CN109933816B - Creep induction period prediction method for coupling residual stress and constraint effect under elastic transient creep condition - Google Patents
Creep induction period prediction method for coupling residual stress and constraint effect under elastic transient creep condition Download PDFInfo
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Abstract
The invention discloses a creep induction period prediction method for a high-temperature structure coupling residual stress and constraint effect under an elastic transient creep condition. And (3) calculating a creep induction period considering the residual stress by introducing an elastic following factor Z by utilizing a reference legislation. Creep experiments were performed using compact tensile specimens (CT) to generate residual stress by precompression and applying a main load. The invention can effectively predict the creep induction period under the elastic transient creep condition by introduction in the structure.
Description
Technical Field
The invention relates to a creep inoculation period engineering critical evaluation of a high-temperature structure coupled with residual stress and constraint effect under an elastic transient creep condition, namely, when a surface crack exists in the structure and the structure is under the transient creep condition, the creep crack initiation life of the high-temperature structure is evaluated.
Background
The energy structure mainly based on coal burning is one of the main causes of haze weather in China, and coal burning power generation is the most main power generation mode in China at present, and the trend exists for a long time. Therefore, besides changing the energy structure, the development of a high-efficiency clean Ultra Supercritical (USC) unit is one of the important ways of energy conservation and emission reduction. However, the service environment of the key high-temperature pipeline of the unit is very severe due to the improvement of parameters such as steam temperature, steam pressure and the like, and particularly, various defects such as cracks, incomplete penetration, welding pores, slag inclusion and the like exist in the pipeline, so that the safe operation of the unit is seriously threatened, and scientific and accurate service life evaluation needs to be carried out on the unit.
For decades, various high temperature creep life assessment criteria and methods have been developed abroad for crack-containing components at high temperatures. The creep induction period is the longest period in the creep process, and the accurate prediction of the induction period has great significance for predicting the creep life of a high-temperature structure; an incubation period prediction model provided by Davies et al based on a toughness dissipation model considers the integrity of stress change in a creep process, but the influence of structural residual stress and restraint effect on the incubation period is not researched; residual stresses, confinement effects, are widely present in machined high temperature components and have a significant impact on the service life of the component. A large number of studies have also been widely conducted on the residual stress and restraint effect in the case of high-temperature creep. Therefore, a creep induction period prediction model coupling the residual stress and the constraint effect is established, and the creep induction period of the composite loading structure can be more accurately and completely evaluated.
Disclosure of Invention
The invention provides a creep induction period prediction model coupling residual stress and constraint effect on the basis of Davies work. By utilizing a reference method, an elastic following factor Z is introduced to calculate a creep induction period considering residual stress. Creep experiments were performed using compact tensile specimens (CT) to generate residual stress by precompression and applying a main load.
The technical scheme adopted for realizing the purpose of the invention is as follows:
the creep induction period prediction method for the high-temperature structure coupling the residual stress and the constraint effect under the elastic transient creep condition comprises the following steps of:
s1, firstly, carrying out compression loading on a CT sample body by using an upper round pin and a lower round pin in a preset size, and then releasing the upper round pin and the lower round pin to generate residual stress distribution near a gap of the CT sample body;
s2, inserting a prefabricated crack at the notch containing the residual stress to perform a creep test;
s3, applying main loads to the upper main load pin hole and the lower main load pin hole by using the pins, and performing a high-temperature creep test;
and S4, obtaining necessary parameters required for calculating the incubation period of the CT sample containing the residual stress through creep finite element simulation. Under elastic transient creep conditions, as shown in FIG. 4, the initial stress at the point of investigation is the elastic stress state, reaching the transitionTime t K-RR Then entering a transient creep stress state;
the method for calculating the induction period mainly comprises the following steps:
(1) Firstly, calculating a stress intensity factor under composite loading, wherein the calculation formula is as follows:
in (I):
wherein:
is a stress intensity factor under the simulation calculation and only contains residual stress, and the unit is MPa (m) 1/2 )；
Is the main load stress intensity factor with the unit of MPa (m) 1/2 ) (ii) a P is the primary load in N; b is the thickness of the specimen in mm, B n Is the net thickness of the sample (B in this application) n = B), in mm; a/W is the length ratio of the prefabricated crack, a is the length of the prefabricated crack, and the horizontal straight line distance from the center of the upper main load pin hole to the rear end of the prefabricated crack is adopted, and the unit is mm; w is the nominal sample width, and the horizontal linear distance from the circle center of the upper main load pin hole to the rear end of the CT sample body is adopted, and the unit is mm; f (a/W) is the geometric coefficient of the CT sample and is only related to a/W; v is a dimensionless plasticity related term calculated as follows:
in (II) V 0 Is a non-dimensional parameter, and the parameter is,
wherein: e' is the effective modulus of elasticity: e' = E/(1-v) 2 ). E is the modulus of elasticity and ν is the poisson's ratio, both of which are described in the literature: (Zhao L, sting H, xu L, han Y, xiu J. Evaluation of related effects on crop grow growth by experimental initiation and numerical simulation. Engng frame Mech 2012.
And J S Extracting by using finite element simulation results;
in (II) L r Is a dimensionless parameter describing the main load amplitude:
wherein: sigma y Is the yield strength in MPa, see literature: (Zhao L, jin H, xu L, han Y, xiu J. Evaluation of constraint efficiencies on crop crack growth by experiment improvemention and numerical simulation.Engng Fract Mech 2012；96:251–66.)；
Is the main load reference stress in MPa, calculated by the following formula:
wherein: n is L For dimensionless crack aspect ratio parameters, the following is calculated:
constant number
(II):
wherein:
is the elastic main load stress intensity factor with the unit of MPa (m) 1/2 )，
Is a plastic main load stress intensity factor with the unit of MPa (m) 1/2 )；
Calculating by using a finite element simulation result:
in the (II), beta describes the amplitude of the residual stress and is a dimensionless parameter;
in the step (II), Z is a dimensionless elastic following factor, a stress-strain relation is extracted from a finite element simulation result, and an equivalent creep strain increment is taken
Equivalent elastic strain increment
The ratio of (A) to (B):
(2) And calculating the integral value of C under the steady-state creep composite stress field, wherein the calculation formula is as follows:
wherein A is creep hardening coefficient in MPa -n ·h -1 ，K I Is a composite stress intensity factor with the unit of MPa (m) 1/2 )。
Is the initial reference stress in MPa;
(3) Then calculating a crack tip parameter C (t) which is a load loop integral value reflecting the transient creep process and has the unit of MPa-mm- (h) -1 ) And calculating by using a reference stress method:
(V) in: sigma ref Is the total reference stress in MPa, calculated using the following integral equation:
wherein:
is the total reference strain rate in units of h -1 ，
Is the primary load reference strain rate in units of h -1 ，
In (V): epsilon ref Is the total reference strain, calculated using the formula:
ε ref ＝ε 0 ref +A ∫σ n ref dt
wherein: epsilon 0 ref Is an initial reference strain, extracted by finite element simulation.
(4) Calculating constraint parameter Q under transient creep condition RR The calculation formula is as follows:
(VI): sigma 22 The opening stress value of the crack front is calculated by using the HRR stress field, the unit is MPa,
wherein: r is the distance from the crack trailing tip to the crack front investigation point in mm, theta is the crack tip angle,
is the creep strain rate of change in units of h -1 Related to the high temperature creep properties of the material, n is the dimensionless creep stress hardening index, n and
see literature: (Zhao L, sting H, xu L, han Y, xiu J. Evaluation of constraint efficiencies on crop crack growth by experimental investigation and numerical simulation.Engng Fract Mech 2012；96:251–66.)，I n Is a non-dimensional function related to n,
is a dimensionless function related to theta and n, I n And
specific values can be found by consulting the literature: shih, C.F. 1983.Tables of Hutchinson-Rice-Rosenggren Single Field Technical Report, MRL E-147.
(5) Calculating transient creep equivalent stress
The calculation formula is as follows:
wherein:
is a dimensionless function related to theta and n, and the specific value can be obtained by looking up the literature: shih, C.F. 1983.Tables of Hutchinson-Rice-Rosenggren Single Field Technical Report, MRL E-147.
Calculating elastic equivalent stress
The calculation formula is as follows:
(6) Calculating the conversion time t by using MATALAB software K-RR : at this moment:
elastic stage damage integrated value:
MSF K the multiaxial stress factor under elastic conditions is calculated according to the relationship of Cocks and Ashby:
wherein: n is a dimensionless creep stress hardening index, sinh is a hyperbolic sine function, h k Three degrees of elastic stress, in the elastic stress state:
wherein: theta is the crack tip angle and ν is the poisson's ratio.
(4) Then calculating the incubation period time t under the transient creep stress field i The calculation formula is as follows:
(VII): d (mm) is the distance extending until the creep damage reaches 1 before the crack tip when the creep initiation occurs, namely the critical distance of the creep initiation.
(VII): MSF RR The multiaxial stress factor under plastic condition is calculated according to the relationship of Cocks and Ashby:
sinh is a hyperbolic sine function, h RR Three degrees of transient creep stress, in the plastic stress state:
wherein the mean stress
The unit is MPa, and the calculation formula is as follows:
wherein: sigma 11 And σ 33 The stress value of the crack front is calculated by utilizing the RRss stress field, the unit is MPa,
wherein:
is a dimensionless function related to theta and n, and the specific value can be obtained by looking up the literature:
Shih,C.F..1983.Tables of Hutchinson-Rice-Rosengren Singular Field Quantities.Brown University Technical Report,MRL E-147.。
preferably, the finite element simulation is a computational simulation using ABAQUS6.14, σ 22 FEM 、
J S 、
ε 0 ref The extraction process comprises the following steps:
(5) Firstly, establishing a finite element model of a pre-compression loaded CT sample, wherein specific dimensions can be shown in figure 1, setting elastic-plastic parameters in a material property module, setting compression load in a load module and constraint conditions: including symmetric conditions and fixed conditions. The contact module is internally provided with a compression round pin which is in rigid contact with the upper surface and the lower surface of the sample, and the analysis step module is internally provided with output parameters: the stress value is used for dividing grids in the grid module;
(6) The task calculation is submitted in the operation module to obtain the calculation result of the residual stress, and the secondary load reference stress can be directly extracted from the field variables in the result file
(7) Establishing a sample model with the same size, carrying out a main load tensile test, referring to fig. 1, setting elastic-plastic creep parameters at high temperature in a material property module, dividing grids in a grid module, setting rigid contact between a tensile pin and a pin hole in a contact module, inserting a prefabricated crack in the model, and setting output parameters in an analysis step module: stress strain value, stress intensity factor K value, rupture parameter J integral value set up tensile load in the load module to and restrain the condition: the method comprises the steps of (1) introducing the calculated residual stress into a preloading stress field under a symmetrical condition and a fixed condition;
(8) Submitting task calculation in the operation module to obtain the calculation result of the creep-tensile experiment containing residual stress, and acquiring initial reference strain from field variables when tensile load is not applied after cracks are inserted in a result file
σ 22 FEM 、
The elastic residual stress intensity factor can be obtained from historical variables
And residual stress rupture parameter J S At the initial moment of applying the tensile load, the plastic main load strength factor can be obtained
Obtaining the change curve of the equivalent stress along with the total strain increment from the historical variables, obtaining the equivalent creep strain increment from the curve,
increment of equivalent elastic strain
And further obtaining an elastic following factor Z calculation method.
Compared with the prior art, the invention has the beneficial effects that:
compared with the existing model, the design method can expand the original prediction model into the model containing the residual stress, so that the simplified method for predicting the creep induction period under the transient creep deformation condition is provided, and the creep induction period under the transient creep deformation condition can be simply and effectively predicted in the structure.
Drawings
FIG. 1 is a schematic structural diagram of a creep induction period prediction model of a high-temperature structure coupling residual stress and constraint effect under elastic conditions according to the present invention.
Wherein: 1-upper round pin, 2-CT sample body, 3-upper main load pin hole, 4-groove, 5-notch, 6-prefabricated crack, 7-lower main load pin hole and 8-lower round pin.
FIG. 2 is a schematic diagram of critical conditions for creep crack initiation.
Fig. 3 shows a method for calculating the elastic tracking factor Z.
Fig. 4 is a schematic diagram of stress conversion.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The creep induction period prediction model of the high-temperature structure coupling the residual stress and the restraint effect under the elastic transient creep condition comprises a CT sample body 1, wherein an upper round pin 1 and a lower round pin 2 are respectively arranged at the upper end and the lower end of the CT sample body, a groove 4 is arranged at the front end of the middle part of the CT sample body, a notch 5 is arranged at the rear part of the groove 4, a prefabricated crack 6 is arranged at the rear part of the notch 5, the groove 4, the notch 5 and the prefabricated crack 6 are on the same plane, an upper main load pin hole 3 and a lower main load pin hole 7 are further arranged on the CT sample body 1, and the upper main load pin hole 3 and the lower main load pin hole 7 are symmetrically arranged up and down and are respectively arranged at the upper end and the lower end of the groove 4.
P92 high-temperature heat-resistant steel was selected, CT samples of B =20mm, W =40mm, a/W =0.5 were used as study objects, and preload of 12000N and a main load of P =12000N were used as study loads. The main material properties are given in the following table:
the creep induction period prediction method for the high-temperature structure coupling the residual stress and the constraint effect under the elastic condition comprises the following steps of:
s1, firstly, carrying out compression loading on a CT sample body by using an upper round pin and a lower round pin in a preset size, and then releasing the upper round pin and the lower round pin to generate residual stress distribution near a gap of the CT sample body;
s2, inserting a prefabricated crack at the notch containing the residual stress to perform a creep test;
s3, applying main loads to the upper main load pin hole and the lower main load pin hole by using the pins, and performing a high-temperature creep test;
and S4, obtaining necessary parameters required for calculating the incubation period of the CT sample containing the residual stress through creep finite element simulation. Under elastic transient creep conditions, as shown in FIG. 4, the initial stress at the point of investigation is the elastic stress state, reaching the transition time t K-RR And then entering a transient creep stress state. Calculating pregnancyThe growing period mainly comprises the following steps:
the technical scheme of the invention is further illustrated by combining the specific examples.
Firstly, calculating each parameter:
(a) Elastic main load strength factor:
the following data were extracted from the finite element results:
(1) First, a finite element model of a pre-compressed loaded CT specimen was built by size. And setting elastic-plastic parameters in the material property module. Set up compression load in the load module to and restrain the condition, restrain the condition and include symmetry condition and fixed condition, set up the rigid contact of compression round pin and sample upper and lower surface in the contact module, set up output parameter in the analysis step module: stress value, dividing grids in the grid module;
(2) And submitting task calculation in the operation module to obtain a calculation result of the residual stress. In the result file, the secondary load reference stress can be directly extracted from the field variable
(3) The same size sample model was built and the main load tensile test was performed, see fig. 1. Elastic-plastic creep parameters under high temperature are set in the material property module, grids are divided in the grid module, rigid contact between a stretching pin and a pin hole is set in the contact module, a prefabricated crack is inserted into the model, and output parameters are set in the analysis step module: stress value, stress intensity factor K value, rupture parameter J integral value set up tensile load in the load module to and the constraint condition: the method comprises the steps of (1) introducing the calculated residual stress into a preloading stress field under a symmetrical condition and a fixed condition;
(4) Submitting task calculation in an operation module to obtain a calculation result of a creep-tensile experiment containing residual stress, wherein in a result file, when no tensile load is applied after a crack is inserted, and when no tensile load is applied after the crack is inserted, an initial reference strain can be obtained from field variables
The elastic residual stress intensity factor can be obtained from historical variables
And residual stress rupture parameter J S =0.013MPa · m, the plastic residual stress intensity factor can be calculated:
at the initial moment of applying the tensile load, the plastic main load strength factor can be obtained
(b) Main load reference stress:
(c) Amplitude of main load:
(d) Residual stress reference stress:
magnitude of residual stress:
(e) Elastic following factor: by step (4) in the above abaqus finite element simulation step, equivalent creep strain increments can be obtained from historical variables, resulting in figure 3,
increment of equivalent elastic strain
As can be read from fig. 3
(f) Plastic related terms:
second, stress intensity factor under composite loading
Initial reference stress:
the value of C integral under the steady state creep composite stress field is:
(III) stress values may then be obtained for the field variables
(a) And (4) looking up a table to obtain:
I n material parameter ε of P92 steel =4.99 crit =0.2; n =5.23, and when calculating creep stress and constraint, we take the distance r = d =0.05mm before the crack tip.
(b) And (6) looking up a table to obtain:
elastic equivalent stress
(IV) looking up a table to obtain:
transient creep equivalent stress
Transition time t K-RR : by using
And MATALAB calculated as: t is t K-RR ＝0h
Elastic stage damage integrated value:
(V) then calculating the germination under the transient creep stress field:
and (4) looking up a table to obtain:
average stress:
stress triaxial degree:
multiaxial stress factor:
d (mm) is the distance extending to 1 from the creep damage before the crack tip when the creep initiation occurs, i.e. the critical distance for the creep initiation, and the grain size of the material under study is generally taken as shown in FIG. 2.
Incubation period under transient creep conditions:
using MATALAB to solve the integral to obtain: t is t i K-RR ＝1755h。
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (3)
1. A creep induction period prediction method for coupling residual stress and constraint effect under elastic transient creep condition is characterized in that S1, an upper round pin and a lower round pin are used for carrying out compression loading with a preset size on a CT sample body, and then the upper round pin and the lower round pin are released, so that residual stress distribution can be generated near a notch of the CT sample body;
s2, inserting a prefabricated crack at the notch containing the residual stress to perform a creep test;
s3, applying main loads to the upper main load pin hole and the lower main load pin hole by using the pins, and performing a high-temperature creep test;
s4, obtaining necessary parameters required for calculating the incubation period of the CT sample containing residual stress through creep finite element simulation, wherein under the condition of elastic transient creep, the initial stress of a research point is in an elastic stress state, and the transition time t is reached K-RR Then entering a transient creep stress state;
the method for calculating the induction period mainly comprises the following steps:
(1) Firstly, calculating a stress intensity factor under composite loading, wherein the calculation formula is as follows:
in (I):
wherein:
is a stress intensity factor under the simulation calculation and only contains residual stress, and the unit is MPa (m) 1/2 )；
Is the main load stress intensity factor with the unit of MPa (m) 1/2 ) (ii) a P is the primary load in N; b is the thickness of the specimen in mm, B n Is the net thickness of the sample, in mm; a/W is the length ratio of the prefabricated crack, a is the length of the prefabricated crack, and the horizontal straight line distance from the center of the upper main load pin hole to the rear end of the prefabricated crack is adopted, and the unit is mm; w is the nominal sample width, and the horizontal linear distance from the circle center of the upper main load pin hole to the rear end of the CT sample body is adopted, and the unit is mm; f (a/W) is the geometric coefficient of the CT sample and is only related to a/W; v is a dimensionless plasticity related term calculated as follows:
in (II) V 0 Is a non-dimensional parameter, and the parameter is,
wherein: e' is the effective elastic modulus: e' = E/(1-v) 2 ) E is the modulus of elasticity, v is the Poisson's ratio,
and J S Extracting by using finite element simulation results;
in (II) L r Is a dimensionless parameter describing the main load amplitude:
wherein: sigma y Is the yield strength in MPa;
is the main load reference stress in MPa, calculated by the following formula:
wherein: n is L For dimensionless crack aspect ratio parameters, calculated by:
constant number
(II):
wherein:
is the elastic main load stress intensity factor with the unit of MPa (m) 1/2 )，
Is a plastic main loadStress intensity factor in MPa (m) 1/2 )；
Calculating by using a finite element simulation result:
in the (II), beta describes the amplitude of the residual stress and is a dimensionless parameter;
in the step (II), Z is a dimensionless elastic following factor, a stress-strain relation is extracted from a finite element simulation result, and an equivalent creep strain increment is taken
Equivalent elastic strain increment
The ratio of (A) to (B):
(2) And calculating the integral value of C under the steady-state creep composite stress field, wherein the calculation formula is as follows:
wherein A is creep hardening coefficient in MPa -n ·h -1 ，K I Is a composite stress intensity factor with the unit of MPa (m) 1 /2 )，
Is the initial reference stress in MPa;
(3) Then calculating a crack tip parameter C (t) which is a load loop integral value reflecting the transient creep process and has the unit of MPa.mm (h) -1 ) And calculating by using a reference stress method:
in (V): sigma ref Is the total reference stress in MPa, calculated using the following integral equation:
wherein:
is the total reference strain rate in units of h -1 ，
Is the primary load reference strain rate in units of h -1 ，
(V) in: epsilon ref Is the total reference strain, calculated using the formula:
ε ref ＝ε 0 ref +A∫σ n ref dt
wherein: epsilon 0 ref Is an initial reference strain, is extracted by finite element simulation,
(4) Calculating constraint parameter Q under transient creep condition RR The calculation formula is as follows:
(VI): sigma 22 The opening stress value of the crack front is calculated by using the HRR stress field, the unit is MPa,
wherein: r is the distance from the crack trailing tip to the crack front investigation point in mm, theta is the crack tip angle,
is the creep strain rate of change in units of h -1 Related to the high temperature creep properties of the material, n is the dimensionless creep stress hardening index, I n Is a non-dimensional function related to n,
is a dimensionless function related to theta and n,
(5) Calculating transient creep equivalent stress
The calculation formula is as follows:
wherein:
is a dimensionless function related to theta and n,
calculating elastic equivalent stress
The calculation formula is as follows:
(6) Calculating the conversion time t by using MATALAB software K-RR : at this moment:
elastic stage damage integrated value:
MSF K the multiaxial stress factor under elastic conditions is calculated according to the relationship of Cocks and Ashby:
wherein: n is a dimensionless creep stress hardening index, sinh is a hyperbolic sine function, h k Three degrees of elastic stress, in the elastic stress state:
wherein: theta is the crack tip angle, ν is the poisson's ratio,
(4) Then calculating the incubation period time t under the transient creep stress field i The calculation formula is as follows:
(VII): d (mm) is the distance extending from the creep damage before the crack tip to 1 when the creep initiation occurs, namely the critical distance of the creep initiation,
(VII): MSF RR Calculating a multiaxial stress factor under a plastic condition according to a relational expression of Cocks and Ashby:
sinh is a hyperbolic sine function, h RR Three degrees of transient creep stress, in the plastic stress state:
wherein the mean stress
The unit is MPa, and the calculation formula is as follows:
wherein: sigma 11 And σ 33 The stress value of the crack front is calculated by utilizing the RRss stress field, the unit is MPa,
wherein:
is a dimensionless function with respect to theta and n.
2. The method of claim 1, wherein the finite element modeling is computational modeling using ABAQUS6.14 to compute σ, a 22 FEM 、
J S 、
ε 0 ref The extraction process comprises the following steps:
(1) Firstly, establishing a finite element model of a pre-compressed loaded CT sample, setting elastic-plastic parameters in a material property module, setting compression load in a load module, and setting a constraint condition: including symmetry condition and fixed condition, set up the rigid contact of compression round pin and sample upper and lower surface in the contact module, set up output parameter in the analysis step module: stress value, dividing grids in the grid module;
(2) The task calculation is submitted in the operation module to obtain the calculation result of the residual stress, and the secondary load reference stress can be directly extracted from the field variables in the result file
(3) Establishing a sample model with the same size, carrying out a main load tensile test, setting elastic-plastic creep parameters at high temperature in a material property module, dividing grids in a grid module, setting rigid contact between a tensile pin and a pin hole in a contact module, inserting a prefabricated crack in the model, and setting output parameters in an analysis step module: stress strain value, stress intensity factor K value, rupture parameter J integral value set up tensile load in the load module to and restrain the condition: the method comprises the steps of (1) introducing the calculated residual stress into a preloading stress field under a symmetrical condition and a fixed condition;
(4) The method comprises the steps of submitting task calculation in an operation module, obtaining a calculation result of a creep-tensile experiment containing residual stress, and obtaining initial reference strain from field variables when tensile load is not applied after cracks are inserted in a result file
σ 22 FEM 、
The elastic residual stress intensity factor can be obtained from historical variables
And residual stress rupture parameter J S At the initial moment of applying the tensile load, the plastic main load strength factor can be obtained
Obtaining the change curve of the equivalent stress along with the total strain increment from the historical variables, obtaining the equivalent creep strain increment from the curve,
increment of equivalent elastic strain
And further obtaining an elastic following factor Z calculation method.
3. The method of claim 1, wherein B is a method of predicting creep induction period coupling residual stress and constraint effect under elastic transient creep conditions n ＝B。
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