Finite deformation plasticity with strain induced anisotropy and shear banding

The Numerical Analysis of the Phenomena of Superficial Hardening of the Hot-Work Tool Steel Elements / Analiza Numeryczna Zjawisk Przypowierzchniowego Hartowania Elementów Ze Stali Narzędziowej Do Pracy Na Gorąco

“…It can be claimed that in the numerical simulation of such hardening the fact that transformation plasticity is included in the model of mechanical phenomena brings about the changes in obtained results [10,11,16]. The phase transformations significantly effect on the changes of the temporary stresses (Fig.…”

“…during heating process -austenitization, cooling -austenite to pearlite or bainite in model are calculated by JM formula. The changes of content of martensite are defined by the empirical kM equation [3,13,23,24]: (7) where is maximal phase fraction for established cooling rate estimated on the basis of CCT diagram, b(t s ,t f ) and n(t s ,t f ) are coefficients calculated assuming the initial fraction ( s (t s )=0.01) and the maximum value of fraction ( f (t f )=0.99), A η is the fraction of forming austenite after heating, m is a constant from experiment; for considered steel m = 3.5, the start temperature of martensite transformation amount M s =548 k, and final temperature of transformation is equal M f =123 k [14,16].…”

“…Therefore, in the modeling of mechanical phenomena the use of the models of elastic-plastic materials is required. Additionally, to ensure the reliability of the results of numerical simulations of mechanical phenomena, except thermal, structural and plastic strains the transformation induced plasticity should be taken into account [3,[12][13][14][15][16][17][18].…”

The numerical model prediction of phase components and stresses distributions in hardened tool steel for cold work

“…They most often focus on analysing phase transformations during cooling and disregard stresses that are generated in this process. Transformation plasticity occurring in heat treatment (in particular during hardening) are also frequently ignored [28][29][30][31][32][33].…”

Kinetics of oriented crystallization of polymers in the linear stress-orientation range in the series expansion approach

“…Equation (1) in the integral form reads (Equation (2)): (2) where the kinetics and the degree of the transformation are determined by the temperature -and orientation -dependent rate function K and its history. Let us observe that in this discussion an analogy appears with the concept of the development of the micro-shear bands contribution in modeling of the deformation mechanisms in polymers and metals [67,68]. The rate function in Equations (1) and (2) expresses by the inverse of the observable crystallization halftime, K(T,f a ) = (ln2) 1/n /t 1/2 (T,f a ), determined for quiescent crystallization at fixed temperature T and orientation f a [46,47].…”