Influence of impact velocity on transition time for V-notched Charpy specimen*

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1 [ 溶接学会論文集第 35 巻第 2 号 p. 80s-84s (2017)] Influence of impact velocity on transition time for V-notched Charpy specimen* by Yasuhito Takashima** and Fumiyoshi Minami** This study investigated the influence of impact velocity for the V-notched Charpy specimen on the transition time, t T, which is defined as the time when the kinetic energy is equal to the deformation energy of the specimen. The t T indicates the point in the response after which inertial effects diminish rapidly. In this study, dynamic stress/strain fields in the V-notched Charpy specimen were numerically analyzed by means of three-dimensional dynamic explicit finite element (FE) analysis. This analysis considered the effect of high-speed strain rate on the flow stress and the increase in temperature during impact loading. The contact problem between the specimen and the striker of Charpy testing machine was solved using the Hertzian contact theory. This FE-analysis shows that the t T decreases slightly with increasing impact velocity over the range from 1 to 10 m/s. The deformation energy increases more rapidly than the kinetic energy with increasing impact velocity. The increase in the deformation energy leads to shorter t T. The t T depends on the strength class of steels. The t T decreased with decreasing in strength of steels, because of the reduction of kinetic energy. Key Words: Charpy impact test, Dynamic finite element analysis, Inertial force, Notch toughness, Structural steels 1. Introduction Charpy impact tests are widely used for evaluating toughness of materials and welds. The high-speed loading provides an inertial force in the specimen and deteriorates toughness of steels. According to the results measured by the instrumented Charpy testing machine, the load applied to the Charpy specimen exhibits significant oscillation by inertial force and reflected stress wave. This oscillation makes it difficult to determine a fracture initiation. The inertial effects on fracture are important to characterize material toughness by the instrumented Charpy impact test. Nakamura et al. 1) introduced the concept of the transition time, t T. The t T indicates the point in the response after which inertial effects diminish rapidly, for pre-cracked three-point bend specimen used for fracture toughness test. The t T is defined as the time when the kinetic energy is equal to the deformation energy of the specimen. After t T seconds passed, the inertial effect on brittle fracture can be neglected and toughness value can be evaluated by quasi-static manner. Koppenhoefer et al. 2) reported that the t T depended on the impact velocity for a pre-cracked Charpy specimen. On the other hand, the V-notched specimen is usually employed for the Charpy impact test. Understanding of the impact velocity effect on the t T for the V-notched specimen is important to evaluate the inertial effect on the result of Charpy impact test. The impact velocity varies with the striker angle from 3 m/s to 6 m/s for the Charpy impact test. In this study, the influence of impact velocity on the t T was investigated for the V-notched Charpy specimen. The kinetic and deformation energies were calculated by means of a dynamic analysis in order to evaluate the t T. 2. Numerical analysis of transition time 2.1 Dynamic finite element analysis of impact behavior of Charpy specimen Dynamic stress/strain fields in the Charpy specimen were numerically analyzed by means of three-dimensional dynamic explicit finite element (FE) analysis. The three-dimensional FE code Abaqus/Explicit Ver-6.12 was used in this study. The time increment used in the explicit analysis was smaller than the stability limit satisfying the Courant Friedrichs Lewy condition. The configuration of the Charpy specimen is shown in Fig. 1. The specimen has a standard V-notch with a depth of c = 2 mm and a root radius of = 0.25 mm. The three-dimensional mesh of the FE model is shown in Fig. 2. Because of the symmetry of the specimen, only one-quarter of it was modeled. Eight-node elements with eight Gaussian integration points were used in the FE analysis; the smallest element near the notch root had dimensions of 0.05 mm 0.05 mm 0.2 mm. * Received: ** Member, Joining and Welding Research Institute, Osaka University Fig. 1 V-notched Charpy specimen.

2 溶接学会論文集 第 35 巻 (2017) 第 2 号 81s Striker (3D shell elements) Impact velocity: 0.5 m/s to 10 m/s B/2 = 5 mm W = 10 mm x z y S/2 = 20 Anvil (3D shell elements) Fig. 2 Mesh division of Charpy specimen (one-quarter model). Table 1 Mechanical properties used for FE analysis. Y (MPa) T (MPa) Y.R.= Y / T T (%) YP YP Y: Yield stress, T: Tensile strength, T : Uniform elongation Table 2 Thermal constants used for FE analysis. Specific Thermal Coefficient of Density, heat, C conductivity, linear expansion, (kg/mm 3 ) (J/kg K) (W/K mm) L (1/K) The mechanical properties of steels used for the FE analysis are listed in Table 1. Two strength classes were employed. The one is 400 MPa yield strength class (YP400), and another is 800 MPa yield strength class (YP800). This analysis included the effect of the strain rate on the flow stress and the increase in temperature during impact loading. Fully coupled thermal stress analysis was conducted together with the dynamic explicit analysis. Under the impact loading conditions, high-speed straining adiabatically generates heat. In this analysis, it was assumed that 90% of the plastic work was transferred to heat 3). The thermal constants adopted in this analysis are given in Table 2. The rate-dependent elastic plastic material behavior of the specimen was considered in the FE analysis. The effect of the strain rate on the tensile properties was evaluated using the strain rate temperature parameter R proposed by Bennett and Sinclair 4). The yield stress Y and tensile strength T are plotted in Fig. 3 with respect to the parameter R used in this analysis. The uniform elongation T was assumed to be independent of the strain rate and the temperature. In the FE analysis, material hardening was modeled based on Swift s power law as Y {1 ( p / )n } (1) where and p are the equivalent stress and equivalent plastic strain, respectively; n is the strain hardening exponent; and Fig. 3 by is a material constant. According to Eq. (1), T and T are given T = Y (n/ ) n exp( n) (2) T = exp(n ) 1 (3) Eqs. (2) and (3) were used to determine the values of n and from Y, T, and T (= 20% or 7%) under various strain rate and temperature conditions. The global response of impact load to Charpy specimen depends on the contact stiffness between the specimen and striker 5). This analysis considered the contact of the specimen with the striker and anvil. The contact problem was solved using the method based on the Hertzian contact theory 5). The striker and anvil were modeled as 3D shell elements, as shown in Fig. 2. The contact pressure of the striker with the specimen is defined as 6) where Yield stress Y and tensile strength T plotted against strain rate temperature parameter R. 2 1 E 2 P ln E R 1 R 2 (4) 2 2P 1 R 1 R 2 is the depth of the indentation and R 1 and R 2 are the radii of the contact body, respectively. In this analysis, the radius of the striker tip (= 2 mm) was adopted as R 1, and R 2 = was assumed for a specimen with a planar surface. In this study, the striker of the testing machine and the specimen are composed of steel. Thus, the Young s modulus E and Poisson s ratio 206,000 MPa and 0.3, respectively. The dynamic explicit analysis was conducted taking into account the contact pressure evaluated by Eq. (4). The vertical displacement of the nodes coming into contact with the anvil was fixed. In this analysis, it was assumed that there was no friction between the specimen and the striker and anvil, but the reaction force was considered under the contact condition. This numerical model for the global response of impact load was validated by means of comparison with experimental results obtained by the instrumented Charpy impact test 5). The impact velocity was employed from 0.5 m/s to 10 m/s. The are

3 82s 研究論文 TAKASHIMA et al.: Influence of impact velocity on transition time for V-notched Charpy specimen previous study by the authors 5) reported that the velocity of the striker was kept constant during the Charpy impact test. In this study, the velocity was assumed to be constant. 2.2 Analysis of transition time for Charpy specimen The t T indicates the point in the response after which inertial effects diminish rapidly. This study calculated the t T for the V-notched Charpy specimen as the elapse time after impact when the kinetic energy is equal to the deformation energy of the specimen. The kinetic and deformation energies of the specimen were calculated by using the dynamic explicit FE analysis. In this study, the elastic plastic strain energy was defined as the deformation energy U. The dissipation of energy by friction energy and others except the plastic deformation of the specimen was not considered in this analysis. The external work applied to the specimen was converted to the kinetic and deformation energies, based on the law of the conservation of energy. Fig. 5 Kinetic and deformation energies as a function of time at impact velocity of 5 m/s. 3. Dynamic response of kinetic and deformation energy The response of impact load subjecting to the V-notched Charpy specimen is shown in Fig. 4. The value of impact load was calculated from the reaction force at the reference node of the striker in the FE analysis. The load-point displacement means the displacement at the reference node of the striker. The impact load oscillated over time. The oscillation of impact load was significant in the early loading stage. The amplitude of the load oscillations decreased with time. In the early loading stage, the difference in the oscillation of impact load is not found between YP400 and YP800. Figure 4 shows the numerical result by the dynamic analysis for an elastic material model, in which the E and are 206,000 MPa and 0.3, respectively. The numerical results indicate that the plastic deformation occurred before the second peak of the oscillation. Fig. 6 Influence of impact velocity on kinetic energy as a function of time. Fig. 7 Influence of impact velocity on deformation energy as a function of time. Fig. 4 Impact response of load displacement curves at impact velocity of 5 m/s. The evolutions of the kinetic and deformation energies are shown in Fig. 5. The time t in the vertical axis means the elapse time after the impact of the striker upon the specimen. The kinetic energy oscillated over the time. On the other hand, the deformation energy continued to increase. The kinetic energy was larger than the deformation energy in the early loading stage.

4 溶接学会論文集 第 35 巻 (2017) 第 2 号 83s The influence of impact velocity on the kinetic energy is shown in Fig. 6. At impact velocity of 1 m/s, the kinetic energy is quite small. The kinetic energy increases with increasing impact velocity. The maximum value of the kinetic energy at impact velocity of 10 m/s is approximately four times larger than 5 m/s. The kinetic energy is proportional to the square of the velocity. The influence of impact velocity on the deformation energy is shown in Fig. 7. The deformation energy increases with increasing impact velocity. Because the increase in impact velocity causes large deformation in the Charpy specimen at the same time, the deformation energy increases. The deformation energy at the same time is proportional to the impact velocity. 4. Effect of impact velocity on transition time The evolution of the energy ratio after impact for the V-notched Charpy specimen is shown in Fig. 8. The transition time t T is equal to ms for the Charpy specimen in the 5 m/s analysis. This value is approximately 13.5W/c 1, where c 1 is the stress wave speed (= 5120 m/s) and W is the width of the specimen (= 0.01 m). This agrees well with the numerical results Fig. 8 Kinetic-to-deformation energy ratio for V-notched Charpy specimen at impact velocity of 5 m/s. Fig. 10 Comparison of kinetic energy for V-notched Charpy specimen of YP400 and YP800. reported by Koppenhoefer et al 2) and Norris 7). This time means that stress wave roughly three times traverses of the span of the specimen. The numerical results of the t T for the V-notched Charpy specimen are plotted in Fig. 9. At impact velocity below 1 m/s, there is no influence of impact velocity on the t T. The t T decreased with increasing impact velocity over the range from 1 to 10 m/s. The numerical results shown in Figs. 6 and 7 indicate that the deformation energy increases more rapidly than the kinetic energy with increasing impact velocity. Therefore, rapid loading decreases the t T. In Fig. 9, the t T for the specimen of YP400 is shorter than that of YP800. The lower strength material is easy to deform plastically. Norris 7) reported that the kinetic energy was lost in plastic deformation. The kinetic energy of the Charpy specimen of YP 400 is compared with YP800 as shown in Fig. 10. As compared with YP800, the kinetic energy for the Charpy specimen of YP400 is small. Because of the reduction of kinetic energy, the t T decreased with decreasing in strength of steels. 5. Conclusions Fig. 9 Influence of impact velocity on transition time for V-notched Charpy specimen. The influence of impact velocity on the transition time, t T for V-notched Charpy specimen was investigated. It was found that the t T decreased with increasing the impact velocity over the range from 1 to 10 m/s. The three-dimensional dynamic explicit finite element analysis of the Charpy specimen showed that the kinetic and deformation energies increase with increasing impact velocity. The numerical results indicated that the kinetic energy of the Charpy specimen is approximately proportional to the square of the impact velocity, and the deformation energy is approximately proportional to the impact velocity. The deformation energy increases more rapidly than the kinetic energy with increasing impact velocity. The increase in the

5 84s 研究論文 TAKASHIMA et al.: Influence of impact velocity on transition time for V-notched Charpy specimen deformation energy leads to shorter t T. The t T depends on the strength class of steels. The t T decreased with decreasing in strength of steels, because of the reduction of kinetic energy. Reference 1) T. Nakamura, C.F. Shih and L.B. Freund: Analysis of a Dynamically Loaded Three-Point-Bend Ductile Fracture Specimen, Eng. Fract. Mech (1986) ) K.C. Koppenhoefer, R.H. Dodds: Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens, Nucl. Eng. Des. 162 (1996) ) G.I. Taylor: The Latent Energy Remaining in a Metal after Cold Working, Proc. Roy. Soc. London. 143 (1934) ) P.E. Bennett, G.M. Sinclair: Parameter representation of low-temperature yield behavior of body-centered cubic transition metals, Trans. ASME, 88 (1966) ) Y. Takashima, T. Handa, F. Minami: Three-Dimensional Dynamic Explicit Finite Element Analysis of Charpy Impact Test, Mater. Sci. Forum. 879 (2017) ) W. Goldsmith: IMPACT The theory and physical behaviour of colliding solids, Edward Arnold Ltd., London, (1960). 7) D.M. Norris: Computer Simulation of the Charpy V-Notch Toughness Test, Eng. Fract. Mech. 11 (1979)