Constitutive relationships for anisotropic high-temperature alloys

A constitutive theory is presented for representing the anisotropic viscoplastic behavior of high temperature alloys that posses directional properties resulting from controlled grain growth or solidification. The theory is an extension of a viscoplastic model that was applied in structural analyses involving isotropic metals. Anisotropy is introduced through the definition of a vector field that identifies a preferential (solidification) direction at each material point. Following the development of a full multiaxial theory, application is made to homogeneously stressed elements in pure shear and to a uniaxially stressed rectangular block in plane stress with the stress direction oriented at an arbitrary angle with the material direction. It is shown that an additional material parameter introduced to characterize the degree of anisotropy can be determined on the basis of simple creep tests

A continuous damage model based on stepwise-stress creep rupture tests

A creep damage accumulation model is presented that makes use of the Kachanov damage rate concept with a provision accounting for damage that results from a variable stress history. This is accomplished through the introduction of an additional term in the Kachanov rate equation that is linear in the stress rate. Specification of the material functions and parameters in the model requires two types of constituting a data base: (1) standard constant-stress creep rupture tests, and (2) a sequence of two-step creep rupture tests

A continuum deformation theory for metal-matrix composites at high temperature

A continuum theory is presented for representing the high temperature, time dependent, hereditary deformation behavior of metallic composites that can be idealized as pseudohomogeneous continua with locally definable directional characteristics. Homogenization of textured materials (molecular, granular, fibrous) and applicability of continuum mechanics in structural applications depends on characteristic body dimensions, the severity of gradients (stress, temperature, etc.) in the structure and the relative size of the internal structure (cell size) of the material. The point of view taken here is that the composite is a material in its own right, with its own properties that can be measured and specified for the composite as a whole

Unified constitutive model development for metal matrix composites at high temperature

Structural alloys used in high temperature applications exhibit complex thermomechanical behavior that is time dependent and hereditary. Recent attention is being focused on metal matrix composite materials for high temperature applications where they exhibit all the complexities of conventional alloys and their strong anisotropy adds further complexities. Here, a proven constitutive model for isotropic materials in which the inelastic strain rate and internal state are expressible as gradients of a dissipation potential is taken to depend on invariants that reflect local transverse isotropy. Applications illustrate the capability of the theory of representing the time dependent, hereditary, anisotropic behavior typical of these materials at high temperature

Constitutive Equations for Use in Design Analyses of Long-life Elevated Temperature Components

Design analysis needs and procedures relative to elevated temperature components in liquid metal fast breeder reactor (LMFBR) system were examined. The effects of the thermal transients on the pressure boundary components are enhanced by the excellent heat transfer properties of the liquid sodium coolant. Design criteria for high temperature nuclear reactor components recognize the potential occurrence of inelastic structural response. Specifically, criteria and limits were developed which reflect a recognition of this potential and employ design by analysis concepts that requires that inelastic (elastic-plastic and creep) analyses be performed. Constitutive equations to represent multiaxial time-dependent responses of LMFBR alloys are established. The development of equations applicable under cyclic loading conditions are outlined

High-temperature constitutive modeling

Thermomechanical service conditions for high-temperature levels, thermal transients, and mechanical loads severe enough to cause measurable inelastic deformation are studied. Structural analysis in support of the design of high-temperature components depends strongly on accurate mathematical representations of the nonlinear, hereditary, inelastic behavior of structural alloys at high temperature, particularly in the relatively small strain range. Progress is discussed in the following areas: multiaxial experimentation to provide a basis for high-temperature multiaxial constitutive relationships; nonisothermal testing and theoretical development toward a complete thermomechanically path dependent formulation of viscoplasticity; and development of viscoplastic constitutive model accounting for initial anisotropy

A theory of viscoplasticity accounting for internal damage

A constitutive theory for use in structural and durability analyses of high temperature isotropic alloys is presented. Constitutive equations based upon a potential function are determined from conditions of stability and physical considerations. The theory is self-consistent; terms are not added in an ad hoc manner. It extends a proven viscoplastic model by introducing the Kachanov-Rabotnov concept of net stress. Material degradation and inelastic deformation are unified; they evolve simultaneously and interactively. Both isotropic hardening and material degradation evolve with dissipated work which is the sum of inelastic work and internal work. Internal work is a continuum measure of the stored free energy resulting from inelastic deformation

Some advances in experimentation supporting development of viscoplastic constitutive models

The development of a biaxial extensometer capable of measuring axial, torsion, and diametral strains to near-microstrain resolution at elevated temperatures is discussed. An instrument with this capability was needed to provide experimental support to the development of viscoplastic constitutive models. The advantages gained when torsional loading is used to investigate inelastic material response at elevated temperatures are highlighted. The development of the biaxial extensometer was conducted in two stages. The first involved a series of bench calibration experiments performed at room temperature. The second stage involved a series of in-place calibration experiments performed at room temperature. A review of the calibration data indicated that all performance requirements regarding resolution, range, stability, and crosstalk had been met by the subject instrument over the temperature range of interest, 21 C to 651 C. The scope of the in-placed calibration experiments was expanded to investigate the feasibility of generating stress relaxation data under torsional loading

Effects of state recovery on creep buckling under variable loading

Structural alloys embody internal mechanisms that allow recovery of state with varying stress and elevated temperature, i.e., they can return to a softer state following periods of hardening. Such material behavior is known to strongly influence structural response under some important thermomechanical loadings, for example, that involving thermal ratchetting. The influence of dynamic and thermal recovery on the creep buckling of a column under variable loading is investigated. The column is taken as the idealized (Shanley) sandwich column. The constitutive model, unlike the commonly employed Norton creep model, incorporates a representation of both dynamic and thermal (state) recovery. The material parameters of the constitutive model are chosen to characterize Narloy Z, a representative copper alloy used in thrust nozzle liners of reusable rocket engines. Variable loading histories include rapid cyclic unloading/reloading sequences and intermittent reductions of load for extended periods of time; these are superimposed on a constant load. The calculated results show that state recovery significantly affects creep buckling under variable loading. Structural alloys embody internal mechanisms that allow recovery of state with varying stress and time

Viscoplastic constitutive relationships with dependence on thermomechanical history

Experimental evidence of thermomechanical history dependence in the cyclic hardening behavior of some common high-temperature structural alloys is presented with special emphasis on dynamic metallurgical changes. The inadequacy of formulating nonisothermal constitutive equations solely on the basis of isothermal testing is discussed. A representation of thermoviscoplasticity is proposed that qualitatively accounts for the observed hereditary behavior. This is achieved by formulating the scalar evolutionary equation in an established viscoplasticity theory to reflect thermomechanical path dependence. To assess the importance of accounting for thermomechanical history dependence in practical structural analyses, two qualitative models are specified: (1) formulated as if based entirely on isothermal information; (2) to reflect thermomechanical path dependence using the proposed thermoviscoplastic representation. Predictions of the two models are compared and the impact the calculated differences in deformation behavior may have on subsequent lifetime predictions is discussed