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金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系, Blue brittleness is exhibited by some steels after being heated to an elevated temperature. Although at high temperature a given strain is associated with a lower stress level, at the temperature at which blue brittleness is observed there is a pronounced work-hardening effect. Furthermore, the temperature at which blue brittleness occurs is a function of the strain rate. Therefore, to improve the accuracy of numerical simulations of hot or warm working which utilizes the thermal softening of steels, a dynamic constitutive equation which can model the blue brittleness phenomenon is needed. In this paper we present such a constitutive equation, which has two parts : one models the ordinary constitutive relation and the other the phenomenon of blue brittleness. Unknown material constants in the equation are determined by a non-linear least-squares method from uniaxial impact and static compressive test results. The equation is then evaluated by comparing it to experiments over a wide temperature range.

金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系, In this paper, a dynamic constitutive equation that is applicable for impact loading and inverse loading was investigated. The numerical calculation was done for aluminum using finite difference method under the boundary condition of measured axial and angular velocities. The calculated stress and strain agreed well with the experimental ones under torsional and inverse torsional loadings about the strain rate of 40 l/s. The comparison of calculated result with experimental one for the combined loadings of impact tension and torsion was also performed, and the validity of this constitutive equation was verified. Moreover, the appearing yield points were discussed based on some simulations under two-stage combined loadings of tension and torsion.

金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系, A practical model of a temperature and strain-rate dependent dynamic constitutive equation for carbon steels is proposed. Unknown material constants involved in the proposed constitutive equation can be determined by the non-linear least squares method, which approximates ordinary-impact-test results with calculated values of elasto-plastic waves propagation analyses. In addition static stress-strain curves, longitudinal elastic modulus and yield stress, which are needed for elasto-plastic waves propagation analyses with the proposed constitutive equation, are expressed as a function of temperature. These results enable elasto-plastic waves propagation analyses under wide strain-rate and temperature ranges easily. The present paper has actually determined material constants involved in the proposed constitutive equation and compared the calculated results with measured ones. As a result, it has been confirmed that the proposed equation is applicable at a wide strain rate range and at a room temperature to less than one in which blue brittleness occurs.

金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系, Previously, we presented the determination method of a dynamic constitutive equation with strain- rate sensitivity from the results of an uniaxial longitudinal impact compression test. The proposed method could derive an appropriate strain-rate sensitive dynamic constitutive equation as a polynomial without consideration based on underlying material physics. However, the method needs a lot of test results over a wide strain-rate range. This paper presents the determination method of a dynamic constitutive equation from a few impact test results. The proposed method determines unknown coefficients involved in a polynomial that appears dynamic constitutive relations of a material by nonlinear least squares method. Furthermore, the proposed method determines the optimum degree of a polynomial constitutive equation by AIC (Akaike information criterion). This paper, further, presents the split Hopkinson pressure bar method using a stepped striker bar. The proposed method can obtain the relations between the dynamic stresses and strain-rates in a wide range from a single impact test.

金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系, This paper presents an easy determination method for the dynamic constitutive equations of materials with strain-rate sensitivity. The proposed method will easily determine a simple constitutive equation from the results of ordinary impact tests. Previously, the determination of dynamic constitutive equations is usually attempted from a metallographical or physical standpoint. Such attempts often need detailed consideration, and most of the derived equations become complex. Furthermore, the estimation of the involved unknown parameters in the equations is also difficult. If simple dynamic constitutive equations can be determined without especially physical considerations, the simulation for mechanical deformations caused by impact will become easy. Thus, this paper tries to determine dynamic constitutive equations as polynomials which can describe various curves and be easily treated. Polynomials approximate given data more precisely with increase in the number of the involved parameters. However, as the number of parameters increases, the calculation of the equations become more difficult. Furthermore, it is not necessarily appropriate that the equation fits measured data considerably precisely, because the measured data usually contain some errors. Therefore this paper proposes the determination method for dynamic constitutive equations based on an information criterion 'AIC'. The information criterion will evaluate the appropriateness of approximate equations and reveal the required minimum number of the parameters to be used. The proposed method demonstrates that 'AIC' will easily determine appropriate dynamic constitutive equations.

金沢大学高度モビリティ研究所 / 金沢大学理工研究域機械工学系

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s −1 . Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s −1 , the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s −1 , the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.