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At least 145 records · Page 8

Constitutive modelling of single crystal and directionally solidified superalloys

The trend towards improved engine efficiency and durability places increasing demands on materials that operate in the hot section of the gas turbine engine. These demands are being met by new coatings and materials such as single crystal and directionally solidified nickel-base superalloys which have greater creep/fatigue resistance at elevated temperatures and reduced susceptibility to grain boundary creep, corrosion and oxidation than conventionally cast alloys. Work carried out as part of a research program aimed at the development of constitutive equations to describe the elevated temperature stress-strain-time behavior of single crystal and directionally solidified turbine blade superalloys is discussed. The program involves both development of suitable constitutive models and their verification through elevated temperature tension-torsion testing of single crystals of PWA 1480.

Jordan, E. H.↗

Constitutive modeling of cyclic plasticity and creep, using an internal time concept

Using the concept of an internal time as related to plastic strains, a differential stress-strain relation for elastoplasticity is rederived, such that (1) the concept of a yield-surface is retained; (2) the definitions of elastic and plastic processes are analogous to those in classical plasticity theory; and (3) its computational implementation, via a 'tangent-stiffness' finite element method and a 'generalized-midpoint-radial-return' stress-integration algorithm, is simple and efficient. Also, using the concept of an internal time, as related to both the inelastic strains as well as the Newtonian time, a constitutive model for creep-plasticity interaction, is discussed. The problem of modeling experimental data for plasticity and creep, by the present analytical relations, as accurately as desired, is discussed. Numerical examples which illustrate the validity of the present relations are presented for the cases of cyclic plasticity and creep.

Watanabe, O.↗

Constitutive Modeling and Testing of Polymer Matrix Composites Incorporating Physical Aging at Elevated Temperatures

Advanced polymer matrix composites (PMC's) are desirable for structural materials in diverse applications such as aircraft, civil infrastructure and biomedical implants because of their improved strength-to-weight and stiffness-to-weight ratios. For example, the next generation military and commercial aircraft requires applications for high strength, low weight structural components subjected to elevated temperatures. A possible disadvantage of polymer-based composites is that the physical and mechanical properties of the matrix often change significantly over time due to the exposure of elevated temperatures and environmental factors. For design, long term exposure (i.e. aging) of PMC's must be accounted for through constitutive models in order to accurately assess the effects of aging on performance, crack initiation and remaining life. One particular aspect of this aging process, physical aging, is considered in this research.

Veazie, David R.↗

A Constitutive Model for the Inelastic Multiaxial Cyclic Response of a Nickel Base Superalloy Rene 80

The objective was to develop unified constitutive equations which can model a variety of nonlinear material phenomena observed in Rene 80 at elevated temperatures. A constitutive model was developed based on back stress and drag stress. The tensorial back stress was used to model directional effects; whereas, the scalar drag stress was used to model isotropic effects and cyclic hardening or softening. A flow equation and evolution equations for the state variables were developed in multiaxial form. Procedures were developed to generate the material parameters. The model predicted very well the monotonic tensile, cyclic, creep, and stress relaxation behavior of Rene 80 at 982 C. The model was then extended to 871, 760, and 538 C. It was shown that strain rate dependent behavior at high temperatures and strain rate independent behavior at the lower temperatures could be predicted very well. A large number of monotonic tensile, creep, stress relation, and cyclic experiments were predicted. The multiaxial capabilities of the model were verified extensively for combined tension/torsion experiments. The prediction of the model agreed very well for proportional, nonproportional, and pure shear cyclic loading conditions at 982 and 871 C.

Ramaswamy, V. G.↗

Constitutive modeling for single crystal superalloys

The inelastic response of single crystal gamma/gamma prime superalloys is quite different from the behavior of polycrystalline nickel base superalloys. Upto a critical temperature the yield stress of single crystal alloys is a function of the material orientation relative to the direction of the applied stress and the material exhibits significant tension/compression asymmetry. This behavior is primarily due to slip on the octahedral slip system. Above the critical temperature there is a sharp drop in the yield stress, cube slip becomes more predominant and the tension/compression asymmetry is reduced. Similar orientation and tension/compression asymmetry is observed in creep and secondary creep above the critical temperature is inferred to occur by octahedral slip. There are two exceptions to this behavior. First, loading near the (111) orientation exhibits cube slip at all temperatures, and; second, loading near the (001) orientation produces only octahedral slip at all temperatures. The constitutive model is based on separating the total global strain into elastic and inelastic components. This model is developed and briefly discussed.

Stouffer, D. C.↗

Accelerated Creep Test Qualification of Creep-Resistance Using the Wilshire–Cano–Stewart Constitutive Model and Stepped Isostress Method

In this paper, a qualification of accelerated creep-resistance of Inconel 718 is assessed using the novel Wilshire–Cano–Stewart (WCS) model and the stepped isostress method (SSM) and predictions are made to conventional creep data. Conventional creep testing is a long-term continuous process; in fact, the ASME B&PV III requires that 10,000+ h of experiments must be conducted to each heat for materials employed in boilers and/or pressure vessel components. This process is costly and not feasible for rapid development of new materials. As an alternative, accelerated creep testing techniques have been developed to reduce the time needed to characterize the creep resistance of materials. Most techniques are based upon the time-temperature-stress superposition principle that predicts minimum-creep-strain-rate (MCSR) and stress-rupture behaviors but lack the ability to predict creep deformation and consider deformation mechanisms that occur for experiments of longer duration. The SSM has been developed, which enables the prediction of creep deformation response as well as reduce the time needed for qualification of materials. The SSM approach has been successful for polymer, polymeric composites, and recently has been introduced for metals. In this study, the WCS constitutive model, calibrated to SSM test data, qualifies the creep resistance of Inconel 718 at 750 °C and predictions are compared to conventional creep testing data. The WCS model has proven to make long-term predictions for stress-rupture, MCSR, creep deformation, and damage in metallic materials. The SSM varies stress levels after time interval adding damage to the material, which can be tracked by the WCS model. The SSM data is calibrated into the model and the WCS model generates realistic predictions of stress-rupture, MSCR, damage, and creep deformation. The calibrated material constants are used to generate predictions of stress-rupture and are postaudit validated using the National Institute of Material Science database. Similarly, the MCSR predictions are compared from previous studies. Finally, the creep deformation predictions are compared with real data and is determined that the results are well in between the expected boundaries. Material characterization and mechanical properties can be determined at a faster rate and with a more cost-effective method. This is beneficial for multiple applications such as in additive manufacturing, composites, spacecraft, and industrial gas turbines.

42 ENGINEERING↗

ACCELERATED CREEP TEST (ACT) QUALIFICATION OF CREEP RESISTANCE USING THE WCS CONSTITUTIVE MODEL AND STEPPED ISOSTRESS METHOD (SSM)

In this study, a qualification of accelerated creep-resistance of Inconel 718 is assessed using the novel Wilshire-Cano-Stewart (WCS) model and the stepped isostress method (SSM) and predictions are made to conventional creep data. Conventional creep testing (CCT) is a long-term continuous process, in fact, the ASME B&PV III requires that 10,000+ hours of experiments must be conducted to each heat for materials employed in boilers and/or pressure vessel components. This process is costly and not feasible for rapid development of new materials. As an alternative, accelerated creep testing techniques have been developed to reduce the time needed to characterize the creep resistance of materials. Most techniques are based upon the time-temperature-stress superposition principle (TTSSP) that predicts minimum-creep-strain-rate (MCSR) and stress-rupture behaviors but lack the ability to predict creep deformation and consider deformation mechanisms that occur for experiments of longer duration. The stepped isostress method (SSM) has been developed which enables the prediction of creep deformation response as well as reduce the time needed for qualification of materials. The SSM approach has been successful for polymer, polymeric composites, and recently has been introduced for metals. In this study, the WCS constitutive model, calibrated to SSM test data, qualifies the creep resistance of Inconel 718 at 750°C and predictions are compared to CCT data. The WCS model has proven to make long-term predictions for stress-rupture, minimum-creep-strain-rate (MCSR), creep deformation, and damage in metallic materials. The SSM varies stress levels after time interval adding damage to the material, which can be tracked by the WCS model. The SSM data is calibrated into the model and the WCS model generates realistic predictions of stress-rupture, MSCR, damage, and creep deformation. The calibrated material constants are used to generate predictions of stress-rupture and are post-audit validated using the National Institute of Material Science (NIMS) database. Similarly, the MCSR predictions are compared from previous studies. Finally the creep deformation predictions are compared with real data and is determined that the results are well in between the expected boundaries. Material characterization and mechanical properties can be determined at a faster rate and with a more cost-effective method. This is beneficial for multiple applications such as in additive manufacturing, composites, spacecraft, and Industrial Gas Turbines (IGT).

36 MATERIALS SCIENCE↗

NEML2: An efficient and modular multiphysics constitutive modeling library for hybrid computing environments

This paper presents NEML2, an open-source, high-performance library developed for constitutive material modeling, designed to support the flexible and modular development of models for complex material behavior. Building on the foundational structure of its predecessor, NEML, the NEML2 library introduces significant improvements, including enhanced vectorization, automatic differentiation, and seamless integration with PyTorch, facilitating the application of machine learning techniques in material simulations. NEML2 provides a C++ backend with Python bindings, enabling users to create custom material models that can be executed efficiently on both CPU and GPU platforms. The library also supports coupling with Multiphysics simulation frameworks like MOOSE, making it suitable for realistic simulations involving coupled physical processes. Rigorous quality assurance through unit and regression testing ensures the reliability of results, while the extensible, user-friendly design encourages collaboration and reproducibility across the scientific community. This paper provides an overview of NEML2’s architecture, core features, and applications, highlighting its impact on accelerating material qualification and advancing computational methods in materials science.

GPU↗

A Multiscale Modeling Approach to Cryocompressed Hydrogen Storage Pressure Vessels – Part II: Constitutive Modeling and Finite Element Analysis

Subjected to thermomechanical cycling, composite cryogenic hydrogen (H2) storage pressure vessels experience high stresses in the carbon fiber (CF)/epoxy overwrap which can lead to vessel failure due to a combination of degradation mechanisms such as matrix cracking, fiber/matrix debonding, delamination, and fiber rupture. The present paper is the second part of a set of two articles on this subject that addresses analysis and design of these pressure vessels. Predictive finite element (FE) modeling capabilities have been used to support a material acceptance process that aims at providing guidance to evaluate specialty resins, vessel liner options, and CF composites through thermomechanical testing. We have applied a multiscale modeling approach recently developed (B.N. Nguyen et al., International Journal of Hydrogen Energy, 2019, https://doi.org/10.1016/j.ijhydene.2019.09.200) to perform three-dimensional (3D) FE analysis and design of a cryo-compressed H2 storage pressure vessel for its operation in a large temperature range from room to cryogenic temperatures. The developed approach termed the micro-meso-macro approach determines the laminar stresses in different layers of the vessel in addition to constituent (i.e., fiber and matrix) stresses that are important to the design of the composite overwrap for its layup and material combination to reduce the risk of vessel failure.

Nguyen, Ba Nghiep↗

Constitutive modeling of inelastic anisotropic material response

A constitutive equation was developed to predict the inelastic thermomechanical response of single crystal turbine blades. These equations are essential for developing accurate finite element models of hot section components and contribute significantly to the understanding and prediction of crack initiation and propagation. The method used was limited to unified state variable constitutive equations. Two approaches to developing an anisotropic constitutive equation were reviewed. One approach was to apply the Stouffer-Bodner representation for deformation induced anisotropy to materials with an initial anisotropy such as single crystals. The second approach was to determine the global inelastic strain rate from the contribution of the slip in each of the possible crystallographic slip systems. A three dimensional finite element is being developed with a variable constitutive equation link that can be used for constitutive equation development and to predict the response of an experiment using the actual specimen geometry and loading conditions.

Stouffer, D. C.↗

An internal variable constitutive model for the large deformation of metals at high temperatures

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.

Brown, Stuart↗

Life prediction and constitutive models for engine hot section anisotropic materials program

This report presents the results from a 35 month period of a program designed to develop generic constitutive and life prediction approaches and models for nickel-based single crystal gas turbine airfoils. The program is composed of a base program and an optional program. The base program addresses the high temperature coated single crystal regime above the airfoil root platform. The optional program investigates the low temperature uncoated single crystal regime below the airfoil root platform including the notched conditions of the airfoil attachment. Both base and option programs involve experimental and analytical efforts. Results from uniaxial constitutive and fatigue life experiments of coated and uncoated PWA 1480 single crystal material form the basis for the analytical modeling effort. Four single crystal primary orientations were used in the experiments: (001), (011), (111), and (213). Specific secondary orientations were also selected for the notched experiments in the optional program. Constitutive models for an overlay coating and PWA 1480 single crystal material were developed based on isothermal hysteresis loop data and verified using thermomechanical (TMF) hysteresis loop data. A fatigue life approach and life models were selected for TMF crack initiation of coated PWA 1480. An initial life model used to correlate smooth and notched fatigue data obtained in the option program shows promise. Computer software incorporating the overlay coating and PWA 1480 constitutive models was developed.

Nissley, D. M.↗

Constitutive modelling of lubricants in concentrated contacts at high slide to roll ratios

A constitutive lubricant friction model for rolling/sliding concentrated contacts such as gears and cams was developed, based upon the Johnson and Tevaarwerk fluid rheology model developed earlier. The friction model reported herein differs from the earlier rheological models in that very large slide to roll ratios can now be accommodated by modifying the thermal response of the model. Also the elastic response of the fluid has been omitted from the model, thereby making it much simpler for use in the high slide to roll contacts. The effects of this simplification are very minimal on the outcome of the predicted friction losses (less than 1%). In essence then the lubricant friction model developed for the high slide to roll ratios treats the fluid in the concentrated contact as consisting of a nonlinear viscous element that is pressure, temperature, and strain rate dependent in its shear response. The fluid rheological constants required for the prediction of the friction losses at different contact conditions are obtained by traction measurements on several of the currently used gear lubricants. An example calculation, using this model and the fluid parameters obtained from the experiments, shows that it correctly predicts trends and magnitude of gear mesh losses measured elsewhere for the same fluids tested here.

Tevaarwerk, J. L.↗

Life prediction and constitutive models for engine hot section anisotropic materials program

This report presents a summary of results from a 7 year program designed to develop generic constitutive and life prediction approaches and models for nickel-based single crystal gas turbine airfoils. The program was composed of a base program and an optional program. The base program addressed the high temperature coated single crystal regime above the airfoil root platform. The optional program investigated the low temperature uncoated single crystal regime below the airfoil root platform including the notched conditions of the airfoil attachment. Both base and option programs involved experimental and analytical efforts. Results from uniaxial constitutive and fatigue life experiments of coated and uncoated PWA 1480 single crystal material formed the basis for the analytical modeling effort. Four single crystal primary orientations were used in the experiments: group of zone axes (001), group of zone axes (011), group of zone axes (111), and group of zone axes (213). Specific secondary orientations were also selected for the notched experiments in the optional program. Constitutive models for an overlay coating and PWA 1480 single crystal materials were developed based on isothermal hysteresis loop data and verified using thermomechanical (TMF) hysteresis loop data. A fatigue life approach and life models were developed for TMF crack initiation of coated PWA 1480. A life model was developed for smooth and notched fatigue in the option program. Finally, computer software incorporating the overlay coating and PWA 1480 constitutive and life models was developed.

Nissley, D. M.↗

Requirements of constitutive models for two nickel-base superalloys

The constitutive behavior of two nickel-base superalloys, Rene '80 and Inconel 718, utilized in gas turbine blade and disk components, respectively, is presented. In turbine blade applications, the high homologous temperatures result in strain-rate effects dominating behavior. In turbine disks, the temperatures are cooler so that mean stress effects become important. The impact of these two variables on the overall crack initiation lifetime and analysis methodology is discussed.

Laflen, J. H.↗