimen crushed by lower impact velocities.
6
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 6 Microstructure of PU foam: (a) Uncrushed, specimen density: low, (b) uncrushed, high, (c) crushed by low impact velocity, low density, (d) crushed by low impact velocity, high density, (e) crushed by high impact velocity, low density, and (f) crushed by high impact velocity, high density. Fig. 7 shows the deformation patterns of PU foam crushed by various velocities of the striker. The images of PU foam crushed by lower impact velocity striker revealed that deformation progressed with cooperative collapse of all layers as shown in Fig. 7(b) and (e). Overall deformation pattern is homogeneous. On the other hand, for the specimen crushed by medium impact velocity (Fig. 7(c)), deformation was mainly concentrated in the plane of upper surface, which was contacted with the striker; whereas bottom surface was almost unchanged. The phenomenon of this local buckling deformation and the occurrence of the higher buckling mode in the upper surface of cylindrical foam impacted axially are mainly due to the effects of stress wave and structural inertia. The initial buckling deflection, occurring near the impacted end, spread forward and developed into the higher mode as the axial stress wave was propagated. The obvious unloading of the axial stress wave appeared in the region near the impacted end when the buckling deformation became large enough in this region. The lower surface remains unchanged because it was found that significant buckling displacements usually appear if the stress wave had moved a long distance along the specimen, the early local buckling did not influence essentially the final buckling form (Lepik et al. 2001). Thus, the adjacent layers of striker moved inward while after next layers spread outward; overall deformation was being considered as inhomogeneous as shown in Fig.7 (f). Finally, the specimen was broken for the highest impact velocity shown in Fig. 7(d).
7
(a)
(b)
(e)
(c)
(d)
(f)
Fig. 7 Deformation pattern of PU foam: (a) Uncrushed, (b) crushed by low impact velocity, (c) crushed by medium impact velocity, (d) crushed by high impact velocity, (e) crushed by low impact velocity; close view and (f) crushed by medium impact velocity; close view. 3 Constitutive models for elastic and plateau regions 3.1 Constitutive models Stress-strain behaviour is expressed by the Sherwood-Frost model (1992), which incorporates the effects of foam density, temperature and strain rate. This model included the modulus function as well as shape function, was applied to the plateau region shown as follows.
10
n 0
H T D 0 a b An n
(ε εd)
(1)
H(T) and D(ρ) represent the temperature and density effects, a and b are material constants which can be determined by quasi-static tests. εd is the onset of densification strain. Strain rate remains constant in quasi-static compression, however, it varies during impact testing. The strain rate can be obtained by the Eq. (2) expressed as follows:
8
d d 1 d v L dt dt L dt L
(2)
where, L is the overall height of the specimen, and v are deformation of the specimen and the transient velocity of the striker at arbitrary strain during impact, respectively. To calculate transient velocity, the Impulse-momentum theory (Beer and Johnston 1981) was employed, as shown below.
mvi Fi t mvi 1
(3)
where, Fi was assumed to be constant within a small t. It is necessary to solve coupled equations, i.e. Eq. (1) and (3) with respect to time, for obtaining transient velocity, stress as well as compressive deformation of the specimen at each stage. Fig. 8 summarises the solving procedure of coupled equations briefly. As the time step becomes smaller, more accurate result would be obtained since the deformation is assumed to be proportional with velocity of that step. In the current study, 4.88 s was chosen for the time step.
START
Input vi value Input ti
Calculate
i (deformation)
Calculate
.
i (strain), i (strain rate) Calculate i using Sherwood-Frost model
Calculate Fi (Force)
Calculate vi+1 using Impulse-momentum
i d
NO
YE S END Fig. 8 Flowchart for solving coupled equations.
9 n An
0 0.01
2 -197
3 1687
Table 2 Coefficients of the shape function 4 5 6 7 -8656 27942 -57375 73627
10
experiment analysis
Transient velocity (m/s)
Transient velocity (m/s)
10
1 13
8 100L3 6 100L2 4 2
8 -55839
10 -3098
experiment analysis
8 100H3 6 100H2 4 2
100L1
100H1 0
0 0
0.2
0.4 Strain
0.6
0
0.8
0.2
(a) experiment analysis
10 200L3
8 200L2
6 4 2
0.4 Strain
0.6
0.8
0.6
0.8
(b)
Transient velocity (m/s)
10
Transient velocity (m/s)
9 21937
200L1
experiment analysis
200H3
8 200H2
6 4 2
200H1
0
0 0
0.2
0.4 Strain
0.6
0.8
0
0.2
0.4 Strain
(c) (d) Fig. 9 Transient velocity curves: (a) Impact energy: 100 J, specimen density: low, (b) 100 J, high, (c) 200 J, low and (d) 200 J, high. Experimental data as well as results from solving coupled equations for obtaining transient velocities were shown in Fig.9. The calculated transient velocity curves showed excellent agreement with the experiments allowing less than 10% error.
10 3
3
experiment
experiment
2
analysis
Stress (MPa)
Stress (MPa)
analysis 100H1
1
2 100H2 1
100L1
100L2
0
0 0
0.2
0.4
0.6
0.8
0
0.2
0.4
Strain
3
experiment
0.8
0.6
0.8
experiment analysis
Stress (MPa)
Stress (MPa)
0.6
(b)
analysis 2 100H3 1
2
200H1
1 200L1
100L3 0
0 0
0.2
0.4
0.6
0.8
0
0.2
0.4
Strain
Strain
(c)
3
(d)
3
experiment
experiment analysis
Stress (MPa)
analysis
Stress (MPa)
0.8
Strain
(a)
3
0.6
200H2
2
1
2 200H3 1
200L2
200L3
0
0 0
0.2
0.4 Strain
(e)
0.6
0.8
0
0.2
0.4 Strain
(f)
Fig. 10 Calculated and experimental stress-strain response of PU foam under impact loading: (a) Impact energy: 100 J, low velocity, (b) 100 J, medium velocity, (c) 100 J, high velocity, (d) 200 J, low velocity, (e) 200 J, medium velocity and (f) 200 J, high velocity.
11
100H1 100L1
6
0
0
0.4
0.6
0.8
(a)
(b)
12
SEA (kJ/kg)
0
0 0.6
0.8
0
(d)
12
200H3
200L3
0
0 0.8
0.8
6 3
0.6
0.6
analysis
9
3
0.4
experiment
200H2
200L2
0.2
0.4
(c)
6
0
0.2
Strain
analysis
9
200L1
Strain
experiment
0.8
200H1
6 3
0.4
analysis
9
3
0.6
experiment
100H3
6
12
0.4 Strain
100L3
0.2
0.2
Strain
analysis
0
100H2 100L2
0
experiment
9
analysis
6 3
0.2
experiment
9
3
12
SEA (kJ/kg)
SEA (kJ/kg)
analysis
9
0
SEA (kJ/kg)
12
experiment
SEA (kJ/kg)
SEA (kJ/kg)
12
0
0.2
0.4
Strain
Strain
(e)
(f)
0.6
0.8
Fig. 11 Comparison between calculated and experimentally obtained specific energy absorption (SEA) vs. strain curves: (a) Impact energy: 100 J, low velocity, (b) 100 J, medium velocity, (c) 100 J, high velocity, (d) 200 J, low velocity, (e) 200 J, medium velocity and (f) 200 J, high velocity.
12 3.2 Evaluation For the Sherwood-Frost model, the base curve selected from the quasi-static results was as follows: Density of the specimen, = 67 kg/m3 Lowest constant strain rate, = 10-3 s-1 Temperature, T = 23C (room temperature) An, coefficients of the shape function, which were specified in Eq. (1), were obtained by regression with 10th order polynomial of quasi-static data as listed in Table 2. The temperature effect H (T) was assumed to be unity since all tests were conducted at room temperature. H (T) function needs to be determined through impact testing at different temperatures. The density effect was determined by comparing two quasi-static experimental results under the strain rate of 10-3 s-1 applied to different densities at room temperature, setting that 67 kg/m3 density specimen has a unity effect. Thus, the density and the temperature effects were:
D 0.046 2.059 , (60 97)
(4)
H (T) = 1; (T = 23 C)
(5)
Using the static test results, the values of a and b in Eq. (1) for the PU foam in the current study were found to be 0.05173 and 0.001553, respectively. The comparison between the analytical and experimental stress-strain curves during impact crush was shown in Fig. 10. Even though the analysis didn’t simulate the oscillation of the curves, analytical stress-strain results under various impact velocities demonstrated a fit quite similar to test data occupying allowable error (within ±5% range of error) in elastic and plateau regions. In general, experimental curves of lower density specimens have a better fit with analytical curves than for the high density specimens, because oscillation in the stress-strain curves was observed more in higher density specimens. Crashworthy characteristics is commonly quoted in the form of the specific energy absorption (SEA), absorbed energy per crushed mass, and it is considered one of the major parameters in designing the structures which undergo high strain rate or impact load applications (Mamalis et al. 1997; Zarei and Kröger 2008). It was possible to calculate SEA of the PU foam from Eq. (6).
u
1
d
(6)
0
Fig. 11 shows the experimental and calculated specific energy absorption curves. Each specific energy absorption curve was evaluated until the onset of densification strain. It is obvious from the figure that high density specimen has more energy absorption capacity. The specific energy absorption curves from the analytical results matched well with the specific energy absorption curves from the experimental data. 4 Conclusions Crashworthy characteristics of the PU foams, with respect to varying the striker velocity under constant impact energy, was investigated. Under the identical impact energy, the energy absorption of the PU foam was increased by the increment of the densification strain as the striker velocity became higher, however, there were no obvious changes in Young’s modulus as well as plateau stress. Crush mode of PU foam was determined by analysing SEM microstructures. Also, coupled equations using Sherwood-Frost model as well as Impulse-momentum theory were solved to predict mechanical behaviour of the PU foam. Analytical stress-strain curves under various impact velocities demonstrate a fit quite similar to test data occupying allowable error for analysing crashworthiness in elastic and plateau regions even though it didn’t simulate the oscillation of the real data. Moreover, the specific energy absorption, which was calculated from the analytical stress-strain curves, showed good agreement with experimental. 5 Societal benefits The improvement of the crashworthiness of automobiles cannot be overestimated. US Department of Traffic (US Department of Transportation, NHTSA, Traffic safety facts 2015: A compilation of motor vehicle crash data from the fatality analysis reporting system and the general estimates system; DOT HS 812 384) estimated that there were 35,092 fatalities and
13 1 million injuries requiring hospitalization in 2015. This, together with a range of environmental concerns and social pressures backed by legislation has led, and will continue to lead, to highly innovative designs, involving advanced materials such as nonferrous alloys, smart structures, composites and foams. The goal of this study is to guide designer use Polyurethane foam in crashworthiness structures such as automotive bumper system by providing crashworthiness data, determining crush mode, and mathematical model of crashworthiness. Therefore, this study will help to reduce deaths and injuries in motor vehicle crashes. Acknowledgements This work was supported by the National Research Foundation of Korea (KR) under the grant number of D00011. Conflicts of interest The authors declare no conflict of interest.
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