**1. Introduction**

The era of nuclear energy in the world started in 1954 by putting into service the first nuclear power plant (NPP)—the Obninsk NPP with a channel-type reactor and power of 5 MW. Since then, leading countries of the world (the USSR-Russia, the USA, Great Britain, France, etc.) have come up with a whole spectrum of a new type of power supply—nuclear-powered.

extremely conditions, a high-loaded power-generating plants with use physical and

*Probability Modeling Taking into Account Nonlinear Processes of a Deformation and Fracture…*

Results of traditional researches and a standardization of strength and life time of NPP in the determined statement in Russia and abroad are both initial scientific baseline of normative documents on design and actual baseline of making of perspective methods of a reliability estimate, survivability, initiation, and evolution of accidents and disasters by risk criteria, and also of makings of new principles, technologies, and engineering complexes ensuring safety service of NPP. These are conditions that are scientifically grounded to prevent initiation of the emergency and disastrous situations and also to minimize probable losses at their initiation at

all stages of life cycle. Such situations within the limits of usual normative

approaches and methods, as a rule, remained the least investigated from the scientific and application points of view owing to the complication, small predictability, and recurrence. At the same time, survivability of power-generating units in emergency situations and risk analysis of probable aftereffects should become weighable arguments in favor of building of nuclear units with a life expectancy from 60 to

The analysis of sources, the reasons, and aftereffects of the heavy disasters occurring during installations of nuclear energetics display both their likeness and essential difference. Accidents known to the world on NPP with radioactivity ejection in a circumambient manner in the USA (the NPP "Three Mile Island (TMI)"— **Figure 2**), in the USSR (the Chernobyl NPP (CNPP)—**Figure 3**), and in Japan (the

A common after effect of NPP accidents and disasters was that direct and indirect economical losses from them reached tens and hundreds of billions of USD. For their forestalling and preventing in the subsequent, the principal changes were made to designer, technological, and service solutions. Heavy emergency situations for NPP service arose earlier at the time of damage to their equipment, such as runners, steam plants, main coolant pumps, heat exchanger pipes, gate valves, and

The abovementioned NPP heavy accidents and disasters originated from unapproved impacts of human controllers, non-observance of technological discipline at emergency situation (TMI, CNPP), heavy-lift seismic loads, and a tsunami (Fukushima-1). Regular systems of the automatize guard of the NPP have been unreasonably disconnected (CNPP) or could not work in an emergency situation (TMI, Fukushima-1). Heavy emergency situations on turbine runners, steam plants,

NPP "Fukushima-1—**Figure 4**) were the heaviest [3, 6, 8, 11, 18].

mathematical modeling [1, 12–17].

*DOI: http://dx.doi.org/10.5772/intechopen.88233*

legs of reactor internals [11, 17].

100 years.

**Figure 2.**

**193**

*The "Three Mile Island" NPP (TMI).*

By 2019, in the Russian Federation, 10 NPPs with 35 power-generating units with a total power of 29 GW are operational. In model of the NPP of Russia, there are 20 pressurized water reactors, including water-moderated power reactors (12 units of VVER-1000 type, 1 unit of VVER-1100 type, 2 units of VVER-1200 type, 5 units of VVER-400 type, and 1 unit of VVER-417 type). There are also 13 units of channel boiling water reactors of a high power of RBMK type (channeltype graphite-moderated power reactor—GMPR)—(10 units of RBMK-1000 type and 3 units of type EPG-6 type with power of 12 MW) and 2 units of fast-neutron reactor (FNPR) of BN type (BN-600 type and BN-800 type).

In 56 states of the world, more than 430 nuclear reactors with a total power 370 GW is now operated. The NPPs in the world produce about 11% of the consumable electric power. Leaders in this production are France (80%), South Korea (32%), and Ukraine (30%). In Russia, this share amounts to 16%. In the long term of 20–25 years, probably accretion of this share will be about 25%.

On changeover to reactors of power plants of first generations of 1960–1970 reactors of new third and fourth breeds come. And if the first reactors were considered as "nuclear boilers" and designed on norms of boiler fabrication for thermal power, up-to-date reactors develop on these details both on scientifically wellfounded norms and on methods of national (Russia, the USA, Great Britain, France, and Germany) and international levels (IAEA).

From stands of classes of hazards detection for technosphere objects, nuclear reactors undoubtedly fall into critically (CRO) and strategically (SRO) relevant objects. These are facts that demand the profound combined analysis and a justification of all design and service solutions for all stages of their life cycle.

In the proximal (till 2020), midrange (till 2030), and kept away (till 2050) prospects, the evolution of nuclear energetics will be carried out on the basis of operating, built, and designed nuclear power plants. Basis of the fundamental and application analysis of strength, life time, reliability, and safety of operation of NPP elements with reactors of VVER, RBMK, and BN types (**Figure 1**) in regular both emergency situations are the equations and criteria linear and nonlinear mechanics of deformation and fracture [1–11]. They contain in home and foreign strength standards and are used as at design, so at manufacture and operation of working in

#### **Figure 1.**

*The Russian reactors of VVER (water-moderated power reactor) (a), RBMK (channel graphite-moderated power reactor) (b) and BN (fast-neutron reactor) (c) types.*

*Probability Modeling Taking into Account Nonlinear Processes of a Deformation and Fracture… DOI: http://dx.doi.org/10.5772/intechopen.88233*

extremely conditions, a high-loaded power-generating plants with use physical and mathematical modeling [1, 12–17].

Results of traditional researches and a standardization of strength and life time of NPP in the determined statement in Russia and abroad are both initial scientific baseline of normative documents on design and actual baseline of making of perspective methods of a reliability estimate, survivability, initiation, and evolution of accidents and disasters by risk criteria, and also of makings of new principles, technologies, and engineering complexes ensuring safety service of NPP. These are conditions that are scientifically grounded to prevent initiation of the emergency and disastrous situations and also to minimize probable losses at their initiation at all stages of life cycle. Such situations within the limits of usual normative approaches and methods, as a rule, remained the least investigated from the scientific and application points of view owing to the complication, small predictability, and recurrence. At the same time, survivability of power-generating units in emergency situations and risk analysis of probable aftereffects should become weighable arguments in favor of building of nuclear units with a life expectancy from 60 to 100 years.

The analysis of sources, the reasons, and aftereffects of the heavy disasters occurring during installations of nuclear energetics display both their likeness and essential difference. Accidents known to the world on NPP with radioactivity ejection in a circumambient manner in the USA (the NPP "Three Mile Island (TMI)"— **Figure 2**), in the USSR (the Chernobyl NPP (CNPP)—**Figure 3**), and in Japan (the NPP "Fukushima-1—**Figure 4**) were the heaviest [3, 6, 8, 11, 18].

A common after effect of NPP accidents and disasters was that direct and indirect economical losses from them reached tens and hundreds of billions of USD. For their forestalling and preventing in the subsequent, the principal changes were made to designer, technological, and service solutions. Heavy emergency situations for NPP service arose earlier at the time of damage to their equipment, such as runners, steam plants, main coolant pumps, heat exchanger pipes, gate valves, and legs of reactor internals [11, 17].

The abovementioned NPP heavy accidents and disasters originated from unapproved impacts of human controllers, non-observance of technological discipline at emergency situation (TMI, CNPP), heavy-lift seismic loads, and a tsunami (Fukushima-1). Regular systems of the automatize guard of the NPP have been unreasonably disconnected (CNPP) or could not work in an emergency situation (TMI, Fukushima-1). Heavy emergency situations on turbine runners, steam plants,

**Figure 2.** *The "Three Mile Island" NPP (TMI).*

power of 5 MW. Since then, leading countries of the world (the USSR-Russia, the USA, Great Britain, France, etc.) have come up with a whole spectrum of a new

By 2019, in the Russian Federation, 10 NPPs with 35 power-generating units with a total power of 29 GW are operational. In model of the NPP of Russia, there are 20 pressurized water reactors, including water-moderated power reactors (12 units of VVER-1000 type, 1 unit of VVER-1100 type, 2 units of VVER-1200 type, 5 units of VVER-400 type, and 1 unit of VVER-417 type). There are also 13 units of channel boiling water reactors of a high power of RBMK type (channeltype graphite-moderated power reactor—GMPR)—(10 units of RBMK-1000 type and 3 units of type EPG-6 type with power of 12 MW) and 2 units of fast-neutron

In 56 states of the world, more than 430 nuclear reactors with a total power 370 GW is now operated. The NPPs in the world produce about 11% of the consumable electric power. Leaders in this production are France (80%), South Korea (32%), and Ukraine (30%). In Russia, this share amounts to 16%. In the long term

On changeover to reactors of power plants of first generations of 1960–1970 reactors of new third and fourth breeds come. And if the first reactors were considered as "nuclear boilers" and designed on norms of boiler fabrication for thermal power, up-to-date reactors develop on these details both on scientifically wellfounded norms and on methods of national (Russia, the USA, Great Britain, France,

From stands of classes of hazards detection for technosphere objects, nuclear reactors undoubtedly fall into critically (CRO) and strategically (SRO) relevant objects. These are facts that demand the profound combined analysis and a justifi-

In the proximal (till 2020), midrange (till 2030), and kept away (till 2050) prospects, the evolution of nuclear energetics will be carried out on the basis of operating, built, and designed nuclear power plants. Basis of the fundamental and application analysis of strength, life time, reliability, and safety of operation of NPP elements with reactors of VVER, RBMK, and BN types (**Figure 1**) in regular both emergency situations are the equations and criteria linear and nonlinear mechanics of deformation and fracture [1–11]. They contain in home and foreign strength standards and are used as at design, so at manufacture and operation of working in

*The Russian reactors of VVER (water-moderated power reactor) (a), RBMK (channel graphite-moderated*

cation of all design and service solutions for all stages of their life cycle.

type of power supply—nuclear-powered.

*Probability, Combinatorics and Control*

reactor (FNPR) of BN type (BN-600 type and BN-800 type).

of 20–25 years, probably accretion of this share will be about 25%.

and Germany) and international levels (IAEA).

*power reactor) (b) and BN (fast-neutron reactor) (c) types.*

**Figure 1.**

**192**

**Figure 3.** *The accident on the Chernobyl NPP (CNPP).*

**Figure 4.** *The accident on the "Fukushima-1" NPP.*

gate valves, and legs arose due to the lack of suitable technical diagnostics of these situations [11, 19], when faults in the form of cracks because of technological or operational fault attained of the limiting, intolerable sizes (10<sup>2</sup> to 1.5 <sup>10</sup><sup>3</sup> mm), affecting 50–70% of carrying cross-section and creating sharp magnification of runner chattering. Thus, the analysis of such situations was not envisioned by normative calculations.

Long-term experience of home nuclear branch organizations and the academic institutes has allowed to form (**Figure 5**) the schematic diagram of the combined

*Probability Modeling Taking into Account Nonlinear Processes of a Deformation and Fracture…*

*DOI: http://dx.doi.org/10.5772/intechopen.88233*

• The determined and statistical researches of deformation and fracture processes of laboratory specimens (with groups from 3–10 to 100–200

*The structure of the main task solution at making and service of the NPP equipment.*

• Model tests of the metallic specimens imitating most important parts (for example, studs of threaded connections with a diameter from 24 to 110 mm) and also nonmetallic specimens of studs with a diameter from

scale 1:10 and from metallic materials in scale 1:5

fracture, and also cyclic forming and radiation damage.

• Tests of the modeling reactor vessels fabricated of nonmetallic materials in

• Full-scale prestarting and starting tests of reactor prototype models of VVER,

In considered norms, there are two cores sections: calculation of principal dimensions predominantly by criteria of a static strength and the verification calculations on a different combination of limiting states at low-cycle and high-cycle, long-term, vibration, seismic loads with initiation of static, cyclic, brittle, corrosion

solution of tasks in view:

**Figure 5.**

**195**

60 to 210 mm

RBMK, and BN types

specimens of one steel)
