3D-FE Implementation of Evolutionary Cyclic Plasticity Model for Fully Mechanistic (non S-N curve) Fatigue Life Evaluation

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1 3D-FE Implementation of Evolutionary Cyclic Plasticity Model for Fully Mechanistic (non S-N curve) Fatigue Life Evaluation Bipul Barua, Subhasish Mohanty 1, Joseph T. Listwan, Saurindranath Majumdar, and Krishnamurti Natesan Argonne National Laboratory Lemont, IL, USA ABSTRACT Large uncertainties exist in the current methods of fatigue life evolution for nuclear components due to the overdependence on approaches that use empirical stress/strain-life (S~N) curves. Argonne National Laboratory (ANL), under the sponsorship of Department of Energy's Light Water Reactor sustainability (LWRS) program, seeks to develop a fully mechanistic approach for more accurate fatigue life estimation of nuclear components. To this end, ANL has developed evolutionary cyclic plasticity models for reactor steels based on uniaxial fatigue tests to capture the material aging behavior such as stress hardening/softening. In this paper, we introduce an implementation of the evolutionary cyclic plasticity model within the commercial finite element software ABAQUS through the use of an in-house developed user material subroutine. The developed FE model can be used for predicting the time-dependent stress hardening/softening of 3D structures. A strain-controlled variable amplitude fatigue experiment is 3D modeled using the developed ABAQUS based FE modeling framework and verified through the experimental data. Keywords: Finite element modeling; cyclic plasticity; low cycle fatigue; stainless steel; material hardening/softening 1. Introduction The current procedures for fatigue life assessment of nuclear reactor components exposed to thermal-mechanical loading cycles and reactor environment are usually based on stress/strain versus life (S~N) curves and/or similar empirical approaches [1-4]. Although these empirical approaches allow engineers to quickly assess the components design lives, they are not based on firm mechanistic understanding of how the stress/strain behavior of material evolve over time and its impact on fatigue damage accumulation. Moreover, the (S~N) curves are usually obtained from a uniaxial fatigue test that may not represent the true stress-strain state of the component under multi-axial loading. Nowadays, with the availability of advanced computation tools such as the FE method along with supercomputers, it is possible to perform mechanistic simulation at system- and component-level under real-loading conditions [5-7]. This will provide engineers with more accurate prediction of fatigue lives of the reactor components as compare to current approaches that have large uncertainties due to the use of empirical relations. We, therefore, are trying to develop a fully mechanistic modeling approach. The aim is to capture the time/cycledependent material ageing behavior such as stress hardening/softening through multi-axial stress-strain evolution of the components based on which the life of the component can be predicted. The overall picture of our mechanic-based fatigue-modeling framework is shown in Figure 1. As shown in the flowchart, mechanics-based fatigue modeling starts with uniaxial fatigue experiments followed by material model (based on an evolutionary cyclic plasticity model) development along with material model parameter estimations. The evolutionary cyclic plasticity model [8] was developed based on Armstrong-Frederick [9] or Chaboche [10] type nonlinear kinematic hardening rule. In the proposed model, it is assumed that the material yield surface and the corresponding hardening and softening behavior evolved over time. Thus, a single set of material parameters is not enough to predict the material behavior for the complete lifetime. In our previous work [8, 11-13], we had demonstrated that material parameters (estimated from uniaxial fatigue experiment) such as elastic modulus, yield stress and kinematic hardening constants do not stay constant but evolve over the lifetime of the specimen. Thus, the material parameters should be functions of time or fatigue cycle/block or any other physical state. The details of the 1 Corresponding author. smohanty@anl.gov; Tel.: ; fax:

2 model development and time/block-dependent material parameter estimation technique are discussed in Ref. [8, 11]. The next step in the mechanics-based fatigue modeling framework is validation of the evolution cyclic plasticity model through analytical and 3D-FE modeling of the specimen. In our recent work [14], we presented results from 1D-analytical modeling of fatigue specimens subjected to constant, variable, and random amplitude loadings. Comparison of the analytical modeling results with experimentally observed data demonstrated that the evolutionary cyclic plasticity model can mechanistically capture all the important stages of material behavior (initial hardening, softening, stabilized cycles, and finally rapid crack propagation followed by failure) during the entire fatigue life of the specimens with great accuracy [14]. The final step of the mechanics-based fatigue modeling framework is to extrapolate uniaxial fatigue test-based material behavior to a multiaxial domain for structural analysis of nuclear reactor components subjected to multiaxial fatigue loading. However, a successful incorporation of the evolutionary cyclic plasticity model in generalized FE code is necessary for the extrapolation of material behavior under uniaxial loading to multiaxial domain. In this work, we present an implementation of the evolutionary cyclic plasticity model for 316 stainless steel (SS) into a commercial finite element code, ABAQUS. To verify the accuracy of the model a variable amplitude strain-controlled fatigue experiment scenario is 3D modeled using the developed ABAQUS based FE modeling framework and compared with experimental results. The verification based on constant amplitude fatigue has been presented in our recent publication [15]. The complete work of the analytical and FE modeling of fatigue tests under any arbitrary loading including constant, variable, and random amplitude can be found in a recent Argonne report [16]. Figure 1 Flowchart showing the steps in ANL s mechanics-based fatigue-modeling framework. 2. FE Implementation of the Evolutionary Cyclic Plasticity Model The evolutionary cyclic plasticity model was incorporated into the developed FE code for Chaboche-type models in the ABAQUS/Standard environment. As ABAQUS uses the backward Euler method [17], it provides unconditional stability for integration of rate equations. However, ABAQUS does not allow the use of time/block-dependent material properties. Note that, during a variable amplitude fatigue experiment, repetitive loading blocks, with each block consisting of multiple cycles with varying amplitudes, are applied to the specimen. To model a variable amplitude fatigue experiment based on evolutionary cyclic plasticity model, therefore, time/block-dependent (i.e. block-by-block) material properties are required. To enable the use of time/block-dependent material properties in the implementation of the evolutionary cyclic plasticity model into ABAQUS, a user subroutine, called USDFLD (written in Fortran), was developed. The time/block-dependent material properties such as elastic modulus, yield stress, and kinematic hardening constant are provided into the ABAQUS input file in tabular form. At the start of

3 each integration, the USDFLD accesses the corresponding block material properties from the table provided in the input file. If properties are not provided for a value of the user-defined field variable, ABAQUS uses interpolation to calculate the values of the material properties. 3. Experimental A strain-controlled variable amplitude uniaxial fatigue test (Test ID: ET-F38) on 316 SS was conducted using a small hourglass type specimen (gage length: 0.5 inch) and a hydraulic-controlled MTS test frame, in air at 300 C. During ET-F38, a repetitive block consists of 12 cycles with different strain amplitudes was applied. Figure 2 depicts the applied cyclic strain input during ET-F38. The strain amplitude was varied by gradually increasing from a minimum value of 0.05% (selected to fall within the elastic limit) to a maximum value of 0.55% and then gradually decreasing to the minimum again. A constant strain rate of 0.1%/s was employed during the test. The corresponding time history of the measured stress data from ET-F38 is shown in Figure 3. As seen in Figure 3, there are significant initial stress hardening followed by stress softening for 316 SS material under strain-controlled mode. Data of a tensile test (Test ID: ET-T04, air, 300 C) from previously published work [11] are also used in the discussion of this paper. Figure 2 Block loading during variable amplitude strain-controlled fatigue test (ET-F38). Data points show minimum and maximum amplitudes.

4 Figure 3 Observed stress during the entire ET-F38 test. 4. Material Model Parameters The ABAQUS implementation of the evolutionary cyclic plasticity model requires elastic material properties such as elastic modulus and Poisson s ratio and plastic material properties such as yield stress and kinematic hardening material constants. The Poisson s ratio was considered constant while time/block-dependent (i.e. block-by-block) data were provided for other material properties. In our previous work [12], we presented a parameter estimation technique to evaluated time/block-dependent material parameters from a variable amplitude fatigue test. Using same technique, block-dependent material parameters for 316 SS were estimated from ET-F38 test data. Figure 4 shows the block variation of the estimated elastic modulus and elastic limit stress, while Figure 5 shows the block variation of the estimated nonlinear kinematic hardening parameters C1 and γ1. It can be seen from the figures that all the material parameters significantly vary over the entire time of the specimen life. Time-independent or fixed material parameters estimated from ET-T04 tensile test are provided in Table 1 [11]. The values of material parameters at half-life of fatigue specimen ET-F38 are provided in Table 1 as well. These time-independent material parameters were also used to simulate the ET-F38 fatigue experiment and compared with the results from simulation using time/block-dependent material properties. Figure 4 Time/block-dependent elastic modulus (left) and elastic limit stress (right) estimated from ET-F38.

5 Figure 5 Time/block-dependent nonlinear kinematic hardening constants, C1 (left) and γ1 (right) estimated from ET- F38. Table 1 Time-independent material parameters Elastic modulus Elastic limit stress Nonlinear hardening constants (GPa) (MPa) C1 (MPa) γ1 Tensile test (ET-T04) Half-life (ET-F38) FE Simulation Results One of our major tasks in mechanics-based fatigue modeling is to develop an FE modeling framework based on the evolutionary cyclic plasticity model. The FE modeling framework can then be used for extrapolating material behavior based on uniaxial tests to a multi-axial domain for stress analysis and fatigue evaluation of realistic reactor components, which are ideally subjected to multi-axial loading. Compared to the conventional FE model, the evolutionary cyclic plasticity FE model would be able to predict the cyclic hardening and softening behavior of a component. However, before the new FE model can be used for component-level stress analysis, the FE framework must be validated with experimental test cases. We used a commercially available FE software, ABAQUS, for FE implementation of the proposed evolutionary cyclic plasticity model. A single 3D brick element (hexahedral: 8-node linear brick element: C3D8) representing the gauge section (0.5 in.) was used for FE simulation of the fatigue experiment. The geometry information of the actual specimen and FE modeled equivalent specimen is shown in Figure 6. The area of cross-section of the brick element was equal to the nominal cross-sectional area of the specimen. A simulation representing the ET-F38 fatigue experiment (variable strain amplitude applied in Z- direction) was performed using time/block-dependent and time-independent material properties.

6 Figure 6 Geometry information of actual specimen and FE modeled equivalent specimen. Figure 7 depicts the comparison between experimentally observed stress and simulated stress for first 50 blocks. The figure shows predicted stress using both time/block-dependent material parameters estimated from ET-F38 fatigue test data and two sets of time-independent or fixed parameters estimated from tensile test ET-T04 and the half-life block of ET-F38. It can be seen from the figures that the evolutionary cyclic plasticity model based on time/blockdependent material properties can well predict the material hardening behavior, while the Chaboche model based on time-independent material properties could not predict the material hardening behavior. The ABAQUS model was then simulated for the entire life of the fatigue specimen in the FE modeling framework. The 3D-FE simulated axial stress along with the experimentally observed stress for the entire life of the specimen is shown in Figure 8. A magnified version of Figure 8, demonstrating initial stress hardening and then softening followed by stabilized cycles, is shown in Figure 9. These figures demonstrate that the evolutionary cyclic plasticity model predicts not only the stress hardening but also the stress softening with significant accuracy. The model also predicts the stabilized cycles, which represent a quasi-stable state during fatigue. Most importantly, as shown in Figure 10, it accurately predicts the fast stress drop toward the end of the fatigue life of the specimen, which represents unstable or rapid crack propagation. Thus, it can be concluded that the evolutionary cyclic plasticity model can predict all stages of the material behavior during its entire fatigue life. This creates a great possibility to replace the current S~N curves based empirical method with mechanistic simulation for fatigue life evaluation.

7 Figure 7 3D-FE simulated vs. experimental axial stress of ET-F38 specimen for first 50 blocks. Predictions are from simulation using time/block-dependent parameters and two sets of time-independent parameters (estimated from tensile test ET-T04 and half-life block of ET-F38). Figure 8 3D-FE simulated (using evolutionary cycle plasticity model) vs. experimental axial stress history of ET- F38 specimen for whole fatigue life.

8 Figure 9 Magnified version of Figure 8 showing that the 3D-FE results can predict the material behavior (such as initial stress hardening, softening, and stabilized cycles) under variable-amplitude loading. Figure 10 Magnified version of Figure 8 showing that the 3D-FE results can predict the material behavior during rapid crack propagation and failure under variable-amplitude loading. 6. Conclusions

9 In this work, Argonne-developed evolutionary cyclic plasticity model for 316 SS is implemented into a commercial FE code, ABAQUS, by utilizing an in-house developed user subroutine. A strain-controlled variable amplitude fatigue test specimen was successfully simulated using a 3D 8-noded brick element representing specimen gage area. The simulated results demonstrate that the evolutionary cyclic plasticity model can mechanistically capture all the important stages of material behavior (initial hardening, softening, stabilized cycles, and finally rapid crack propagation followed by failure) during the entire fatigue life of the specimens with great accuracy. We believe the findings of this research work is a significant step toward the development of mechanics-based fatigue life estimation technique which will greatly reduce the uncertainty in the estimated fatigue life using current S~N curve based empirical methods. ACKNOWLEDGEMENTS This research was supported through the U.S. Department of Energy s Light Water Reactor Sustainability (DOE- LWRS) program under the work package of environmental fatigue study, program manager Dr. Keith Leonard. REFERENCES 1. The American Society of Mechanical Engineers, Rules for Construction of Nuclear Facility Components (ASME Boiler and Pressure Vessel Code, Section III, Division1, 2013). 2. O.K. Chopra, and W.J. Shack, Effect of LWR Coolant Environments on the Fatigue Life of Reactor Materials (Report NUREG/CR-6909, U.S. Nuclear Regulatory Commission, 2007). 3. BSi, Unfired Pressure Vessels (BS EN :2009+A1:2012, Part 3: Design, 2012). 4. AFCEN, Design and Construction Rules for Mechanical Components of PWR Nuclear Islands (RCC-M- Edition 2007 Addendum December 2008, 2007). 5. S. Mohanty, W.K. Soppet, S. Majumdar, S., and K. Natesan, System-Level Heat Transfer Analysis, Thermal- Mechanical Cyclic Stress Analysis, and Environmental Fatigue Modeling of a Two-Loop Pressurized Water Reactor. A Preliminary Study (Report ANL/LWRS-15/01, Argonne National Laboratory, 2015) S. Mohanty, W.K. Soppet, S. Majumdar, S., and K. Natesan, Thermal mechanical stress analysis of pressurized water reactor pressure vessel with/without a preexisting crack under grid load following conditions Nuclear Engineering and Design, 310 (2016), S. Mohanty, W.K. Soppet, S. Majumdar, S., and K. Natesan, Full-scale 3-D finite element modeling of a twoloop pressurized water reactor for heat transfer, thermal mechanical cyclic stress analysis, and environmental fatigue life estimation Nuclear Engineering and Design, 295 (2015), S. Mohanty, W.K. Soppet, S. Majumdar, S., and K. Natesan, Tensile and Fatigue Testing and Material Hardening Model Development for 508 LAS Base Metal and 316 SS Similar Metal Weld under In-air and PWR Primary Loop Water Conditions (Report ANL/LWRS-15/02, Argonne National Laboratory, 2015) P.J. Armstrong, and C.O. Frederick, A Mathematical Representation of the Multiaxial Bauschinger Effect (Research & Development Department, Central Electricity Generating Board and Berkeley Nuclear Laboratories, 1966). 10. J.L. Chaboche, and G. Rousselier, On the Plasticity and viscoplasticity Constitutive Equations part II: Application of Internal Variable Concepts to the 316 Stainless Steel Journal of Pressure Vessel Technology, 105 (1983), S. Mohanty, W.K. Soppet, S. Majumdar, and K. Natesan, Effect of Pressurized Water Reactor Environment on Material Parameters of 316 Stainless Steel: A Cyclic Plasticity Based Evolutionary Material Modeling Approach ASME 2015 Pressure Vessels and Piping Conference, 2015, PVP S. Mohanty, B. Barua, W.K. Soppet, S. Majumdar, S., and K. Natesan, Study the Cyclic Plasticity Behavior of 508 LAS under Constant, Variable and Grid-Load-Following Loading Cycles for Fatigue Evaluation of PWR Components (Report ANL/LWRS-16/03, Argonne National Laboratory, 2016).

10 13. S. Mohanty, W.K. Soppet, S. Majumdar, S., and K. Natesan, Chaboche-Based Cyclic Material Hardening Models for 316 SS 316 SS Weld under In-air and Pressurized Water Reactor Water Conditions Nuclear Engineering and Design, 305 (2016), B. Barua, S. Mohanty, J.T. Listwan, S. Majumdar, K. Natesan, A Cyclic-Plasticity-Based Mechanistic Approach for Fatigue Evaluation of 316 Stainless Steel Under Arbitrary Loading Journal of Pressure Vessel Technology, 140:1 (2018), B. Barua, S. Mohanty, J.T. Listwan, S. Majumdar, K. Natesan, Is it Possible to Get-rid of SN Curve for Fatigue Evaluation?: A Fully Mechanistic Model of 316SS Reactor Steel for Fatigue Life Evaluation ASME 2017 Pressure Vessels and Piping Conference, 2017, PVP S. Mohanty, B. Barua, J.T. Listwan, S. Majumdar, S., and K. Natesan, Final Report on CFD and Thermal- Mechanical Stress Analysis of PWR Surge Line under Transient Condition Thermal Stratification and an Evolutionary Cyclic Plasticity Based Transformative Fatigue Evaluation Approach without Using S~N Curve (Report ANL/LWRS-17/03, Argonne National Laboratory, 2017). 17. Systémes, Dassault. (2016) "Abaqus Theory Guide.