A mathematical model for the formation and development of defects in metals

Effect of hardening friction treatment with hard-alloy indenter on microstructure, mechanical properties, and deformation and fracture features of constructional steel under static and cyclic tension

“…Plastic deformation of metallic materials is accompanied by the formation of fracture microdefects in the form of micropores and microcracks, leading to the formation of a fracture crack at a certain stage of their development. In the mechanics, the process of the evolutionary accumulation of microdamage is described by phenomenological cumulative models (e.g., [25][26][27][28]). The basic conceptual and calculation parameter in the majority of the models is the damage ω, which is assumed to be ω=0 prior to deformation and becomes ω=1 by the moment a fracture crack appears.…”

Improved ductile fracture criterion for cold forming of spheroidised steel

“…Eqs. (23) and (24) for I 4 and I 5 were found to be functions of ε θf and ε zf . If ε θf and ε zf exhibit linear relationship, then I 4 and I 5 will also have linear relationship:…”

“…Continuum damage mechanics techniques have also been used to predict ductile fracture [17,18]. Kolmogorov and coworkers have introduced a phenomenological metal fracture model, which is used in practice of the metal forming in Russia [19][20][21][22][23][24][25][26][27][28][29][30]. Shabara et al [31] have assessed six widely recognised ductile fracture criteria utilising the experimental data from the cold upsetting of spheroidised steel specimens.…”

Numerical Simulation of a Class of Three‐Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method

“…Many researchers [10][11][12][13][14][15][16][17][18][19][20] studied the dynamics of three dimensional Kolmogorov model with different type of functional response in theory. They found some chaotic dynamics [13,[18][19][20][21][22][23] of the three-dimensional Kolmogorov model.…”