CN106980735A - The method for numerical simulation of fragile material thermal fracture - Google Patents

The method for numerical simulation of fragile material thermal fracture Download PDF

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CN106980735A
CN106980735A CN201710219950.7A CN201710219950A CN106980735A CN 106980735 A CN106980735 A CN 106980735A CN 201710219950 A CN201710219950 A CN 201710219950A CN 106980735 A CN106980735 A CN 106980735A
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stress
fragile material
unit
calculating
node
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CN106980735B (en
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王大国
王哲
徐兵
李斌
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Southwest University of Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

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  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)

Abstract

The invention discloses the method for numerical simulation of fragile material thermal fracture, it includes carrying out calculating mesh generation to fragile material using engineering object mathematical model；Material parameter, temperature boundary, stress limited boundary and offset qualification border during simulation is set；Calculate stress field；When calculating the first principal stress that there is a node in grid more than or equal to tensile strength of fragile material, cracking processing is carried out to the unit to be cracked at where the node, and return to calculating stress field step；When the first principal stress that there are multiple nodes is more than or equal to tensile strength of fragile material, cracking processing is carried out to bearing the unit to be cracked at the node place of maximum first principal stress, and return to calculating stress field step；When the first principal stress of all nodes is respectively less than tensile strength of fragile material, and simulated time is when being not up to setting simulation duration, calculates stress field step by being returned behind setting value increasing temperature border, otherwise stops simulated operation.

Description

The method for numerical simulation of fragile material thermal fracture
Technical field
The present invention relates to rock mechanics and engineering, mining engineering field, and in particular to a kind of number of fragile material thermal fracture It is worth analogy method.
Background technology
Thermal stress is a key factor for causing the Brittle Material Damages such as rock, when thermal stress exceedes the strong of material itself The limit is spent, material will be made to produce rupture.Thermal fracture can cause very big influence to the elasticity and mechanical disruption property of rock, and Cause the change of petrophysical parameter (such as porosity, permeability), so as to cause significant impact to many engineerings.For example： In the storage of nuke rubbish, country rock temperature is significantly raised because nuke rubbish is fissioned, cause the thermal fracture of rock, underground water oozes Membership is further exacerbated by surrounding rock failure, even results in nuclein migration, causes underground water pollution；In oil exploitation, rock is utilized Thermal fracture, increase rock permeability.At present, the method for numerical simulation of fragile material thermal fracture mainly has discontinuous change Conformal analysis method, FInite Element, particle method etc., these method generally existing part mechanics parameters are difficult accurate estimation, it is impossible to work Cheng Shiji accurately simulate and emulate.
Conventional finite element method simulating crack usually requires splitting point structure singular elements when extending, and with Crack Extension Grid reconstruction is constantly carried out, this method is realized difficult and poorly efficient.The problem of although boundary element method avoids grid reodering, But depend critically upon the elementary solution of problem, for it is non-linear, heterogeneous the problems such as its advantage substantially reduce.The cracks of the present invention Reason is carried out grid adjustment, discontinuous position is not related to using triangular unit grid cracking technology, technology counterincision point local unit The process problem of field is moved, extra discretion need not be also introduced, it is easier, efficient, with preferable applicability.
The content of the invention
For above-mentioned deficiency of the prior art, the present invention is intended to provide a kind of numerical simulation side of fragile material thermal fracture Method, is simulated to the tension destructive process that fragile material is produced under thermal stress effect, to analyze the heat damage of fragile material Process and mechanism provide a kind of new finite element method.
In order to reach foregoing invention purpose, the technical solution adopted by the present invention is：
A kind of method for numerical simulation of fragile material thermal fracture is provided, it comprises the following steps,
Calculating mesh generation is carried out to fragile material using engineering object mathematical model；
Material parameter, temperature boundary, stress limited boundary and offset qualification border during simulation is set；
Calculate stress field：
{ σ }=[D] ([B] { δ }e-{ε0})
Wherein, [D] is elastic matrix；[B] is strain matrix；{ε0Deformed caused by temperature change；{δ}eFor unit position Move；
When calculating the first principal stress that there is a node in grid more than or equal to tensile strength of fragile material, to the section Unit to be cracked at where point carries out the calculating grid that cracking processing is newly formed, and returns to calculating stress field step；
When the first principal stress that there are multiple nodes is more than or equal to tensile strength of fragile material, led to bearing maximum first Unit to be cracked at where the node of stress carries out the calculating grid that cracking processing is newly formed, and returns to calculating stress field Step；
When the first principal stress of all nodes is respectively less than tensile strength of fragile material, and simulated time is not up to setting simulation During duration, stress field step is calculated by being returned behind setting value increasing temperature border, otherwise stops simulated operation；
The unit to be cracked splits to be more than or equal to the unit of the node of its tensile strength comprising first principal stress and being located at Unit on line propagation direction.
Beneficial effects of the present invention are：This programme can be by the material parameter and various boundary condition imitation fragility of setting The thermal stress damage pattern that material is produced by different heat expansion coefficient, and cracking processing is carried out to the unit destroyed, to drop Low-heat ruptures the influence caused to the elasticity and mechanical disruption property of fragile material；Can be accurately anti-using the method for numerical simulation Mirror under temperature load, fragile material tension destructive process, and can effectively analyze crack initiation rule and stress transfer change Change process.
During the Crack handling of the present invention, crackle can directly rive a unit, or be extended along elementary boundary, therefore Crackle can not be limited by initial mesh to be extended along free routing；Compared with existing grid reconstruction algorithm, this method need only Counterincision point local unit carries out grid cracking or node motion, easier, efficient, with preferable applicability.
Brief description of the drawings
Fig. 1 is the flow chart of method for numerical simulation one embodiment of fragile material thermal fracture.
Fig. 2 is the triangular element cracking schematic diagram of the method for numerical simulation of fragile material thermal fracture.
Fig. 3 is interlocking particles circular specimen model schematic in fragile material.
Interlocking particles circular specimen first principal stress schematic diagram when Fig. 4 a are T=350 DEG C.
Interlocking particles circular specimen first principal stress schematic diagram when Fig. 4 b are T=370 DEG C.
Interlocking particles circular specimen crack propagation process and stress transfer process first principal stress are shown when Fig. 5 is T=390 DEG C It is intended to.
Interlocking particles circular specimen crack propagation process and stress transfer process first principal stress are shown when Fig. 6 is T=400 DEG C It is intended to.
Fig. 7 is sample analog result and experimental result Contrast on effect schematic diagram.
Embodiment
The embodiment to the present invention is described below, in order to which those skilled in the art understand this hair It is bright, it should be apparent that the invention is not restricted to the scope of embodiment, for those skilled in the art, As long as various change is in the spirit and scope of the present invention that appended claim is limited and is determined, these changes are aobvious and easy See, all are using the innovation and creation of present inventive concept in the row of protection.
With reference to Fig. 1, Fig. 1 schematically shows the flow of method for numerical simulation one embodiment of fragile material thermal fracture Figure；As shown in figure 1, the method comprising the steps of 101 to step 106.
In a step 101, calculating mesh generation is carried out to fragile material using engineering object mathematical model；Wherein, model In grid be divided into Atria node unit.The model built in this programme is to use numerical analysis general graphical user What interface was created.
In a step 102, material parameter, temperature boundary, stress limited boundary and the offset qualification border during simulation are set； Material parameter therein includes density of material, modulus of elasticity, Poisson's ratio, thermal coefficient of expansion, the coefficient of heat conduction and tensile strength.
In step 103, stress field is calculated：
{ σ }=[D] ([B] { δ }e-{ε0})
Wherein, [D] is elastic matrix, and it is the isotropism matrix controlled by elastic modulus E and Poisson's ratio ν；[B] is should Become matrix；{ε0Deformed caused by temperature change；{δ}eFor element displacement.
Because stress field is obtained based on temperature field and displacement field, this programme is also needed to before stress field is obtained Temperature field and displacement field are solved.
In one embodiment of the invention, the acquisition methods in temperature field are：
Temperature calculating uses Fourier heat conduction laws：
Wherein, ρ is density of material kg/m3；K is the coefficient of heat conduction (W/m DEG C) in x, y direction；C is specific heat of combustion (J/ m3·℃)；T is the time；T is temperature (DEG C).
Because this programme is simulated mainly for Heat Conduction, so when temperature is not changed over time, then kii▽2T =0, now, i=1,2, bring the obtained coefficient of heat conduction into Fourier heat conduction law formula, obtain temperature field T.
The acquisition methods of displacement field are to solve displacement field using conventional finite elements method：
[K] { δ }={ Q }T
Wherein, [K] is stiffness matrix, { Q }TFor hot load (suitable load formed by expanded by heating).
During implementation, calculate stress use due to caused by temperature change deform { ε0Expression formula be：
{ε0}=α T [1 1 0]
Wherein, α is the thermal coefficient of expansion of material, and T is the change of temperature.
At step 104, when the first principal stress that there is a node in calculating grid is more than or equal to fragile material tension During intensity, the calculating grid that cracking processing is newly formed is carried out to the unit to be cracked at where the node, and return to calculating Stress field step.
In step 105, when the first principal stress that there are multiple nodes is more than or equal to tensile strength of fragile material, to holding The calculating grid that cracking processing is newly formed is carried out by the unit to be cracked at where the node of maximum first principal stress, and is returned Return and calculate stress field step.
Wherein, unit to be cracked is comprising first principal stress is more than or equal to the unit of the node of its tensile strength and is located at Unit on direction of crack propagation.
The unit to be cracked of this programme destroys principle based on tension and determined, wherein tension destruction principle is：Work as section When point first principal stress is more than or equal to the tensile strength of rock, tension destruction occurs for rock；If the first master of multiple nodes When stress is more than or equal to tensile strength, the point rupture of maximum first principal stress is born.
In one embodiment of the invention, the expression formula of first principal stress is：
Wherein, σ1For first principal stress；σxFor the stress on x-axis direction；σyFor the stress on y-axis direction；τxyFor in y-axis Shearing stress；
Angle is between first principal stress and X-axis：
During implementation, this programme preferred pair unit to be cracked carries out cracking processing and further comprised：Obtain direction of crack propagation The intersection point formed with the cracking side of unit to be cracked；Increase is more than or equal to the node of tensile strength of fragile material with first principal stress The newly-increased node coincided；According to newly-increased node and intersection point, unit to be cracked is split along direction of crack propagation.
After unit cracking, unit geometric properties may be caused bad, especially work as direction of crack propagation and unit During angle very little between side, it will form poor calculating grid.
During implementation, this programme preferably also includes to new between the calculating grid and return newly formed calculates stress field step The calculating grid of formation is modified processing.After correcting process, the precision for calculating grid computing ensure that.
In one embodiment of the invention, concrete methods of realizing during correcting process is：
When the angle between unit and direction of crack propagation is less than setting value, judging unit short side and the ratio on long side are It is no to be less than setting minimum ratio (real value for being less than 1)：
If being less than, the side for calculating grid is moved to direction of crack propagation, is less than by merge node deletion angle and set The unit of definite value.
In step 106, when the first principal stress of all nodes is respectively less than tensile strength of fragile material, and not up to setting When simulating duration, stress field step is calculated by being returned behind setting value (time step) increasing temperature border, otherwise stops simulated operation.
To realize the processing of the numerical simulation result to the processing procedure that ftractures, this programme automatically saves number according to time step According to file, i.e., the cell data of calculating grid in the time step is automatically saved every setting time step-length, afterwards again to be next Temperature loading is calculated and prepared.
Below in conjunction with the accompanying drawings 2 be described in detail Atria node units dehiscence process：
1. cracking unit is judged.If node N5Tension destruction principle is met, searches and includes node N5All units, Unit on direction of crack propagation is the unit for needing to ftracture, i.e. unit E1-3-5And E7-5-9；
2. intersection point is increased.The intersection point N for needing to ftracture on unit cracking side is found along direction of crack propagation2And N8；
3. increase overlaps node.Increase and cracking node N5The node N of coincidence10；
4. rive unit.According to newly-increased node (including overlapping node), unit is rived along direction of crack propagation, that is, ftractureed Unit E1-3-5And E7-5-9Can be in the node N newly increased2, N8And N10On the basis of rive as four independent unit E1-2-5, E10-2-3And E7-5-8, E8-10-9；
5. amending unit grid.Non- cracking unit E3-5-6, E9-5-6Unit information can be repaiied on the basis of newly-increased coincidence node It is changed to E3-10-6, E9-10-6, unit E1-5-4And E7-5-4Then keep constant.
The method for numerical simulation of this programme is illustrated with reference to specific example：
The present embodiment is a kind of numerical simulation form of the material breaks pattern caused by thermal coefficient of expansion is different, and it has Body step is：
(1) engineering object mathematical model is set up, as shown in figure 3, calculated examples are the circular specimen with particle, model is Be made up of two concentric circles, a diameter of 12mm of inner circle, outside diameter is 25mm, inside and outside concentric circles represent respectively two kinds it is different Material, is respectively designated as particle and matrix.
(2) the specific material parameter of application material parameter, particle and matrix is shown in Table 1；
The mechanical parameters of table 1
(3) time control step-length, total time t=40s, time step (every setting time step-length) Δ t=1s are set；
(4) the particle application identical temperature conditionss of temperature boundary condition, Setup Experiments model matrix and center are applied, just T=0 DEG C of beginning temperature, is constantly heated up with T=10 DEG C of temperature increment of Δ.
(5) computation model temperature field, displacement and stress fields, the material parameter according to acquired in step (2), step (3) And boundary condition, it is worth by each of finite element program automatic creation system FEPG computation models.
(6) first principal stress and deflection are calculated.By step (5) calculate obtained by stress value bring into, further calculate the One principal stress and its deflection.
(7) determine whether that unit ftractures.Determine whether that unit meets Cracking Condition by criterion of strength, if there is unit to expire Sufficient Cracking Condition, unit of riving (cracking flow refers to Fig. 2), repeat step (5)~(7)；If no unit meets Cracking Condition, The cracking result of current time step is preserved, and judges whether to reach the total time of setting, if being not reaching to the total time of setting, is increased Heating degree increment Delta T, i.e. temperature Tn+1=Tn+ Δ T, repeat step (4)~(7)；If reaching the total time of setting, terminate program Calculate.
(8) the cracking result of thick wall cylinder sample in first principal stress off field is checked.
Interlocking particles circular specimen first principal stress schematic diagram when Fig. 4 a are T=350 DEG C.It is embedded when Fig. 4 b are T=370 DEG C Particle circular specimen first principal stress schematic diagram.Interlocking particles circular specimen dehiscence process first, which is led, when Fig. 5 is T=390 DEG C answers Power schematic diagram.Interlocking particles circular specimen dehiscence process first principal stress schematic diagram when Fig. 6 is T=400 DEG C.
It can be seen that in temperature-rise period, because matrix and particle have different thermal coefficient of expansions, make from these views What is deformed on into the interface of matrix and particle is uncoordinated, stress concentration phenomenon is then generated around particle, at the beginning of heating Stress is in accumulation process in stage beginning, model, but is unsatisfactory for Cracking Condition, does not there is breakoff phenomenon；At T=390 DEG C, examination Destruction takes place in region in sample matrix close to particle, and T=400 DEG C of crackle is further expanded on the basis of original, finally A lead crack is formed to destroy matrix insertion.
Fig. 7 is sample analog result and experimental result comparison diagram, the as seen from Figure 7 final failure mode of sample and experiment As a result it is consistent.

Claims (8)

1. the method for numerical simulation of fragile material thermal fracture, it is characterised in that including：
Calculating mesh generation is carried out to fragile material using engineering object mathematical model；
Material parameter, temperature boundary, stress limited boundary and offset qualification border during simulation is set；
Calculate stress field：
{ σ }=[D] ([B] { δ }e-{ε0})
Wherein, [D] is elastic matrix；[B] is strain matrix；{ε0Deformed caused by temperature change；{δ}eFor element displacement；
When calculating the first principal stress that there is a node in grid more than or equal to tensile strength of fragile material, to the node institute Unit to be cracked at place carries out the calculating grid that cracking processing is newly formed, and returns to calculating stress field step；
When the first principal stress that there are multiple nodes is more than or equal to tensile strength of fragile material, to bearing maximum first principal stress Node where the unit to be cracked at place carry out the calculating grid that is newly formed of cracking processing, and return to calculating stress field and walk Suddenly；
When the first principal stress of all nodes is respectively less than tensile strength of fragile material, and simulated time is not up to setting simulation duration When, stress field step is calculated by being returned behind setting value increasing temperature border, otherwise stops simulated operation；
The unit to be cracked is more than or equal to the unit of the node of its tensile strength and positioned at crackle expansion comprising first principal stress Open up the unit on direction.
2. the method for numerical simulation of fragile material thermal fracture according to claim 1, it is characterised in that in the meter newly formed Calculate also includes being modified processing to the calculating grid newly formed between grid and return calculating stress field step.
3. the method for numerical simulation of fragile material thermal fracture according to claim 2, it is characterised in that described to be cracked Unit carries out cracking processing and further comprised：
Obtain direction of crack propagation and the intersection point of the cracking side formation of unit to be cracked；
The newly-increased node that the node that increase is more than or equal to tensile strength of fragile material with first principal stress coincides；
According to newly-increased node and intersection point, unit to be cracked is split along direction of crack propagation.
4. the method for numerical simulation of fragile material thermal fracture according to claim 3, it is characterised in that the amendment cracking The calculating grid newly formed after processing further comprises：
When the angle between unit and direction of crack propagation is less than setting value, whether judging unit short side and the ratio on long side are small In setting minimum ratio：
If being less than, the side for calculating grid is moved to direction of crack propagation, deleting angle by merge node is less than setting value Unit.
5. according to the method for numerical simulation of any described fragile material thermal fractures of claim 1-4, it is characterised in that described to split Line propagation direction is perpendicular to the direction of the first principal stress.
6. the method for numerical simulation of fragile material thermal fracture according to claim 5, it is characterised in that first master should Power is：
σ 1 = 1 2 [ ( σ x + σ y ) + ( σ x - σ y ) 2 + 4 τ x y 2 ]
Wherein, σ1For first principal stress；σxFor the stress on x-axis direction；σyFor the stress on y-axis direction；τxyShould to be cut in y-axis Power；
Angle is between first principal stress and X-axis：
7. according to claim 1-4, the method for numerical simulation of 6 any described fragile material thermal fractures, it is characterised in that also wrap Include the cell data that calculating grid in the time step is automatically saved every setting time step-length.
8. according to claim 1-4, the method for numerical simulation of 6 any described fragile material thermal fractures, it is characterised in that described Material parameter includes density of material, modulus of elasticity, Poisson's ratio, thermal coefficient of expansion, the coefficient of heat conduction and tensile strength.
CN201710219950.7A 2017-04-06 2017-04-06 Numerical simulation method for thermal fracture of brittle material Expired - Fee Related CN106980735B (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109101675A (en) * 2018-06-19 2018-12-28 中国地质大学（武汉） A kind of simulation solid material thermal fracture method
CN111462839A (en) * 2020-04-21 2020-07-28 浙江水利水电学院 Multiscale prediction method for thermal expansion coefficient of hardened cement mortar
CN111883216A (en) * 2020-06-22 2020-11-03 北京电子工程总体研究所 Simulation grid division method and system based on material attribute optimization
CN112084647A (en) * 2020-09-03 2020-12-15 武汉大学 Large-scale granular material internal stress and crushing simulation analysis method and device

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101462854A (en) * 2009-01-12 2009-06-24 山东大学 Brittle material for manufacturing rocks and preparation of specimen prefabricated crack thereof
US20110256786A1 (en) * 2010-04-15 2011-10-20 Mark Bomberg Exterior building wall insulation systems with hygro thermal wrap
CN102852516A (en) * 2012-04-19 2013-01-02 北京大学 Full-sew-length three-dimensional crushing data simulation method and device for oil and gas reservoir development

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101462854A (en) * 2009-01-12 2009-06-24 山东大学 Brittle material for manufacturing rocks and preparation of specimen prefabricated crack thereof
US20110256786A1 (en) * 2010-04-15 2011-10-20 Mark Bomberg Exterior building wall insulation systems with hygro thermal wrap
CN102852516A (en) * 2012-04-19 2013-01-02 北京大学 Full-sew-length three-dimensional crushing data simulation method and device for oil and gas reservoir development

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109101675A (en) * 2018-06-19 2018-12-28 中国地质大学（武汉） A kind of simulation solid material thermal fracture method
CN109101675B (en) * 2018-06-19 2023-05-26 中国地质大学（武汉） Method for simulating thermal cracking of solid material
CN111462839A (en) * 2020-04-21 2020-07-28 浙江水利水电学院 Multiscale prediction method for thermal expansion coefficient of hardened cement mortar
CN111462839B (en) * 2020-04-21 2023-10-13 浙江水利水电学院 Multiscale prediction method for thermal expansion coefficient of hardened cement mortar
CN111883216A (en) * 2020-06-22 2020-11-03 北京电子工程总体研究所 Simulation grid division method and system based on material attribute optimization
CN111883216B (en) * 2020-06-22 2023-12-26 北京电子工程总体研究所 Simulation grid division method and system based on material attribute optimization
CN112084647A (en) * 2020-09-03 2020-12-15 武汉大学 Large-scale granular material internal stress and crushing simulation analysis method and device

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