School of Engineering, The University of Birmingham, Edgbaston, UK. Abstract: The use of predictive finite element (FE) models in tyre design and analysis has ...
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Finite element simulation of the tyre burst test E O Bolarinwa and O A Olatunbosun* School of Engineering, The University of Birmingham, Edgbaston, UK
Abstract: The use of predictive finite element (FE) models in tyre design and analysis has become widely popular in recent times. This is largely due to the introduction of high-performance computers in addition to the enhancement in the capabilities of existing proprietary finite element software, thus enabling the efficient use of such tyre models in solving the challenging problems of pneumatic tyre behaviour as an alternative to experimental tests routinely carried out on tyre prototypes. This present work investigates tyre burst behaviour when the tyre is inflated well beyond the manufacturer’s recommended maximum pressure. This will help to predict the extent to which a tyre can be loaded before failing catastrophically, thus simulating one of the mandatory tyre qualification tests. Consequently, an axisymmetric finite element tyre model has been developed using the improved capabilities in ABAQUS FE code, which allows the modelling of the tyre burst phenomenon, based on the ultimate strengths of the constituent reinforcement materials. A summary of the results obtained from this model for a passenger car tyre P195/65R15 H91 is presented together with a study of the effect of some tyre design parameters on the tyre burst pressure. Also some recommendations are made for enhancing the functionality of the model. Keywords: tyre, finite element method, geometrical non-linearity, burst pressure
1 INTRODUCTION Destructive tests such as the application of burst pressure, high-speed free rotation, and plunger energy are sometimes performed on new tyres to ascertain their ultimate strengths [1] or to comply with legislative requirements. These tests are used for the qualification of a new tyre design as well as to determine the extent to which the tyre can be loaded beyond the manufacturer’s recommended service conditions before failing. The current work is part of an on-going development of an integrated CAD/FE tyre design system, which seeks to integrate tyre design and virtual testing for the purposes of design verification and optimization. Coincidentally, such tests equally subject a tyre to a large state of strain and deformation and thus pose an interesting challenge for a numerical tyre model. Such a numerical tyre model would reduce the cost of carrying out routine destructive tests on tyre prototypes, while avoiding safety-related issues surrounding such destructive tests. To this end, a new tyre model is developed and used to simulate the tyre burst test. The MS was received on 1 April 2004 and was accepted after revision for publication on 14 June 2004. * Corresponding author: Vehicle Dynamics Research Group, School of Engineering, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK. D07104 © IMechE 2004
A tyre primarily owes its ability to withstand different loading conditions, such as inflation pressure and vehicle load, to the network of fabrics sandwiched between its rubber components [2, 3]. Indeed the importance of using reinforcement material in pneumatic tyres had long been recognized by J. B. Dunlop [4] who made the first pneumatic tyre with an Irish flax fabric. However, as requirements imposed by the severity of tyre operational conditions have increased over the years and tyre manufacturers seek inexpensive but high-quality fabrics, new tyre reinforcement materials made of cotton, rayon, polyester, steel, Kevlar and fibreglass are increasingly being introduced into the tyre reinforcement cords market. The different characteristic properties (adhesion to rubber, heat ageing resistance, thermal stability, fatigue resistance) of these cords, which can be altered by heat or chemical treatments, are employed during the tyre manufacturing stage to achieve the desired tyre behaviour. Typically, in carcass plies, nylon’s high strength is required to provide adequate carcass strength, while polyester’s high elastic modulus and low elongation reduce tyre deformation under service conditions, leading to a better high-speed performance and tread wear, reduced tread cracking and better steering characteristics or manoeuvrability [5]. However, in most passenger car tyres, steel wire cords are used for the belt cords of radial tyres so as to provide directional stability for the tread Proc. Instn Mech. Engrs Vol. 218 Part D: J. Automobile Engineering
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Table 1 Mechanical properties of reinforcement materials Material
Young’s modulus (GPa)
Poisson’s ratio
Yield tensile strength (MPa)
Ultimate tensile strength (MPa)
Elongation at break (%)
Nylon Polyester Steel
3 9.5 200
0.3 0.3 0.3
66 130 350
– – 420
21 16 10
during steering, thus keeping it flat in contact with the road despite the induced lateral deflection on it. Since no single commercial cord can satisfy the entire reinforcement material requirement in a tyre, combinations of these cords are used in the making of a tyre depending on the ultimate desired tyre properties. Although rubber matrices, in which these cords are embedded, exhibit large elastic deformation, they are weak in tension and unable to withstand high tensile load, which a tyre is normally subjected to during operational conditions such as inflation, preload, and rolling. Hence, the failure or breakage of the cords signals the failure of a tyre. Such a failure criterion will be employed in this paper to predict the catastrophic tyre burst phenomenon.
2 FINITE ELEMENT MODEL It is sufficient to use a two-dimensional axisymmetric tyre model for the numerical simulation of tyre inflation [3, 6–11]. This simulation option represents a computationally inexpensive alternative to a full threedimensional tyre model when screening tyres designed for severe loading or extreme operational conditions such as the burst pressure test [1]. A model similar to that used to correlate inflation pressure predictions with experimental test results will be used here [12]. However, in order to determine the pressure at which the ultimate strength of the tyre reinforcements is achieved, the ultimate strength properties of the cords, modelled with rebar elements, are used as inputs, as shown in Tables 1 and 2. In addition, perfectly plastic cord behaviour is assumed at such extreme loading condition for the nylon and polyester rebars, while the steel breakers are assumed to stress-harden up to an ultimate strength of 420 MPa. The P195/65R15 passenger car half-tyre section was modelled using ABAQUS 6.3–1. The resulting twodimensional axisymmetric FE model used for the burst pressure analysis comprises 24 quad-continuum elements Table 2 Geometric properties of reinforcement materials Material
X-sectional area (mm2)
Spacing (mm)
Orientation (°)
Nylon Steel Steel Polyester
0.4208352 0.2118683 0.2118683 0.4208352
1.19 1.16 1.16 1.00
0 +20 −20 90
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and a triangular continuum element required to accurately model the geometry transition region–shoulder. The model discretization having 89 nodal points with the load and boundary conditions is as shown in Fig. 1. The non-linear and isotropic rubber material component is defined in terms of a hyperelastic strain energy model possessing experimentally obtained material properties shown in Table 3 [13]. The reinforcement materials, modelled as homogeneous, elastic–plastic, and orthotropic (unidirectional ) rebars comprising two axisymmetric layers of belts (breakers) made of steel cords, are positioned in the circumferential tyre direction with a nylon layer (bandage) on top of these belts. On the other hand, the carcass ply, made of polyester, assumes a radial orientation, running from bead to bead, as shown in Fig. 2. Also, a negligible rubber viscoelastic property is assumed. The rim is considered to be of negligible compliance, rigidly attached to the tyre to represent the tyre– rim interface. Since a half-tyre section is being used, a symmetric boundary condition is imposed at the tyre centre-line. Finally, the non-linear geometric ( large displacement) analysis in ABAQUS [14] is used for the simulation in order to account for the large state of strain a tyre is subjected to under inflation pressure.
3 SIMULATION RESULTS The tyre model’s response to an extremely large, but progressively applied, inflation pressure was simulated by inflating the tyre up to a limit of 1000 kPa pressure, representing a 300 per cent increase in the tyre’s rated inflation pressure (248 kPa). The resulting plot of the deformed geometry superimposed on the undeformed one at a pressure of 887 kPa is shown in Fig. 3. This plot shows an extremely large displacement in the crown region with an outwardly expanding sidewall having a thinned shoulder. The tyre burst pressure, under this extreme loading condition, can be predicted by identifying the pressure at which the maximum strength and the maximum sustainable elongation (i.e. the elongation at break) of Table 3 Hyperelastic material properties Material
C (MPa) 10
C (MPa) 01
D (MPa) 1
Rubber
1
0
0 D07104 © IMechE 2004
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Fig. 1 Two-dimensional axisymmetric tyre model with reinforcement materials
Fig. 2 Reinforcement materials
Fig. 3 Deformed versus undeformed plot at 887 kPa (129 psi)
the reinforcement materials is attained. In addition, the plot of the tensile stress of each constituent rebar against the inflation pressure reveals their responses to pressure loading leading to tyre burst. For example, in Fig. 4, the most stressed element (28) in the first layer of belt D07104 © IMechE 2004
(MEM_SURF1) is seen to attain its yield strength at an inflation pressure of 496 kPa, while further increase in pressure is sustained by its post-yield hardening behaviour up to the maximum strength value. A similar response to inflation pressure is exhibited by the rebars contained in the second belt layer, but with the most stressed element attaining its yield strength at 532 kPa. A somewhat different response was observed in the layers of nylon rebars or bandage (MEM_SURF3) on top of the belt layers as shown in Fig. 5. Below the pressure at which the steel belt cords yield (between 493 kPa and 496 kPa), all the rebars displayed very light loading. However, the reduction in stiffness of the breakers exposed this layer to a greater proportion of the increased inflation pressure, resulting in a rapid increase in stress up to its yield strength. The high elastic modulus of the polyester in the carcass ply (MEM_carcass) is responsible for the high contribution of this layer, compared to the nylon cords in MEM_SURF3, in sustaining the inflation pressure in the crown region (crown rebar as shown in Fig. 6). Also, the sidewall carcass ply equally maintained high stiffness behaviour until the highly stressed polyester sidewall rebar closest to the bead region attained its yield strength and began to undergo plastic deformation until the simulation run terminated at a pressure of 887 kPa, well before the pre-set limit of 1000 kPa. Figure 7 shows the maximum elongation of the reinforcement materials in the tyre model expressed in terms of the percentage of their elongation under increasing inflation pressure. This chart reveals that above 580 kPa, the sidewall carcass ply element (66) closest to the bead region undergoes severe elongation until it reaches its maximum strain (16 per cent). The inflation pressure of 700 kPa, at which the rebar element Proc. Instn Mech. Engrs Vol. 218 Part D: J. Automobile Engineering
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Fig. 4 Stress in selected (MEM_SURF1) elements versus inflation pressure
Fig. 5 Stress in selected nylon (MEM_SURF3) elements versus inflation pressure
Fig. 6 Stress in selected polyester (MEM_carcass) element versus inflation pressure Proc. Instn Mech. Engrs Vol. 218 Part D: J. Automobile Engineering
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Fig. 7 Reinforcement materials’ strain response versus inflation pressure—one carcass layer
breaks, is assumed to correspond to the tyre model burst pressure. This proves to be reasonably close to the burst pressure of 1000 kPa (M. Burnett, October 2003, personal communication), obtained in tests on similar steel-belted radial tyres, though from another manufacturer. In summary, Table 4 gives an insight into the maximum strain in each rebar layer at the tyre burst pressure, indicating the extent to which the reinforcement is elongated prior to tyre burst.
Table 4 Elongation of reinforcement materials at 700 kPa Rebar layer
Representative element
Maximum strain (%)
Strain at break (%)
MEM_SURF1 MEM_SURF2 MEM_SURF3 MEM_carcass
28 36 42 66
3.9 3.8 4 16
10 10 21 16
4 PARAMETRIC STUDIES In view of the dependence of the predicted tyre burst pressure on the carcass strength closest to the bead region, an attempt was made to investigate the sensitivity of the burst pressure to the carcass strength and geometrical properties. As discussed earlier, the burst pressure is taken as the earliest pressure at which the specified ‘strain at break’ for any of the reinforcement elements is attained. In this case, the 16 per cent ‘strain at break’ for the carcass rebar was the first to be attained at a pressure of 700 kPa (see Fig. 7 and Table 4). To further demonstrate the capability of the FE model as a tyre design tool, the impact of changing the number of carcass layers and the geometric properties (cross-sectional area and rebar spacing) on tyre burst pressure is presented. By increasing the number of carcass layers in the original model, the reinforcement materials exhibit a similar response to inflation pressure (Fig. 8), as observed
Fig. 8 Reinforcement materials’ strain response versus inflation pressure—two carcass layers D07104 © IMechE 2004
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in the case of a single carcass layer. However, there is a 64 per cent increase in the burst pressure, as shown in Fig. 9, thus making the tyre sidewall stiffer and more resistant to the pressure load. An important feature of the FE tyre model is that it provides a cost-effective means of carrying out parametric studies on the tyre so as to optimize desired performance output. As a result of this, the carcass properties can be optimized to achieve a target burst pressure. In this section, the main and combined effects of changing the yield strength, cross-sectional area, and spacing of the carcass rebars on the tyre burst pressure will be investigated using an organized approach popularly referred to as the Design of Experiment (DOE) for determining the effects of process parameters on its output [15, 16 ]. To this end, percentage changes in the nominal values (for the base model ) of these properties to be used as input for the burst pressure simulation are presented in Table 5.
From this table of properties, a matrix of eight experiments (simulation runs) and a resulting output burst pressure are generated, as shown in Table 6. Each run in the matrix has different combinations of high (coded as 1) and low (coded as −1) settings of the properties based on the DOE orthogonal array scheme. From the simulation results shown in Table 6, the average burst pressure for the entire simulation is estimated as 700 kPa. In addition to this, the average contributions of the low and high settings of each property to the burst pressure are respectively computed in the Avg− and Avg+ rows, graphically shown in Fig. 10, while the ‘D’ row gives the difference between the Avg+ and Avg− values. Looking at the last three rows in Table 6, the yield strength, Y, and the cross-sectional area, X, are found to have the greatest impact on the burst pressure, while the combined effect of the crosssectional area and spacing, S, has the least effect. Furthermore, it can be seen that the burst pressure is
Fig. 9 Sensitivity of burst pressure to the number of carcass layers Table 5 Carcass properties for burst pressure sensitivity study Properties
Base model 0
Increment ±%
Low setting −1
High setting 1
Yield strength (MPa) ‘Y ’ X-sectional area (mm2) ‘X’ Spacing (mm) ‘S’
130 0.42 1.0
20 19 15
104 0.336 0.85
156 0.5 1.15
Table 6 An orthogonal array for burst pressure simulation Interactions Run/test
Yield strength (Y )
X-area (X )
Spacing (S)
YX
YS
XS
YXS
Burst pressure (Pa)
Base 1 2 3 4 5 6 7 8
0 −1 1 −1 1 −1 1 −1 1
0 −1 −1 1 1 −1 −1 1 1
0 −1 −1 −1 −1 1 1 1 1
0 1 −1 −1 1 1 −1 −1 1
0 1 −1 1 −1 −1 1 −1 1
0 1 1 −1 −1 −1 −1 1 1
0 −1 1 1 −1 1 −1 −1 1
7.00E+05 5.65E+05 7.60E+05 7.55E+05 9.75E+05 5.00E+05 6.10E+05 6.15E+05 8.05E+05
7.13E+05 6.84E+05 −2.88E+04
7.10E+05 6.86E+05 −2.38E+04
Avg− Avg+ D
6.09E+05 7.88E+05 1.79E+05
6.09E+05 7.88E+05 1.79E+05
7.64E+05 6.33E+05 −1.31E+05
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6.85E+05 7.11E+05 2.63E+04
6.91E+05 7.05E+05 1.38E+04
7.0E+05 (average)
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service condition such as burst pressure. Typically, based on the result of the parametric studies, burst pressure can be taken to be dependent on the carcass reinforcement yield strength, cross-sectional area, and spacing. However, in order to enhance the versatility of the tyre model for carrying out the simulation of the tyre burst event, the following issues must be considered:
Fig. 10 Graphical interpretation to the DOE for the burst pressure sensitivity study
directly proportional to the carcass yield strength, with a 20 per cent increase in the yield strength of the material resulting in a 13 per cent increase of the burst pressure. Similarly, increasing the carcass rebar’s volume fraction, achieved either by increasing the cross-sectional area of the rebar or reducing the rebar spacing, can elevate the tyre burst pressure. For example, the burst pressure also increased by 13 per cent with a 19 per cent increase in the crosssection area, while 15 per cent reduction in the rebar’s spacing only resulted in about a 9 per cent increase in the burst pressure. From this result, it is evident that the fourth simulation run with high settings for Y and X, combined with a low setting for S, produced the highest burst pressure of 975 MPa, corresponding to an increase of about 39 per cent above the average burst pressure.
5 CONCLUSIONS A numerical approach for modelling tyre burst phenomenon under severe inflation pressure has been presented by making use of a commercial FE code. The model has the double advantage of serving as a valuable tool to confirm the robustness of the FE tyre model and for identifying the extreme inflation pressure at which the tyre is likely to burst. In addition, it offers better understanding of the tyre failure mechanism under inflation pressure, revealing the behaviour of tyre reinforcements leading to failure. It can therefore be used as an alternative to destructive tyre tests. It will form the basis of one of the tyre qualification tests to be provided in the integrated tyre design and virtual testing system under development. Finally, the model developed in this study shows significant flexibility in being used as a tyre design sensitivity tool for optimizing design parameters, such as the number of carcass plies and the geometrical and mechanical properties of the carcass ply, for a severe D07104 © IMechE 2004
1. in order to generate an accurate model for the prediction of tyre burst pressure, reliable test data for the elastic–plastic behaviour of the reinforcement materials are required; 2. model predictions of tyre burst pressure should be correlated with test data, in which case the tyre is hydro-tested to destruction; 3. a three-dimensional model of the tyre should be used to investigate the interply shear effects between the layers of rebars under severe inflation pressure condition.
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14 ABAQUS/Standard User’s Manual, vols I–III, 2002 (Hibbitt, Karlson and Sorenson Inc., USA). 15 Coppola, A. Design of experiments. In Total Quality Management Toolkit, 1993, pp. 75–93. 16 Bryne, D. M. and Taguchi, S. The Taguchi approach to parameter design. In Taguchi Methods: Applications in World Industry, 1989, IFS, pp. 57–76.
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