Annex B
(Normative)
Design by Analysis – Direct Route
This annex is currently
limited to sufficiently ductile materials, like the whole standard, but it is,
for components operating in the creep range, also limited to sufficiently creep
ductile materials.
A material is considered to
be sufficiently creep ductile if the average elongation or reduction of area at
creep rupture is greater than five times the product, at the same temperature
and stress, of the average minimum creep rate and the average time to rupture.
The steels and steel castings
listed in Table A.2-1 of EN 13445-2:2002 for which, for the relevant temperature
regime, creep strengths are given in the referred to material standards, are
considered to be sufficiently creep ductile. This is, without proof, not valid
for weldments, for which sufficient creep ductility shall be proven.
Design-by-analysis (DBA) provides rules for the design of any component under any action. It may be used:
— as an alternative to design-by-formulas (see 5.4.1)
— as a complement to design-by-formulas for:
Due to the advanced methods applied, until
sufficient in-house experience can be demonstrated, the involvement of an
independent body, appropriately qualified in the field of DBA, is required in
the assessment of the design (calculations) and the potential definition of
particular NDT requirements.
For components which, under
reasonably foreseeable conditions, may operate in the creep range, the lifetime
of this creep load case (or the lifetimes for more than one of such load cases)
shall be specified (by the user or his representative). For each load case
which includes operation in the creep range, the specified time for operation
in the creep range shall not be less than 10 000 hours. If none is specified,
the manufacturer shall assume a reasonable time, but at least 100 000 hours.
NOTE: Whereas for structures
with solely non-creep load cases the load cases can be specified quite
independently, the specification of load cases for structures with creep load
cases requires careful consideration of the total design life taking into
consideration all reasonably foreseeable load cases. Alternative total design
lives may be used.
The (specified or assumed)
design life shall be stated in the Technical Documentation.
If the minimum of the two
values:
a) the product of 1,2 and the creep rupture strength at
calculation temperature and for the relevant lifetime,
b) the product of 1,5 and the 1% creep strain strength at
calculation temperature and for the relevant lifetime
is larger than the 0,2% proof
strength at calculation temperature, no creep design checks are required, and
subclause B.5.1.2 and clause B.9 do not apply. If the minimum of the two values
is not larger than the 0,2% proof strength at calculation temperature, creep
design checks are required, and subclause B.5.1.2 and clause B.9 apply.
The designations
creep rupture strength and 1% creep strain strength refer to mean values, as
specified in the material standard, for which a scatter band of experimental
results of ± 20% is assumed. For larger scatter bands 1,25
times the minimum band values shall be used instead of mean values.
For interpolation
and possible extrapolation of strength values, and for the determination of
time to creep rupture or 1% creep strain, the procedures given in Annex R shall
be used.
B.2.8 design model
(physical) model used in the determination of effects of actions.
B.5
Methodology
To each relevant failure mode,
relevant with regard to the scope of this standard, there corresponds a single
design check (DC). Each design check represents one or more failure modes.
The design checks shall be carried
out for the following (classes of) load cases,
where relevant
- normal operating load cases, where normal
conditions apply
- special load cases, where conditions for testing, construction, erection or repair apply
- exceptional load cases, see 5.3.5
In general, each design check
comprises various load cases; load cases being combinations
of coincident actions, that can occur simultaneously under reasonably
foreseeable conditions.
To each design check a simple principle is stated. For each principle, one or more application rules are given, to indicate different means by which an assessment can be made. The most relevant application rule or rules shall be selected. It is permissible to use other application rules, provided they accord with the relevant principle, and are at least equivalent with regard to safety, reliability and durability.
The design checks to be considered are:
- Gross Plastic Deformation Design Check (GPD-DC), see B.8.2
- Progressive Plastic Deformation Design Check (PD-DC) , see B.8.3
- Instability Design Check (I-DC) , see B.8.4
- Fatigue Design Check (F-DC) , see B.8.5
- Static Equilibrium Design Check (SE-DC) , see B.8.6
NOTE: The design checks are named after the main failure
mode they deal with. Some design checks may not be relevant for a particular
design. The
list of design checks is not exhaustive. In some cases, it may be necessary
to investigate additional limit states. For example, with austenitic stainless
steel, failure by GPD shall be checked (as an ultimate limit state) but leakage
may also need to be checked (as either an ultimate or a serviceability limit
state), see Table B.4-1.
If creep design checks are
required, see B.1.3, the design checks which shall be considered, in addition
to those listed in B.5.1.1, are:
- Creep Rupture Design Check (CR-DC), see B.9.4,
- Excessive Creep Strain Design Check (ECS-DC), see B.9.5,
- Creep Fatigue Interaction Design Check (CFI-DC), see B.9.6.
NOTE: For some load cases
creep rupture design checks may make corresponding gross plastic deformation
design checks superfluous.
For the determination of the
effects of (design) actions specific (physical) models shall be used, these
depend on the design check. Detail specifications for these specific
models are given in the subclauses of B.8 dealing with the specific design
checks, general descriptions and requirements in the following.
Whenever the initial (and
weightless) stress state of the model is of importance in a design check, the
stress-free state shall be used.
With the two exceptions
stated in the following, first-order-theory shall be used, i. e. geometrically
linear kinematic relations and equilibrium conditions for the undeformed
structure
Instability design checks shall
be based on non-linear geometric relations – equilibrium
conditions for the deformed structure and non-linear kinematic relations. Second order theory – linear kinematic relations and equilibrium conditions
for the deformed structure – may be used, if it can be shown to be accurate enough.
In case of structures and
actions where deformation does not improve but decreases the carrying capacity,
has an unfavourable (weakening) effect, geometrically non-linear effects shall
be taken into account in gross plastic deformation, in creep rupture, in creep
excessive strain, and in fatigue design checks.
B.7.4
Constitutive laws
The constitutive law to be
used in the model depends on the design check:
- in
the gross plastic deformation design check, B.8.2, a linear-elastic
ideal-plastic law with Tresca's yield condition (maximum shear stress
condition) and associated flow rule;
- in the progressive plastic deformation design check, B.8.3, in the creep rupture design check, B.9.4, in the creep excessive strain design check, B.9.5, a linear-elastic ideal-plastic law with Mises' yield condition (maximum distortion energy condition) and associated flow rule;
- in the fatigue design check, B.8.5, a linear-elastic law;
- in the instability design check, B.8.4, either a linear-elastic or a linear-elastic ideal-plastic law, depending on the approach;
NOTE1: In the GPD-DC Mises' yield condition may also be used, but the design material strength parameter (design yield strength) shall then be modified, see NOTE in B.8.2.1.
NOTE2: In the F-DC, which shall be performed by usage of the requirements of Clause 18, continuing plastification is accounted for by application of plasticity correction factors, see 18.8.
NOTE3: In the creep-fatigue interaction design check results of F-DC and ECS-DC are used.
B.7.5.1 Material strength parameters
The design value of the
material strength parameter (design yield strength) of plastic constitutive
laws RMd shall be determined
by division of the parameter's characteristic value by the relevant partial
safety factor, in general terms:
RMd
= RM / gR ...(B.7-1)
where RM is the characteristic
value of the relevant material strength and gR the relevant partial safety factor.
Details for the determination
of the characteristic values of the material strengths, and the partial safety
factors, are specified in the sub-clauses of the design checks, B.8.2 through B.8.5.
For exceptional situations,
the partial safety factor gR shall be agreed upon by
the parties concerned, but shall not be less than the one for testing situations.
a) Short-term characteristic values
In the determination of the
short-term characteristic values RM, for load cases with temperatures below the
creep regime, the minimum specified material strength data shall be used, i. e.
values for ReH, Rp0.2 / tT, Rp1.0
/t T,
Rm/t,T
, which apply to the materials in the final fabricated condition, which shall
conform with the minimum specified values of the appropriate material
specification.
NOTE:
These values will generally be achieved when the heat treatment procedures
conform with EN 13445-4:2002.
These minimum values,
guaranteed for the delivery condition, may be used unless the heat treatment is
known to lead to lower values.
If welding gives lower strength
values after fabrication and/or heat treatment, these shall be used.
Temperature dependent material
strength data, used in the determination of a characteristic strength value,
Rp0.2 / t, Rp1.0 /t and Rm / t, shall be for the reference
temperature specified in the relevant sub-clauses of the design checks
/
load cases, B.8.2 through B.8.5.
If short-term material
strength parameters for load cases with temperatures in the creep regime are
not specified in the material standards for the (high) calculation
temperatures, linear extrapolation in temperature from specified values shall
be used.
b) Long-term characteristic values
For the determination of the
long-term characteristic values RM, relevant for load cases with calculation
temperatures in the creep regime, see B.9.3.
B.7.5.2 Other material parameters
For the modulus of elasticity, Poisson's
ratio, and the coefficient of linear thermal expansion, time-invariant design
values given by the corresponding instantaneous value of the material may be used, see Annex 0, for
a reference temperature which depends on the design check /
load case. This reference temperature shall not be less than
a) 0.75 tc max + 5 K in the gross plastic deformation design check, and where tc max is the maximum calculation temperature of the load case
b) 0.25 tc min + 0.75 tc max in the progressive plastic deformation, the fatigue design check, B.9.5.4.2 and of the application rule 2 of the excessive creep design check, and where tc min and tc max are minimum and maximum calculation temperatures in the action cycles considered
c) tc max in the instability design check, the creep rupture design check, and application rule 1 of the excessive creep design check, and where tc max is the maximum calculation temperature of the load case
NOTE: The reference
temperature may be space dependent.
All of the design checks
specified in the sub-clauses of this clause B.8 shall be considered, and all
relevant load cases shall be dealt with.
B.8.2 applies mainly
to failure by gross plastic deformation (GPD), in either operation or test, but
deals also with excessive local strains. The other sub-clauses apply as
follows: For failure by progressive plastic deformation (PD), see B.8.3; by
instability (I), see B.8.4; by cyclic fatigue (F), see B.8.5; and by
overturning and global displacement, i. e. with rigid body motions, static
equilibrium (SE), see B.8.6.
B.8.2
After Table B.8.2 (incl. footnote) change text to :
As reference temperature of the temperature dependent material strength parameters a temperature not less than the maximum calculation temperature of the load case shall be used.
NOTE 1: The reference
temperature may be chosen as a function of space, or space-independent
NOTE 2: The deformations at
this material strength may be large for austenitic steels, and it is advisable
to check against leakage at bolted connections, bolted ends, etc.
The
principle is fulfilled, if the model with stress/strain concentrations shakes
down to linear-elastic behaviour under the action cycles considered
The principle is fulfilled if
both of the following conditions are satisfied:
a) The equivalent stress-concentration-free model, see
B.2.16, or any model which deviates from the model with local stress/strain
concentrations solely in the local stress/strain concentrations, shakes down to
linear-elastic behaviour under the cyclic action considered,
b) For the (detailed) model, with local stress/strain
concentrations, any time-invariant self-equilibrating stress field can be found
such that the sum of this stress field and the cyclically varying stress field
determined with the (unbounded) linear-elastic constitutive law for the cyclic
action considered is compatible with the relevant yield condition continuously
in a core of the structure which encompasses at least 80% of every wall
thickness.
NOTE 1: A self-equilibrating stress field is a stress field which satisfies the equilibrium conditions (in the interior and on the surface) for zero imposed forces, i. e. for zero mass forces in the interior points and for zero forces in all surface points with the exception of those where displacements are prescribed.
NOTE 2: In surface points where displacements are prescribed
self-equilibrating stress fields may correspond to non-vanishing surface
forces.
NOTE 3: A stress field is compatible with the relevant yield condition,
if the Mises equivalent stress does at no time and nowhere exceed the design
strength parameter.
This application rule applies for load cases without thermal stresses
and without stresses induced by prescribed displacements.
The principle is fulfilled (without specific proof) for all action
cycles within the range of actions allowable according to the Gross Plastic
Deformation Design Check (GPD-DC).
NOTE: There are load cases with prescribed displacements which can be
converted via global equilibrium conditions into cases with prescribed forces,
e. g. load cases with prescribed vanishing vertical displacements at brackets,
where the corresponding forces may be determined via the global equilibrium
conditions.
B.8.5 (Cyclic) Fatigue
failure (F)
B.8.5.1 Principle
The design value of the fatigue
damage indicator
, for cyclic fatigue, obtained
for all the (cyclic) design functions of
pressure / temperature and variable actions shall not exceed 1.
B.9 Creep design checks (Clause totally NEW)
All of the design checks
specified in the sub-clauses of this clause shall be considered, in addition to
the design checks specified in Clause B.8. All relevant load cases shall be
dealt with.
NOTE: There may be load cases
where the creep rupture design check may replace the corresponding gross
plastic deformation design check.
The sub-clauses apply as
follows: For creep rupture failure (CR), see B.9.4; for failure by excessive
creep strain (ECS), see B.9.5; by creep and cyclic fatigue interaction (CFI),
see B.9.6.
Creep properties of welded
joints may differ essentially from those of the base metal, strain
concentrations may result. Weld joints, where the maximum stress component
normal to the joint direction exceeds 80% of the relevant design value of the
creep material strength parameter, shall be included in the model as a separate
region, slightly larger than the likely maximum weld joint region including the
heat influence zone.
The design values of the
creep material strength parameters of this weld region shall
‑ be 64% of the base metal values, if neither of
the corresponding values for the weld joint nor for the weld metal are known,
‑ be 80% of the lesser of the corresponding
values for base metal and weld metal, if the corresponding weld metal are known
‑ not exceed the corresponding values of the base
metal.
It is a pre-condition of the
use of this clause that all regions which are creep crack critical are
accessible for in-service inspection and in-service non-destructive testing,
and that instructions for appropriate maintenance and inspection are
established and included in the operating instructions. Means for tracking
creep deformation shall be provided, including appropriate design details, such
as dedicated measurement points.
NOTE:
Recommendations on appropriate maintenance and inspection are given in Annex M?
(TG Creep to act!)
In the determination of the
characteristic values of the material creep strength parameters RM the mean
specified material creep strength data shall be used which apply to the
materials in the final fabricated condition. These values shall conform with
the values specified in the appropriate material specification.
The temperature for which
these characteristic values are determined shall be the reference temperature specified
in the relevant sub-clauses of the creep design checks, B.9.4 through B.9.6.
For each creep load case, the
design value of an action, or of a combination of actions, shall be carried by
the design model with
‑ a nonlinear-elastic ideal-plastic constitutive law,
‑ Mises' yield condition (maximum distortion energyhypothesis) and
associated flow rule
‑ a material strength parameter RM and a partial safety factor
as specified in Table
B.9-2, and the maximum absolute value of the principal structural strains is
less than 5%.
‑ for proportional increase of all actions and a stress-free
initial state
With the exception of cases
where deformation has a weakening effect, see B.7.1, first-order-theory shall
be used; where deformation has a weakening effect, geometrical non-linear
effects shall be taken into account.
If it can be shown that any
lower bound limit value of the action or combination of actions, determined
with the design model specified in the principle, is reached without violation
of the strain limit, the principle is fulfilled, if the design value of the
action or combination of actions does not exceed that lower bound limit value.
a) Design checks are required for normal operating load cases only
b) Partial safety factors for actions shall be as given in Table B.9-1
Table B.9-1: Partial safety factors for actions for CR load cases
|
Action |
Condition |
Partial safety
factor |
|
Permanent |
For
actions with an unfavourable effect |
|
|
Permanent |
For
actions with an favourable effect |
|
|
Variable |
For
unbounded variable actions |
|
|
Variable |
For
bounded variable actions and limit values |
|
|
Pressure |
|
|
c) Combination rules shall be as follows:
All permanent actions shall
be included in each load case.
Each pressure action shall be
combined with the most unfavourable variable action.
Each pressure action shall be
combined with the corresponding sum of the variable actions; the design values
of stochastic actions, see B.6-1 and Table B.6-1, may be multiplied by the
combination factor Y = 0,9, if these stochastic actions are combined with
pressure and/or at least one other stochastic action.
NOTE: Since
it is most unlikely that all the variable stochastic actions would be at their
maximum together, they may each be multiplied by Y
= 0,9 when combined with pressure or another stochastic action.
Favourable variable actions
shall not be considered.
d) Material
strength parameters (RM) and partial safety factors (
) shall be as given in Table B.9-2.
e) As reference
temperature t a temperature not less than the maximum calculation temperature
of the load case shall be used.
As reference time T the specified lifetime in the
creep range, for the component, or part, see B.1.3, shall be used.
NOTE: The reference
temperature t may be chosen as a function of space, but may also be chosen
space ‑ independent.
Table B.9-2: RM and
for CR load cases
|
Material |
RM |
|
|
Steel |
|
1,25 if |
|
Steel castings |
|
19/12 if (19/15) |
In each point of the
structure at which the calculation temperature in any load case is in the creep
range, the accumulated equivalent structural creep strain, accumulated over all
design lifetimes in the creep regime, shall not exceed 5%.
Until agreement on the design
creep constitutive laws, based essentially on data in material standards, is
reached, the Principle shall not be used, but the Application Rules shall be
used instead.
Denoting the components of
the creep strain by
, the equivalent creep strain
is defined by
![]()
This application rule applies
for creep load cases of sufficiently long creep periods with essentially
time-independent temperature and with time-independent other relevant actions,
such that a calculation with time-independent upper bounds of all relevant
actions gives a reasonably good approximation of the structure's creep
behaviour. The creep periods shall be long enough such that the influence of
initial conditions on the lifetime can be reasonably neglected.
NOTE: In case of doubt, the
validity of this pre-supposition should be checked with reasonable constitutive
models
The principle is fulfilled,
if in each point of the structure at which the calculation temperature in any
load case is in the creep regime, the accumulated weighted design lifetime in
the creep regime, accumulated over all design lifetimes in the creep regime,
does not exceed unity. The weight function shall be the reciprocal of the
allowable lifetime for the reference stress
determined for the
relevant load case, see B.9.5.3.2.
For each interval of a load
case in which the calculation temperature is in any point in the creep regime
the creep design temperature
shall be specified
such that it bounds the calculation temperature
from above
![]()
NOTE: This creep design
temperature, to be specified for each interval of all load cases in which the
calculation temperature is in the creep regime, may be specified as a function
of space, or space- independent .
a) Determination of the
elastic limit action
.
For each interval of a load
case, of duration
, in which the calculation temperature is in the creep range,
the value
of the action, or the
combination of actions, relevant for creep, shall be determined, which
corresponds to the on-set of plastification in the region with calculation
temperatures in the creep regime in a design model with
-
linear-elastic ideal-plastic
constitutive law,
-
Mises' yield condition
(maximum distortion energy hypothesis)
-
material strength parameters
and partial safety factors as described in b) below
and
-
for proportional increase of
all actions, with the exception of temperature, which shall be
time-independent, and
-
a stress free initial state.
b) Material strength
parameters and partial safety factors
Material strength parameters (RM)
and partial safety factors
shall be as in Table
B.9-2, but
-
the reference temperature
shall be the creep design temperature, determined with the procedure outlined
in B.9.5.3.1,
-
the reference time shall be
the (sufficiently long) interval duration
, see B.9.5.3.2a).
NOTE 1: For structures of
more than one material the material strength parameters, and their design
values, will be space-dependent.
NOTE 2: For structures of one material, the material strength parameters, and their design values, may be space-dependent or space-independent, depending on the choice of the creep design temperature.
c) Determination of the
(strain limiting) limit action
.
For each interval, of
duration
, in which the calculation temperature is in the creep range,
the maximum value of the action, or the combination of actions, shall be
determined which can be carried by the design model with
-
linear-elastic ideal-plastic
constitutive law,
-
Mises' yield condition
(maximum distortion energy hypothesis) and associated flow rule,
-
a material strength
parameters and partial safety factors as in B.9.5.3.2b)
and for
-
proportional increase of all
actions, with the exception of temperature, which shall be time-independent,
-
a stress free initial state,
with a maximum absolute value
of the principal structural strains less than 5%.
d) Reference stress
For each of these intervals,
of duration
, the design reference stress is given by
![]()
where, in addition to
,
,
as in a), b), c)
above,
denotes the design
value of the relevant action, or the relevant combination of actions. These
design values shall be determined for actions other than temperature from
specified steady upper bounds of these actions with partial safety factors as
in Table B.9-1. The specified steady upper bounds shall bound the actions at
least in the relevant interval.
NOTE 3: The reference stress may be
space-independent but also space-dependent, depending on the choice of the
creep design temperature and on the number of materials, see NOTE 1 and NOTE 2.
Since the very same reference time
has been chosen, the
estimate of creep rupture endurance is space-independent. Therefore, any
convenient position
may be chosen, e. g.
the point of maximum equivalent stress, or the point of maximum temperature,
and reference stress and reference temperature in this point used in the
determination of the weighted lifetime.
For each interval of a load
case, of duration
, in which the calculation temperature is in the creep range,
the weight function is given by
![]()
where
is the allowable
lifetime for a stress equal to
and a limit strength
given by the design strength parameter specified in B.9.5.3.2b), i. e.
according to Table B.9-2.
The weighted design lifetime,
corresponding to this interval in this load case, is given by
![]()
The creep damage indicator is
equal to the accumulated weighted design lifetime, is given by the sum of all
weighted design lifetimes, summed up over all intervals of all load cases where
the calculation temperature is in the creep range, i. e. by
![]()
where the sum extends over
all intervals of all load cases, and over all specified (design) occurances of
the load cases, in which the calculation temperature is in the creep range.
This application rule applies
for load cases of sufficiently long creep periods, as in application rule 1,
but which are interrupted by action cycles resulting in responses of negligible
creep and without plastification, see B.9.5.4.1 and B.9.5.4.2.
For such load cases, creep
and cyclic periods may be treated separately and the individual interrupted
creep periods may be combined into one total (non-interrupted) creep period.
The principle is fulfilled if
the creep and cyclic fatigue design check B.9.6 is fulfilled, with the creep
damage indicator determined for the total creep period by usage of application
rule 1.
Action cycles, which
interrupt long creep periods, are considered to be of negligible creep, if the
maximum duration of calculation temperatures above
-
400°C for ferritic steels,
-
500°C for austenitic steels,
is less than 100 hours.
Action cycles, which
interrupt long creep periods, are considered to be without plastification, if
the maximum Mises equivalent stress of the response of the model, described
below, to the cyclic actions and with initial conditions, described below, does
not exceed the short-term design material strength parameter, described below:
a) The constitutive low of the model shall be
linear-elastic with material parameters for a temperature given in B.7.5.2b).
b) The initial stress distribution shall be the one
obtained like in the determination of the limit action B.9.5.3.2c), for a
reference time, required for the determination of the material strength
parameters in B.9.5.3.2b), given by the total creep period.
c) The short-term design material strength parameter,
with which the maximum equivalent stress is compared, shall be the minimum
specified values of
-
Rp0,2 / tc for
ferritic steels,
-
Rp1,0 / tc for
austenitic steels,
where tc is the respective temperature at each point and each
time.
a) Design checks are required for normal operating load
cases only
b) Partial safety factors for actions, combination rules,
material strength parameters, reference temperature and reference time for the
creep periods, shall be as for the CR-DC, in B.9.4.3. Partial safety factors
shall be 1.
B.9.6 Creep and cyclic fatigue (CFI)
For each point of the
structure, the sum of the design value of the creep damage indicator, see
B.9.5.3, and the design value of the fatigue damage indicator (for cyclic
actions), see B.8.5, shall not exceed unity.
Interpolation and extrapolation procedures for creep strengths