Cyclic-and time-dependent behavior can significantly affect the life of aerospace propulsion components. Consequently, one needs an accurate constitutive model that can represent both reversible and irreversible behavior under such loading conditions. To accomplish this, researchers at the NASA Glenn Research Center adopted a complete-potential-based framework, wherein strain, stress, and the thermodynamic functions (stored energy and dissipation) are appropriately partitioned to form a general viscoelastoplastic, multimechanism, deformation model (see ref. 1). This framework, named Generalized VIscoelastoplasticity with Potential Structure (GVIPS), attempts to capture the underlying physical processes associated with microscopic defects (e.g., dislocations, grain boundaries, and voids in metals) and their complicated interactions, which span an entire spectrum of time and length scales, through the introduction of a multiplicity of mechanisms in the mathematical description. The use of multimechanisms in the GVIPS-class formulation enables the specialization of this general model into simpler (more restricted in scope) formulations--for example, purely elastic, linear viscoelastic, classical rate-independent elastoplastic--as well as more elaborate forms of hereditary descriptions--involving such phenomena as viscous effects, nonlinear hardening, dynamic recovery, thermal/static recovery, relaxation, ratcheting, or shakedown phenomena under load cycles.
Previously, a six-mechanism viscoelastic and a three-mechanism viscoplastic
GVIPS model was characterized with three constant total-strain-rate
(
=
10-4, 10-5, and 10-6 1/sec) tensile
tests, three constant-load creep tests, one three-step creep test,
three relaxation histories, and a single fully reversed hysteresis
loop. The predictive ability was then validated with multiple-step
relaxation tests and a creep-plasticity interaction test (see ref.
2). Recently, the predictive capabilities of this original model
and its higher fidelity counterparts (i.e., ones with additional
viscoplastic mechanisms) were examined in the context of 12 specifically
designed cyclic tests at 650 °C, with and without mean stresses
(wherein significant ratcheting can take place). In addition, three
complex cyclic-relaxation history tests, also performed at 650 °C,
were reserved for validation purposes. The details of these experiments
are discussed in reference 3. The motivation behind the selection
of this specific test matrix was to gain insight into the appropriate
functional forms to be taken for flow and hardening as well as to
identify the appropriate state variables and material parameters
to best describe the path and history dependence of TIMETAL 21S.
The graphs show representative predictive results obtained for multiple cycles of one of the three complex cyclic-relaxation histories reserved for validation purposes, given a six-mechanism reversible and a seven-mechanism irreversible viscoelastoplastic model. The corresponding material parameters were obtained using tensile, creep, relaxation, and fully reversed cyclic data and mean stress cyclic ratcheting characterization tests. Clearly, the model can accurately predict these complex cyclic-relaxation histories. Note that the top graphs illustrate the stress-strain response corresponding to three block loading histories consisting of two interrupted cycles followed by 50 uninterrupted cycles each. The bottom graphs show the subsequent material response for three similar block loading histories; however, in this case the interrupted cycles are reversed from those in on the top. A specially designed and developed python script for ABAQUS (ABAQUS, Inc., Providence, RI) was required to obtain the more complex load histories in which the control variable and target variable differ in character (e.g., strain-controlled, stress-limited; or stress-controlled, strain-limited).
Strain-controlled, strain-limited, complex cyclic-relaxation block histories conducted at 650 °C (i.e., path 1). IC 1 (as are IC 53 and IC 105) is an interrupted cycle (IC) containing eight 2-hr relaxation histories. This is then followed immediately by a second cycle (IC 2) that has four 2-hr relaxation histories (similar cycles are IC 54 and IC 106). Note that in between each set (e.g., IC 1 + IC 2 and IC 53 + IC 54) 50 uninterrupted strain-controlled, strain-limited (°0.005 in./in.) cycles are performed.
Strain-controlled, strain-limited, reversed complex cyclic-relaxation block histories conducted at 650 °C (i.e., path 2) that had prior histories related to path 1 in the preceding graphs. IC 157 (as are IC 209 and IC 261) is an interrupted cycle (IC) containing eight 2-hr relaxation histories. This is then followed immediately by a second cycle (IC 158) that has four 2-hr relaxation histories (similar cycles are IC 210 and IC 262). Note that in between each set (e.g., IC 157 + IC 158 and IC 209 + IC 210) 50 uninterrupted strain-controlled, strain-limited (± 0.005 in./in.) cycles are performed.
Last updated: October 17, 2006
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