Irreversible deformation in a cubic metal on temperature change

  • K. M. Rusinko
  • I. M. Goliboroda
Article
  • 18 Downloads

Summary

Temperature swings applied to cubic metals and alloys result in temperature hardening and temperature aftereffects.

In particular, a series of temperature shocks applied under conditions where the upper temperature exceeds the threshold Tcr accelerates the creep (no temperature hardening then occurs), while in the opposite case, the creep is retarded (when both effects occur).

A model is proposed that gives unified equations for rapid plastic strain within yield theory, as well as for creep and the above effects.

The associated yield law is considered for an initially isotropic material showing linear translational hardening; the equation for the loading surface f is
$$f = ({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2})(S_{ij} - \alpha _{ij} )(S_{ij} - \alpha _{ij} ) - \sigma _y^2 = 0.$$
The parameterαij defining the center of the loading sphere is given by
$$dx_{ij} = Cd\varepsilon _{ij} - K(\lambda ,\tau )(\alpha _{ij} - \alpha _{ij}^ \cap )dt.$$
The tensor parameter α ij 0 , which is dependent on temperature and controls the thermal hardening, is defined by
$$d\alpha _{ij}^ \cap = L(q\alpha _{ij} - \alpha _{ij}^0 )dt.$$
The radius of the loading sphereαy is specified as
$$\sigma _y = \sigma _0 (\lambda )(1 + aI(t) - bQ(t)),$$
in which I(t) is the local peak stress function occurring in active loading and Q(t) is an isotropic measure for the thermostructural stresses arising on temperature change.

Keywords

Plastic Strain Peak Stress Stress Function Local Peak Active Loading 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    M. M. Myshlyaev, ‘Polygonized-structure creep,” in: Structure Imperfections and Martensite Transformations [in Russian], Nauka, Moscow (1972) pp. 194–233.Google Scholar
  2. 2.
    G. V. Vladimirova and V. A. Likhachev, “Temperature aftereffects in aluminum,” Fiz. Met. Metalloved.,24, No. 3, 556–562 (1967).Google Scholar
  3. 3.
    V. A. Likhachev and G. A. Malygin, “A study on creep at variable temperatures: review,” Zavod. Lab., No. 1, 70–85 (1966).Google Scholar
  4. 4.
    G. V. Vladimirova, V. A. Likhachev, and M. M. Myshlaev, “Temperature hardening and temperature aftereffects in creep in metals and allows,” Fiz. Met. Metalloved.,28, No. 5, 907–914 (1969).Google Scholar
  5. 5.
    K. N. Rusinko, Plasticity Theory and Nonstationary Creep [in Russian], Vishcha Shk., Lvov (1981).Google Scholar
  6. 6.
    T. W. Bailey, “Note on the softening of strain-hardening metals and its relation to creep,” J. Inst. Met.,5, 27–40 (1926).Google Scholar
  7. 7.
    E. Orowan, “The creep of metals,” J. West. Scotland Iron Steel Inst.,54, 45–53 (1946).Google Scholar
  8. 8.
    Hart, “Equations of state for inelastic metal strain,” Proc. ASME, Ser. D,98, No. 3, 1–11 (1976).Google Scholar
  9. 9.
    Ostrom and Lagneborg, “A creep model based on incorporating recovery and athermal slip,” ibid. No. 2, 21–34 (1976).Google Scholar
  10. 10.
    Miller, “A mathematical model for monotone and cyclic strain variation and creep based on inelastic-strain analysis, Part 1,” ibid. No. 1, 1–11 (1976).Google Scholar
  11. 11.
    Ponter and Lecky, “Definitive equations for time-dependent metal strain,” ibid. No. 1, 51–56 (1976).Google Scholar
  12. 12.
    Delf, “Comparative study of two theoretical models in terms of state parameters,” ibid.,102, No. 4, 11–22 (1980).Google Scholar
  13. 13.
    Merzer, “Use of generalized state equations for steady-state and transient creep,” ibid.,104, No. 1, 21–30 (1982).Google Scholar
  14. 14.
    Slavik and Santoglu, “Definitive models incorporating thermal loading,” ibid.,108, No. 4, 10–24 (1986).Google Scholar
  15. 15.
    N. N. Malinin and J. M. Khadjinsky, “Theory of creep with anisotropic hardening,” Int. J. Mech. Sci.,14, 235–246 (1972).Google Scholar
  16. 16.
    K. N. Rusinko, Features of Inelastic Strain in Solids [in Russian], Vishcha Shk., Lvov (1986).Google Scholar
  17. 17.
    Yu. I. Kadashevich, “Various forms of linear tensor relation in plasticity theory,” in: Researches on Elasticity and Plasticity [in Russian], No. 6 (1967), pp. 39–46.Google Scholar
  18. 18.
    Yu. I. Kadashevich and M. A. Kuz'min, “Describing viscoplastic yield in cyclically unstable materials,” Prikl. Probl. Prochn. Plastichn. Issue 12, 110–119 (1979).Google Scholar
  19. 19.
    V. A. Likhachev, G. V. Vladimirova, and M. M. Myshlyaev, “Hardening in aluminum on temperature steps during creep,” Fiz. Met. Metalloved.,29, No. 6, 1280–1287 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • K. M. Rusinko
    • 1
  • I. M. Goliboroda
    • 1
  1. 1.Lenin Komsomol L'vov Polytechnic InstituteUSSR

Personalised recommendations