Pure Bending for the Multimodulus Material Beam at Creep Conditions

The paper deals with the solution of pure bending of rectangular beam AK4-1T at constant temperature loaded constant bending moment. The research of construction for creep and long-term strength with the whole distribution pattern of stress until the beginning of destruction is considered. The numerical calculation of the problem is solved with the equations of the energy variant of the creep theory, as well as the solution continuation with respect to a parameter and the best parameterization, using three methods of numerical integration of ordinary differential equations: Euler method, Euler-Cauchy method and fourth-order Runge-Kutta method. The paper also considers the comparison of two methods for the solution of numerical results and a comparison of the numerical solutions with the experimental data as well.

Keywords

creep; fracture; specific dissipation power; damage parameter; method of solution continuation with respect to a parameter; the best parameterization; the system of differential-algebraic equations.

References

1. Rabotnov Ju.N. shape Polzuchest' jelementov konstrukcij [Creep Problems in Structural Members]. Moscow, Nauka, 1966. 752 p.
2. Kachanov L.M. shape Teorija polzuchesti [The Theory of Creep]. Moscow, Fizmatgiz, 1960. 455 p.
3. Lepin G.F., Bondarenko Yu.D. Creep of a Straight Beam Bending with the Damaging Material [Polzuchest' pryamogo brusa pri izgibe s uchetom povrezhdaemosti materiala]. shape Problemy prochnosti [Problems of Strength], 1970, no. 7, pp. 68-70.
4. Nikitenko A.F., Sosnin O.V. Bending of Beam with Different Characteristics of Creep in Tension and Compression [Izgib balki s raznymi kharakteristikami polzuchesti pri rastyazhenii i szhatii]. shape Problemy prochnosti [Problems of Strength], 1971, no. 6, pp. 67-70.
5. Sosnin O.V., Gorev B.V., Nikitenko A.F. shape Jenergeticheskij variant teorii polzuchesti [Energy Variant of the Creep Theory]. Novosibirsk, Institut gidrodinamiki SO AN SSSR, 1986. 95 p.
6. Gorev B.V. To Calculation for Transient Creep Beam Bending of Material with Different Characteristics in Tension and Compression [K raschetu na neustanovivshuyusya polzuchest' izgibaemogo brusa iz materiala s raznymi kharakteristikami na rastyazhenie i szhatie]. shape Dinamika sploshnoy sredy [Continuum Dynamics], 1973, vol. 14, pp. 44-51.
7. Gorev B.V., Klopotov I.D. Description of the Creep and Rupture of Beams Bending and Shafts Torsion by the Equations with Scalar Damage Parameter [Opisanie protsessa polzuchesti i razrusheniya pri izgibe balok i kruchenii valov uravneniyami so skalyarnym parametrom povrezhdaemosti]. shape Prikladnaja mehanika i tehnicheskaja fizika [Journal of Applied Mechanics and Technical Physics], 1999, vol. 40, no. 6, pp. 157-162.
8. Gorev B.V., Panamarev V.A., Peretyat'ko V.N. Energy Variant of the Creep Theory in Metal Forming [Energeticheskiy variant teorii polzuchesti v obrabotke metallov davleniem]. shape Izv. Vuzov. Chernaya metallurgiya [Sci. Iron and steel], 2011, no. 6, pp. 16-18.
9. Sosnin O.V., Gorev B.V., Nikitenko A.F. Justification of the Energy Variant of the Theory of Creep and Long-Term Strength of Metals [K obosnovaniyu energeticheskogo varianta teorii polzuchesti i dlitel'noy prochnosti metallov]. shape Prikladnaja mehanika i tehnicheskaja fizika [Journal of Applied Mechanics and Technical Physics], 2010, vol. 51, no. 4, pp. 188-197.
10. Formalev V.F., Reviznikov D.L. shape Chislennye metody [Numerical Methods]. Moscow, Fizmatlit, 2004. 400 p.
11. Shalashilin V.I., Kuznetsov E.B. Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics. Dordrecht, Boston, London, Kluwer Academic Publishers, 2003. 236 p.