Constitutive modeling of trip steel and its application to the improvement of mechanical properties

Finite Element Modeling of Thermo-mechanical and Metallurgical Behavior of Type 304 Stainless Steel in Cold Strip Rolling

“…The detailed finite element formulation may be seen in the references. 9,10) The flow stress s of the strip within two phases of austenite and martensite may be represented by the mixed rule 4,5) : Where C g1 -C g5 , and C aЈ1 -C aЈ5 , taken from the references, 4,5) were described in Table 2.…”

“…Assume that the strain rate may be decomposed into the Where ė trans and ė v denote the phase transformation induced plastic strain rate and volume change rate due to phase transformation, respectively, which were taken from the references 4,5) and shown as follows: Parameters R and Dh, taken from the references, 4,5) may be found in Table 1. With respect to the high process speed in the tandem cold rolling process, ė trans and ė v may be neglected when comparing to ė p , which was verified from the comparison of mean values among these three components by FEM analysis.…”

“…Furthermore, a generalized rate form of Olson-Cohen model for the evaluation of the martensite evolution, which was function of plastic strain, temperature, and stress state, was proposed by Stringfellow et al 3) Then, a constitutive relationship defining the flow strength of the coexist of twophase composite was proposed. Recently, Tomita et al 4) further spread the generalized constitutive relationship by Stringfellow by taking the strain rate effect into account only in tension state; and the extensive application both in tension and compression state was made by Iwamoto et al 5) In the past, various numerical techniques have been applied to predict the metal flow and heat transfer occurring in the strip in rolling process, to a degree far beyond the scope that the elementary theories can cover. Among them, finite element (FE) model was especially successful with regard to revealing the most detailed aspects of the metal flow characteristics and thermal behaviors in rolling process.…”

“…1(a) and 1(b), respectively. n, ė y , and M, taken from the references, 4,5) are described in Table 1. The predicted fraction of martensite evolution was in good agreement with the measurements, as shown in Fig.…”

“…Note that Qϭse¯in the strip and Qϭ0 in the roll, when the roll deformation is purely elastic. Q l represents the latent heat discharged during phase transformation according to the references, 4 Where, f˙m, the rate of the fraction of martesite, was determined by finite difference method.In the strip and also in the roll, a large amount of heat is transported to the downstream by convection due to high processing speed. It is well known that when the convection term governs heat transfer more significantly than the diffusion term, solutions based on the standard Galerkin formulation are often corrupted by spurious node to node oscillations.…”