Abstract
We propose a mathematical model of jumpwise deformation under conditions of deep cooling based on an analysis of the localized adiabatic heat release, inertial properties, and accumulated elastic energy of loading forces. The model enables one to give a qualitative description of the kinetics of intermittent flow of metals and establish quantitative estimates of the parameters of the jumps of strains, which are in reasonably good agreement with the experimental data and adequately describe the mechanical behavior of the material depending on the conditions of loading and deformation. We also consider the influence of various factors on the possibility of suppressing of the effect of mechanical instability of metals, which is of significant practical interest.
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Abbreviations
- T :
-
absolute temperature, K
- T 0 :
-
initial temperature, K
- ΔT :
-
increment of temperature in the zone of flow, K
- C :
-
stiffness of the specimen-machine system, N/m
- K :
-
effective modulus of the system, MPa
- ε,\(\dot \varepsilon \), and\(\ddot \varepsilon \) :
-
plastic component of strains, strain rate for this component, and acceleration, respectively
- σ Y :
-
yield limit of the material of the specimen, MPa
- σ0 :
-
initial stress corresponding to the beginning of a jump, MPa
- μ:
-
viscosity factor, MPa·s
- Θ:
-
strain-hardening coefficient, MPa
- α:
-
coefficient of linear thermal expansion, K−1
- E :
-
elasticity modulus, MPa
- c v :
-
specific heat capacity, J·m−3·K−1
- β p :
-
coefficient of transformation of the work of plastic deformation into heat
- k t :
-
coefficient of thermal softening, MPa·K−1
- τ c :
-
duration of a jump of strains, s
- t :
-
time, s
- m :
-
added mass, kg
- g :
-
gravitational acceleration, m/s2
- l :
-
length of a part of the specimen, m
- F :
-
cross-sectional area of the specimen, m2
- ω:
-
frequency of the exciting action, s−1
- ωλ :
-
natural frequency of the specimen-machine system, s−1
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Additional information
Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 41–52, January–February, 1999.
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Vorob’ev, E.V., Strizhalo, V.A. Development of low-temperature jumpwise deformation of metals and possibilities of its elimination. Strength Mater 31, 28–37 (1999). https://doi.org/10.1007/BF02509737
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DOI: https://doi.org/10.1007/BF02509737