johnson-cook模型原始论文-1983-johnson-cook

HARDNESS GRAIN ELASTIC SIZE
___~
o.D%-0.150 d
PROPERTIES E (GPaJ 0.34 IGPal (GPa) I 207 0.29 200 0.29
ELASTIC MODULUS, POISSON’S
RATIO, Y E/2(1 + VI E/3(1 -2 Y i _”
Air Force Armament

Ahstrac-This paper considers fracture characteristics of OFHC copper, Armco iron and 4340 steel. The materials are subjected to torsion tests over a range of strain rates, Hopkinson bar tests over a range of temperatures, and quasi-static tensile tests with various notch geometries. A cumulative-damage fracture model is introduced which expresses the strain to fracture as a function of the strain rate, temperature and pressure. The model is evaluated by comparing computed results with cylinder impact tests and biaxial (torsion-tension) tests.
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G. R. JOHNSON Table I. Physical properties of OFHC
and W. H. COOK
copper,
Armco
iron and 4340 steel
HEAT TREATMENT TEMPERATURE -__ TIME AT TEMPERATURE tK) (MINUTES) e~OCKWELL~ (mm1 F-30 0.060-0.090 j -__ F-72 j c -30 < 0.010
HEAT, cp k/pi+, COEF.
MELTING TEMPERATURE,
cannot be accurately evaluated after necking occurs in the tensile specimen. While these data can be helpful in examining strength characteristics, fracture characteristics can be determined only by examining post-tested specimens as shown in Fig. 4. The photographs of Fig. 4 and the metallographic sections of Fig. 5 both show the relatively ductile fracture of the OFHC copper and Armco iron, when compared to the 4340 steel. In Fig. 5, voids are most evident in the Armco iron and some are present in the OFHC copper. The 4340 steel also shows some void formation at elevated temperatures. Quasi-static tensile data are shown in Fig. 6. The notched geometry specimens are identical to those used elsewhere and give a concentration of hydrostatic tension in the test specimen [6]. This is clearly shown in the data of Fig. 6. For a specified true strain, the stress (including hydrostatic tension) increases as the notch becomes more severe. It can also be seen that the presence of the hydrostatic tension significantly decreases the strain at which the material fractures. Figure 7 shows metallographic sections of the quasi-static tensile test specimens. The OFHC copper and Armco iron fail in a more ductile manner than the 4340 steel, as expected. The formation of voids is apparent in the unnotched OFHC specimen and all of the Armco iron specimens. No voids are evident in the 4340 steel specimens.
INTRODUCTION WHENMATERIALS are subjected to dynamic loading conditions such as high velocity impact, explosive detonation or metal forming operations, a wide range of strains, strain rates, temperatures and pressures may be experienced. In some instances there has been a tendency to distinguish “dynamic” material properties from “static” material properties. The underlying assumption is that the differences between the “dynamic” and “static” properties must be due to strain rate effects only. Often associated with high strain rates, however, are large strains, high temperatures and high pressures. Therefore, it is important that the effects of each variable be properly assessed, rather than assuming all distinguishing characteristics are due to strain rate alone. This paper considers fracture characteristics of OFHC copper, Armco iron and 4340 steel. A series of laboratory tests has been performed to determine the effects of strain rate, temperature and pressure on the strain to fracture. A cumulative-damage fracture model is developed and evaluated with an independent series of tests and computations. TEST DATA A description of the three materials is given in Table 1. All of the test specimens were fabricated from the same material stock and the heat treatment was always as specified in Table 1. The torsion test data are shown in Fig. 1. The torsion tester is described in Ref. [I] and the procedure for analyzing the data is given in Ref. [2]. Data for a wide range of other materials are presented in Refq. [3] and [4]. For the data in Fig. 1 the average shear strain, 7, is assumed to occur only in the thin test section, and to occur uniformly along that section. At the higher strain rates, however, there may be some localizations of strain due to adiabatic heating[2]. The average shear strains at fracture are clearly shown for the Armco iron and the 4340 steel. None of the OFHC copper specimens in Fig. 1 fractured due to rotational limitations of the torsion tester. Another shorter-gage, OFHC copper specimen was tested at 3 = 0.008 s-’ and it fractured at 7 = 8.7. Metallographic sections of three torsion specimens are shown in Fig. 2. The OFHC copper specimen appears to exhibit a strain localization near the center of the gage section. There are no voids evident in any of the sections. The tensile Hopkinson bar data are shown in Fig. 3. A representative Hopkinson bar apparatus and data for various materials are presented in [5]. The specific Hopkinson bar used for the data of Fig. 3 is located at the Air Force Armament Laboratory (AFATL) at Eglin Air Force Base. The elevated temperatures were obtained by surrounding the in-place test specimen by an oven such that the temperatures were applied for several minutes prior to testing. The true tensile strain in Fig. 3 is based on the assumption that there is uniform axial strain in the tensile specimen. The stress-strain data are shown only for relatively small strains because they