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Modeling the Temperature Dependence of Tertiary Creep Damage of a Ni-Based Alloy

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Modeling the Temperature Dependence of Tertiary Creep Damage of a Ni-Based Alloy Modeling the Temperature Dependence of Tertiary Creep Damage of a Ni-Based Alloy To capture the mechanical response of Ni-based materials, creep deformation and rup- ture experiments are typically performed. Long term tests, mimicking service conditions at 10,000 h or more, are generally avoided due to expense. Phenomenological models such as the classical Kachanov–Rabotnov (Rabotnov, 1969, Creep Problems in Struc- Calvin M. Stewart tural Members, North-Holland, Amsterdam; Kachanov, 1958, “Time to Rupture Process Under Creep Conditions,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashin., 8, pp. Ali P. Gordon 26–31) model can accurately estimate tertiary creep damage over extended histories. Creep deformation and rupture experiments are conducted on IN617 a polycrystalline Department of Mechanical, Materials, and Ni-based alloy over a range of temperatures and applied stresses. The continuum damage Aerospace Engineering, model is extended to account for temperature dependence. This allows the modeling of University of Central Florida, creep deformation at temperatures between available creep rupture data and the design Orlando, FL 32816-2450 of full-scale parts containing temperature distributions. Implementation of the Hayhurst (1983, “On the Role of Continuum Damage on Structural Mechanics,” in Engineering Approaches to High Temperature Design, Pineridge, Swansea, pp. 85–176) (tri-axial) stress formulation introduces tensile/compressive asymmetry to the model. This allows compressive loading to be considered for compression loaded gas turbine components such as transition pieces. A new dominant deformation approach is provided to predict the dominant creep mode over time. This leads to development of a new methodology for determining the creep stage and strain of parametric stress and temperature simulations over time. ͓DOI: 10.1115/1.3148086͔ Keywords: gas turbine, tertiary creep damage, IN617, Ni-based alloy, constitutive model, tensile/compressive asymmetry 1 Introduction strain history and component life estimates of limited accuracy. Using a more advanced tertiary creep damage model with tensile/ Gas turbines generate electric power through a compression- compressive asymmetry improves the ability to predict compo- combustion process that forces superheated highly pressurized ex- nent life. Creep deformation and rupture experiments are used to haust gas through various components. High pressure in the com- determine the constants of the constitutive model. As a part of this pression area coupled with combustion chamber exit temperatures investigation, the material model is evaluated and a numerical of up to 1350°C creates a situation where material design and parametric study is carried out to determine the total strain expe- selection play a major role in the long term reliability of gas rienced at various combinations of uni-axial stress, temperature, turbine parts. Drives to increase gas turbine efficiency require and time. raising turbine firing temperatures, which negatively impact com- ponent life. Under these conditions high strength materials are 2 Tertiary Creep Damage Model needed to provide long life at elevated temperatures. The traditional method of determining the service life of gas A method has been established for modeling tertiary creep at turbine components employs practical experience, experimental high temperatures. This method is based on the Norton power law data, and finite element analysis ͑FEA͒. The boundary conditions, for secondary creep, i.e., temperature and stress gradients, environmental conditions, and ␧ ␴n ͑ ͒ ˙ cr = A¯ 1 time-dependent variations induce a number of damage mecha- nisms, which cause crack initiation and eventual rupture. Com- where A and n are the creep strain coefficient and exponent, re- ␴ mon practice in the gas turbine industry is to conduct high tem- spectively, and ¯ is the von Mises effective stress. The coefficient perature mechanical testing on a sample-sized specimen over a A exhibits Arrhenian temperature dependence, e.g., period of time and use practical experience ͑from previous design͒ Q A = B expͩ− crͪ ͑2͒ to extend empirical models to failure time. Creep rupture life is RT typically estimated using experience and secondary creep ͑i.e., steady state͒ modeling with temperature dependence. Unfortu- Here Qcr is the activation energy for creep deformation, and T is nately, this method neglects the effects of both strain-softening the temperature measured in K. The term R is the universal gas behavior ͑tertiary creep modeling͒ and tensile/compressive asym- constant. Both A and its temperature-independent counterpart, B, −n −1 metry. Not including these damage mechanisms creates both have units MPa h . The exponent n may also exhibit tempera- ture dependence. As shown in Eq. ͑1͒, the creep strain rate is stress dependent due to ¯␴. For most materials, traditional methods Contributed by the Pressure Vessel and Piping Division of ASME for publication tend to find A and n to be stress independent but there are excep- in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 19, tions ͓1͔. The secondary creep constants are determined by con- 2008; final manuscript received February 28, 2009; published online September 3, 2009. Review conducted by Douglas Scarth. Paper presented at the ASME Early sidering the minimum strain rate versus the applied stress, and Career Technical Conference 2008. using a regression analysis. Hyde et al. ͓2͔ showed for a Ni-based Journal of Pressure Vessel Technology Copyright © 2009 by ASME OCTOBER 2009, Vol. 131 / 051406-1 Downloaded From: https://pressurevesseltech.asmedigitalcollection.asme.org on 08/13/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 1 Creep Deformation data for IN617 Time to strain, t Temperature, T Stress, ␴ Min Rupture ͑h͒ Stress ratio, strain rate strain ␴/␴ ͑ ͒ ͑ ͒ °C °F MPa ksiys %/h % 0.25% strain 1% strain 5% strain Rupture 649 1200 310 45 1.22 0.0006 1.1 204 1338 N/A 1485 649 1200 310 45 1.22 0.0008 1.2 69 904 N/A 1090 649 1200 345 50 1.36 0.0024 1.2 54 353 N/A 412 649 1200 345 50 1.36 0.0024 1.2 40 296 N/A 341 760a 1400 145 22 0.53 0.0098 16.0 7 57 355 748 760 1400 145 22 0.53 0.0051 19.8 14 138 581 981 760 1400 158 23 0.58 0.0031 13.3 19 188 577 852 760 1400 158 23 0.58 0.0035 14.0 16 171 560 828 871 1600 62 9 0.29 0.0022 22.0 54 224 563 1050 871 1600 62 9 0.29 0.0022 19.3 33 200 533 1082 871 1600 69 10 0.32 0.0082 19.8 17 84 251 585 871 1600 69 10 0.32 0.0088 28.5 14 74 231 488 982a 1800 24 3.5 0.19 0.0002 19.0 170 256 384 520 982 1800 24 3.5 0.19 0.0002 14.5 228 384 614 946 982 1800 28 4 0.22 0.0011 20.2 162 259 416 658 982 1800 28 4 0.22 0.0021 17.8 53 240 404 654 aRemoved from consideration. alloy Waspaloy that once a critical value of applied stress is steady-state creep strain is expressed as a modified secondary reached the relationship between minimum creep strain and stress creep rate: evolves. This leads to a two-stage relationship and stress depen- dence of the secondary material constants. Table 1 shows that for ¯␴ n ␧˙ = Aͩ ͪ ͑5͒ the collected creep deformation data, only two stress levels per cr 1−␻ temperature were conducted. Any possible stress dependence of A and n is not visible in the current data. Therefore, stress depen- The isotropic damage variable is scalar valued from 0 for an ini- dence of the secondary material constants is neglected. tial state ͑e.g., undamaged͒ to 1 at final state ͑e.g., completely Jeong et al. ͓3͔ demonstrated that while under stress relaxation ruptured͒. Its evolution was given by Rabotnov ͓4͔ as short term transient behavior occurs where Qcr and n are both stress dependent at relativity short times ͑e.g., less than 10 min͒. M¯␴␹ ␻˙ = ͑6͒ After this transient stage, the Norton power law becomes indepen- ͑1−␻͒␾ dent of initial stress and strain. This transient behavior has been neglected here since the current study focuses on longer periods where M is the creep damage coefficient having units of MPa−␹. ͑e.g., 1–100,000 h͒. This damage evolution formulation allows the model to account During the transition from secondary to tertiary creep, stresses for tertiary creep. In an earlier study, Kachanov ͓5͔ developed a in the vicinity of voids and microcracks along grain boundaries of similar formulation with the exception that the creep damage ex- polycrystalline materials are amplified. The stress concentration ponents, ␹ and ␾, were equivalent. Time hardening, tensile/ due to the local reduction in cross-sectional area is the phenom- compressive asymmetry, and multi-axial behavior can be ac- enological basis of the Kachanov–Rabotnov ͓4,5͔ damage vari- counted for in the model by replacing the effective stress with one able, ␻, that is coupled with the creep strain rate and has a stress- that considers multi-axial stress, e.g., dependent evolution, i.e., ␴␹ ␧ ␧ ͑␴ ␻ ͒ M r m ˙ cr = ˙ cr ¯ ,T, ,... ␻˙ = t ͑7͒ ͑ ␻͒␾ ͑3͒ 1− ␻ ␻͑␴ ␻ ͒ ˙ = ˙ ¯ ,T, ,... The exponent, m, accounts for time hardening and the units of M A straightforward formulation implies that the damage variable is are in MPa−n h−m−1; however, m is defined to be 0.0 in most cases the net reduction in cross-sectional area due to the presence of ͓7,8͔. Here ␴r describes the Hayhurst ͑tri-axial͒ stress and is re- ␴ ͑ ͒ ␴ defects such as voids and/or cracks, e.g., lated to the principal stress, 1, and hydrostatic mean stress, m, and ¯␴. The Hayhurst stress ͓9͔ is given as A ¯␴ ¯␴ ¯␴ = ¯␴ 0 = = ͑4͒ net ␻ Anet A0 − Anet 1− ␴ = ␣␴ +3␤␴ + ͑1−␣ − ␤͒¯␴ ͑8͒ ͩ1− ͪ r 1 m A 0 where ␣ and ␤ are the weighing factors valued between 0 and 1 ␴ ͑ ͒ where ¯ net is called the net area reduction stress, A0 is the un- and are determined from multi-axial creep experiments.
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