CN112329301B - Optimal self-compaction pressure determining method suitable for metal lining composite gas cylinder - Google Patents
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- 239000002131 composite material Substances 0.000 title claims abstract description 32
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- 238000005056 compaction Methods 0.000 title claims abstract description 29
- 229910052751 metal Inorganic materials 0.000 title claims abstract description 14
- 239000002184 metal Substances 0.000 title claims abstract description 14
- 239000000835 fiber Substances 0.000 claims abstract description 36
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- 238000004364 calculation method Methods 0.000 claims abstract description 18
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- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 description 2
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Abstract
An optimal self-compaction pressure determining method suitable for a metal lining composite gas cylinder belongs to the technical field of high-pressure gas cylinder manufacturing. Firstly, determining the size, layering and material properties of a gas cylinder to be analyzed, establishing a finite element model of the gas cylinder made of the composite material, modeling a fiber winding layer in a straight section by adopting equal thickness, and modeling a sealing head section by adopting variable thickness. Secondly, selecting a gas cylinder self-tightening condition, and using ANSYS finite element software to simulate the gas cylinder self-tightening. Again, the ultimate strength and fatigue life under the different autofrettage conditions as described in the second step were calculated by ANSYS finite element software. And finally, comparing and determining the optimal self-tightening pressure according to the condition to be met by the self-tightening treated gas cylinder. The invention provides a calculation method of the self-tightening pressure of a gas cylinder on the premise of considering the strength and the fatigue life; the influence of various failure modes on the rigidity of the composite material is considered by adopting a degradation criterion, the ultimate strength and the fatigue life of the gas cylinder can be accurately calculated, and then the optimal self-compaction pressure is selected.
Description
Technical Field
The invention belongs to the technical field of high-pressure gas cylinder manufacturing, and relates to an optimal self-compaction pressure determining method suitable for a metal lining composite gas cylinder.
Background
Currently, aluminum liner fiber fully-wound composite gas cylinders are widely applied to high and new technical fields such as aerospace, pressure vessels, new energy automobiles and the like. Because of the different mechanical properties of the aluminum inner container and the carbon fiber winding layer, under the same strain state, even if the aluminum inner container is in a plastic state and yields, the carbon fiber is in an elastic low-stress state. To solve this problem, the cylinder may be subjected to a self-tightening process prior to the application of the operating pressure. The self-tightening treatment is to apply a self-tightening pressure higher than the working pressure to the inside of the gas cylinder before the gas cylinder is used so as to make the metal lining generate plastic deformation, and the fiber winding layer is still in the elastic deformation state. After pressure unloading, the metal lining cannot recover the original size due to residual deformation, so that certain compressive stress (prestress) is generated on the liner, and the fiber winding layer is in a tensile state due to the obstruction of the residual deformation of the metal lining, and has certain tensile stress. Under working pressure, the stress generated by the internal pressure of the gas cylinder is superposed with the prestress, so that the stress of the metal lining tends to be uniform along the wall thickness distribution, and the elastic bearing capacity and the safety life of the metal lining are improved.
Chinese patent CN 106909708A relates to a method for determining the optimal self-tightening pressure of an aluminum liner fiber fully-wound composite gas cylinder, in particular to a finite element method for determining the optimal self-tightening pressure of an aluminum liner fiber fully-wound composite gas cylinder. The patent CN 106909708A does not consider the effect of fatigue life on self-tightening pressure in the method of determining the optimal self-tightening pressure of an aluminum liner fiber fully wrapped composite gas cylinder.
The fatigue failure is a main failure factor in the use process of the gas cylinder, and the invention provides an optimal self-compaction pressure determination method suitable for the gas cylinder made of the metal lining composite material on the basis of considering the fatigue life.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for determining the optimal self-compaction pressure of a metal lining composite gas cylinder, which can solve the following problems in the prior art: fatigue failure is one of the main forms of cylinder failure, but existing self-tightening pressure determination methods only consider ultimate strength, resulting in a self-tightening pressure that is not the optimal solution. The invention simultaneously considers the ultimate strength and fatigue strength of the gas cylinder and performs finite element analysis of the low-temperature gas cylinder under different self-tightening conditions. And comparing and analyzing calculation results under different self-tightening conditions, and finally determining the optimal self-tightening pressure of the low-temperature gas cylinder.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an optimal self-compaction pressure determination method suitable for a metal lining composite gas cylinder comprises the following steps:
firstly, determining the size, layering and material properties of a gas cylinder to be analyzed, establishing a finite element model of the gas cylinder made of a composite material, modeling a fiber winding layer in a straight section with equal thickness, and modeling a sealing head section with variable thickness; wherein, the thickness t of the end socket section of the fiber winding layer is changed f The calculation formula of (2) is as follows:
wherein: r is the distance from the point of the end socket to the central axis, r 0 The radius of the polar axis, R, is the outer diameter of the straight section, t, determined for the manufacturing process fα Is equal to the thickness of the spiral group of the cylinder body at the equatorial circle.
Second, selecting the self-tightening condition of the gas cylinder
The self-tightening pressure of the gas cylinder is 1.3-1.5 times of working pressure. Within the range, the normal temperature self-compression pressure a of the gas cylinder can be arbitrarily set i And low temperature self-compaction force b j The method comprises the steps of carrying out a first treatment on the surface of the N and m self-compaction pressure values are selected from the equal difference between the working pressures of 1.3 times and 1.5 times and are respectively used as a i (i=1, 2, … n) and b j (i=1, 2, … m), all the selected room temperature self-compaction forces a i With low temperature self-compaction force b j Permutation and combination are performed to generate n multiplied by m groups of calculation combinations for the next step of self-tightening simulation.
And thirdly, simulating the self-tightening of the gas cylinder by using ANSYS finite element software. First, normal temperature self-tightening force a is applied i The liner enters the yield stage and then is gradually unloaded, after which the cylinder will have residueStress (residual stress which is not completely unloaded), and continuously applying a low-temperature self-tightening pressure b on the gas cylinder with residual stress j And then gradually unloading to finish the self-tightening treatment process of the composite material low-temperature gas cylinder.
Fourthly, calculating the ultimate strength and the fatigue life under different self-tightening conditions (as described in the second step) through ANSYS finite element software;
(1) The ultimate strength is solved and the flow chart is shown in figure 3.
The ultimate strength is solved by adopting the progressive failure analysis of a composite material structure, wherein the progressive failure analysis comprises stress analysis and failure analysis;
and calculating by using an ANSYS linear static solver, wherein other solving control options are set according to ANSYS default options. Applying an initial load P 0 Failure analysis is carried out, and the bottle mouth of the gas bottle is provided with a reinforcing design, so that the end socket section and the straight barrel section of the liner are used as judging ranges. And extracting Mises equivalent strain in the finite element calculation result, taking the ultimate strain of the material as a criterion, and considering that the gas cylinder fails when the Mises equivalent strain of the lining exceeds the ultimate strain, so as to obtain the ultimate strength.
If the cylinder has not failed, a stress analysis is performed. The cells are checked using failure criteria to check if any cells in the structure are corrupted. And judging the cracking of the gas cylinder composite material matrix by adopting a Tsai-Wu criterion, and judging the fiber breakage by adopting a maximum stress criterion.
The Tsai-Wu criterion:
wherein: x, Y, S the axial strength, transverse strength and shear strength, respectively; superscript t denotes tensile, c denotes compressive; sigma, tau are normal and shear stresses, subscript 1 denotes fibre direction, subscript 2 denotes in-plane matrix direction, subscript 3 denotes out-of-plane matrix direction, sigma 1 Representing fiber direction stress, sigma 2 Represents in-plane matrix directional stress, τ 12 Representing in-plane shear stress; s is S 12 Represents in-plane shear strength;
x, Y, S is the material property, sigma, tau is the finite element calculation result. When the calculated σ, τ is brought into formula (1), and left is equal to or greater than 1, the matrix cracking is considered to occur based on the Tsai-Wu criterion.
The maximum stress criterion:
σ 1 ＜X (2)
wherein X is the tensile strength of the fiber, respectively. Sigma (sigma) 1 Is the tensile stress of the fiber.
σ 1 Obtained by finite element calculations, X being a known fixed material property, when calculated sigma 1 When the value is equal to or greater than X, fiber breakage is considered to occur based on the maximum stress criterion.
When the structure is damaged initially, the structure does not fail immediately, but still has a certain bearing capacity, but the rigidity of the structure is degraded to a certain extent, and the rigidity of the failure unit needs to be reduced. And for the unit judged to be invalid, adopting a Camanho stiffness degradation criterion to carry out stiffness reduction. The reduced macroscopic material stiffness at failure of a single component material can be expressed as:
wherein w is s (w s ＝E 1 ,E 2 ,G 12 ,G 23 ,μ 12 ) Stiffness properties that are good materials;w is respectively s The coefficient of compromise of the j-th stiffness properties of the matrix, the upper right corner mark α (α=f, m) of which indicates the type of component material, f-fiber, m-matrix, in which the failure has occurred.
If the failure unit is damaged, carrying out stress analysis again under the same load after adopting rigidity reduction on the failure unit; if no unit is broken, 1 load increment delta P is increased, and the process is repeated until the whole gas cylinder fails.
(2) The fatigue life of the aluminum alloy lining of the gas cylinder is calculated by adopting a Manson-Coffin formula:
wherein: epsilon a Is the total strain amplitude; sigma'. f Known as the fatigue strength coefficient; epsilon' f Known as the fatigue ductility coefficient; sigma (sigma) m Is the average stress; e is the elastic modulus; b is the fatigue strength index; c is the fatigue ductility index and N is the calculated fatigue life.
Wherein ε a ，σ′ f ，ε′ f ，σ m And E is a known elastic modulus, b and c are engineering constants (for most metal materials, the fatigue strength index b is generally-0.06 to-0.14, and the fatigue ductility index c is generally-0.5 to-0.7).
And fifthly, determining the optimal self-compaction force.
Firstly, according to the design rule of DOT CFFC in the United states, the gas cylinder after self-tightening treatment should satisfy the following conditions:
(1) At zero pressure, the maximum compressive stress of the liner must be between 60% and 95% of its material yield limit;
(2) The maximum tensile stress of the liner should be less than 60% of its material yield limit at the operating pressure.
Screening the self-tightening conditions meeting the design criteria, comparing and analyzing the ultimate strength and the fatigue life of the gas cylinder under different self-tightening conditions, and selecting the result with excellent fatigue life and ultimate strength as the comprehensive optimal self-tightening pressure.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention provides a calculation method of the self-tightening pressure of a gas cylinder on the premise of considering strength and fatigue life. The importance and necessity is that fatigue failure is the most dominant failure mode of the gas cylinder, and the result is not reliable regardless of fatigue life.
(2) The composite material has strong anisotropism, multiple failure modes and mutual connection. The method adopts progressive failure analysis to consider the accumulated damage of the composite material, and compared with the prior art, the method adopts a degradation criterion (formula 3) to consider the influence of various failure modes on the rigidity of the composite material, so that the ultimate strength and fatigue life of the gas cylinder can be accurately calculated, and the selected self-tightening pressure is the optimal self-tightening pressure.
Drawings
FIG. 1 is a 1/8 geometric model of the present invention
Fig. 2 is a flow chart of the present invention.
Fig. 3 is a flow chart of progressive failure analysis.
Detailed Description
The invention will be further illustrated with reference to specific examples.
The method for determining the optimal self-compaction pressure of the gas cylinder made of the metal lining composite material comprises the following steps:
and firstly, determining the size, layering and material properties of the gas cylinder, and establishing a finite element model of the composite gas cylinder. The fiber winding layer is modeled by adopting equal thickness in the straight barrel section, and is modeled by adopting variable thickness in the end socket section;
wherein the thickness t of the end socket section of the fiber winding layer is changed f Using the formula
Wherein: r is the distance from the point of the end socket to the central axis, r 0 The radius of the polar axis, R, is the outer diameter of the straight section, t, determined for the manufacturing process fα Is equal to the thickness of the spiral group of the cylinder body at the equatorial circle.
And secondly, selecting the self-tightening condition of the gas cylinder.
The self-tightening pressure of the gas cylinder is 1.3-1.5 times of working pressure. Within the range, the normal temperature self-compression pressure a of the gas cylinder can be arbitrarily set i And low temperature self-compaction force b j The method comprises the steps of carrying out a first treatment on the surface of the 4 self-tightening pressure values are selected from the equal difference between 1.3 times and 1.5 times of self-tightening pressure, the normal temperature self-tightening pressure is 45, 47, 49 and 51Mpa, the low temperature self-tightening pressure is 45, 47, 49 and 51Mpa, and all the selected normal temperatureThe self-compaction force and the low-temperature self-compaction force are arranged and combined to generate 16 groups of calculation combinations for the next self-compaction simulation.
And thirdly, simulating the self-tightening of the gas cylinder by using ANSYS finite element software.
First, normal temperature self-tightening force a is applied i The lining enters the yielding stage and then is gradually unloaded, after unloading, the gas cylinder has residual stress (stress residual which is not completely unloaded), and the gas cylinder with the residual stress continuously applies a low-temperature self-tightening pressure b j And then gradually unloading to finish the self-tightening treatment process of the composite material low-temperature gas cylinder.
In the fourth step, the third step is that,
calculating the ultimate strength and fatigue life of the gas bottle under different self-compaction pressures at low temperature and low temperature respectively through ANSYS finite element software;
(1) The method comprises the steps of solving the ultimate strength, wherein the ultimate strength is solved by adopting the progressive failure analysis of a composite material structure, and the progressive failure analysis comprises stress analysis and failure analysis;
and calculating by using an ANSYS linear static solver, wherein other solving control options are set according to ANSYS default options. Applying an initial load P 0 Failure analysis is carried out, and the bottle mouth of the gas bottle is provided with a reinforcing design, so that the end socket section and the straight barrel section of the liner are used as judging ranges. And extracting Mises equivalent strain in the finite element calculation result, taking the ultimate strain of the material as a criterion, and considering that the gas cylinder fails when the Mises equivalent strain of the lining exceeds the ultimate strain, so as to obtain the ultimate strength.
If the cylinder has not failed, a stress analysis is performed. The cells are checked using failure criteria to check if any cells in the structure are corrupted. And judging the cracking of the gas cylinder matrix by adopting a Tsai-Wu criterion, and judging the fiber breakage by adopting a maximum stress criterion.
The Tsai-Wu criterion:
wherein: x, Y, S the axial strength, transverse strength and shear strength, respectively; superscript t denotes stretch, cRepresenting compression; sigma, tau are normal and shear stresses, subscript 1 denotes fibre direction, subscript 2 denotes in-plane matrix direction, subscript 3 denotes out-of-plane matrix direction, sigma 1 Representing fiber direction stress, sigma 2 Represents in-plane matrix directional stress, τ 12 Representing in-plane shear stress; s is S 12 Represents in-plane shear strength;
x, Y, S is the material property, sigma, tau is the finite element calculation result. When the calculated σ, τ is brought into formula (1), and left is equal to or greater than 1, the matrix cracking is considered to occur based on the Tsai-Wu criterion.
The maximum stress criterion:
σ 1 ＜X (2)
wherein X is the tensile strength of the fiber, respectively. Sigma (sigma) 1 Is the tensile stress of the fiber.
σ 1 Obtained by finite element calculations, X being a known material property, when calculated sigma 1 When the value is equal to or greater than X, fiber breakage is considered to occur based on the maximum stress criterion.
When the structure is damaged initially, the structure does not fail immediately, but still has a certain bearing capacity, but the rigidity of the structure is degraded to a certain extent, and the rigidity of the failure unit needs to be reduced. And checking whether a unit in the structure is damaged according to a failure criterion, and carrying out rigidity reduction on the unit judged to be failed by adopting a Camanho rigidity degradation criterion. The reduced macroscopic material stiffness at failure of a single component material can be expressed as:
wherein w is s (w s ＝E 1 ,E 2 ,G 12 ,G 23 ,μ 12 ) Stiffness properties that are good materials;w is respectively s The coefficient of compromise of the j-th stiffness properties of the matrix, the upper right-hand corner mark α (α=f, m) representing the type of component material in which failure occurs, f-fibersThe method for degrading the rigidity of the m-matrix is specifically as follows:
matrix stretching or shear cracking:
E 2 d ＝0.2E 2 G 12 d ＝0.22G 12 v 12 d ＝0.15v 12
fiber stretch breaking:
E 1 d ＝0.07E 1 E 2 d ＝0.07E 2 G 12 d ＝0.07G 12 v 12 d ＝0.07v 12
both matrix stretch or shear cracking and fiber stretch breaking occur:
E 1 d ＝0.07E 1 E 2 d ＝0.2E 2 G 12 d ＝0.22G 12 v 12 d ＝0.15v 12
wherein E is i For modulus of elasticity, V ij For Poisson's ratio, G ij The shear elastic modulus is a material parameter.
Subscript 1 indicates the fiber direction, subscript 2 indicates the in-plane matrix direction, and subscript 3 indicates the out-of-plane matrix direction.
If the failure unit is damaged, carrying out stress analysis again under the same load after adopting rigidity reduction on the failure unit; if no unit is broken, 1 load increment delta P is increased, and the process is repeated until the whole gas cylinder fails.
(2) The fatigue life of the aluminum alloy lining of the gas cylinder is calculated by adopting a Manson-Coffin formula:
wherein: epsilon a Is the total strain amplitude; sigma'. f Known as the fatigue strength coefficient; epsilon' f Known as the fatigue ductility coefficient; sigma (sigma) m Is the average stress; e is the elastic modulus; b is the fatigue strength index; c is the fatigue ductility index and N is the calculated fatigue life.
Wherein ε a ，σ′ f ，ε′ f ，σ m And E is a known elastic modulus, b and c are engineering constants (for most metal materials, the fatigue strength index b is generally-0.06 to-0.14, and the fatigue ductility index c is generally-0.5 to-0.7).
And fifthly, determining the optimal self-compaction force.
Firstly, according to the design rule of DOT CFFC in the United states, the gas cylinder after self-tightening treatment should satisfy the following conditions:
(1) At zero pressure, the maximum compressive stress of the liner must be between 60% and 95% of its material yield limit;
(2) The maximum tensile stress of the liner should be less than 60% of its material yield limit at the operating pressure.
And screening out self-tightening conditions meeting the design criteria, comparing and analyzing the ultimate strength and the fatigue life of the gas cylinder under different self-tightening conditions, and selecting the result with excellent fatigue life and ultimate strength as the comprehensive optimal self-tightening pressure.
The examples described above represent only embodiments of the invention and are not to be understood as limiting the scope of the patent of the invention, it being pointed out that several variants and modifications may be made by those skilled in the art without departing from the concept of the invention, which fall within the scope of protection of the invention.
Claims (4)
1. The method for determining the optimal self-compaction pressure of the gas cylinder made of the metal lining composite material is characterized by comprising the following steps of:
firstly, determining the size, layering and material properties of a gas cylinder to be analyzed, establishing a finite element model of the gas cylinder made of a composite material, modeling a fiber winding layer in a straight section with equal thickness, and modeling a sealing head section with variable thickness; wherein, the thickness t of the end socket section of the fiber winding layer is changed f The calculation formula of (2) is as follows:
wherein: r is the distance from the end socket to the central axis, r 0 The radius of the polar axis, R, is the outer diameter of the straight section, t, determined for the manufacturing process fα The thickness of the spiral group of the cylinder body is equal to that of the equatorial circle;
second, selecting the self-tightening condition of the gas cylinder
The selection range of the self-tightening pressure of the gas cylinder is 1.3 to 1.5 times of the working pressure; within the range, the normal temperature self-compression pressure a of the gas cylinder can be arbitrarily set i And low temperature self-compaction force b j The method comprises the steps of carrying out a first treatment on the surface of the N and m self-compaction pressure values are selected from the equal difference between the working pressures of 1.3 times and 1.5 times and are respectively used as a i (i=1, 2, … n) and b j (i=1, 2, … m), all the selected room temperature self-compaction forces a i With low temperature self-compaction force b j Performing permutation and combination to generate n multiplied by m groups of calculation combinations for the next step of self-tightening simulation;
thirdly, using ANSYS finite element software to simulate the self-tightening of the gas cylinder; first, normal temperature self-tightening force a is applied i The lining enters a yielding stage and then is gradually unloaded, the gas cylinder has residual stress after unloading, and the gas cylinder with the residual stress continuously applies low-temperature self-tightening pressure b j Then gradually unloading to finish the self-tightening treatment process of the composite material low-temperature gas cylinder;
fourthly, calculating the ultimate strength and the fatigue life under different self-tightening conditions as in the second step through ANSYS finite element software;
(1) Ultimate strength solution:
the ultimate strength is solved by adopting the progressive failure analysis of a composite material structure, wherein the progressive failure analysis comprises stress analysis and failure analysis;
calculating and using an ANSYS linear static solver, wherein other solving control options are set according to ANSYS default options; applying an initial load P 0 Performing failure analysis, and taking the end socket section and the straight section of the liner as judging ranges; extracting Mises equivalent strain in a finite element calculation result, taking the ultimate strain of a material as a criterion, and considering that a gas cylinder fails when the Mises equivalent strain of the lining exceeds the ultimate strain to obtain ultimate strength;
if the gas cylinder is not in failure, performing stress analysis; checking the units by applying a failure criterion to check whether the units in the structure are damaged; judging the cracking of the gas cylinder composite material matrix by adopting a Tsai-Wu criterion, and judging the fiber breakage by adopting a maximum stress criterion;
when the structure is initially damaged, the rigidity of the failure unit is required to be reduced; for the judged failure unit, adopting a Camanho stiffness degradation criterion to carry out stiffness reduction; the reduced macroscopic material stiffness at failure of a single component material is expressed as:
wherein w is s (w s ＝E 1 ,E 2 ,G 12 ,G 23 ,μ 12 ) Stiffness properties that are good materials;w is respectively s The coefficient of compromise of the j-th stiffness property, the upper right corner mark alpha (alpha=f, m) of which represents the type of component material, f-fiber, m-matrix, in which failure occurs;
if the failure unit is damaged, carrying out stress analysis again under the same load after adopting rigidity reduction on the failure unit; if no unit is damaged, increasing 1 load increment delta P, and repeating the ultimate strength solving process until the whole gas cylinder fails;
(2) The fatigue life of the aluminum alloy lining of the gas cylinder is calculated by adopting a Manson-Coffin formula:
wherein: epsilon a Is the total strain amplitude; sigma'. f Known as the fatigue strength coefficient; epsilon' f Known as the fatigue ductility coefficient; sigma (sigma) m Is the average stress; e is the elastic modulus; b is the fatigue strength index; c is the fatigue ductility index, N is the calculated fatigue lifeThe method comprises the steps of carrying out a first treatment on the surface of the Wherein ε a ，σ′ f ，ε′ f ，σ m Extracting the finite element calculation result in the fourth step, wherein E is a known elastic modulus, b and c are engineering constants, b represents a fatigue strength index, and c represents a fatigue ductility index;
fifthly, determining optimal self-compaction force;
the gas cylinder after self-tightening treatment should satisfy:
(1) At zero pressure, the maximum compressive stress of the lining is between 60% and 95% of the yield limit of the material;
(2) At operating pressures, the maximum tensile stress of the liner should be less than 60% of its material yield limit;
screening the self-tightening conditions meeting the design criteria, comparing and analyzing the ultimate strength and the fatigue life of the gas cylinder under different self-tightening conditions, and selecting the result with excellent fatigue life and ultimate strength as the comprehensive optimal self-tightening pressure.
2. The method for determining the optimal self-compaction pressure for a metal-lined composite cylinder according to claim 1, wherein the Tsai-Wu criterion:
wherein: x, Y, S the axial strength, transverse strength and shear strength, respectively; superscript t denotes tensile, c denotes compressive; sigma, tau are normal and shear stresses, subscript 1 denotes fibre direction, subscript 2 denotes in-plane matrix direction, subscript 3 denotes out-of-plane matrix direction, sigma 1 Representing fiber direction stress, sigma 2 Represents in-plane matrix directional stress, τ 12 Representing in-plane shear stress; s is S 12 Represents in-plane shear strength;
x, Y, S is the property of the material, sigma and tau is the finite element calculation result; when the calculated σ, τ is brought into formula (1), and left is equal to or greater than 1, the matrix cracking is considered to occur based on the Tsai-Wu criterion.
3. The method for determining the optimal self-compaction pressure for a metal-lined composite cylinder according to claim 1, wherein the maximum stress criterion in the fourth step is:
σ 1 ＜X (2)
wherein X is the tensile strength of the fiber and is a known property of the fixing material; sigma (sigma) 1 Is fiber tensile stress and is obtained by finite element calculation;
when calculated sigma 1 When the value is equal to or greater than X, fiber breakage is considered to occur based on the maximum stress criterion.
4. The method for determining the optimal self-compaction pressure for a metal-lined composite cylinder according to claim 1, wherein the fatigue strength index b is-0.06 to-0.14; the fatigue ductility index c is-0.5 to-0.7.
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