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

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 equation_θAnd radial stress σ_r:

${\mathrm{\σ}}_{\mathrm{\θ}}=\frac{a^{2}p}{b^2-a^2}(1+\frac{b^2}{r^2})$

${\mathrm{\σ}}_r=\frac{a^{2}p}{b^2-a^2}(1-\frac{b^2}{r^2})$

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:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$c=(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L})$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

Wherein, E is the elastic modelling quantity of material, and ν is the Poisson's ratio of material, V_HRepresent hydrogen partial molar volume in mother metal, V_M 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, N_L= N_A/V_MFor the metallic atom quantity of per unit volume, N_AFor Avogadro's number, N_TRepresent 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, W_BHydrogen trap for material combines Energy.

Step 3: calculate axial stress σ_z

${\mathrm{\σ}}_z=\mathrm{\ν}({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_r)-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

Step 4: calculate circumferential strain ε_θAnd radial strain ε_r

${\mathrm{\ϵ}}_{\mathrm{\θ}}=\frac{1}{E}{\mathrm{\σ}}_{\mathrm{\θ}}-\frac{\mathrm{\ν}}{E}({\mathrm{\σ}}_r+{\mathrm{\σ}}_z)+\frac{1}{3}\frac{V_H}{V_M}(c-c_0)$

${\mathrm{\ϵ}}_r=\frac{1}{E}{\mathrm{\σ}}_r-\frac{\mathrm{\ν}}{E}({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_z)+\frac{1}{3}\frac{V_H}{V_M}(c-c_0).$

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:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

Step 203: calculate following functional value g:

$g=c-(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L})$

Step 204: judge g value size, if | g | >=ε_err, then execution step 205 is to step 206, otherwise terminates to calculate, To hydrogen concentration c, wherein ε_errFor convergence tolorence, desirable ε_err=10^-6；

Step 205: calculate hydrogen concentration c according to the following formula₁

$c_1=c-\frac{g}{g^{\′}}$

Wherein

$g^{\′}=1+\[\mathrm{\β}+\mathrm{\α}\frac{N_T}{N_L}\frac{K_T}{{(1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L)}^2}\]\frac{{\mathrm{\θ}}_L^0(1-{\mathrm{\θ}}_L^0)}{{(1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0)}^2}\frac{K_L{V}_H}{3RT}\frac{E}{3}\frac{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 shell_θAnd radial stress σ_r:

${\mathrm{\σ}}_{\mathrm{\θ}}=\frac{a^{2}p}{b^2-a^2}(1+\frac{b^2}{r^2})$

${\mathrm{\σ}}_r=\frac{a^{2}p}{b^2-a^2}(1-\frac{b^2}{r^2})$

Step 2: solve below equation group, calculating hydrogen concentration c:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$c=(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L})$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

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:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

Step 203: parameter step 202 obtained brings following functional value into, calculating functional value g:

$g=c-(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L})$

Step 204: judge g value size, if | g | >=ε_err, then execution step 205 is to step 206, otherwise terminates to calculate, To hydrogen concentration c, wherein convergence tolorence takes ε_err=10^-6；

Step 205: calculate hydrogen concentration c according to the following formula₁

$c_1=c-\frac{g}{g^{\′}}$

Wherein

$g^{\′}=1+\[\mathrm{\β}+\mathrm{\α}\frac{N_T}{N_L}\frac{K_T}{{(1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L)}^2}\]\frac{{\mathrm{\θ}}_L^0(1-{\mathrm{\θ}}_L^0)}{{(1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0)}^2}\frac{K_L{V}_H}{3RT}\frac{E}{3}\frac{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 σ_z

${\mathrm{\σ}}_z=\mathrm{\ν}({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_r)-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

Step 4: circumferential stress σ that step 1 and step 3 are obtained_θ, radial stress σ_rWith axial stress σ_zBring following formula meter into Calculate circumferential strain ε_θAnd radial strain ε_r

${\mathrm{\ϵ}}_{\mathrm{\θ}}=\frac{1}{E}{\mathrm{\σ}}_{\mathrm{\θ}}-\frac{\mathrm{\ν}}{E}({\mathrm{\σ}}_r+{\mathrm{\σ}}_z)+\frac{1}{3}\frac{V_H}{V_M}(c-c_0)$

${\mathrm{\ϵ}}_r=\frac{1}{E}{\mathrm{\σ}}_r-\frac{\mathrm{\ν}}{E}({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_z)+\frac{1}{3}\frac{V_H}{V_M}(c-c_0).$

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. the Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress, it is characterised in that the method comprises the following steps:

Step 1: calculate circumferential stress σ of heavy wall cylindrical shell according to below equation_θAnd radial stress σ_r:

${\mathrm{\σ}}_{\mathrm{\θ}}=\frac{a^{2}p}{b^2-a^2}(1+\frac{b^2}{r^2})$

${\mathrm{\σ}}_r=\frac{a^{2}p}{b^2-a^2}(1-\frac{b^2}{r^2})$

Wherein a is cylindrical shell inside radius, and b is cylindrical shell outer radius, and p is inner pressuring load, and r is the position needing to ask for ess-strain Put.

Step 2: solve below equation group, calculating hydrogen concentration c:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$c=\left(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L}\right)$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

Wherein, E is the elastic modelling quantity of material, and ν is the Poisson's ratio of material, V_HRepresent hydrogen partial molar volume in mother metal, V_MFor mother The molal volume of material, α is the hydrogen trap number of per unit lattice, the interstitial void binding site number of β per unit lattice, N_L=N_A/V_M For the metallic atom quantity of per unit volume, N_AFor Avogadro's number, N_TRepresent the trap number of per unit volume.R is reason Thinking gas constant, T is Kelvin's thermometric scale, c₀For the hydrogen concentration in cylindrical shell during no-load, W_BHydrogen trap for material combines energy.

Step 3: calculate axial stress σ_z

${\mathrm{\σ}}_z=\mathrm{\ν}({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_r)-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

Step 4: calculate circumferential strain ε_θAnd radial strain ε_r

${\mathrm{\ϵ}}_{\mathrm{\θ}}=\frac{1}{E}{\mathrm{\σ}}_{\mathrm{\θ}}-\frac{\mathrm{\ν}}{E}({\mathrm{\σ}}_r+{\mathrm{\σ}}_z)+\frac{1}{3}\frac{V_H}{V_M}(c-c_0)$

${\mathrm{\ϵ}}_r=\frac{1}{E}{\mathrm{\σ}}_r-\frac{\mathrm{\ν}}{E}\left({\mathrm{\σ}}_{\mathrm{\θ}}+{\mathrm{\σ}}_z\right)+\frac{1}{3}\frac{V_H}{V_M}\left(c-c_0\right).$

A kind of Forecasting Methodology facing the strain of hydrogen heavy wall cylindrical shell elastic stress the most according to claim 1, it is characterised in that 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:

${\mathrm{\σ}}_{kk}=\frac{2(1+\mathrm{\ν})a^{2}p}{b^2-a^2}-\frac{E}{3}\frac{V_H}{V_M}(c-c_0)$

$K_L=\exp \left(\frac{{\mathrm{\σ}}_{kk}{V}_H}{3RT}\right)$

$K_T=\exp \left(\frac{W_B}{RT}\right)$

${\mathrm{\θ}}_L=\frac{K_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}$

${\mathrm{\θ}}_L^0=c_0/\mathrm{\β}$

Step 203: calculate following functional value g:

$g=c-(\frac{{\mathrm{\βK}}_L{\mathrm{\θ}}_L^0}{1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0}+\frac{{\mathrm{\αN}}_T}{N_L}\frac{K_T{\mathrm{\θ}}_L}{1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L})$

Step 204: judge g value size, if | g | >=ε_err, then execution step 205 is to step 206, otherwise terminates to calculate, obtains hydrogen Concentration c, wherein ε_errFor convergence tolorence, desirable ε_err=10-⁶；

Step 205: calculate hydrogen concentration c according to the following formula₁

$c_1=c-\frac{g}{g^{\′}}$

Wherein

$g^{\′}=1+\[\mathrm{\β}+\mathrm{\α}\frac{N_T}{N_L}\frac{K_T}{{(1-{\mathrm{\θ}}_L+K_T{\mathrm{\θ}}_L)}^2}\]\frac{{\mathrm{\θ}}_L^0(1-{\mathrm{\θ}}_L^0)}{{(1-{\mathrm{\θ}}_L^0+K_L{\mathrm{\θ}}_L^0)}^2}\frac{K_L{V}_H}{3RT}\frac{E}{3}\frac{V_H}{V_M}$

Step 206: make c=c₁, return step 202.