Numerical Simulation Of Tensile Impact Process For Filament Yarns

The investigation of tensile impact behavior of high performance filament yarns, which are extensively used in circumstances subject to impact loads, is of increasingly importance nowadays. The Split Hopkinson Tensile Bar (SHTB) provides a popular experimental approach to obtain the properties of filament yarns at high stain rates. However, since the signal of transmitted wave of filament yarns is too weak to avoid disturbances, it is difficult to obtain correct signals for further study. As an alternative technique, numerical simulation would be more practical to obtain accurate stress wave so that the rupture mechanism of filament yarns under impact loads at high strain rates could be investigated more effectively.The objective of the present study is to develop a numerical approach towards the simulation of tensile impact process of filament yarns. For this purpose, a one-dimensional model for the SHTB apparatus with variable cross-section is firstly established. Then a numerical method is developed, together with the model, to simulate the impact process of the SHTB apparatus. After that the tensile impact process of filament yarns is simulated, and the effect of strain rates on the tensile properties of filament yarns is analyzed. The study is carried out as follows:The working principle of the SHTB system is introduced and it is emphasized that the hypostasis of the device is the propagation of stress wave in the system comprised of Hopkinson bar and specimen. Therefore, the dynamic tensile properties of the specimen can be calculated by means of the recorded signals of transmitted wave and reflected wave. To obtain the signal strong enough for the effective analysis, the number of yarn bundles in the specimen is estimated. For the purpose of firmly holding the specimen with multiple strands of iflament yarns, a commercial adhesive with great shear strength is used, in addition to an increase in the slot length of the Hopkinson bar. Then, the tensile impact performances of carbon and PVA filament yarns are tested and the corresponding stress waves are recorded. The testing data provide useful information for evaluating the present method of numerical simulation.A one-dimensional model for the SHTB apparatus in consideration of the variable cross-section is established. Two key problems are solved in developing the model. One is the introduction cross-section variation into one-dimensional governing equation. The other is the determination of the dynamic failure criterion of filamentyarns. In solving the first problem, both mass and momentum conservation equations in continuity mechanics are modified in such a way that the stress is represented by dividing load by cross-section area and that the density is replaced by diving linear density by cross-section area. The model suitable for approaching the wave propagation in variable area system is thus established. In solving the second problem, the failure criterion for the strain of filaments is determined. In addition, single and bimodal Weibull distribution functions are used respectively to describe the breaking tenacity of carbon and PVA filaments to obtain the constitutive relations of each material, which are then applied in analyzing the experimental data.A numerical simulation scheme based on the Smoothed Particle Hydrodynamics (SPH) method is proposed for simulating impact process. Two key issues for successful simulation of tensile impact process by means of the SPH method, namely boundary treatment and kernels evaluation, are pointed out. For the boundary conditions, free end boundary and fixed end boundary are treated separately by adding virtual particles outside the boundary. For the evaluation of a suitable kernel, the approximation equations of SPH particle for functions and their derivatives are analyzed in a stable field. Three criterions for determining suitable kernels are proposed to evaluate the accuracy of computation. The effects of the position of estimated particles and the smoothing length on behaviors of kernels are analyzed. Thus, the evaluation method of the kernels is established. Eight selected SPH kernels of different functions are choosen to demonstrate the feasibility of the criterions. After a suitable kernel is determined, the impact problem of two elastic bars is solved by simulation to verify the accuracy of the boundary treatment and kernels evaluation method in wave propagation issues. The simulation results show that the treatment of boundary conditions in this study can accurately represent the variation of stress waves passing through the boundary, namely, the signal of the stress inversed at the free end while the signal of velocity inversed at the fixed end.By means of the one-dimensional model and the numerical simulation scheme, wave propagations in bars with sudden or gradual changing cross-section areas, stepped bars and conical bars, respectively, are simulated. The stress waves from simulation are compared with the analytical solutions to verify the validity of the model. The simulation results of wave propagation in stepped bars show that the stress changes abruptly at the position where the cross-section has sudden change, while the load and velocity keep continuous. Both the transmitted wave and reflectedwave show no aberration during the passing of stress wave through the bar. The simulation results in the case of conical bars show that the stress, load and velocity are changed continuous with non-linear nature. In addition, the transmitted wave and reflected wave show aberration. Good agreements between simulation and analytic solutions demonstrate the feasibility of the proposed model in solving the problem of wave propagation in variable cross-section bars.The wave propagation in the Hopkinson bar system is then simulated. The conditions of equilibrium assumptions for stress and strain are evaluated at first. Then the effects of the break position, cross-section area, length and elastic modulus of specimen on the propagation of stress wave in the system are studied. The results show that the stress and strain distribution in specimen with large cross-section area is of non-equilibrium at the beginning of wave propagation through the specimen, and it tends to be equilibrium after several repeats of wave propagation. The equilibrium of stress and strain depends also upon the cross-section area of specimen. The smaller the cross-section area is, the more quickly reaching the equilibrium of the distribution of stress and strain is. Further analysis shows that the sum of the incident wave and reflected wave is not equal to the transmitted wave. It also shows that the phase difference of the waves depends on the length of the specimen. Hence, when the length of specimen exceeds a certain value, the experiment could not provide acceptable results. The simulation results of wave propagation with regard to the different break position, cross section, length and modulus of specimen show that the break of specimen will cause fluctuation in both transmitted and reflected wave, and the frequency and magnitude of which depends on the break position of specimen. In addition, when the cross-section of specimen decreases, transmitted wave becomes weaker, and the stress in specimen greater and the specimen is easier to break. The length of specimen directly influences the shape, strength and width of the transmitted and reflected waves. The longer the specimen is, the weaker the transmitted wave and the harder specimen to break. With the increase of the modulus of specimen, the strength of transmitted wave increases and more time is needed to break the specimen.Finally, the tensile impact process of filament yarns is simulated with three aspects. First, the statistical distribution of the tensile strength of a single filament is considered in the simulation of filament yarns. In other words, the broken possibility of yarns under certain stress levels are determined by a statistical distribution model and then the cross-section area and stress of the yarn is modified. Second, thecorrelation between the experimental results and the simulated ones is evaluated. Third, the tensile impact process of carbon fibers and PVA ones are simulated. The transmitted wave, reflected wave and the stress-strain curve of the specimen are compared to experiment ones to verify the accuracy of simulation. Furthermore the effect of strain rate on the tensile impact test is analyzed via adjusting the strength of the incident wave. The simulation results show that the obtained transmitted wave, reflected wave and the stress-strain curve of the filament yarns agree well with the experimental results, although the maximum stress of simulation value is somewhat lower than the experimental ones, especially for PVA filaments. It could be attributed to the stress wave transmitted by the breoken filaments, which is neglected in the simulation. The simulation results under different strain rates show that the effect of strain rate depends on the strain rate sensitivities of filament material. For the insensitive materials, the strength of transmitted wave keeps unchanged while the increasing rate of stress increases and the break time decreases. For sensitive ones, the increasing rates of transmitted wave and stress both increase with the strain rate, the time to break is related to the integrated effects of sensitivity to strain rate of the material and the range of strain rate. In general, the time to break decreases when the strain rate increases.