Numerical Simulation Study Of Fatigue Failure And Hysteretic Heat Build-up Based On Thermo-mechanical Coupling Approach For Natural Rubber Nanocomposites

Rubber, as one of the strategic supplies and important engineering materials, is widely used in the products applied in the dynamic loading condition such as tires, conveyor belt, vibration isolation bearings, damper, etc.In the external dynamic condition, rubber materials generate two responses because of viscoelastic characteristics: energy storage due to elasticity and energy dissipation due to viscosity. On the one hand, the initial micro-cracks,also known as crack precursors, in the rubber materials would propagate until fracture and damage due to energy storage, which lead to fatigue failure of rubber. On the other hand, part of the external work would be converted into heat because of the energy dissipation, which lead to hysteretic heat build-up.Moreover, the rising temperature affect the mechanical and thermal properties of rubber in turn, leading toa thermo-mechanical coupling problem. Fatigue failure and hysteretic heat build-up are two main complex problems for rubber materials and products working at dynamic loading conditions. Rubber nanocomposites are composed of complex structures with the characteristics of multi-scale and multi-level interactions, and then traditionally experimental methods are difficult to establish the quantitative relations between material properties, loading conditions and the properties of final rubber products.Furthermore, the time cycles of experiments are long and the costs are high.Finite element analysis (FEA) method is an efficient and reliable approach used to study the fatigue failure and hysteretic heat build-up behaviors of rubber materials, which can give preliminary guides for the design of high-performance rubber materials and products. The acquisition of reliable constitutive equation of rubber materials is one of the key factors to obtain highly precious numerical results.Based on the above academic background, the work focus on the numerical simulation of fatigue failure and hysteretic heat build-up behaviors of natural rubber materials. The main points are summarized as follows:(1) We systematically summarized the selection method and fitting precision of different constitutive model of carbon black (CB) filled natural rubber (NR) nanocomposites from the perspectives of stress-strain test data and hyperelastic constitutive equations based on the analysis of uniaxial compressive deformation of a cylindrical rubber component. From the perspective of stress-strain test data, the results indicate that the fitting precision cannot used to determine the strengths and weaknesses of relative constitutive model when only uniaxial tensile (UT) test data supplied. The overall precisions of calculating results with UT, planar tensile (PT) and equibiaxial tensile (ET) test data supplied are more higher compared with those with UT test data supplied, and the fitting precision can determine the strengths and weaknesses of the constitutive model. From the perspective of hyperelastic constitutive equations, the results indicate that O Ni, P_Ni, VdW and Mar models with high fitting precisions are proper hyperelastic equations when UT, PT and ET test data are all supplied. RP_Ni, AB and Marlow models are proper, and O-Ni and P_N2 models are improper when only UT test data are supplied. The compressive deformation analysis of solid rubber tire and the comparison between test data of tearing energy and FEA data of J integral for a planar tensile rubber specimen further prove the necessity of UT,PT and ET test data when fitting hyperelastic constitutive equations of rubber nanocomposites. The mechanical behavior of hysteresis loop of CB filled NR compounds under a quasistatic cyclic loading experiment was modeled.Marlow hyperelastic model fitted the time-independent behavior of the loading curve with the highest precision. The viscoelastic behavior of the unloading curve was studied with Mullins model (stress softening model).Mullins model could describe the unloading curve well for the larger strains,but permanent set could not be predicted using Mullins model only. The combination of plastic model with Marlow and Mullins equations could accurately describe the mechanical behaviors including loading/unloading and permanent set behaviors. The work would be instructive for the determination of rubber constitutive equationsin the finite element analysis of rubber materials and products.(2) Fatigue life prediction for a dumbbell cylindrical natural rubber component under uniaxial tensile loading conditions was performed based on the crack growth law which including the Thomas fatigue crack growth model for relaxing (R = 0) load cycles and the Mars-Fatemi model for non-relaxing(R > 0) load cycles. The calculating results were composed of three parts: the first location in which the component breaks, the fatigue life and the orientation direction plane in which the crack prone to grow. The visualization of the calculating fatigue life and orientation angles were realized based on our code written by Python. The effect of strain induced crystallization on fatigue crack growth rate under different R ratio were systematically studied.By using a self-written program, we proposed a new approach to establish the relation between the power law exponent (F) and the load ratio (R) in the Mars-Fatemi model. The approach is based on rubber fatigue life (S-N) data rather than crack growth rate and tearing energy (da/dN-T) data, avoiding certain difficulties often encountered using the crack growth method. The results indicate that the relation between F and R is a quadratic or cubic function over the range 0 < R < 0.3. The crack precursor sizes were obtained from S-N data and iterative inverse algorithm. The quantitative effect of initial crack size on fatigue life was studied. We found that the inferred mean size of crack precursors in the rubber component is around 30-40 ?m under both relaxing and non-relaxing loading conditions, and the fluctuation of fatigue life is due to the inhomogeneity of crack precursor size except the factors such as unavoidable variations in testing conditions and specimen variations. The good agreement of inferred crack precursor sizes from different R ratio loading conditions is a strong indication that the Mars-Fatemi model provides a proper accounting for the effects of strain crystallization. The work can help to understand mechanism of fatigue failure and to guide the design of rubber materials and products with high fatigue life.(3) Based on nonlinear viscoelastic theory and thermo-mechanical coupling approach, heat build-up (HBU) analysis of a cylindrical natural rubber specimen under cyclic loading was performed through finite element analysis. The thermo-mechanical coupling approach can be divided into three major parts: deformation, dissipation, and thermal modules. In the deformation module, uniaxial, planar, and equibiaxial tensile tests were used to determine the hyperelastic constitutive equation. In the dissipation module,an analytical method for calculating the energy dissipation rate was established, and the dynamic properties were updated as a function of the strain, temperature and frequency based on the modified Kraus model. In the thermal module, the dependence of thermal parameters including thermal conductivity and specific heat capacity on temperature was established based on experimental data. The determination of the rubber material properties attracted particular attention, and a highly sophisticated equipment which can measure the temperature rise curves both on the surface and at the heart of the rubber specimen was used to verify the calculated results. Most importantly,the effect and mechanism of creep and dynamic property softening behaviors on the HBU were systematically studied. The consideration of dynamic property softening effect on the viscoelastic properties was necessary. The comparison between numerical results and experimental data shows that the proposed analysis method provides a satisfactory way to predict heat build-up for rubber compounds. Based on the code, the effect of material parameters such as specific heat capacity, thermal conductivity and loss factor on the HBU were studied by parametric numerical experiments. The results indicate the temperature rising and cooling rate was high with the increasing specific heat capacity, but the balanced temperature kept constant. When the value of thermal conductivity was higher, the heart temperature (TH) in the cylindrical rubber specimen was lower, the surface temperature (TS) at cylindrical rubber specimen was higher, the temperature difference was smaller, and a more homogeneous temperature distribution was obtained. TS and TH increase linearly with loss factor (tan ?). When tan 6 value increases 0.01, TH and TS increase 6.9? and 3.1?, respectively.(4) The transient temperature and rolling resistance (RR) of a solid rubber tire at the loading conditions of different compressive displacement and rotating speed were performed accurately based on the thermo-mechanical coupling approach and nonlinear viscoelastic theory. Particular attention was paid to the strain cycles as the solid tire rolling on the road presents non-sinusoidal deformation. First, a static three dimensional tire-road contact analysis with the tire rolling effect neglected was conducted to obtain the principal strain cycles during a rotation period. Second, the strain amplitude at the centroid point of the element was set to be the average value of the half amplitude of the three principal strains, and the 100th-order Fourier sine series was used to approximate the strain amplitude with high precision. Third, the heat generation rate proportional to the product of the loss modulus and the square of strain amplitude was calculated with great care. The loss modulus was updated as a function of strain amplitude, temperature and frequency based on the modified Kraus model and linear interpolation method. Loss modulus softening effect wasalso considered. Fourth, a practical method was proposed to compute the rolling resistance and transient temperature distributions by establishing a 2-D axisymmetric geometric model. A rubber rolling tester which can record the surface temperature and RR of the solid tire was used to verify the numerical results. The comparison between numerical data and test data reveals that the proposed analytical method is a reliable approach to predict RR and transient temperature distribution for solid rubber tires. The transient temperature increases with the compressive displacement and with rotating speed. The effect of thermal conductivity and loss rotating speed, and the RR increases with the compressive displacement but decreases factor on the steady temperatures on the surface and at the heart and RR of the tire were studied by parametric numerical experiments based on the above code. The results indicate that when the value of thermal conductivity was higher, TH was lower and TS kept almost constant, the temperature difference was smaller, and a more homogeneous temperature distribution was obtained.TS, TH and RR increase linearly with tan ?. When tan 8 value increases 0.01,TS, TH and RR increase 2.5?,4.6? and 0.6N, respectively. The work can be used to guide the design of natural rubber nanocomposite and high-performance tire with low fuel consumption and high safety.