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1、Lesson content:Sequentially Coupled Analysis Thermal-Stress Modeling ConsiderationsExample Methods for Assigning Temperature DataDirectUser subroutineOutput database/results fileMapped fieldsTemperature Application for Solid ElementsTemperature Application for Shell ElementsTemperature Application f

2、or Beam ElementsSummaryWorkshop 5: Reactor: Stress Response (IA)Workshop 5: Reactor: Stress Response (KW)Lesson 7: Sequentially-Coupled Thermal-Stress Analysis2 hoursBoth interactive (IA) and keywords (KW) versions of the workshop are provided. Complete only one.Sequentially Coupled Analysis (1/11)A

3、 sequential thermal-stress analysis requires two analyses:Heat transfer analysis must first be performed.Temperature is the unknown variable.Thermal response is not influenced by the mechanical behavior and thus, can be obtained independently.Subsequently a stress analysis is performed in which temp

4、eratures are applied as external nodal loads to generate thermal strain.Displacement is the unknown variable.Mechanical response is influenced by temperatures through.Thermal expansionTemperature-dependent material propertiesFor constant coefficient of thermal expansion a :For a 1-D linear elastic m

5、aterial, Abaqus calculates the elastic (i.e., mechanical) strain and corresponding stress asSequentially Coupled Analysis (2/11)Thermal expansionAn unrestrained body subject to temperature increase will normally expand with the increase in temperature, where the proportionality factor between strain

6、 and temperature is the coefficient of thermal expansion (CTE).CTEs can depend on temperature or predefined field variables. CTEs can also be isotropic, orthotropic, or anisotropic.*EXPANSION, TYPE=ISO, ZERO=201.0e-6, 100., 1.1.5e-6, 200., 1.2.0e-6, 100., 2.2.5e-6, 200., 2.Sequentially Coupled Analy

7、sis (3/11)Some common values:* Stress generated by fully constrained 1 C temperature increase.For all but rubber, constrained in the sense of a bar fixed at its ends.For rubber, constrained 3D solid.* Compression* Bulk ModulusMaterial a (me per oC) E (MPa)Thermal Stress Capacity* (MPa)Cast Iron12.11

8、70,000*2.05Aluminum23.270,0001.62Steel11.7207,0002.42Rubber220.02,000*1.32Sequentially Coupled Analysis (4/11)Abaqus/Standard calculates thermal strains at element material locations according towherea (q ) is the coefficient of thermal expansion,q is the current temperature,q I is the initial tempe

9、rature, andq 0 is the reference temperature for the expansion coefficient. (at this temperature the thermal expansion is assumed to be zero).CTEs generally increase slightly with temperature.The second term in the thermal strain expression represents the strain due to the difference between q 0 and

10、q I. Since it is assumed that there is no thermal strain at the initial conditions, this strain must be subtracted to obtain the thermal strain at temperature q. Therefore, the difference between q and q I creates thermal strain.If the expansion coefficient is not a function of temperature, q 0 is n

11、ot needed.Sequentially Coupled Analysis (5/11)If the thermal expansion of a material is a complex function of temperature and other variables, user subroutine UEXPAN can be used to define the increments of thermal strain, De th, directly. To indicate that the thermal strains will be defined with thi

12、s subroutine:*EXPANSION, USERSequentially Coupled Analysis (6/11)Abaqus calculates total thermal expansion coefficients from a reference value (see figure). Often, you will have thermal expansion data in differential form. Formulas are provided in the Abaqus Analysis Users Guide for converting diffe

13、rential values to total values.qe thq 0q 1q 2a 1a 2Sequentially Coupled Analysis (7/11)Example: Yielding in highly constrained structures Even small temperature increases may cause yielding.Typical properties: structural steelYoungs modulus: 200 103 MPaYield stress: 300 MPaThermal expansion coeffici

14、ent: 12 10-6/C strain to cause yield 125C (225F) fully constrained thermal expansion will cause yieldDq = 125Ce th = aDqSequentially Coupled Analysis (8/11)Temperature-dependent material propertiesMaterial response is often strongly dependent on temperature.Temperature-dependent material propertiesT

15、emperature, qYoungs modulus, EYield stress, syTemperature, qSequentially Coupled Analysis (9/11)It is often important to include these effects when the material is subjected to large temperature changes. Most material models in Abaqus allow for variation of mechanical properties with temperature. Da

16、ta are entered in tabular form. Abaqus/Standard interpolates as necessary to obtain material properties at the current material point temperature (see the following figures).Abaqus/Explicit interpolates regularized data for efficiency reasons.Sequentially Coupled Analysis (10/11)*MATERIAL, NAME=SS30

17、4*ELASTICE1, n1, q1E2, n2, q2E3, n3, q3E4, n4, q4E5, n5, q5E6, n6, q6Values held constant outside range of dataYoungs modulus and Poissons ratio vs. TemperatureSequentially Coupled Analysis (11/11)*MATERIAL, NAME=METAL*ELASTICE1, n1 *PLASTICs01, e01, q 1s11, e11, q 1s21, e21, q 1s31, e31, q 1s02, e0

18、2, q 2s12, e12, q 2s22, e22, q 2s32, e32, q 2yield stressplastic strainq increasingq = q 1q = q 2Thermal-Stress Modeling Considerations (1/13)Thermal-stress analyses are typically performed to investigate stresses and strains caused by:CTE mismatches in a structure.Rapid temperature changes (thermal

19、 shock) in localized regions of a structure.In both types of problems localized cracking or yielding is usually a concern. Furthermore, the resultant deformation in such cases is very often a bending response (see following figure).During model design consider whether bending is likely to be a domin

20、ant mode of the deformation and whether high thermal gradients are expected in regions that are close to the surface of the structure.Thermal-Stress Modeling Considerations (2/13)CTE mismatching example:steelcopperceramiccool downpossible cracking of ceramic at copper interfaceq highq lowacopper = 1

21、.6 10-5/Caceramic = 2.7 10-6/Casteel = 1.2 10-5/CCTE mismatch in a brazed copper jointThermal-Stress Modeling Considerations (3/13)Thermal shock example:Reference: Abaqus Benchmark Problem 1.6.4, Quenching of an infinite plate.Objectives:Motivate discussion of thermal-stress analysis.Consider a simp

22、le geometry and loading with a complex response.Discuss how to take advantage of symmetry in thermal-stress problems.Understand some basic effects in transient thermal-stress response.Thermal-Stress Modeling Considerations (4/13)Consider a thick plate with very large (i.e., infinite) lateral dimensi

23、ons:Material properties are that of steelThickness = 914 (36 in)convective cooling from both sidesy-xzInfinite plateThermal-Stress Modeling Considerations (5/13)Problem:Initially the plate is at uniform high temperature (near melting).The surfaces are cooled suddenly by oil spray (quenching).Questio

24、ns:How can we analyze this problem? What mesh and boundary conditions are suitable?What symmetries exist in the thermal and structural regimes, and how can we model them?meshSymmetry planeThermal-Stress Modeling Considerations (6/13)What qualitative conclusions can be made regarding the stress state

25、 in the plate?Hints: Are there any external forces on the plate at any time during the analysis?No external forces.Only in-plane stresses (sxx,szz): there is no restriction on expansion/contraction in the y-direction.midplanez-xyszzsxxsyysin-planemeshThermal-Stress Modeling Considerations (7/13)Anal

26、ysis modelsHeat transferStressElement type DC2D8 CPEG8RBCs/Loads Surface film conditions Displacement BCs and temperature“l(fā)oads” via ODB fileMaterial Specific heatDensityConductivity ElasticityPlasticityThermal expansionProcedure Heat Transfer: DELTMX=10. END=SS General staticThermal-Stress Modeling

27、 Considerations (8/13)Thermal Model*HEADING:*ELEMENT,TYPE=DC2D8:*INITIAL CONDITIONS,TYPE=TEMPERATUREALL,1900.*STEP,INC=500*HEAT TRANSFER,DELTMX=10., END=SS20.,4.0E6,0.5,1.E-6*SFILMTOP,F,70.,6.559E-5*OUTPUT, FIELD*NODE OUTPUTNT, *END STEPDefault BC at sides and bottom: insulated boundarysymmetryTOPTh

28、ermal-Stress Modeling Considerations (9/13)Stress Model*HEADING:*ELEMENT,TYPE=CPEG8R:*EQUATION2 SIDE,1,1., BOT,1,-1.*INITIAL CONDITIONS,TYPE=TEMPERATUREALL,1900.*STEP,INC=100*STATIC10.,9.616E4*TEMPERATURE,FILE=heat.odb,BSTEP=1,BINC=1,ESTEP=1,EINC=483*END STEPBOTi th node in set SIDEImpose generalize

29、d plane strain conditions in the 1-direction.BCs: symmetry about left and bottom edges; free out-of-plane expansionThermal-Stress Modeling Considerations (10/13)How does the temperature evolve at various points through the plates thickness? Sketch the variations of temperature with time at the cente

30、rline and surface of the plate.centersurfaceCooling curves for plateThermal-Stress Modeling Considerations (11/13)How does the stress state evolve with time? Sketch the variations of stress with time at the centerline and surface of the plate.Stresses in PlateEarly on The surface cools quickly and c

31、enter remains hotsurface wants to contract but contraction is limited by hot centersurface in tension.Conversely, the rapid cooling of the surface forces the center to contract more than it wantscenter in compression.Later As surfaces cool, temperature difference decreases and surface allowed to con

32、tract (compression) and center goes into tension.Thermal-Stress Modeling Considerations (12/13)Sketch the stress distribution through the plates thickness at times:early in the cool-down,later in the cool-down, andat room temperature (steady-state thermal conditions).Residual stress distributionsC/L

33、Outside surfaceBending is the dominant deformation mode.Thermal-Stress Modeling Considerations (13/13)What possible benefits or disadvantages can be obtained from such a residual stress distribution? Can you think of any structures or components in which you would like to have such a stress distribu

34、tion?Stress distribution on a concrete slab: built-in compression at surface to fight cracking.Methods for Assigning Temperature Data (1/18)Recall that in a sequential thermal-stress analysis, two analyses are generally required:Heat transfer analysis using heat transfer elementsTemperature is treat

35、ed as a boundary conditionTemperature distribution is the objective of the analysisThermal response is not influenced by the mechanical behaviorStress analysis using stress/displacement elements in which temperatures are applied as nodal loadsTemperature is treated as a predefined field because it i

36、s known beforehandStress distribution is the objective of the analysisThermal solution is obtained independently of the mechanical solution; thus, the stress analysis is performed using a known temperature field.Methods for Assigning Temperature Data (2/18)Temperatures typically vary with position a

37、nd time, (x, t).Spatial dependence is plished by assigning a different temperature to each nodal point throughout the finite element grid.Abaqus then interpolates the nodal temperatures to material points that are used for thermal-strain calculations and for evaluation of any temperature-dependent m

38、aterial properties that are used in the constitutive calculations.Initial temperatures are assigned to the nodal points with the *INITIAL CONDITIONS, TYPE=TEMPERATURE option.Time dependence is possible because temperature can be applied as a load in an Abaqus stress analysis model.Methods for Assign

39、ing Temperature Data (3/18)Temperature history data can be assigned in any one of four possible ways.Direct specification.Temperatures can be assigned directly to nodes or sets. This is most often used for uniform or very simple temperature distributions. An amplitude can be referred to using the AM

40、PLITUDE parameter to vary the temperature with time.The INPUT parameter can be used to read temperatures from an ASCII file, which is a convenient way of reading in temperatures from another heat transfer program.*TEMPERATURE,AMPLITUDE=amp_name, INPUT=file_namenode or node set, reference magnitude1M

41、ethods for Assigning Temperature Data (4/18)User subroutine UTEMP (Abaqus/Standard only).Nodal temperatures can be prescribed within user subroutine UTEMP. This allows temperatures to be programmed as a function of position or time.The form of the user subroutine is as follows: SUBROUTINE UTEMP(TEMP

42、, NSECPT,1 KSTEP, KINC, TIME, NODE, COORDS) . . user coding to define TEMP . RETURN END*TEMPERATURE, USERnode or node set, (magnitude ignored)2Methods for Assigning Temperature Data (5/18)Abaqus/Standard output database or results file.Temperatures can be supplied to a stress analysis from an Abaqus

43、 output database (.odb) or results (.fil) file generated in a previously run heat transfer analysis.*TEMPERATURE, FILE=file_name This method is only available for solid and shell elements.The meshes used for the heat transfer and stress analysis may be compatible or patible.3Methods for Assigning Te

44、mperature Data (6/18)Abaqus/Standard output database or results file (contd)Compatible meshesBoth models have the same mesh topology and the same corner nodes (positions and labels).Element order can be different, however.Can read data from either the results (.fil) or output database (.odb) file.St

45、ress meshHeat transfer meshDC3D20C3D20RDC3D10C3D10M3Methods for Assigning Temperature Data (7/18)Abaqus/Standard output database or results file (contd) patible meshesMesh topology is different between the two models.Element order can also be different.Interpolation is based on the heat transfer mes

46、h.Can read data only from output database (.odb) file.Stress meshHeat transfer mesh3Methods for Assigning Temperature Data (8/18)Aside on patible meshes: Controlling the source and target regions when reading data from an ODB fileFree surfaces in a heat transfer analysis that are very close or touch

47、ing each other may cause ambiguities in the temperature mapping Specify the source region from where the temperatures are read and the target region onto where the temperatures are mapped to eliminate the ambiguityKeywords usage:*INITIAL CONDITIONS, TYPE=TEMPERATURE, FILE=*.ODB, INTERPOLATE, DRIVING

48、 ELSETSSource element set label, target node set label*TEMPERATURE, FILE=*.ODB, INTERPOLATE, DRIVING ELSETSSource element set label, target node set labelAbaqus/CAE usage: not currently supported (use the Keywords Editor)Methods for Assigning Temperature Data (9/18)Example: Finite gap conductance at

49、 an interface in contactGlobal model mesh with gap exaggeratedGlobal model resultsTemperature mapping without DRIVING ELSETSTemperature mapping with DRIVING ELSETSMethods for Assigning Temperature Data (10/18)Example (contd)set init-outringset init-inringset nset_outringset nset_inringMethods for As

50、signing Temperature Data (11/18)Abaqus/Standard output database or results file (contd)Element orderThe same element order does not have to be used in each analysis. For example: First-order heat transfer elements might be used to capture strong discontinuities in the temperature gradients.Second-or

51、der stress/displacement elements might be needed in the thermal-stress analysis because the structure bends.For compatible meshes, Abaqus can calculate the temperatures at the midside nodes of the second-order elements using the corner node values.A compatible mesh implies both models have the same

52、mesh topology and the same corner nodes (positions and labels).3Methods for Assigning Temperature Data (12/18)Mapped fields (3D only).Abaqus/CAE tool to define spatially varying parameter values from an external data source (not limited to temperature data)Point cloud dataODB mesh dataPoint cloud da

53、ta: x, y, z, q4The spatial distribution for point cloud data can be reviewed in the Visualization module.Methods for Assigning Temperature Data (13/18)Mapped fields (contd)Mesh-to-mesh mapping is based on a previously existing ODB fileSelect a viewport with an open and displayed ODB to indicate mapp

54、ing settingsAll settings of the viewport will be used in the mappingMeshes can be dissimilar4Methods for Assigning Temperature Data (14/18) Clearly there are some similarities between the option to read data from an ODB file and mapped fieldsFor example, both techniques will transfer temperature dat

55、a between dissimilar meshesSome differences exist, however:ODB fileLimited to temperature mapping for solids and shells2D and 3D geometryTemperature data not imported into Abaqus/CAEIn fact, usage is such that can directly access temperature data for different steps/increments during analysis runtim

56、e Mapped fieldsMore general purpose: not limited to temperature mapping (shell thickness, sink temperatures, and other scalar values are also supported) and does not require ODB3D geometry onlyTemperature data is imported into Abaqus/CAEMust map data separately for different steps/increments (intera

57、ctive operation)Methods for Assigning Temperature Data (15/18)Reconciling incrementation differences between the thermal and stress analysesTypically, the temperatures in the output database or results file will appear in the form of temperature data for all nodes at discrete points in time througho

58、ut the transient. An exception would be a steady-state analysis run in one increment.A transient heat transfer analysis that uses the Abaqus/Standard automatic time incrementation scheme will produce sets of temperature data points at times that do not necessarily correspond with the times generated

59、 by the automatic time incrementation scheme used by the subsequent structural analysis.Abaqus will interpolate linearly between the time points stored for the heat transfer analysis to obtain temperature values at the time points required by the structural analysis. Ensure that the heat transfer ou

60、tput contains sufficient data (that is, enough increments are stored) to make this interpolation meaningful.Methods for Assigning Temperature Data (16/18)Reconciling time scale differences between the thermal and stress analysesThe thermal-stress analysis is most often a general static procedure for