Constitutive model development for isotropic materials

The objective is to develop a unified constitutive model for finite-element structural analysis of turbine engine hot section components. This effort constitutes a different approach for nonlinear finite-element computer codes which were heretofore based on classical inelastic methods. A unified constitutive theory will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. Model development will be directed toward isotropic, cast nickel-base alloys used for aircooled turbine blades and vanes. The contractor will select a base material for model development and an alternate material for verification purposes from a list of three alloys specified by NASA. The candidate alloys represent a cross-section of turbine blade and vane materials of interest to both large and small size engine manufacturers. Material stock for the base and alternate materials will be supplied to the Contractor by the government

A multiscale constitutive model for intergranular stress corrosion cracking in type 304 austenitic stainless steel

Intergranular stress corrosion cracking (IGSCC) is a fracture mechanism in sensitised austenitic stainless steels exposed to critical environments where the intergranular cracks extends along the network of connected susceptible grain boundaries. A constitutive model is presented to estimate the maximum intergranular crack growth by taking into consideration the materials mechanical properties and microstructure characters distribution. This constitutive model is constructed based on the assumption that each grain is a two phase material comprising of grain interior and grain boundary zone. The inherent micro-mechanisms active in the grain interior during IGSCC is based on crystal plasticity theory, while the grain boundary zone has been modelled by proposing a phenomenological constitutive model motivated from cohesive zone modelling approach. Overall, response of the representative volume is calculated by volume averaging of individual grain behaviour. Model is assessed by performing rigorous parametric studies, followed by validation and verification of the proposed constitutive model using representative volume element based FE simulations reported in the literature. In the last section, model application is demonstrated using intergranular stress corrosion cracking experiments which shows a good agreement

A multiscale constitutive model for intergranular stress corrosion cracking in type 304 austenitic stainless steel

Intergranular stress corrosion cracking (IGSCC) is a fracture mechanism in sensitised austenitic stainless steels exposed to critical environments where the intergranular cracks extends along the network of connected susceptible grain boundaries. A constitutive model is presented to estimate the maximum intergranular crack growth by taking into consideration the materials mechanical properties and microstructure characters distribution. This constitutive model is constructed based on the assumption that each grain is a two phase material comprising of grain interior and grain boundary zone. The inherent micro-mechanisms active in the grain interior during IGSCC is based on crystal plasticity theory, while the grain boundary zone has been modelled by proposing a phenomenological constitutive model motivated from cohesive zone modelling approach. Overall, response of the representative volume is calculated by volume averaging of individual grain behaviour. Model is assessed by performing rigorous parametric studies, followed by validation and verification of the proposed constitutive model using representative volume element based FE simulations reported in the literature. In the last section, model application is demonstrated using intergranular stress corrosion cracking experiments which shows a good agreement

Constitutive model for plasticity in an amorphous polycarbonate

A constitutive model for describing the mechanical response of an amorphous glassy polycarbonate is proposed. The model is based on an isotropic elastic phase surrounded by an SO(3) continuum of plastic phases onto which the elastic phase can collapse under strain. An approximate relaxed energy is developed for this model on the basis of physical considerations and extensive numerical testing, and it is shown that it corresponds to an ideal elastic-plastic behavior. Kinetic effects are introduced as rate-independent viscoplasticity, and a comparison with experimental data is presented, showing that the proposed model is able to capture the main features of the plastic behavior of amophous glassy polycarbonate

A constitutive model for an overlay coating

Coatings are frequently applied to gas turbine blades and vanes to provide protection against oxidation and corrosion. The results of an experimental and analytical study to develop a constitutive model for an overlay coating is presented. Specimens were machined from a hot isostatically pressed billet of PWA 286. The tests consisted of isothermal stress relaxation cycles with monotonically increasing maximum strain and were conducted at various temperatures. The results were used to calculate the constants for various constitutive models, including the classical, the Walker isotropic, a simplified Walker, and Stowell models. A computerized regression analysis was used to calculate model constants from the data. The best fit was obtained for the Walker model, with the simplified Walker and classical models close behind

A micromechanics-inspired constitutive model for shape-memory alloys

This paper presents a three-dimensional constitutive model for shape-memory alloys that generalizes the one-dimensional model presented earlier (Sadjadpour and Bhattacharya 2007 Smart Mater. Struct. 16 S51–62). These models build on recent micromechanical studies of the underlying microstructure of shape-memory alloys, and a key idea is that of an effective transformation strain of the martensitic microstructure. This paper explains the thermodynamic setting of the model, demonstrates it through examples involving proportional and non-proportional loading, and shows that the model can be fitted to incorporate the effect of texture in polycrystalline shape-memory alloys

Constitutive Model for Material Comminuting at High Shear Rate

The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high strain rates can dissipate a large portion of the kinetic energy of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate is enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate shear strain of forming particles. For simplicity, the shape of these particles in the plane of maximum shear rate is considered to be regular hexagons. The rate of release of free energy density consisting of the sum of this energy and the fracture energy of the interface between the forming particle is minimized. The particle sizes are assumed to be distributed according to Schuhmann's power law. It is concluded that the minimum particle size is inversely proportional to the (2/3)-power of the shear strain rate, that the kinetic energy release is to proportional to the (2/3)-power, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of the shear strain rate.Comment: 13 pages, 2 figure

Effect of consolidation on the behaviour of excavations in fine-grained soils

This study deals with the detrimental effects of consolidation on the behaviour of excavations carried out in fine-grained soils. With the aim of reproducing the main aspects of the mechanical behaviour of medium-soft clays, an advanced constitutive model was adopted, which is based on bounding surface plasticity and can take into account the damage to the soil microstructure induced by plastic strains. In a first stage of the work, this constitutive model was implemented into a finite element program, and its response was studied through a series of single-element tests, evidencing the effect of the different soil parameters and initial conditions. In the present paper, the constitutive model was used to simulate the behaviour of an idealised excavation, studying the effect of the progressive dissipation of the excess pore water pressures generated during the excavation stages. It was found that, under certain conditions, the initial degree of structure can be progressively lost during consolidation. This detrimental effect produces significant deformation increments and in some cases can drive the system to collapse

A constitutive model for unsaturated cemented soils under cyclic loading

On the basis of plastic bounding surface model, the damage theory for structured soils and unsaturated soil mechanics, an elastoplastic model for unsaturated loessic soils under cyclic loading has been elaborated. Firstly, the description of bond degradation in a damage framework is given, linking the damage of soil's structure to the accumulated strain. The Barcelona Basic Model (BBM) was considered for the suction effects. The elastoplastic model is then integrated into a bounding surface plasticity framework in order to model strain accumulation along cyclic loading, even under small stress levels. The validation of the proposed model is conducted by comparing its predictions with the experimental results from multi-level cyclic triaxial tests performed on a natural loess sampled beside the Northern French railway for high speed train and about 140 km far from Paris. The comparisons show the capabilities of the model to describe the behaviour of unsaturated cemented soils under cyclic loading