Influence of alloying elements on the strain rate and temperature dependence of the flow stress of steels
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INTRODUCTION
«˙ 0 5 rm b L n0 /MT
AT temperatures T & 0.3Tm (Tm 5 melting temperature in K), elastic-plastically deformed metallic polycrystals show a characteristic dependence of flow stress s on temperature T and strain rate «˙ according to thermally activated glide of mobile dislocations across short-range obstacles. The quantitative description of this correlation[1] demonstrates that at temperatures lower than the critical temperature T0, which is dependent on the strain rate, the flow stress s is additively composed of an athermal component sG (depending on temperature only in the same manner as the shear modulus G or Young’s modulus E) and a thermal component s*:
where rm 5 density of mobile dislocations; b 5 amount of Burgers vector; L 5 average distance of short-range obstacles; n0 5 frequency factor, which correlates with the Debye frequency; and MT 5 Taylor factor. DG(s *) is determined by the interaction energy of slip dislocations and the shortrange obstacles, which can be described by force-distance curves (F*, x curves), as shown in Figure 1. The area below the curve characterizes the free-activation enthalpy of the entire obstacle, DG0. If DG 5 DG0, no external force F*, and therefore no thermal flow stress, is neccessary for slip. In this case, Eq. [2] leads to
s 5 sG 1 s * 5 sG,0
G(T ) 1 s *(T, «˙ ) G(0 K)
[1]
The first component arises from the effect of long-range dislocation obstacles; the second is caused by short-range obstacles, which may be overcome by slip dislocations due to thermal fluctuations. The s * increases with decreasing temperature and increasing strain rate. At T 5 0 K, where the probability that thermal fluctuations occur becomes zero, s * shows its maximum value s *0 , which is independent of strain rate. II. THEORETICAL BACKGROUND The free activation enthalpy DG for thermally activated glide of mobile dislocations across short-range obstacles is correlated to the thermal flow stress s *, the strain rate «˙ , the temperature T, and the Boltzmann constant k by «˙ (T, s *) 5 «˙ exp [2DG(s *)/kT ] [2] 0
with ¨V. SCHULZE, Head of Laboratory of Materials Testing, and O. VOHRINGER, Head of Group Plasticity and Fracture, are with the Institut ¨ ¨ fur Werkstoffkunde I, Universitat Karlsruhe (TH), D-76128 Karlsruhe, Germany. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials-Part II,” held during the 1998 Fall TMS/ ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees. METALLURGICAL AND MATERIALS TRANSACTIONS A
T0 5
DG0 k ln («˙ 0 /«˙ )
[3]
as the critical temperature above which s * 5 0 is valid. At temperatures 0 K , T , T0, the thermally activated part of DG decreases, thus requiring a mechanical force F*, which rises to its maximum F 0* at T 5 0 K. Figure 1 shows that the F*(x) curves may be transformed to s*(v) curves with the activation volume v 5 b LD (D 5 effective thickness of the short-range obstacle)
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