Ure-etal-IJPVP-2014-Integrated-structural-analysis-tool-part
Contents
1. Demet 3 SEN EA fu tee Bense PIOTTA ON Module Part iz Moi Tools About Plug ins EAS Models 1 l Model 1 flg Parts Pe Materials Sections E Profiles A Assembly H ola Steps 1 Ea Field Output Requests Ba History Output Reque aac Time Points fis ALE Adaptive Mesh Cc TL Interactions GF Interaction Properties H Contact Controls jr Contact Initializations Constraints TE Connector Sections F Fields Ss Amplitudes 4 Loads mn i Fig 2 An Abaqus CAE interface showing the linear matching method plug in The Linear Matching Method The Linear Matching Method LMM ts an analysis technique which determines the steady state response of structures subject to cyclic loading to find the strict shakedown and ratchet limits This plug in takes material and load cycle data and then automatically configures the Abaqus CAE model for an analysis with the LMM user subroutines To begin the LMM process please select a model and analysis type below Select Model Select Analysis Type Please select a model to analyse with Strict Shakedown the Linear Matching Method Steady State Cycle select Model fel Steady State Cycle Ratchet Limit The LMM subroutines and plug in have been created by Haofeng Chen and James Ure Any enquiries should be directed to haofeng chengistath ac uk Use of this method is at your own risk Both the d2. B Field Output Requests 2 rh Pt em VP EE Ma ie abe PV Output field Node Output NT U Element Output directions YES E S SDV k HISTORY OUTPUT LMM H_output Output history frequency 99999 Energy Output ETOTAL NODE PRINT FREQUENCY 0 EL PRINT FREQUENCY 0 ENERGY FILE SDV End Step EL FILE POSITION INTEGRATION POINTS Block Add After Remove Discard All Edits Fig 9 Keyword block after the ENERGY FILE command has been added a Ho gt G P Total Total Step Time LPF Iter Time Freq Time LPF Inc 44 47 44 45 48 45 46 49 46 47 50 47 47 50 47 Message File Status File EEE IEE JE IEE JEJEJE JEJE IE FEJE JEJEJE EEE EEE IAI AAI AAA I AAA SALA SUMMARY REPORT STRICT SHAKEDOWN NOT ACHIEVED FURTHER ANALYSIS NEEDED UPPER BOUND SHAKEDOWN LIMIT MULTIPLIER 0 8623670915 LOWER BOUND SHAKEDOWN LIMIT MULTIPLIER 0 8455374651 DIFFERENCE BETWEEN LOWER AND UPPER BOUNDS 1 952 ODB OUTPUTS SDV 1 CONSTANT RESIDUAL STRESS EQUIVALENT SDV 2 7 CONSTANT RESIDUAL STRESS TENSOR SDV 8 EFFECTIVE STRAIN INCREMENT i e THE MECHANISM AT THE SHAKEDOWN LIMIT SDV 10 11 STEADY STATE EFFECTIVE STRESS AT EACH LOAD POINT SDV 12 13 STEADY STATE EFFECTIVE STRAIN AT EACH LOAD POINT SDV 14 15 YIELD STRESS AT EACH LOAD POINT SDV 16 17 YIELD FRACTION AT EACH LOAD POINT SDV 18 19 TEMPERATURE AT EACH LOAD POINT SDV 20 25 LMM
3. Staat M Heitzer M LISA a European Project for FEM based Limit and Shakedown Analysis Nuclear Engineering and Design 2001 206 151 166 Spiliopoulos KV Panagiotou KD A direct method to predict cyclic steady states of elastoplastic structures Computational Methods in Applied Mechanics and Engineering 2012 223 224 186 198 Maier G Pastor J Ponter ARS Weichert D Direct Methods of Limit and Shakedown Analysis Comprehensive Structural Integrity Volume 3 de Borst R Mang HA Eds Amsterdam Elsevier Pergamon 2003 637 684 14 10 11 12 13 14 15 16 17 Chen HF Ponter ARS Shakedown and limit analyses for 3 D structures using the linear matching method International Journal of Pressure Vessels and Piping 2001 78 443 451 Chen HF Lower and Upper Bound Shakedown Analysis of Structures with Temperature Dependent Material Properties ASME Journal of Pressure Vessel Technology 2010 132 1 011202 Chen HF Ponter ARS A Direct Method on the Evaluation of Ratchet Limit ASME Joutnal of Pressure Vessel Technology 2010 132 4 041202 Chen HF Ure J Tipping D Calculation of a Lower Bound Ratchet Limit Part 1 Theory Numerical Implementation and Verification European Journal of Mechanics A Solids 2013 37 361 368 Chen HF Ponter ARS Linear matching method on the evaluation of plastic and creep behaviours for bodies subjected to cyclic thermal and mechanical loading Intern
4. Load Tension SCALABLE 0 00000 0 50000 Load Temperature Difference NOT_SCALABLE 0 00000 1 00000 Explanation The analysis type May also have a value of STEADY_CYCLE_ONLY or STEADY_CYCLE_AND_RATCHET Max number of increments defined by the user should convergence prove elusive The convergence option chosen and the value The Diff flag is present when the percentage difference convergence option is used It is not present when the difference between upper bounds is selected Dimensionality flag May also have a value of THREE_D AXISYMMETRIC PLANE_STRESS or PLANE_STRAIN The number of loads including temperature distributions and load instances in the cycle The multipliers for each load as entered in the Loadcycle table The LMM uses these multipliers to construct the load cycle in the code and so determine the elastic stress at each load point The SCALABLE NOT_SCALABLE flag dictates whether the load can be scaled using the calculated in each increment 17 Table 3 Material properties section of the LMM text file LMM Text File Material Properties Number of materials 3 Material SA508 Temperature Independent Modulus Temperature Independent Yield Stress Perfectly Plastic Material Material NCONEL 82 182 Temperature Independent Modulus Temperature Dependent Yield Stress 2 3 7860000000e 002 20 000 3 1580000000e 002 320 000 Perfectly Plastic Material Material STEEL 316 Temperature Ind
5. Ramberg Osgood Material Poissons Ratio 03 Use R O model ae E Temperature Dependent Calculate 0 2 proof stress Calculate The default material mode of the LMM is perfectly plastic If the Use R O model is ticked then a Ramberg Osgood 7 model is used for the selected material A 11893 The coefficients A and Beta are those for the stress and strain ranges see section A1 4 2 of R5 The values of A and beta can also be temperature dependent Beta 03 The R O model is used in the steady cycle stage of the analysis It is not used in a ratchet limit assessment In regions where the steady cycle analysis shows yielding i e stresses above the stress specified in the Yield Stress box this hardened stress is brought forward into the ratchet limit calculation and used as the yield stress with the perfect plasticity model Dismiss Fig 5 a Material properties dialog with Ramberg Osgood option b Tip box E Loadeycle Tip Definition of the Load Cycle For each point in the load cycle enter multipliers to scale the loads to the correct level for that load point In addition select the temperature field which corresponds to that load point and scale it accordingly If the temp Is zero then enter none for the temperature field For example consider the plate with central hole in the opposite diagram The axial tension is constant with time The temperature at the outer edge remains zero whilst the
6. arose This testing also highlighted some small additional functions which would be beneficial in regular use For example in Figure 5a the function which calculates the 0 2 proof stress was added in this way Therefore the plug in overall has been tailored based on the requests from industry making the tool more convenient for their engineers to use 6 Conclusions This paper has described the development of the LMM into an integrated structural analysis tool which can be used on a regular basis by industrial engineers for assessing the load carrying capacity shakedown limit ratchet limit and steady state cyclic behaviour of components subjected to cyclic thermal and mechanical load condition This has involved re structuring the subroutines for multiple CPU solution and developing a plug in for Abaqus CAE This plug in tool has been created to provide an intuitive and simple way to perform a LMM analysis The data for the analysis is gathered through Abaqus CAE which is a familiar environment for industrial engineers The plug in implements all of the functionality possible in the subroutines and includes extensive error checking to ensure that only permissible combinations of options are used The plug in and subroutines have been written so that the configuration of the subroutines for each analysis is performed automatically thus making a LMM analysis more convenient and less prone to errors Further demonstration of this new LM
7. the applied load is below the elastic shakedown limit ratchetting and plastic shakedown will not occur under repeated loading However in some situations for example in nuclear power applications with cyclic thermal loading this elastic shakedown limit can also be over conservative Thus an alternative approach is required to allow plastic shakedown to occur but preclude ratchetting In ratchetting a net increment of plastic strain occurs with each cycle of load and leads to an incremental plastic collapse over a number of cycles Guarding against incremental plastic collapse by the determination of plastic shakedown limit or ratchet limit is crucial in any design involving cyclic thermal and mechanical loads Under plastic shakedown condition a low cycle fatigue LCF analysis would also be undertaken to ensure the structure does not fail by low cycle fatigue associated with local alternating plasticity where the number of cycles to failure is determined by the maximum plastic strain range A steady state cyclic analysis is often sought to evaluate the LCF life and address whether shakedown or ratchetting occurs under the defined cyclic load condition Design limits in plasticity for components subjected to cyclic thermal and mechanical load conditions including both shakedown and ratchet limits have attracted the attention of many researchers The incremental finite element FE analysis 2 allows the investigation of any type of load cycle bu
8. to obtain the elastic stresses for each load in turn return the subroutine variables to zero and then carry out the shakedown steady cycle ratchet analysis The boundary conditions are moved to the first step and set to propagate through the entire analysis The original analysis steps are suppressed allowing the user to recover the original state of the model The materials are the next area to receive attention The LMM requires a User material to be defined in Abaqus to link with the UMAT subroutine In Abaqus CAE a copy of each active material is made which is defined as a User material for the LMM analysis The original material is retained so that the user may recover the original material properties Values for temperature independent Young s modulus Poisson s ratio yield stress and the Ramberg Osgood parameters are entered as constants in this material A User material is only able to include multiple constants not tables Therefore if a property is temperature dependent then a value of zero is entered for this constant and the temperature dependent values are appended to the bottom of the LMM text file An example of this is given in Table 3 11 After a materials configuration the field and output requests are created Once again any original requests in the model are suppressed rather than deleted The most important of the LMM output requests is the variable SDV which is the user defined output from the UMAT subroutine Requesti
9. INTERNAL VARIABLES SDV 26 31 32 33 LOAD 1 ELASTIC STRESS TENSOR EFFECTIVE STRESS AND TEMPERATURE SDV 34 39 40 41 LOAD 2 ELASTIC STRESS TENSOR EFFECTIVE STRESS AND TEMPERATURE DE HE IEH IE HE IE HE IE HE IE HE HE IE HE IE HEIE HEIE HE IE HE IE HE IE IE HE HE HEIE HE IEH IE HE IE HE IE HE IE HEIE IE IE IE IE IE IE IE E M VA Search Text Text to find Match case J Next f Previous Fig 10 Monitor dialog box showing the LMM summary report
10. Integrated Structural Analysis Tool using the Linear Matching Method part 1 Software Development James Ure Haofeng Chen David Tipping Dept of Mechanical and Aerospace Engineering University of Strathclyde 75 Montrose Street Glasgow G1 1XJ Scotland United Kingdom Central Engineering Support EDF Energy Nuclear Generation Ltd Barnwood Gloucester GL4 3RS United Kingdom Abstract A number of direct methods based upon the Linear Matching Method LMM framework have been developed to address structural integrity issues for components subjected to cyclic thermal and mechanical load conditions This paper presents a new integrated structural analysis tool using the LMM framework for the assessment of load carrying capacity shakedown limit ratchet limit and steady state cyclic response of structures First the development of the LMM for the evaluation of design limits in plasticity is introduced Second preliminary considerations for the development of the LMM into a tool which can be used on a regular basis by engineers are discussed After the re structuring of the LMM subroutines for multiple central processing unit CPU solution the LMM software tool for the assessment of design limits in plasticity is implemented by developing an Abaqus CAE plug in with graphical user interfaces Further demonstration of this new LMM analysis tool including practical application and verification is presented in an accompanying pa
11. M analysis tool including practical application and verification is presented in an accompanying paper 17 13 Acknowledgments The authors gratefully acknowledge the support of the Nuclear EngD Centre of the United Kingdom EDF Energy and the University of Strathclyde during the course of this work The authors would also like to thank Prof Alan Ponter from University of Leicester for his advice and discussions on the theoretical and software developments of the LMM References 1 2 3 4 5 6 7 8 9 R5 An assessment procedure for the high temperature response of structures Revision 3 British Energy Generation Limited Gloucester UK 2003 Abaqus User s Manual Dassault Syst mes Simulia Corp 2009 Vu DK Yan AM Nguyen Dang H A primal dual algorithm for shakedown analysis of structures Computer Methods in Applied Mechanics and Engineering 2004 193 4663 4674 Muscat M Mackenzie D Hamilton R Evaluating shakedown under proportional loading by non linear static analysis Computers amp Structures 2003 81 1727 1737 Ponter ARS Carter KF Shakedown state simulation techniques based on linear elastic solutions Computer Methods in Applied Mechanics and Engineering 1997 140 259 279 Adibi Asl R Reinhardt W Non cyclic shakedown ratcheting boundary determination Part 1 Analytical approach International Journal of Pressure Vessels and Piping 2011 88 311 320
12. as the way convergence was judged or can use the difference between lower and upper bounds A steady state cycle convergence is based on volume integrals of modulus between consecutive increments If there is little change in this value then the stress fields are not changing and so have reached a converged steady state behaviour The value of convergence in the dialog box represents the percentage change of this volume integral in consecutive increments A ratchet limit analysis requires convergence values for both stages of the procedure Stage 1 is identical to that of a steady state cycle analysis and the convergence options for stage 2 are identical to those for the strict shakedown analysis Once again the Tip box gives additional information and help to the user if required If the data entered in the Analysis Parameters box passes the error checking stage then the user interface portion of the plug in is complete In total the dialog boxes will have gathered the following information model name analysis type material properties temperature dependent load cycle which loads are scalable job name max number of increments convergence criteria and working directory The next stage of the plug in is then to use this 10 information to configure the Abaqus model and write the LMM text file containing the information for the subroutines The changes to the model have been designed so that the original model is entirely recoverable
13. ational Journal for Numerical Methods in Engineering 2006 68 1 13 32 Chen HF Ponter ARS Structural integrity assessment of superheater outlet penetration tubeplate International Journal of Pressure Vessels and Piping 2009 86 7 412 419 Tipping D The Linear Matching Method A Guide to the ABAQUS User Subroutines British Energy Generation Ltd Report E REP BBGB 0017 GEN 07 2008 Chen HF Ure J Integrated Structural Analysis Tool using the Linear Matching Method part 2 Application and Verification International Journal of Pressure Vessels and Piping 2014 15 Table 1 Functions available in each LMM analysis Steady Steady State Strict Analysis Option State Cycle Cycle Shakedown Only Ratchet Limit All structural continuum element types 3D axisymmetric plane strain and plane stress Y p Y Temperature dependent Young s modulus and yield stress d Y p Ramberg Osgood Material Model which may also be temperature dependent Y y Any number of points possible in the load ev l v v v ycle Ability to select which loads to scale during solution Y Y eee ee E 16 Table 2 LMM text file example LMM Text File Analysis Type STRICT SHAKEDOWN Max Number of Increments 350 Convergence DIff 5 00000 Dimensionality THREE D Number of Applied Loads 4 Number of Load Instances 2 Load Bending Moment NOT_SCALABLE 0 00000 1 00000 Load Internal Pressure SCALABLE 0 00000 1 00000
14. customising Abaqus In Section 3 a re structuring of the LMM user subroutines for multiple CPU solution is proposed The creation of a Graphical User Interface GUI via an Abaqus Plug in is presented in Section 4 Section 5 briefly discusses the installation and testing of the LMM software tool for the assessment of design limits in plasticity Section 6 concludes this paper 2 Preliminary Considerations 2 1 Previous LMM Versions The original incarnation of the LMM code was created as Abaqus user subroutines and has been mainly used for research purposes A typical LMM analysis consists of two stages 12 13 In the first stage an elastic analysis for each applied load and temperature distribution is performed using the elastic analysis UMAT subroutine For each of these analyses the elastic stress tensor for each integration point is written to a text file and the integration point temperature is written to a separate text file The second stage of this analysis uses a second UMAT subroutine and these text files to perform the shakedown or ratchet limit calculation In this second stage some changes are required to the UMAT code in order to set up the analysis For example the number of integration points per element and the total number of elements in the model needed to be changed so that the arrays could be sized appropriately The code defining the load cycle also requires updating which reads the stress and temperature text files to ge
15. d convergence levels are printed for the current increment so the user can see the progress of the solution When an analysis is complete a summary is printed which declares the shakedown status of the model the final values of the load multipliers and lists the SDV numbering so the user can view contour plots of the results A sample summary given in the Monitor dialog box is shown in Figure 10 When complete the user may view contour plots of the results in the same way as any other Abaqus analysis 5 Installation and Testing The plug in and subroutines described here have been installed and tested on the computer system of our industrial partner Once it is successfully installed this new integrated LMM structural analysis tool will take into effect in the Abaqus CAE as a plug in shown in Figure 2 The independent users from industry have contributed to extensively test the LMM software tool and give feedback on any problems encountered or additional functions which would be of benefit 12 This external perspective was a valuable asset A lot of effort was invested in error checking of the inputs of each dialog box However it is very difficult for a single programmer to foresee every eventuality or combination of events which could lead to an error The testing within the industrial partners highlighted some additional situations which should be avoided and minor errors with the plug in itself and these were rectified on site when they
16. db outputs Fig 7 Analysis parameters dialog boxes for a strict shakedown b steady state cycle c steady state cycle ratchet analysis fa Load N Name LMM Bendin LMM Interna LMM Tension LMM Temper LMM Null Bending Moment Inactive Inactive Inactive Inactive Inactive Move Left Internal Pressure Created Inactive Inactive Inactive Inactive _ ry vw Tension Created Inactive Inactive Inactive Move Right Actrvate Deactivate Step procedure Static General Load type Concentrated force Load status Created in this step LMM Bendin LMM Interna LMM Tension LMM Tempe LMM Null LMM Shaked Edit Created Reset to initial Inactive Move Left Move Righ t Step procedure Predefined Field type Temperature Predefined Field status Create Fig 8 Load and predefined field manager dialogs i Abaqus CAE 6 9 1 Model Database C job 8 Plug in Holed Plate Structural S File Model Viewport View Load BC Predefined Field Load Ca DERA te SQ BA lam Module Load sS Model Database TA amp v la g Models 1 E Mod gigi Switch Context Ctrl Space n of o Copy Model gr Edit Attributes l Edit Keywords Rename oh ad Folk Delete Del iv Set As Root Expand All Under les Collapse All Under p ension Ta gt a LMM Temperature Difference xyz om LMM Null JG om LMM Shakedown 0 X Step 1
17. e plug in will then be read by the subroutine at the beginning of the analysis This means that the UMAT subroutine is called for each integration point which has been defined as a User material from within Abaqus CAE Defining areas of the model as a User material within Abaqus CAE tells the solver to look to the UMAT subroutine for the material behaviour of those areas This solution stage of the analysis uses the number of CPUs requested by the user and so this UMAT subroutine must be coded to accommodate this As part of the restructuring all the elastic calculations for the applied loads and the LMM calculation itself have been incorporated into a single Abaqus analysis Each elastic calculation is carried out as a single analysis step within this Abaqus analysis with the LMM calculation being performed in the final analysis step This consolidation into a single Abaqus analysis means that the passing of stresses and temperatures in text files is no longer required Instead the results file itself can be used for storage and access of this information When defining a User material in Abaqus CAE the user is able to specify the number of Solution Dependent State Variables SDV for that material This is the number of memory spaces available to the UMAT in the output database file and so is commonly used to provide contour plots of user defined variable fields calculated during the UMAT solution However the direct access of SDVs within UMAT mea
18. e scaled during the solution At least one load must be selected so that the Epdedleneel feet 3 solution can converge on the shakedown limit Fig 6 Loadcycle dialog box and Tip box for Loadcycle definition a Linear Matching Method Analysis Paramters Job Name Sample_Name Max Number of Increments 1300 set Select working directory C job Convergence Level Analysis Paramters Job Name Select working directory Convergence Level 0 001 Clicking OK converts the model and creates an analysis job During solution please refer to the data tab in the Analysis Paramters Job Name Max Number of Increments Ei COO Select working directory C job Steady Cycle Convergence Level C difference between consecutive UB monitor dialog or the dat file for load multipliers and odb outputs Steady Cycle Convergence 0 001 difference between UB and LB Ratchet Limit Convergence Level difference between consecutive UB Clicking OK converts the model and creates an analysis job During solution please refer to the data tab in the Diff 5 Tip monitor dialog or the dat file for load multipliers and z odb outputs difference between UB and LB Clicking OK converts the model and creates an analysis job During solution please refer to the data tab in the monitor dialog or the dat file for load multipliers and o
19. ependent Modulus Temperature Independent Yield Stress Temperature Independent Ramberg Osgood Explanation The number of materials is printed so that UEXTERNALDB knows how many materials to look for in the file The material name is printed to be read by UEXTERNALDB The modulus and yield for each material may be either Temperature Independent or Temperature Dependent Temp independent values are written to the User Material in Abaqus Where temperature dependent properties are found these are printed in a formatted way so that UEXTERNALDB is able to read them For each material the words Perfectly Plastic Material are printed unless a Ramberg Osgood material is selected Where a Ramberg Osgood model is used with temperature dependent properties then a formatted list of these is provided in the same way as modulus or yield Otherwise it is declared as temperature independent and the values are written in the User Material 18 Start the Analysis UEXTERNALDB Read the LMM text file Perform elastic analysis for first applied load K Does K number of applied loads Perform Null step to return variables to zero Carry out an LMM increment Calculate convergence and load multipliers for next increment as the convergence criteria been met End the Analysis Fig 1 Overall structure of a LMM solution 7 Abaqus CAE File Model Viewport View Part Shape Feature Tools Plug ins Help
20. ercial FE software Abaqus 2 using user subroutines developed by FORTRAN programming language which is difficult for non experts to operate Another drawback of this implementation is the level of programming experience required to create and submit an analysis the alterations to the subroutines required to run each analysis present issues for everyday use by engineers generally not familiar with FORTRAN To remedy this situation and enable widespread adoption of the LMMs in industry an integrated software tool is required to not only removes the requirement for manual subroutine alterations but also provide additional functionality for subsequent life assessment calculations The main objective of this paper is to develop a new integrated structural analysis tool using the LMM framework for the assessment of design limits in plasticity including the evaluation of limit load shakedown limit ratchet limit and steady state cyclic behaviour of the structure It will deliver the LMM in a form where it can be readily used by engineers with the responsibility for design and life assessment decisions on a regular basis The software tool would allow engineers to access the LMM solution methods without having to make any of the changes to the subroutines required to run a LMM analysis as was previously required The paper is organized as follows In Section 2 preliminary considerations are discussed by examining previous LMM versions and the way of
21. evelopers and the University of Strathohde take no responsibility for any loss incurred directhy or indirecthy through use of the LMM Copyright 20123 LMM All Rights Reserved waw thelmm co uk LMM modifications from a previous analysis have been detected in this model Existing jobs may become obsolete by continuing this process Dismiss At lease one mechanical load must be applied to perform a ratchet limit assessment Dismiss Fig 3 Main dialog box and possible error messages B Uir nea r Matc hi NG N ethod i Invalid values detected Coefficients must N not be less than zero and poisson s ratio Input Properties for Material Steel must have a value between 0 0 and 0 5 Material Properties Young s Modulus Yield Stress Dismiss Temperature Dependent Temperature Dependent f Youngs Modulus 208000 0 Yield Stress Temp 300 20 285 50 Thermal Expansion 5e 005 Poissons Ratio 0 3 E Abaqus CAE Note Right click to add remove rows to Temperature dependent material data must be entered the tables in order of increasing temperature and therfore decreasing modulus yield values Fig 4 Material properties dialog box and possible error messages a Linear Matching Method Material Properties Input Properties for Material Steel Young s Modulus Yield Stress E Temperature Dependent Temperature Dependent Youngs Modulus 208000 0 Yield Stress 293 39966 Thermal Expansion 5e 005
22. g the component is meshed It also includes checks more specific to the LMM such as ensuring that at least one mechanical load is applied when a ratchet limit analysis is selected Any error found is displayed to the user so that it may be remedied as shown in Figure 3 Upon passing these checks a series of subsequent dialogs are posted This begins with the material data A Material dialog box is posted for each material which is used in the current model Within each of these dialogs the user is prompted to enter the Young s modulus yield stress Poisson s ratio and the thermal expansion coefficient The Young s modulus and yield stress may be temperature dependent which is enabled by selecting this in a check box In many situations the model will have already been used in a previous analysis meaning material property data has already been defined in CAE If this is the case the Extract function can be used which queries the current material for the four properties required for the LMM analysis and populates the dialog box accordingly The Material dialog box is shown in Figure 4 alongside some of the possible error messages When either a steady state cycle analysis or a ratchet analysis is chosen the user has an option of using a Ramberg Osgood R O plastic model In this case the Material dialog is shown in Figure 5a The Ramberg Osgood parameters may be temperature dependent or independent in the same way as the modulus and yield
23. i e nothing of the original model is deleted Instead items are suppressed or copied so that the LMM configuration of the model can be applied All the model data is passed into a set of scripts which write relevant information to the LMM text file and perform a series of changes to the model Firstly a LMM text file is created and populated with information about the analysis An example of this is shown in Table 2 Once this information has been written to the LMM text file the next stage is to configure the loads and boundary conditions in the Abaqus CAE model Two basic requirements dictate the way in which this is achieved The first requirement is that the elastic stress for each applied load must be known so that superposition can be used to construct the load cycle in the subroutines The second requirement is that the same boundary conditions are used for all elastic analyses and the shakedown steady cycle ratchet analysis Therefore one analysis step is created for each of these applied loads and predefined fields and the corresponding load or field is applied in isolation in that step Figure 8 shows example Load Manager and Predefined Field Manager tables from Abaqus to illustrate this A Null analysis step is created where no loads are applied which allows the subroutines to return key variables to zero The final analysis step created is for the shakedown steady cycle global shakedown analysis This situation allows the LMM subroutines
24. lied loads and temperature may be selected for scaling These loads and temperature fields will be scaled by the load multiplier A to find the strict shakedown limit The loads which are not checked as scalable are left at the magnitudes given in the load cycle table A steady state cycle analysis has no option for scaling loads This is because the load levels given in the table are fixed at those values and a steady state cycle analysis determines the steady state response due to this predefined cyclic load condition The ratchet analysis procedure requires that an additional steady state load is scaled to find the global shakedown limit The user may select which of these loads are to be added as additional loads Detailed advice on the load scaling for each analysis type is given in the Tip box Figure 6 The Analysis Parameters dialog shown in Figure 7 is the final dialog box and gathers the data required to create the analysis such as the job name and working directory and the solution controls e g convergence level and maximum number of increments The current working directory is automatically detected and displayed but the user may choose to change this Default values of convergence levels are also displayed for inexperienced users There are different convergence options available depending on the analysis type chosen A strict shakedown analysis can use either the difference between consecutive upper bounds which historically w
25. nerate the applied stresses at each point in the load cycle For an analysis using this set of subroutines both the elastic analyses and the further shakedown or ratchet calculation are submitted using the Abaqus batch command i e the Abaqus input file for the model is required This input file is generated using Abaqus CAE for a complete model The majority of the content of the input file is common between the elastic and shakedown calculations such as geometry and boundary conditions However there are some differences which must be performed manually such as requesting the energy outputs associated with a UMAT subroutine A further upgrade of these subroutines was carried out 16 so that the LMM could be used with minimal code changes where the load cycle is defined via a formatted text file which was read by the subroutines This significantly reduces the code changes required for an analysis However the changes to the Abaqus input file still needed to be performed manually The creation of a formatted text file to configure the LMM analysis was a major step in the usability of the LMM and in fact draws a parallel with the way in which any conventional 4 Abaqus analysis operates In an Abaqus analysis a FE model needs to be created in Abaqus CAE and submitted for analysis although other pre and post processors are often used Abaqus CAE then creates a formatted text file Abaqus input file which is passed to the Abaqus solver fo
26. ng this output allows the user to view contour plots of the variables calculated within the UMAT routine and so it is vital that this is included In addition to the field and history outputs an energy file output must be requested so that the volume integrals needed for the upper bound load multiplier can be accessed The only way to achieve this is by adding commands to the keyword block for the model which contains all the commands printed to the input file when the analysis begins shown in Figure 9 Part of this script inserts the commands to the keyword block as if a user had manually typed them To recover the initial state of the model a user simply clicks the button Discard All Edits which removes any user added commands The final script creates the LMM analysis job with the correct subroutine for the analysis type selected When created the user may edit the job in the same way as any other Abaqus job by selecting the number of CPUs to solve with queue options etc Finally the user may submit the analysis for solution Whilst solving any Abaqus job the progress of the solution may be seen in the Monitor dialog box Information such as the current step and increment are displayed along with any warnings and errors encountered The URDFIL subroutine contains code which prints additional information about the LMM to the Data file which can be read by this dialog box During the solution the lower and upper bound load multipliers an
27. ns that they can also be used as a way of storing values and data to be used during the analysis Hence this has been used to pass elastic stresses and temperatures between the elastic analyses and the LMM analysis removing the need for text files and therefore removing this restriction to multiple CPU solution Returning to Figure 1 the UMAT subroutine is divided into elastic and LMM sections An elastic analysis is performed for each applied load and the stresses and temperatures are stored in the SDV slots When all applied loads have been considered an intermediate null step is included This allows key variables in the subroutine to return to zero before commencing the LMM solution The LMM solution itself uses the stresses and temperatures from the SDVs along with the load cycle and material property data read in the UEXTERNALDB subroutine to perform the calculations Within the LMM solution stage the data previously stored in model sized arrays is now stored using the SDVs Abaqus itself manages the multiple CPUs accessing the results files as it would during any analysis which uses multiple CPUs These existing methods for managing multiple CPU solution mean that the UMAT subroutine can use Abaqus itself to manage the multiple CPUs accessing the data simultaneously The alternative placing these model sized arrays into common memory would mean the CPUs would have to queue for access to the array The URDFIL subroutine is called b
28. o stages of calculation 12 the first a steady state cyclic analysis for a cyclic history of residual stress and the second for the ratchet limit due to an extra constant load This set of subroutines require that the Abaqus model is configured in a certain way e g one analysis step per applied load and so provides a set of requirements which has dictated the design of the plug in and its operation 4 Graphical User Interface via an Abaqus Plug in Upon selecting the LMM plug in from the plug ins menu in Abaqus CAE Figure 2 the user is then guided through the Main dialog box seen in Figure 3 The Main dialog box is posted which prompts the user to select which model from within the current CAE session they would like to analyse and which type of LMM analysis strict shakedown steady state cycle or steady state cycle ratchet limit Selecting a steady state cycle analysis means that only stage 1 of the ratchet analysis procedure 12 is performed to give the steady cyclic state of the component along with the associated strain ranges which provide information concerning fatigue crack initiation in low cycle fatigue The second stage to find the ratchet limit is not performed when selecting a steady state cycle analysis With the information from this dialog background scripts perform a series of checks on the selected model to ensure it is possible to perform a LMM analysis successfully This includes very basic checks such as ensurin
29. odate this presents an opportunity to re write them for multiple CPU solution especially since even basic desktop computers now have dual or quad core as standard Some features of the UMAT code written by Chen 12 14 and Tipping 16 are not amenable to solution with multiple CPUs With all of these considerations a plug in has been created and the LMM subroutines have been re written The plug in posts dialog boxes to gather the required information and data from the user When the process is complete the plug in configures the model for the LMM analysis using scripts The plug in also writes the text file containing relevant data for the subroutines The subroutines themselves have been re written to allow multiple CPU solution in the UMAT routine The structure and function of the plug in is dictated by many of the features of the subroutines and their re structuring for multiple CPU solution Therefore the subroutines will be described in the next section followed by a description of the plug in created to use them 3 Re structuring of the Subroutines Figure 1 shows the general structure of a LMM solution with the new set of subroutines for various plastic analyses The starting point of this process assumes that the plug in has created a formatted text file containing information about the analysis such as the convergence tolerance analysis type load cycle and temperature dependent material data This LMM text file produced by th
30. per Keywords Linear Matching Method LMM Structural Integrity Load Carrying Capacity Shakedown limit Ratchet limit Steady State Cycle Corresponding author Tel 44 1415482036 E mail address Haofeng chen strath ac uk 1 Introduction Many Engineering components and structures in defence aerospace petrochemical automobile and power industries operate under cyclic thermal and mechanical load conditions and would include such diverse products as advanced internal combustion IC engine and gas turbine components high altitude ramjet and rocket motors chemical reactor vessels in plastics manufacture prototype fusion reactors power boilers etc In all of these applications it is important to ensure the equipment can operate safely for the specified design life under the arduous environmental conditions This requires engineers to identify possible failure mechanisms and guard against these during the design process 1 Engineering structures subjected to cyclic loading histories will experience either elastic plastic shakedown or ratchetting depending upon the applied load level Limiting the behaviour of the structure or component to the elastic range is not an effective approach to a problem as this leads to over conservative design In many applications it is acceptable to allow limited plastic deformation to occur provided it can be shown that the structure shakes down to elastic action in the first few cycles of load If
31. qus is a very powerful tool because options also exist to use this language to customise the CAE user interface itself This can be achieved by creating either an entirely custom CAE interface or a plug in to the standard CAE The ability to create a custom GUI is a powerful tool as the modules and toolsets which are not desired can be removed and custom functions can be added Abaqus Viewer is an example of this where all the analysis toolsets and modules have been removed leaving only the visualisation module for viewing output databases Plug ins form another useful avenue of adding functionality to the Abaqus CAE interface Plug ins can be created for a variety of purposes commonly they are used to streamline tasks which are complex to perform or are performed regularly For the LMM application a plug in has been selected over a custom CAE interface A plug in can be accessed through the conventional CAE interface during normal use whereas a custom CAE would need to be opened separately An engineer with an existing Abaqus model will be able to access the LMM through CAE and the plug in will guide them through the process of entering the information needed to run a LMM analysis The creation of a plug in to gather the required data and format the model will require a set of subroutines which are compatible with this model configuration and the text file used to pass in the data for the analysis The re structuring of the subroutines to accomm
32. r solution The text file for the LMM analysis is equivalent to the input file the only difference being that it is created manually The creation of a text file is also adopted here as it is a simple and robust method for passing information from the LMM user interface into the subroutines The major aim of this software tool is that the text file is generated by the user interface rather than manually 2 2 Customising Abaqus Abaqus 2 contains a large number of options for the user to customise a model or analysis for their particular situation To obtain user generated solution options the user subroutines can be used which is how the LMM has been implemented In addition to this Abaqus CAE contains the option to use scripts to perform operations on the model or results databases These scripts are written in the Python open source scripting language 2 and Abaqus has extended this language to allow operations to be performed within CAE itself These scripts can be used to perform all operations which are available through the CAE interface i e applying loads meshing plotting results etc and can also query the model or Abaqus output file odb for values A typical example where scripts serve a useful function is in a sensitivity analysis where an automatic process can vary a particular value in a model re submit for solution query the results and decide whether a further iteration is required The use of python scripting within Aba
33. stress A function is also included to link the R O parameters to the yield stress This function calculates the 0 2 proof stress from the R O parameters entered and populates the yield stress fields accordingly Additional advice is available for the R O model by selecting the Tip button which displays the box shown in Figure 5b It is worth noting that each active material in the FE model will allow users to define the material properties through a separate Material dialog box meaning that the LMM software tool is capable of analysing components or structures with multiple materials such as composites or welded components When this is complete the plug in moves on from materials to the load cycle The definition of the load cycle is crucial for all analyses This is done through the Load cycle dialog boxes where the Loadcycle table at the top of the box is present This table allows the user to define a load cycle by adding any number of time points and scaling the loads to the appropriate level for that time point in the cycle At each time point a temperature field can also be applied by selecting desired predefined field from the drop down list Selecting the Tip button displays a box with additional information on populating this table and a simple worked example as shown in Figure 6 A subtle difference between the three analysis options comes when selecting the loads which may be scaled In a strict shakedown analysis any of the app
34. t inevitably requires significant computer effort for complex 3D structures There has been a recent trend towards the development of direct methods that combine the convenience and efficiency of rule based methods 1 and the accuracy of incremental FE simulation techniques Of these simplified direct methods 3 9 the Linear Matching Method LMM 10 14 has become one of the most powerful numerical methods for generating approximate inelastic solutions and answering specific design related issues using standard finite element codes The basis of the LMM is through an idea of representing histories of stress and inelastic strain as the solution of a linear problem where the linear moduli are allowed to vary both spatially and in time The LMM has been formulated and implemented for the evaluation of shakedown limit 10 11 and ratchet limit 12 13 And more recently a new LMM framework was developed to evaluate the steady state cyclic behaviour of component for the LCF assessment purpose 14 The LMM is distinguished from the other upper bound or lower bound direct methods by ensuring that both the equilibrium and compatibility conditions are satisfied to produce exact solution at each stage of calculations 13 and is counted to be one of the methods most amenable to practical engineering applications involving complicated thermo mechanical load history 15 However as many other direct methods the LMM was initially implemented into comm
35. temp at the bore varies between zero and maximum This creates two significant points in the load cycle Load point 1 has the tension applied and a temperature at the bore of zero meaning zero degrees everywhere in the plate Load point 2 has the tension applied and the temperature at the bore is at its maximum creating a temperature difference and a thermal stress To replicate this in the Load Cycle table each load point J gt Is a in turn and the arse ail are entered At load point EEE ea 1 the tension is applied so a multiplier of 1 is entered The Load Cycle temperature at load point 1 is zero everywhere and so none Load Points is entered in the Temp Field box At load point 2 the tension 1 2 3 is still applied and so a multiplier of 1 is entered The Tensi 1 1 0 temperature field at load point 2 is described by a predefined and so this is selected in the Temp Field box A multiplier of Temp Field None Predefined Field 1 Predefined Field 1 1 is selected but entering any other number would scale the Temp Multiplier men 1 1 entire temp field by this value Load Scaling During Solution Note Right click to add remove Load Scaling During Solution ku C Select which loads may be scaled Selecting loads from this list will allow the LMM to scale to find the strict shakedown limit these loads to find the strict shakedown limit Leaving a i E e P Tension V load un ticked means that the load will not b
36. y Abaqus at the end of every increment and plays a number of key roles Firstly the URDFIL can be used to access the results file and so is able to obtain the volume integrals required to calculate the upper bound multipliers of equations 16 in 11 and 29 in 12 Being called at the end of the increment means that the URDFIL is used to provide a summary of the increment to the user to give an indication of how the solution is progressing Finally the URDFIL routine can also be used to terminate an analysis Convergence calculations are performed in URDFIL and if the convergence criteria are satisfied then the analysis is ended If convergence is not met then the solution continues for a further increment where the UMAT is called and the LMM calculations are performed once again With these subroutines there are three LMM analyses possible for the design limits in plasticity strict shakedown steady state cycle only and ratchet limit i e the global shakedown limit It is worth noting that when having only one load time point the shakedown analysis automatically reduces to a limit analysis and the limit load or load carrying capacity of the component can be evaluated as a special case of this shakedown analysis The subroutines have been programmed to be flexible and allow as many options as possible within these three analyses These options are summarised in Table 1 As shown in Table 1 the calculation of the ratchet limit includes tw
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