A microstructural lattice model for strain oriented problems: A combined Monte Carlo finite element technique

A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature

The fracture morphology of nickel-base superalloys tested in fatigue and creep-fatigue at 650 C

The fracture surfaces of compact tension specimens from seven nickel-base superalloys fatigue tested at 650 C were studied by scanning electron microscopy and optical metallography to determine the nature and morphology of the crack surface in the region of stable growth. Crack propagation testing was performed as part of an earlier study at 650 C in air using a 0.33 Hz fatigue cycle and a creep-fatigue cycle incorporating a 900 second dwell at maximum load. In fatigue, alloys with a grain size greater than 20 micrometers, HIP Astroloy, Waspaloy, and MERL 76, exhibited transgranular fracture. MERL 76 also displayed numerous fracture sites which were associated with boundaries of prior powder particles. The two high strength, fine grain alloys, IN 100 and NASA IIB-7, exhibited intergranular fracture. Rene 95 and HIP plus forged Astroloy displayed a mixed failure mode that was transgranular in the coarse grains and intergranular in the fine grains. Under creep-fatigue conditions, fracture was found to be predominantly intergranular in all seven alloys

Creep-fatigue behavior of NiCoCrAlY coated PWA 1480 superalloy single crystals

Single crystal specimens of a Ni base superalloy, PWA 1480, with a low pressure plasma sprayed NiCoCrAlY coating were tested in various 0.1 Hz fatigue and creep fatigue cycles both at 1015 and 1050 C. Creep fatigue tests of the cp, pc, and cc types were conducted with various constant total strain ranges employing creep dwells at various constant stresses. Considerable cyclic softening occurred as was evidenced particularly by rapidly increasing creep rates in the creep fatigue tests. The cycle time in the creep fatigue tests typically decreased by more than 80 percent at 0.5 N sub f. Though cyclic life did correlate with delta epsilon sub in a better correlation existed with sub f for both the fatigue and creep fatigue tests, and poor correlations were observed with either sigma sub max or the average cycle time. A model containing both delta sigma and delta sigma (sub in), N sub f = alpha delta sigma (sub in) beta delta sigma gamma, with best fit values of sigma for each cycle type, but the same values of beta and gamam, was found to provide good correlations. Life lines were not greatly different among the cycle types, differing only by a factor of about three. The cp cycle life line was lowest for both test temperatures, however among the other three cycle types there was no consistent ranking. For all test types failure occurred predominately by multiple internal cracking originating at pores. The strong correlation of life with delta sigma may reflect a significant crack growth period in the life of the specimens

Fatigue crack propagation of nickel-base superalloys at 650 deg C

The 650 C fatigue crack propagation behavior of two nickel-base superalloys, Rene 95 and Waspaloy, is studied with particular emphasis placed on understanding the roles of creep, environment, and two key grain boundary alloying additions, boron and zirconium. Comparison of air and vacuum data shows the air environment to be detrimental over a wide range of frequencies for both alloys. More in-depth analysis on Rene 95 shows at lower frequencies, such as 0.02 Hz, failure in air occurs by intergranular, environmentally-assisted creep crack growth, while at higher frequencies, up to 5.0 Hz, environmental interactions are still evident but creep effects are minimized. The effect of B and Zr in Waspaloy is found to be important where environmental and/or creep interactions are presented. In those instances, removal of B and Zr dramatically increases crack growth and it is therefore plausible that effective dilution of these elements may explain a previously observed trend in which crack growth rates increase with decreasing grain size

Isothermal and bithermal thermomechanical fatigue behavior of a NiCoCrAlY-coated single crystal superalloy

Specimens of single crystal PWA 1480 with group of zone axes (100) orientation, bare, or with NiCoCrAlY coating PWA 276, were tested in low cycle fatigue (LCF) at 650, 870, and 1050 C, and in simplified bithermal thermomechanical fatigue (TMF) tests between these temperatures. These tests were examined as a bridge between isothermal LCF and general TMF. In the bithermal test, an inelastic strain is applied at one temperature, T sub max, and reversed at T sub min. The out-of-phase (OP) test type imposing tension at T sub min and compression at T sub max received most study, since it was more damaging than the in-phase type. Specifically investigated were the effects of: inelastic strain range, the coating, delta T, T sub max, T sub min, and the environment

Orientation and temperature dependence of some mechanical properties of the single-crystal nickel-base superalloy Rene N4. 3: Tension-compression anisotropy

Single crystal superalloy specimens with various crystallographic directions along their axes were tested in compression at room temperature, 650, 760, 870, and 980 deg C. These results are compared with the tensile behavior studied previously. The alloy, Rene N4, was developed for gas turbine engine blades and has the nominal composition 3.7 Al, 4.2 Ti, 4 Ta, 0.5 Nb, 6 W, 1.5 Mo 9 Cr. 7.5 Co, balance Ni, in weight percent. Slip trace analysis showed that primary cube slip occurred even at room temperature for the 111 specimens. With increasing test temperature more orientations exhibited primary cube slip, until at 870 deg C only the 100 and 011 specimens exhibited normal octahedral slip. The yield strength for octahedral slip was numerically analysed using a model proposed by Lall, Chin, and Pope to explain deviations from Schmid's Law in the yielding behavior of a single phase Gamma prime alloy, Ni3(Al, Nb). The Schmid's Law deviations in Rene N4 were found to be largely due to a tension-compression anisotropy. A second effect, which increases trength for orientations away from 001, was found to be small in Rene N4. Analysis of recently published data on the single crystal superalloy PWA 1480 yielded the same result

Effect of Microstructure on Time Dependent Fatigue Crack Growth Behavior In a P/M Turbine Disk Alloy

A study was conducted to determine the processes which govern hold time crack growth behavior in the LSHR disk P/M superalloy. Nineteen different heat treatments of this alloy were evaluated by systematically controlling the cooling rate from the supersolvus solutioning step and applying various single and double step aging treatments. The resulting hold time crack growth rates varied by more than two orders of magnitude. It was shown that the associated stress relaxation behavior for these heat treatments was closely correlated with the crack growth behavior. As stress relaxation increased, the hold time crack growth resistance was also increased. The size of the tertiary gamma' in the general microstructure was found to be the key microstructural variable controlling both the hold time crack growth behavior and stress relaxation. No relationship between the presence of grain boundary M23C6 carbides and hold time crack growth was identified which further brings into question the importance of the grain boundary phases in determining hold time crack growth behavior. The linear elastic fracture mechanics parameter, Kmax, is unable to account for visco-plastic redistribution of the crack tip stress field during hold times and thus is inadequate for correlating time dependent crack growth data. A novel methodology was developed which captures the intrinsic crack driving force and was able to collapse hold time crack growth data onto a single curve

A Monte Carlo-finite element model for strain energy controlled microstructural evolution: "rafting" in superalloys

A specialized microstructural model, MCFET, has been developed which simulates microstructural evolution in materials in which strain energy plays an important role in determining morphology. The elastic contribution to the energy of the system is estimated by way of a finite element procedure which is employed in a Monte Carlo procedure to determine the microstructural evolution. This model is currently capable of accounting for externally applied stresses, surface tension, misfit, elastic inhomogeneity, elastic anisotropies (cubic) and arbitrary temperatures. The MCFET analysis has been validated by comparison with analytical calculations of the equilibrium morphologies of isolated particles in an infinite matrix. Larger simulations yield microstructures which are in good agreement with experimental observations (including the influence of applied stress). Simulations on the coarsening of two-phase microstructures containing misfitting particles suggest that the presence of strong elastic interactions greatly decreases the rate of microstructural coarsening.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28083/1/0000529.pd

Factors Influencing Dwell Fatigue Cracking in Notches of Powder Metallurgy Superalloys

The influences of heat treatment and cyclic dwells on the notch fatigue resistance of powder metallurgy disk superalloys were investigated for low solvus high refractory (LSHR) and ME3 disk alloys. Disks were processed to produce material conditions with varied microstructures and associated mechanical properties. Notched specimens were first subjected to baseline dwell fatigue cycles having a dwell at maximum load, as well as tensile, stress relaxation, creep rupture, and dwell fatigue crack growth tests at 704 C. Several material heat treatments displayed a bimodal distribution of fatigue life with the lives varying by two orders-of-magnitude, while others had more consistent fatigue lives. This response was compared to other mechanical properties, in search of correlations. The wide scatter in baseline dwell fatigue life was observed only for material conditions resistant to stress relaxation. For selected materials and conditions, additional tests were then performed with the dwells shifted in part or in total to minimum tensile load. The tests performed with dwells at minimum load exhibited lower fatigue lives than max dwell tests, and also exhibited early crack initiation and a substantial increase in the number of initiation sites. These results could be explained in part by modeling evolution of peak stresses in the notch with continued dwell fatigue cycling. Fatigue-environment interactions were determined to limit life for the fatigue cycles with dwells

Fatigue Resistance of the Grain Size Transition Zone in a Dual Microstructure Superalloy Disk

Mechanical property requirements vary with location in nickel-based superalloy disks. To maximize the associated mechanical properties, heat treatment methods have been developed for producing tailored microstructures. In this study, a specialized heat treatment method was applied to produce varying grain microstructures from the bore to the rim portions of a powder metallurgy processed nickel-based superalloy disk. The bore of the contoured disk consisted of fine grains to maximize strength and fatigue resistance at lower temperatures. The rim microstructure of the disk consisted of coarse grains for maximum resistance to creep and dwell crack growth at high temperatures up to 704 C. However, the fatigue resistance of the grain size transition zone was unclear, and needed to be evaluated. This zone was located as a band in the disk web between the bore and rim. Specimens were extracted parallel and transverse to the transition zone, and multiple fatigue tests were performed at 427 and 704 C. Mean fatigue lives were lower at 427 C than for 704 C. Specimen failures often initiated at relatively large grains, which failed on crystallographic facets. Grain size distributions were characterized in the specimens, and related to the grains initiating failures as well as location within the transition zone. Fatigue life decreased with increasing maximum grain size. Correspondingly, mean fatigue resistance of the transition zone was slightly higher than that of the rim, but lower than that of the bore. The scatter in limited tests of replicates was comparable for all transition zone locations examined