Application of the Theory of Dimensionalities to the Evaluation of the Influence of Corrosive Media on the Long-Term Str
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APPLICATION OF THE THEORY OF DIMENSIONALITIES TO THE EVALUATION OF THE INFLUENCE OF CORROSIVE MEDIA ON THE LONG-TERM STRENGTH OF MATERIALS D. A. Kulagin and G.-Yu. Krist
UDC 539.376
The methods used for the investigation of long-term strength are based on the relations of phenomenological theories generalizing significant amounts of empirical data. This is explained by the complexity of the physical fracture processes on the micro- and mesolevels of structures. It is thus an extremely difficult problem to get a physically grounded model with relatively small number of experimentally measured parameters, which seems to be quite important because the experimental investigation of long-term strength is connected with significant technical and economical difficulties. This is even more urgent for the investigation of the influence of corrosive media on the long-term strength of materials. In deducing phenomenological relations, the researcher chooses the most significant parameters of the problem (e.g., time, stresses and/or strains, etc.) and constructs the relationships for these quantities on the basis of the experimental data. In the present work, we demonstrate some advantages of the analysis of dimensionalities used to establish regularities in some limiting cases. The form of these regularities can be useful for subsequent generalization and formulation of correct and adequate phenomenological relations. Long-Term Fracture We consider the problem of tension of a rod under a constant stress σ0 . If we assume that the time to fracture t* is a function of the acting stress, then we can select the following dimensional parameters: t*, σ 0 , and σu . Here, σu is the short-term ultimate stress at testing temperature. However, the defining relation must contain at least one more dimensional parameter. Otherwise, it is impossible to construct a dimensionless combination of the indicated three parameters. Assume that the missing parameter t0 has the dimensionality of time. Then we can construct two dimensionless combinations of the introduced parameters, namely, τ =
t* t0
and
s =
σ0 . σu
Hence, the required relation must have the form τ = f ( s ).
(1)
We now study the behavior of this relation as s → 0. It is clear that, as σ0 tends to zero, the parameter t* tends to infinity. In this case, the required relation can be represented in the following form (solutions of this type are called self-similar solutions of the second kind [1]): Institute of Mechanics at the Lomonosov Moscow State University, Moscow, Russia. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 117–119, March–April, 2005. Original article submitted October 9, 2004. 1068–820X/05/4102–0275
© 2005
Springer Science+Business Media, Inc.
275
276
D. A. KULAGIN
f ( s ) = s– n + o ( s– n),
n > 0.
AND
G.-YU. KRIST
(2)
Substituting this relation in (1), we get t* ⎛ σ0 ⎞ = ⎝ σu ⎠ t0
−n
.
(3)
It is easy to see that relation (3) agrees with the classical power-type relationship between the time to fracture and the lev
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