ESTIMATION OF DEGRADATION OF STRENGTH PROPERTIES
OF A MATERIAL OF STRUCTURES INTENDED FOR A LONG
SERVICE LIFE USING A COMBINATION OF MATHEMATICAL
MODELS AND "PRACTICABLE" MEASUREMENTS
V. I. Makhnenko
E.O.Paton Electric Welding Institute
Kyiv, Ukraine
ABSTRACT. Using non-destructive methods for estimation of degradation of strength properties of a
material of structures intended for a long-time operation at high temperatures, in aggressive
environments or under radioactive radiation is very important for prediction of the residual safe life of
such structures. This is especially important for the cases where the life of the structures is close to the
design service limit. The search for such methods is a real challenge, as they are very helpful for
solving the problems associated with prevention of accidents and extension of service life. The paper
considers a number of approaches based on a combination of mathematical models of degradation of
strength properties of structural steels under certain service conditions with practicable measurements
of variations in the corresponding physical properties of a material, correlating with the degree of
degradation of the strength properties.
INTRODUCTION
There are many structures in operation at present (including welded ones), the
design service limit of which is 40-60 years. Naturally, after 30-50 years of being in
service, while they are still in good condition exteriorly, nevertheless their safe further
operation up to the design service limit and the possibility of extension of their life are the
issues which are of great concern both to the public and to the corresponding specialists.
Such structures include bridges, main pipelines, power reactor casings, large storage tanks,
etc. These structures are expensive, and their unforeseen accidents involve high losses.
Therefore, estimation of actual condition of such structures is of a high practical
importance.
The latter requires appropriate monitoring of strength properties of structure
materials, especially in the cases where service conditions are associated with certain degra-
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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dation effects on these properties (intercrystalline corrosion, radiation, temperature aging,
hydrogen saturation, etc.). The use of traditional approaches related to tests of standard
specimens is far from being readily realizable on a structure in operation, even with the
archive information or witness specimens available. The absence of the latter adds
complexity to the problem. An ideal solution to this problem could be the use of nondestructive testing methods to determine actual values of the required strength
characteristics of a material. There are certain advances in this area [1, etc.]. Success in
prediction of the degree of degradation of a material using non-destructive measurements
was achieved in the cases where degradation was related to dislocations, porosity,
submicrocracks and other defects accumulated in the material, which could be measured
using a combination of up-to-date electromagnetic and acoustic methods with microhardnes
measurements [2]. This concerns the material degradation associated with accumulation of
fatigue damages, intercrystalline corrosion and, to a certain extent, thermal aging. A more
difficult problem is to predict changes in resistance of the material to microfractures (e.g.
microcleavage) caused, in particular, by migration of phosphorus under the radiation effect
at a mass fraction of phosphorus in casing steels equal to less than 0.01 %. Such effects are
characteristic of strength properties of materials, such as toughness fracture KIC, without
which the estimation of safe life of structures by the up-to-date methods is impossible in
many cases.
Unfortunately, detection of such microscopic changes in structural materials by the
non-destructive methods and their quantitative interpretation at a required accuracy in terms
of fracture resistance seems hardly feasible so far, despite some attempts made to derive
non-existent dependencies, such as the dependence of the following type:
(1)
where Y is the desired hard-to-measure characteristic, e.g. KJC, and Xj is the vector
of characteristics which are "easy-to-measure" by the non-destructive methods.
In a number of cases a more flexible approach is that based on a combination of
appropriate mathematical models and practicable measurements.
For example, for the above case of radiation embrittlement of the nuclear reactor
casing steel, it is possible to develop on the experimental basis the dependence
(mathematical model) of KJC upon the degree of radiation (fluence F) for a material of a
specific chemical composition and microstructure, and then measure the F value with a
sufficient accuracy during operation by the non-destructive methods. Therefore, this allows
following the kinetics of the required KJC value. Unfortunately, this approach is not always
feasible, considering high costs of development of the said model: KIC =f(F)9m view
of actual chemical and microstructural states of the "hot spots" material of a specific object.
The more realistic approach is that based on quantitative data on such characteristics as
microhardness, elasticity modulus, yield stress, impact toughness (KCV) and
microstructure, evaluated experimentally (possibly, by destructive methods) on the "hot
spots" material of a structure. Combined with the chemical composition data, this approach
allows development of relatively simple models for K1CMany such models are known in the art, which is indicative of their limited
application fields. To illustrate, consider the following simple model from [3]:
KK =
P'TsEl-vln(l-W
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(2)
where p is the microstructure parameter, TS is the shear yield stress, E is the
elasticity modulus, vis the Poisson's ratio and !Pis the reduction in area of the material in
tensile fracture. The p, TS, E and *F values can be determined by quite practicable
measurements (on samples of small sizes or by non-destructive methods), which is
especially important for sufficiently ductile materials and samples of large thickness (50100 mm) required to determine KIC. Figure 1 shows results of application of dependence
(2) with variable p, Ts and *Ffor characteristic structural steels after different treatments. It
can be seen that model (1) is in good agreement with the experimental measurements of
KK? , although in some cases the probability exists of substantial deviations (for steel 40X
at KIC « 50 — 70MTla V M ). It can be shown that in a case where steel is exposed to
radiation at a temperature below 300 °C, where coarse macrostructure remains almost
unchanged (p « const), TS grows and V decreases just slightly, it is difficult to obtain from
formula (1) a dramatic decrease in fracture toughness Klc associated, for example, with
diffusion of phosphorus, mentioned above, leading to a decrease in strength of the grain
boundaries, etc. [5]. In other words, characteristics p, Ts, E, !Pand v are insufficiently
sensitive to the effect of phosphorus on materials (casing steels) exposed to radiation,
whereas the KIC value is sufficiently sensitive to this phenomenon.
This example shows that with the non-destructive methods of measuring mechanical
properties of materials, the vector of the measured parameters X^ according to (1), should
be sufficiently sensitive to physical changes in the materials, which determine the desired
hard-to-measure characteristic T(e.g.
DESCRIPTION OF THE APPROCH PROPOSED
In this connection, in terms of estimation of the value of KIC m the "hot spots"
zones of steel structures which have been in service for a long time, worthy of attention are
the methods which are based on practicable measurements and sufficiently profound
mathematical models, allow for physics of probable local changes in a material and are
responsible for the value of KIC. Description of one of such methods is given below.
Here the use is made of the results of studies [4, 5].
Considered is a specimen for standard tensile or three-point bending tests intended
for estimation of K1C. The stressed state in the zone near the crack apex (Fig. 2) is
unambiguously determined by the specimen loading conditions which, in turn, allow the
stress intensity factor KIC to be determined from standard dependencies [3]. Polycrystalline
11
A-/
a-2
• -3
31,0
31,0 46,5
62,0
K^MPa-VST
FIGURE. 1. Calculated K%! and experimental
40X.
values for steels: 1 - 4340; 2 - 45KhN2MFA; 3 -
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FIGURE 2. Prediction KIC (T) curve based on Margolin's probabilistic model.
material of the specimen is assumed to be a set of elementary cells with size p
corresponding to a mean grain size of the polycrystalline material. This parameter can be
determined by non-destructive methods.
The following local criterion of brittle fracture was assumed to hold for a cell [4, 5]:
(3)
where a/ is the maximum principal stress and Od is the effective strength of
initiation of cleavage microcracks in the given cell. The latter is a stochastic value, and the
three-parameter Weibull distribution is used to describe the distribution function of this
value:
-a.do
(4)
where P(&d) is the probability that the minimum strength of brittle fracture by the
above mechanism in the elementary cell is lower than od.
ado, od and rj are the Weibull parameters. In dependence (3) mT(T) allows for the
temperature effect. It is suggested in [6] that m(T) should be calculated as follows:
mT(T)=ffy(0)-<ry(T]-m0
(5)
where <jy(T) is the yield stress of the material at temperature T, ay(0) is the same at
temperature T ~ 0, and m0 is determined experimentally.
= S0/Sc(K)
(6)
where Sc(K) is the critical brittle fracture stress, K = \dspeq is the Odquist
parameter, d£gq is the increment of the equivalent plastic strain, and So = Sc(K = 0).
The 0y(T) and SC(K) values are estimated on specimens of small sizes [5]. The
stressed state in all elementary cells of the zone near the crack apex at a given value of Kj
being known, it is possible to calculate the probability of brittle fracture of the specimen
with a crack at temperature T:
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J
dO
Pf(K,\=l-eXp
I M .
v
= 1- exp
(7)
| ~
where aw -1 ^[a] -odo) >
is the Weibull stress and M is the number of the
elementary cells in a volume under consideration (Fig. 2).
In this case, according to (3), if a\ < ado or o] < SC(K), the cell will have a 100 %
probability of non-fracture, and, according to (7), a] -odo =0 for such "z". This allows the
M value to be limited to a substantial degree, as the elementary cells make a zero
contribution to the probability of fracture at some distance from the apex. Naturally, the
thicker the specimen, the higher the M value.
The use of the plane deformation hypothesis [5] makes it possible to consider the
stress state only in plane x, y (Fig. 2). The M value decreases B/p times, but the
corresponding factor should be allowed for before the sum in (7). Here B is the specimen
thickness and p is the mean size of the elementary cell.
In the model under consideration the Weibull distribution parameters ado, ad and r|
can be determined on relatively small specimens with a crack, at low temperatures leading
to brittle fracture.
Therefore, the method for estimation of Klc of the "hot spots" material of a structure
in operation, which normally requires that specimens of substantial thickness be tested by
standard methods, is reduced to testing specimens of small sections taken directly from a
degraded structural material in order to obtain the calculation model parameters, i.e. values
ay(r), SC(K), odo, mo, p, od , and //. Then for different values of temperature T and
specific thickness B, as well as a preset load acting on a standard specimen, i.e. at preset KI,
the stressed state near the crack apex in each elementary cell is numerically estimated, and
the probability of brittle fracture P/K])\ T is calculated from (7).
Figure 3 shows an example of such calculations for the radiation embrittled
specimen of casing steel 15Kh2NMFA with thickness B = 50 mm against the experimental
data [5]. Characteristics cry(T), SC(K)., odo, £7, ad and r/ required for the calculations
were obtained by processing the data of testing the small-size specimens of the above steel
after equivalent radiation.
-200
-100
T,°C
FIGURE 3. Curves KIC(T) calculated by the probabilistic model for specimens of thickness B = 50 mm of
casing steel in an embrittled condition compared to experimental data.
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It can be well seen that the calculated and experimental data are in good agreement.
CONCLUSION
As follows from the above-said, the combination of practicable measurements
(including by the non-destructive methods) of mechanical properties in the "hot spots" zone
of a structure with sufficiently profound mathematical models, reflecting physics of a
corresponding type of fracture, allows a considerable widening of the possibilities of
generating actual data on the degree of degradation of a material, such as decrease in brittle
fracture resistance.
REFERENCES
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Acoustic Waves Measurements. QNDE V. 2IB, 2001, Editors D.O.Tompson,
D.E.Chimenti, p.p. 1629-1637.
2. Milman Ju.V., Galanov B.F., Chugunova S.I., Plasticity Characteristic Obtained
Through Hardness Measurement // Acta Metall. Mater. - 1993. - 71, # 9. - P. 25232532.
3. S.T.Rolfe, J.M.Barson. Fracture and Fatigue Control in Structures. Application of
Fracture Mechanics. - 1977, Prentice-Hall, New Jersey, 560 p.
4. Beremin F.M. A Local Criterion for Cleavage Fracture of a Nuclear Pressure Vessel
Steel / Met. Trans. - 1983. - 14A. - P. 2277-2287.
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for Reactor Pressure Vessel Steels: I. Brittle Fracture Toughness Predictions // Int. J.
Pres. Ves. Piping. - 1999. - 76. - P. 715-729.
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