=Paper=
{{Paper
|id=Vol-2514/paper70
|storemode=property
|title=Criteria basis for development the system of engineering requirements and tests in the field of engineering safety
|pdfUrl=https://ceur-ws.org/Vol-2514/paper70.pdf
|volume=Vol-2514
|authors=Nikolay Makhutov,Dmitry Reznikov,Mikhail Gadenin
}}
==Criteria basis for development the system of engineering requirements and tests in the field of engineering safety==
https://ceur-ws.org/Vol-2514/paper70.pdf
Criteria for the development of the system of combined engineering
calculations and tests to justify technological safety
Nikolay A. Makhutov
Mechanical Engineering Research Institute
101990, 4, Maly Kharitonievsky lane, Moscow, Russia
kei51@mail.ru
Mikhail M. Gadenin
Mechanical Engineering Research Institute
101990, 4, Maly Kharitonievsky lane, Moscow, Russia
imash-ru@mail.ru
Dmitry O.Reznikov
Mechanical Engineering Research Institute
101990, 4, Maly Kharitonievsky lane, Moscow, Russia
mibsts@mail.ru
Abstract: The modern theory and practice of ensuring high per-
formance characteristics of critical engineering systems use pa-
rameters describing the level of the system’s protection from ac-
cidents and catastrophes as well as parameters of technological
risks, safety, damage tolerance, reliability, service life and
strength. To fulfill these requirements and avoid the occurrence
of limit states various safety factors are introduced by research
institutions, design organizations and supervising agencies. These
safety factors are established by conducting analytical and nu-
merical calculations and experiments focused on assessment of
stress-strain states and through tests carried out on laboratory
specimens, models, test benches and full-scale structures. The
amount of calculations and tests are determined by the level of
novelty and criticality of the designed and used equipment.
Keywords: strength, service life, safety, mechanical characteris-
tics, safety factor
1 Introduction
Basic research in the field of risk theory, mechanics of catastrophes, deformation and fracture mechanics [1-3] forms the
basis of modern approaches to insuring safe operation of high-load engineering facilities. At the same time the criterion
base for developing and improving approaches to ensuring the required conditions for accident-free operation includes
standard-based parameters of risk and safety. These parameters are substantiated by sets of criteria of strength, service life,
reliability, and damage tolerance. Safe and reliable operation of high loaded facilities can be ensured through experimental
and calculation formation of an appropriate criteria base for risk regulation and management. This criteria base should take
into account both normal operating conditions and the possibility of occurrence of various incidents, accidents and catastro-
phes [1, 2, 4-7]. With regard to the practice of operating engineering facilities (EF) in Russia, they can be divided into the
following categories: facilities subjected to technical regulation (TRF), this category numbers 106÷107 facilities; hazardous
production facilities (HPF), 104÷5 105 facilities in total; critically important facilities (CIF) with the number 103÷5 103; and
strategically important facilities (SIF) with the number 102÷103.
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
117
In historical retrospective ensuring structural integrity and safety of engineering facilities is characterized by solving the
following sequence of problems: strength stiffness resilience service life reliability damage tolerance
safety risk protection. Each of these problems requires accumulation of basic scientific knowledge, developing a
criteria base, elaborating engineering design and testing methods, creating norms and rules for EF designing and manufac-
turing that would allow one to ensure EF operation within the specified limits of design modes and parameters. In other
words when analyzing the problem of ensuring structural integrity and safety in the most general form, the following gov-
erning parameters should be considered:
Rσ is strength determined by the capacity of the load carrying (structural) components that are subjected to normal and
extreme impacts to resist fracture;
Rλ is stability determined by the capacity load-carrying components to resist buckling under normal and abnormal load-
ing;
Rδ is the rigidity determined by the resistance of the load-carrying components to the unacceptable deformations δ under
the impact of normal and abnormal loads;
RNτ is a service life determined by the time τ or the number of cycles N before either fracture, or loss of stability occurs;
PQR is reliability determined by the ability of an facility (in its normal or damaged state) to fulfill its functions under giv-
en loads Q;
Lld is damage tolerance (or flaw resistance) determined by the ability of the facility with damage d (or defect size l) that
exceeds the acceptable level to fulfill (at least partially) its functions;
S is safety determined by the ability of the facility avoid catastrophic states;
R is risk determined by the probability of the occurrence of unfavorable situations at the facility and possible conse-
quences of these situations;
Zc is protection level determined by the ability of the facility to resist the occurrence and development of adverse conse-
quences in normal and emergency situations.
Parameters Rσ, Rλ, Rδ should be used for assessment of facilities subjected to technical regulation; Rσ, Rλ, Rδ, RNτ should
be estimated when hazardous production facilities are considered; Rσ, Rλ, Rδ, RNτ, PQR, Lld, S should be included into consid-
eration for critically important facilities; Rσ, Rλ, Rδ, RNτ, PQR, Lld, S, R, Zc are characteristics of strategically important facili-
ties.
2 Analysis of limit states
Modern trends in the design and operation of high-load equipment are focused on increasing strength and service life of its
load-bearing elements in order to ensure operational safety. It means that strength assessment should be carried out not only
in linear elastic, but also in nonlinear elastoplastic formulation [2]. Since the considered EF along with static loading are
also subjected to cyclic nonstationary loading, both static and cyclic elastic and elastoplastic strains in stress concentration
zones should be analyzed [2, 8]. In the view of the above the analysis of conditions and the formation of the criteria base of
reaching limit states is a necessary step for justifying parameters of EF safe operation [2, 7, 9].
The assessment of accumulated damage of engineering facilities for various stages of their lifecycle and estimation of
conditions for their transition to critical states due to the application of multifactor loading regimes are generally based on
application of computational and experimental methods for determining strength, service life, reliability, resilience, and
safety (Fig. 1). At the same time, the development of proposals related to various design schemes and design cases for all
stages of EF life cycle is implemented using the criteria that take into account the changes of the mechanical properties of
materials at all stages of the facility life cycle.
At the design stage, the initial mechanical properties of the material are included in the calculations of strength and ser-
vice life. Estimates of the current state of the considered structural components are made with the account of the actual me-
chanical properties of the material obtained during control experiments. Assessment of the remaining service life according
to the criteria for reaching limit states are carried out using current mechanical properties of the material and their estimated
(predicted) values [2, 10]. In this case, the operational loads that influence the current mechanical properties of structural
materials at various stages of EF life cycle are determined by the following main parameters: the number of cycles N, the
loading time , temperature t, level of accumulated damage (size of the defects) l, environmental conditions . Moreover,
the parameters N and affect the lifetime of the facility as a whole, and t affects its heat resistance.
The scientific substantiation of strength, service time, damage tolerance, and safety requires an analysis of the results of
complex basic and applied research in an interdisciplinary formulation with the formation of relevant criteria and governing
equations. Some of these equations that use safety factors for strength and service life assessment were initially quite sim-
ple. But the development of new formulations that take into account the conditions of impact, sustained and cyclic loadings,
and also high-speed, high-temperature, and low-temperature loading requires more complicated governing equations.
118
Figure 1 – The flowchart of the analysis of the conditions for attaining limit states
The analysis of processes of deformation and fracture in the elastoplastic formulation requires a transition from the tradi-
tional stress based approach which is adequate for solving the problems of linear mechanics of deformation and fracture to
the strain-based approach. This formulation of the problem has been introduced into a number of design standards, includ-
ing standards adopted in the nuclear industry. It will be certainly developed further when the problems of ensuring safe op-
eration of engineering facilities in extreme situations will also be included in the scope of consideration with the detailed
assessment of parameters of stress σ, strain e, durability according to the number of cycles N and time τ, as well as the ef-
fects of the environment Φ.
The criteria base and the system of design equations for assessment of limit states at all (design, manufacture, operation)
stages of the EF life cycle that should be considered for justification of the strength, service life, reliability, survivability,
safety, risks and security of facilities become more complex. The effects of stress concentration, boundary problems of the
theory of elasticity and plasticity have now been transformed into an analysis of very complex scientific, design, technolog-
ical, social and economic problems. This requires analytical, numerical and experimental methods to be applied for the
stages of nonlinear behavior of materials and structures when their mechanical properties start to vary in the process of EF
manufacture and operation.
3 Determination of the parameters of limit states
The basic tasks of substantiating the design characteristics and the formation of relevant criteria in the framework of theo-
retical and experimental mechanics, deformation and fracture mechanics, and catastrophe mechanics include three main
ones:
- calculated-experimental analysis of stress-strain states (, e) taking into account mechanical Qs, thermal Qst, aero-
hydrodynamic Qsah impacts as well as impacts of external radiation and corrosive environment Qsrc. In this case, local
stresses σsmax and strains esmax prove to be dependent on the number of loading cycles Ns, time s, and temperature ts;
s s
max , emax F P , Q , Q , Q , N , , t ;
s
s
t
s s
ah
s
rc
s s s
(1)
- analysis of the trends of static, dynamic, cyclic and sustained elastic and elastoplastic deformation for varying frequen-
cies f, amplitudes of stresses and strains eas, temperatures ts and time s;
s s
max , emax F f , , e , t , ;
1s
s
a
s
a
s s
(2)
- analysis of the criteria and conditions for the accumulation of damage ds, as well as cyclic durability NcS for the stages
of crack initiation and propagation:
d , N F f , , e , t ,
s s
c 2s
s
a
s
a
s s
(3)
The results of experimental and numerical studies on specimens, models and full-scale constructions make it possible to de-
termine safety factors for stresses n,, strains ne, number of cycles nN, time n, exposure to environment nФ and crack size nl:
n , ne , n N , n , n , nl s c , es c , N cs , cs , cs , lcs , (4)
max emax N l
where the subscript "c" refers to the critical (limit) value of the relevant characteristics of strength, durability, crack re-
sistance, and the index "s" refers to the corresponding values during operation.
119
The available computational and experimental information on the loads Q, temperatures t, stresses and strains e, as
well as the criterion values of safety factors for stresses of the resistance to deformation and fracture of the structural mate-
rials forms the basis for constructing the curves of limit states:
Qc mod , emod max k , t , , N , (5)
where Qc is the critical (limit) combination of mechanical, temperature and other types of impacts for different loading
modes fot time , number of cycles N, temperature t.
The values of Qc, as a rule, are established according to the criterion values of local stresses (mod)maxk or strains
(emod)maxk. The following equations are used for this purpose:
- curves of isothermal low- or high-cycle fatigue for corresponding materials
mod max k , emod max k c f N N , b , c , S c , (6)
p,m
Where σb is the ultimate strength, σp is the yield strength, Sс is stress at fracture, ψc is the relative narrowing in the neck
of the specimen at fracture, m is the stress hardening exponent in the elastic-plastic region;
- curves of sustained isothermal strength
mod max k , emod max k c f , b , c , S c , (7)
p,m
- static strength curves at varying temperatures t
mod max k , emod max k c f t t , b , c , S c . (8)
p,m
The curves described by expressions (6) and (7) for metal structural materials, have as a rule, a monotonic form: when
the values of N and go up the limit values of stresses and strains at fracture decrease.
According to expression (8) the temperature dependences of the critical stresses and strains in the low temperature region
can be non monotonic: for radiation brittle or cold brittle metal states, strength and plasticity in this case can decrease.
The limit curves constructed in accordance with expressions (6) - (8) for a given loading mode defined by the val-
ues mod max k , emod max k i are used for determination of the limit (critical) values of parameters Nci, ci, tci, Фсi.. If the
values of Ni, i, ti, Фi, for the specific loading mode are known then using the curves of fatigue, crack resistance, long-term
strength and resistance to external impacts, one can estimate the level of the accumulated damage.
In the general case spatial three-dimensional surfaces of limit and allowable states can be constructed to analyze the con-
ditions of critical damage occurrence (Fig. 2). The space that contains these surfaces has the following coordinate axes:
- axis of operational loading factors (forces Q, nominal stresses n, stress intensity factors KI, maximum local stresses
(mod)max k in stress concentration zones);
- the axis of temperature-time and cyclic operation parameters (temperature t, time , number of loading cycles N);
- the axis of the accumulated damage (dimensions l of defects with accounting for their shape and spatial location).
The occurrence of fracture, unacceptable plastic deformations or critical cracks in the analyzed structural components
corresponds to the reaching of the limit state (the surface of the limit states in Fig. 2). The limit load Q in this case is a vec-
tor passing through the origin of coordinates with angles corresponding to the given state of the structure in terms of the
parameters l, t, , N, n, KI, (mod)max k. If you introduce the necessary safety factors n against the specified parameters, then
from the surface of limit states one can go, through the region between the dashed and solid curves in Fig. 2, to the surface
of acceptable states and the acceptable load [Q]. In this case, the specified strength, service life and safety can be considered
as ensured if the length of the vector of the operational load for certain specific conditions Qs is less than or equal to the
length of the vector of the load that is acceptable for these conditions [Q], i.e. Qs [Q].
Traditional methods for calculation of strength and service life were developed on the assumption of the defect-free state
of the structural material (l= 0). In this case from the surfaces of limit and acceptable states (fig. 2) one can go to the limit
and acceptable curves (in the plane «Q, n, KI, (mod)max k – t, , N» - static strength (at a predetermined temperature t), long-
term sustained static strength (for a given time ) and cyclic strength (for a given number of cycles N).
The strength and flaw resistance at the early stages were determined by the criteria of linear fracture mechanics for the
plane «Q, n, KI, (mod)max k – l». For modern design methods for strength, service life and flaw resistance assessment that
use the concepts of limit and acceptable states, it is important to adopt unified constitutive equations, uniform fracture crite-
ria and uniform sets of design characteristics regardless of the type of construction, properties of structural materials and
operational loading modes.
120
Figure 2 – Scheme of construction of the surface limit and allowable states in the analysis of strength and service life
The considered laws of deformation and fracture of structural materials are used for carrying out comprehensive risk
based assessments of technological safety and protection level of the EF subjected to complex operational impacts. These
laws that are taken into account at the design stage and combined with diagnostic and monitoring data on the current state
of the EF forms the foundation of databases and knowledge bases for assessment of its strength, service life and durability.
4 Criterion base of technological safety
Conditions for reaching the limit states (fracture, the formation of critical cracks, loss of resilience, unacceptable plastic
deformations, etc.) under a wide range of loading parameters can be characterized by the following groups of situations
occurring during equipment operation [1, 5]:
- normal (regular) situations when the requirements of strength, service life, reliability and damage tolerance are satisfied
at specified levels of safety factors n and material imperfection ls; in this case the EF operation continues according to the
existing rules and regulations;
- incidents or deviations from normal conditions in terms of operating impact parameters (σ)smax, mechanical properties
and defectness level ls with a decrease in safety factors n; in this case damages and failures may occur. This requires diag-
nostic and repair work;
- design basis emergencies when there is a significant increase in the levels of operational impacts, a decrease in strength
(p, b) and plasticity , an increase of the defectness level ls. In these cases, the operation of the equipment should be ter-
minated, its condition analyzed, repair and restoration, as well as residual strength and service life assessment should be
carried out;
- beyond design basis emergencies when safety factors n and design characteristics are transferred to an unacceptable ar-
ea (n≤1); in this case, there is a normal or abnormal shutdown of the equipment, work is underway to restore them, and de-
cisions are made whether it is possible or not to continuer the work of the EF;
- hypothetical emergencies in the implementation of the most dangerous, unforeseen impacts (σ)smax accompanied by
significant damage (lslс) of load carrying elements.
Each of these types of emergencies corresponds to a certain level of the reduction of technological safety that can be as-
sessed by values of risk Rs(τ) at a current stage s of operation. The values of risk are determined by the probabilities Pis(τ)
of each of these i situations and economic consequences Uis(τ) of their occurrence:
R s ( ) FR Pi s ( ),U is ( ) (9)
In this case the safety parameter can be quantified as a corresponding safety factor:
nR Rc ( ) Ris ( ) (10)
where Rc(τ) is the critical, or unacceptable risk for a specific facility; Ris(τ) is a design value of risk for the moment of
operation τ in i-th situation; nR is a risk-based safety factor.
The main task of the indicated above transition from traditional methods for ensuring the specified operating conditions
of manmade facilities to the new ones is to solve the problem of ensuring a certain level of risks R(τ) of possible accidents
and disasters, and require to use such norms of calculations and tests that would provide an acceptable level of risks. This
121
approach determines (Fig. 3) all the main groups of the above design characteristics: protection Zc(τ), safety S(τ), and risks
R(τ); service life RNτ(τ), and damage tolerance Lld(τ); strength Rσ(τ), stiffness Rδ(τ), and resilience Rλ(τ).
Figure 3 – Sequence of analysis of hazardous conditions of facilities and corresponding risks
At the same time, the trajectories of the development of hazardous events that lead to equipment failures can be of dif-
ferent type (Fig. 3), characterized by an increase of the values of risk R(τ) over the time τ .
Damage accumulation, initiation of failure, accident, and catastrophe, as well as risks R(τ) that correspond to them can
be considered in time τ as both short-term and long-term processes that include various stages of deviations from the nor-
mal operating modes, the accumulation of mechanical damage, failures, as well as violation of control over the quality and
state of the equipment and personnel. This is taken into account when developing a risk analysis algorithm R(τ), as well as
scenarios of hazardous events development and determining the key parameters of assessed facilities.
The first stage of damage accumulation d, failures, and partial destructions with the development of local damage (cracks
l) ends in an emergency situation at the facility, which may be associated with the beginning of cascade fracture and irre-
versible deviations from normal operation conditions. An accident or catastrophe with the occurrence of a limit state in the
structural components and the formation of critical defects lc is the final stage of unfavorable situations and is characterized
by the highest, unacceptable (critical) risks R(τ)=Rc(τ).
The limit state of a facility may be reached along different trajectories, depending on the conditions, modes, and type of
loading. At certain stages of the facility life cycle (including those defined by the regulations), its current states are subject-
ed to automated diagnostic control with determination of the accumulated damage (Fig. 4). This allows one to make deci-
sions about the possibility of further operation of the facility [1, 11-13].
Figure 4 – Trajectories of damage accumulation at different stages of the facility life cycle
A fairly fully developed criteria and regulatory framework was developed for assessment of facilities that operate under
normal operation conditions. The system of calculations of parameters characterizing design basis situations, beyond design
basis, and hypothetical ones is founded on the analysis and consideration of the conditions for the occurrence of failures and
damaged states leading to emergency and disastrous situations. This requires essential improvement and clarification of the
criteria, approaches and methodologies that were developed for assessment of normal situations. In the transition from the
assessment of normal situations to the assessment of beyond design basis situations and possible hypothetical ones that are
122
typical for severe accidents and catastrophes, one should note that the relevant criteria and regulatory frameworks are miss-
ing.
The operating conditions of the engineering facilities and the scenarios of their changes are important for the analysis of
scenarios of reaching limit states [1, 6, 14, 15]. Fig. 5 illustrates such scenarios. The horizontal axis describes factors of
operation conditions (loading cycles, times, temperatures, corrosive environments) Fs, while the vertical axis describes the
system response to these conditions S*.
The lower area in fig. 5 up to the dotted line corresponds to the acceptable states. It includes normal situations with the
operation of the facility within the parameters assigned in accordance with the design standards. In this area the Each point
«Ss-Fs» of this area characterizes the current operational state of the EF.
Figure 5 – States, scenarios and factors of operation of facilities with the possibility of accidents and disasters
A critically loaded element of the facility can transit from this point into dangerous (limit) states along different paths
characterized by an angle (scenario parameter). For example, moving from it current position to the right (when = 0)
one can assess the acceptable service life with respect to N or (up to the crossing with the dotted line) and limit service
life (up to crossing with solid line). Rising from the current point upwards (at =900), a facility can reach the limit state
beyond which a disaster occurs. In this case the task of analyzing safety of the facility in such a scenario should be solved
according to a completely different methodology. At the same time, the existing regulatory stress-based design approach
that uses standard mechanical properties determined using the existing experimental base is insufficient.
5 Experimental determination of design characteristics
As noted above, the results of mechanical tests play an important role in calculations of strength, service life and safety un-
der various modes of loading of engineering facilities. They are included as the main parameters in the corresponding crite-
ria expressions [2, 3, 7, 10, 16, 17]. As machines and structures are being improved and their loading conditions become
more complex, the range of structural materials, technologies and types of mechanical tests expanded in order to obtain
characteristics of their mechanical properties as basic criteria parameters (Table 1).
Already at the stage I (according to Table 1) the basic approaches to the assessment of the main characteristics became
established. Their essence is that the maximum operational impacts QSmax on the load carrying elements should not exceed
the acceptable values [Q] that in turn are determined by critical values of Qc with the introduction of the corresponding
safety factors nQ.
s Qc
Qmax [Q] . (11)
nQ
When the problem of ensuring strength is considered, the term dangerous loads Qc reefers to loads causing destruction
Qb or plastic deformations (fluidity) Qp. Then condition (11) can be rewritten as:
э
Q Q p
Qmax [Q] min c , (12)
nQ nQp
If it is necessary to satisfy stiffness conditions then the critical forces Qc in expression (11) are the forces Q that cause
the specified critical strains c.
If the condition of resilience should be ensured then the critical forces Qс in (11) are the forces Qst that cause the loss of
resilience. In these cases safety factors against strain nQ or stability nQst are introduced into expression (12). Safety factors n
in all the considered cases should be greater than one (n>1).
123
Table 1 - Types of methods of mechanical tests and criterial characteristics of materials obtained using these methods
Calculation Material
Stage Types of materials Test type
section characteristic
Metals, composites, ceramics, Testing for fracture and Qc, lc, Nc, τc
V Safety
nano-materials catastrophe (Qs, Ns, τs)
Tests for crack KIc, KIec, c, Jc
IV Metals, composites, ceramics Resilience
resistance (KIs, s, Js)
Reliability v p , v b , v -1
III Metals, composites Combined safety tests
(νs)
-1, N0, lt, τ0
II Metals Durability Cyclic, long-term tests
(san , sa max)
b, p, Е, μ
I Strength, rigidity, resilience Static, dynamic tests
(ns)
Expressions (11) and (12) are valid for each of individual load carrying component, its dangerous sections S, geometric
shape and size, loading conditions and the type of structural material. There is an infinite number of such combinations of
impacts, forms, loading conditions and types of materials. In this regard in order to get an invariant conditions of strength,
rigidity and resilience, the calculations by expressions (11) and (12) are replaced by calculations at maximum nominal
stresses max n, determined using the equations of the strength of materials.
э
Qmax N M M
max
э
n , b , t , (13)
S F Wax W p
where F is the area cross section, N is axial force, Wax is area moment of inertia, Mb is bending moment, Wp is polar mo-
ment of inertia of area, Mt is torsion moment). Then using equations (11) and (13):
c
max
э
n [ ] . (14)
n
The criterion values of critical stresses с are the ultimate strengths b, yield strengths p, stresses at the given strain
, stresses st at the loss of resilience.
The main types of mechanical testing of structural materials to ensure the conditions of strength, rigidity and resilience
are standard static tests of smooth laboratory specimens under tension (compression), bending or torsion. Moreover, for
most engineering products the following conditions are met:
1npnstn