CN106295021A - A kind of Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress - Google Patents

A kind of Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress Download PDF

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CN106295021A
CN106295021A CN201610670679.4A CN201610670679A CN106295021A CN 106295021 A CN106295021 A CN 106295021A CN 201610670679 A CN201610670679 A CN 201610670679A CN 106295021 A CN106295021 A CN 106295021A
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theta
sigma
cylindrical shell
hydrogen
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陈志平
黄淞
徐烽
郑晨超
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Zhejiang University ZJU
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Abstract

The invention discloses a kind of Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress, the HELP of the method application hydrogen embrittlement is theoretical, with the elastic stress strain under hydrogen environment of the cylindrical shell directly prediction cylindrical shell of the elastic stress strain under atmospheric environment.Compared to the method for structural stress strain under existing prediction hydrogen environment, the present invention has the simple advantage of principle.Straining Forecasting Methodology compared to existing cylindrical shell elastic stress, the impact of cylindrical shell ess-strain is taken into account, engineering design is had some reference value by the present invention by hydrogen environment.

Description

A kind of Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress
Technical field
The present invention relates to face the elastic response prediction field of hydrogen carrying structure, specifically based on hydrogen embrittlement HELP theoretical prediction The elastic stress strain of heavy wall cylindrical shell.
Background technology
Cylindrical shell is the crucial pressure restraining element in hydrogen system during hydrogen storage and defeated hydrogen, determines that heavy wall cylindrical shell is at hydrogen environment Under the elastic response problem that must take into when being the design hydrogen-contacting equipment such as hydrogen container, hydrogenation reactor.Due to this structure of hydrogen damage The complexity of relation, the method for existing prediction material mechanical response under hydrogen environment is to the competency profiling of research worker very Height, simultaneously need to a large amount of programing work, it is difficult to promote in engineering.The most do not occur that being specifically designed to prediction faces hydrogen cylindrical shell stress The method of strain.It is proposed that a kind of method that hydrogen cylindrical shell ess-strain is faced in simple prediction has engineering significance.The present invention The hydrogen of hydrogen embrittlement is promoted, and plasticity localization theoretical (HELP) is applied to heavy wall cylindrical shell, it is proposed that a kind of with atmospheric environment cylinder bullet Property ess-strain prediction face hydrogen cylindrical shell elastic stress strain method.
Summary of the invention
Present invention aims to the deficiencies in the prior art, it is provided that one faces the strain of hydrogen heavy wall cylindrical shell elastic stress Forecasting Methodology, the method predicts the elasticity facing hydrogen cylindrical shell based on the cylindrical shell elastic stress strain in classical atmospheric environment Ess-strain.
It is an object of the invention to be achieved through the following technical solutions: one faces the strain of hydrogen heavy wall cylindrical shell elastic stress Forecasting Methodology, the method comprises the following steps:
Step 1: calculate circumferential stress σ of heavy wall cylindrical shell according to below equationθAnd radial stress σr:
σ θ = a 2 p b 2 - a 2 ( 1 + b 2 r 2 )
σ r = a 2 p b 2 - a 2 ( 1 - b 2 r 2 )
Wherein a is cylindrical shell inside radius, and b is cylindrical shell outer radius, and p is inner pressuring load, and r is to need to ask for ess-strain Position.
Step 2: solve below equation group, calculating hydrogen concentration c:
σ k k = 2 ( 1 + ν ) a 2 p b 2 - a 2 - E 3 V H V M ( c - c 0 )
c = ( βK L θ L 0 1 - θ L 0 + K L θ L 0 + αN T N L K T θ L 1 - θ L + K T θ L )
K L = exp ( σ k k V H 3 R T )
K T = exp ( W B R T )
θ L = K L θ L 0 1 - θ L 0 + K L θ L 0
θ L 0 = c 0 / β
Wherein, E is the elastic modelling quantity of material, and ν is the Poisson's ratio of material, VHRepresent hydrogen partial molar volume in mother metal, VM For the molal volume of mother metal, α is the hydrogen trap number of per unit lattice, the interstitial void binding site number of β per unit lattice, NL= NA/VMFor the metallic atom quantity of per unit volume, NAFor Avogadro's number, NTRepresent the trap number of per unit volume. R is ideal gas constant, and T is Kelvin's thermometric scale, c0For the hydrogen concentration in cylindrical shell during no-load, WBHydrogen trap for material combines Energy.
Step 3: calculate axial stress σz
σ z = ν ( σ θ + σ r ) - E 3 V H V M ( c - c 0 )
Step 4: calculate circumferential strain εθAnd radial strain εr
ϵ θ = 1 E σ θ - ν E ( σ r + σ z ) + 1 3 V H V M ( c - c 0 )
ϵ r = 1 E σ r - ν E ( σ θ + σ z ) + 1 3 V H V M ( c - c 0 ) .
Further, described step 2 uses Newton Algorithm hydrogen concentration c, specifically includes following sub-step:
Step 201: hydrogen concentration initial value c=c is set0
Step 202: according to current hydrogen concentration c, calculates parameters according to the following formula:
σ k k = 2 ( 1 + ν ) a 2 p b 2 - a 2 - E 3 V H V M ( c - c 0 )
K L = exp ( σ k k V H 3 R T )
K T = exp ( W B R T )
θ L = K L θ L 0 1 - θ L 0 + K L θ L 0
θ L 0 = c 0 / β
Step 203: calculate following functional value g:
g = c - ( βK L θ L 0 1 - θ L 0 + K L θ L 0 + αN T N L K T θ L 1 - θ L + K T θ L )
Step 204: judge g value size, if | g | >=εerr, then execution step 205 is to step 206, otherwise terminates to calculate, To hydrogen concentration c, wherein εerrFor convergence tolorence, desirable εerr=10-6
Step 205: calculate hydrogen concentration c according to the following formula1
c 1 = c - g g ′
Wherein
g ′ = 1 + [ β + α N T N L K T ( 1 - θ L + K T θ L ) 2 ] θ L 0 ( 1 - θ L 0 ) ( 1 - θ L 0 + K L θ L 0 ) 2 K L V H 3 R T E 3 V H V M
Step 206: make c=c1, return step 202.
The invention have the advantages that and use the method solving Nonlinear System of Equations, according to the cylindrical shell being easy to get at air The elastic stress strain of cylindrical shell under elastic stress strain in environment directly prediction hydrogen environment, it is not necessary to write the hydrogen loss of complexity Hindering the finite element program of material constitutive model, application threshold is relatively low.
Accompanying drawing explanation
Fig. 1 is the objective for implementation sketch of the present invention;
Fig. 2 is the distribution on different radii of the present example calculated stress;
Fig. 3 is present example calculated strain distribution on different radii.
Detailed description of the invention
Below with the example shown in Fig. 1 and Biao 1 as objective for implementation, the invention will be further described.
Example shown in Fig. 1 is the heavy wall cylindrical shell of a two ends constraint, and its inside radius and outer radius are respectively a and b, hold Being subject to constant internal pressure load p, under unstress state, concentration is c0Hydrogen be uniformly distributed in cylindrical shell.The present invention can predict The cylindrical shell being in hydrogen environment stress and strain under intrinsic pressure p effect.
Material parameter that table 1 example is used and geometric parameter
The inventive method to realize process as follows:
Step 1: choose a radius r (a≤r≤b), such as, take r=a, by the inside radius a in table 1, outer radius b and Inner pressuring load p brings below equation into and calculates circumferential stress σ of heavy wall cylindrical shellθAnd radial stress σr:
σ θ = a 2 p b 2 - a 2 ( 1 + b 2 r 2 )
σ r = a 2 p b 2 - a 2 ( 1 - b 2 r 2 )
Step 2: solve below equation group, calculating hydrogen concentration c:
σ k k = 2 ( 1 + ν ) a 2 p b 2 - a 2 - E 3 V H V M ( c - c 0 )
c = ( βK L θ L 0 1 - θ L 0 + K L θ L 0 + αN T N L K T θ L 1 - θ L + K T θ L )
K L = exp ( σ k k V H 3 R T )
K T = exp ( W B R T )
θ L = K L θ L 0 1 - θ L 0 + K L θ L 0
θ L 0 = c 0 / β
The most each parameter is all shown in Table 1, and step 2 specifically includes following sub-step:
Step 201: hydrogen concentration initial value c=c is set0
Step 202: according to current hydrogen concentration c bring into following formula calculate parameters:
σ k k = 2 ( 1 + ν ) a 2 p b 2 - a 2 - E 3 V H V M ( c - c 0 )
K L = exp ( σ k k V H 3 R T )
K T = exp ( W B R T )
θ L = K L θ L 0 1 - θ L 0 + K L θ L 0
θ L 0 = c 0 / β
Step 203: parameter step 202 obtained brings following functional value into, calculating functional value g:
g = c - ( βK L θ L 0 1 - θ L 0 + K L θ L 0 + αN T N L K T θ L 1 - θ L + K T θ L )
Step 204: judge g value size, if | g | >=εerr, then execution step 205 is to step 206, otherwise terminates to calculate, To hydrogen concentration c, wherein convergence tolorence takes εerr=10-6
Step 205: calculate hydrogen concentration c according to the following formula1
c 1 = c - g g ′
Wherein
g ′ = 1 + [ β + α N T N L K T ( 1 - θ L + K T θ L ) 2 ] θ L 0 ( 1 - θ L 0 ) ( 1 - θ L 0 + K L θ L 0 ) 2 K L V H 3 R T E 3 V H V M
Required each parameter is calculated by step 202;
Step 206: make c=c1, return step 202.
Step 3: hydrogen concentration c step 2 obtained is brought following formula into and calculated axial stress σz
σ z = ν ( σ θ + σ r ) - E 3 V H V M ( c - c 0 )
Step 4: circumferential stress σ that step 1 and step 3 are obtainedθ, radial stress σrWith axial stress σzBring following formula meter into Calculate circumferential strain εθAnd radial strain εr
ϵ θ = 1 E σ θ - ν E ( σ r + σ z ) + 1 3 V H V M ( c - c 0 )
ϵ r = 1 E σ r - ν E ( σ θ + σ z ) + 1 3 V H V M ( c - c 0 ) .
Different r values is used to repeat the stress and strain distribution that step 1 to step 4 can be calculated on whole cross section, Result as shown in Figure 2 and Figure 3, additionally can be seen that hydrogen concentration distribution in cylindrical shell is uniform.

Claims (2)

1.一种临氢厚壁圆柱壳弹性应力应变的预测方法,其特征在于,该方法包括以下步骤:1. A method for predicting elastic stress-strain of a thick-walled cylindrical shell near hydrogen, characterized in that the method may further comprise the steps: 步骤1:按照以下公式计算厚壁圆柱壳的周向应力σθ及径向应力σrStep 1: Calculate the circumferential stress σ θ and radial stress σ r of the thick-walled cylindrical shell according to the following formula: σσ θθ == aa 22 pp bb 22 -- aa 22 (( 11 ++ bb 22 rr 22 )) σσ rr == aa 22 pp bb 22 -- aa 22 (( 11 -- bb 22 rr 22 )) 其中a为圆柱壳内半径,b为圆柱壳外半径,p为内压载荷,r为需要求取应力应变的位置。Where a is the inner radius of the cylindrical shell, b is the outer radius of the cylindrical shell, p is the internal pressure load, and r is the position where the stress and strain need to be calculated. 步骤2:求解以下方程组,计算氢浓度c:Step 2: Calculate the hydrogen concentration c by solving the following system of equations: σσ kk kk == 22 (( 11 ++ νν )) aa 22 pp bb 22 -- aa 22 -- EE. 33 VV Hh VV Mm (( cc -- cc 00 )) cc == (( βKβK LL θθ LL 00 11 -- θθ LL 00 ++ KK LL θθ LL 00 ++ αNαN TT NN LL KK TT θθ LL 11 -- θθ LL ++ KK TT θθ LL )) KK LL == expexp (( σσ kk kk VV Hh 33 RR TT )) KK TT == expexp (( WW BB RR TT )) θθ LL == KK LL θθ LL 00 11 -- θθ LL 00 ++ KK LL θθ LL 00 θθ LL 00 == cc 00 // ββ 其中,E为材料的弹性模量,ν为材料的泊松比,VH表示氢在母材中的偏摩尔体积,VM为母材的摩尔体积,α为每单位晶格的氢陷阱数,β每单位晶格的晶格间隙结合位点数,NL=NA/VM为每单位体积的金属原子数量,NA为阿伏伽德罗常数,NT表示每单位体积的陷阱个数。R为理想气体常数,T为开氏温标,c0为无载荷时圆柱壳内的氢浓度,WB为材料的氢陷阱结合能。where E is the elastic modulus of the material, ν is the Poisson's ratio of the material, V H is the partial molar volume of hydrogen in the base material, V M is the molar volume of the base material, and α is the number of hydrogen traps per unit lattice , β The number of lattice interstitial binding sites per unit lattice, N L =N A /V M is the number of metal atoms per unit volume, N A is Avogadro's constant, NT represents the number of traps per unit volume number. R is the ideal gas constant, T is the Kelvin temperature scale, c0 is the hydrogen concentration in the cylindrical shell at no load, and WB is the hydrogen trap binding energy of the material. 步骤3:计算轴向应力σz Step 3: Calculate the axial stress σ z σσ zz == νν (( σσ θθ ++ σσ rr )) -- EE. 33 VV Hh VV Mm (( cc -- cc 00 )) 步骤4:计算周向应变εθ及径向应变εr Step 4: Calculate the circumferential strain ε θ and the radial strain ε r ϵϵ θθ == 11 EE. σσ θθ -- νν EE. (( σσ rr ++ σσ zz )) ++ 11 33 VV Hh VV Mm (( cc -- cc 00 )) ϵϵ rr == 11 EE. σσ rr -- νν EE. (( σσ θθ ++ σσ zz )) ++ 11 33 VV Hh VV Mm (( cc -- cc 00 )) .. 2.根据权利要求1所述的一种临氢厚壁圆柱壳弹性应力应变的预测方法,其特征在于,所述步骤2采用牛顿法求解氢浓度c,具体包括以下子步骤:2. The method for predicting the elastic stress and strain of a hydrogen-facing thick-walled cylindrical shell according to claim 1, wherein said step 2 uses Newton's method to solve the hydrogen concentration c, specifically comprising the following sub-steps: 步骤201:设置氢浓度初值c=c0Step 201: Set the initial value of hydrogen concentration c=c 0 ; 步骤202:根据当前氢浓度c,按照下式计算各个参数:Step 202: According to the current hydrogen concentration c, calculate various parameters according to the following formula: σσ kk kk == 22 (( 11 ++ νν )) aa 22 pp bb 22 -- aa 22 -- EE. 33 VV Hh VV Mm (( cc -- cc 00 )) KK LL == expexp (( σσ kk kk VV Hh 33 RR TT )) KK TT == expexp (( WW BB RR TT )) θθ LL == KK LL θθ LL 00 11 -- θθ LL 00 ++ KK LL θθ LL 00 θθ LL 00 == cc 00 // ββ 步骤203:计算以下函数值g:Step 203: Calculate the following function value g: gg == cc -- (( βKβK LL θθ LL 00 11 -- θθ LL 00 ++ KK LL θθ LL 00 ++ αNαN TT NN LL KK TT θθ LL 11 -- θθ LL ++ KK TT θθ LL )) 步骤204:判断g值大小,若|g|≥εerr,则执行步骤205至步骤206,否则结束计算,得到氢浓度c,其中εerr为收敛容差,可取εerr=10-6Step 204: Determine the value of g, if |g| ≥εerr , execute step 205 to step 206, otherwise, end the calculation to obtain the hydrogen concentration c, where εerr is the convergence tolerance, and εerr = 10-6 ; 步骤205:按照下式计算氢浓度c1 Step 205: Calculate the hydrogen concentration c 1 according to the following formula cc 11 == cc -- gg gg ′′ 其中in gg ′′ == 11 ++ [[ ββ ++ αα NN TT NN LL KK TT (( 11 -- θθ LL ++ KK TT θθ LL )) 22 ]] θθ LL 00 (( 11 -- θθ LL 00 )) (( 11 -- θθ LL 00 ++ KK LL θθ LL 00 )) 22 KK LL VV Hh 33 RR TT EE. 33 VV Hh VV Mm 步骤206:令c=c1,返回步骤202。Step 206: set c=c 1 , return to step 202 .
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CN115238557A (en) * 2022-07-28 2022-10-25 中国空气动力研究与发展中心超高速空气动力研究所 An evaluation method for hydrogen loss life of shock tube body

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20190137337A (en) * 2018-06-01 2019-12-11 경희대학교 산학협력단 A method for determining average radial stress and pressure vs. volume relationship of a compressible material
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CN115238557A (en) * 2022-07-28 2022-10-25 中国空气动力研究与发展中心超高速空气动力研究所 An evaluation method for hydrogen loss life of shock tube body
CN115238557B (en) * 2022-07-28 2025-03-18 中国空气动力研究与发展中心超高速空气动力研究所 A method for evaluating hydrogen damage life of shock tube

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