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NASA NTRS1987

Structural optimization of an alternate design for the space shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the shuttle solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in. diameter and 135 studs of 1 3/16 in. diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonliner displacement analysis. The minimum weight design has 135 studs of 1 3/16 in. diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, J.-F. M.↗

NASA NTRS1986

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of elastoplastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, the Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗

NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗

NASA NTRS1988

A fiber-resin micromechanics analysis of the delamination front in a DCB specimen

A 3-D finite element model was developed to analyze the fiber-resin behavior near the delamination front in a graphite-epoxy double cantilever beam (DCB) specimen. The specimen interior was analyzed using a typical one-fiber slice, represented by a local 3-D fiber-resin model. The resin stresses were computed for the resin-rich layer at the ply interface as well as for the regions between the fibers close to the delamination front. However, the computed strain energy release rate G sub I along the delamination front varied by less than two percent, and was within about four percent of the plane-strain value. The von Mises yield criterion was used to estimate the extent of yielding near the delamination front. The yielding extended ahead of the delamination and also developed between the fibers. Although the fibers had only a negligible effect on G sub I, they caused yielding within the ply and therefore could influence delamination fracture toughness. The normal and shear stresses at the fiber-resin interface were computed near the delamination front. These results suggest that multi-axial stress criteria may be required to analyze fiber-resin interfaces.

Crews, J. H.↗

NASA NTRS1985

An experimental study of biaxial yield in modified 9Cr-1Mo steel at room temperature

Described are two biaxial experiments which investigated yield, hardening, and flow behavior in modified 9Cr-1Mo steel at room temperature. The aim of these experiments was to determine whether the procedures recommended in NE Standard F9-5T for inelastic design analysis are applicable for this material in normalized and tempered condition. The first experiment investigated small offset yield behavior subsequent to radial preloads (sq rt of 3 sub sigma 12 = sub sigma 11) in tension-torsion stress space. The second experiment investigated yield behavior subsequent to nonradial preloads and also the time-dependent flow occurring during 0.5 hour periods at constant stress. The results of these experiments were qualitatively similar to those obtained earlier for types 304 and 316 stainless steel. Specifically, the von Mises yield criterion was found to provide a reasonable approximation of initial yield behavior. Although the subsequent yield surfaces suffered considerable distortion from their near-circular form after both radial and nonradial preloads, the hardening behavior was to the first order kinematic in nature. The strain-time data obtained during the 0.5 hr hold periods showed characteristics typical of creep curves. As in the case of earlier experiments, the high initial flow rates diminished more rapidly than would be estimated from elevated temperature data.

Ellis, J. R.↗

NASA NTRS1987

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Shay, R. M., Jr.↗

NASA NTRS1989

A numerical model for the thermo-elasto-plastic behaviour of a material

This paper presents a numerical model for the thermo-elasto-plastic behavior of an isotropic material. The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening. This unique model can be used both for isothermal and non-isothermal cases. The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided. The finite element implementation of this model is also outlined.

Ray, Sujit K.↗

NASA NTRS1990

Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process

The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures.

Wheeler, J. T.↗

NASA NTRS1991

Computed stress fields in GaAs during vertical Bridgman growth

The thermoelastic stress field of GaAs crystals grown by the vertical Bridgman method has been approximated using a linear elastic, axisymmetric stress model. The model included the effects due to the thermal field and the gravitational field, as well as the interaction with the ampoule, but did not fully account for the elastic anisotropy of the crystal. Realistic thermal fields for different furnace temperatures and insulation zone thicknesses were computed with a similar model. The difference between the Von Mises stress and the critical resolved shear stress (CRSS) was used as a measure of the number of dislocations present. Different sets of growth parameters were examined to determine which produced the lowest amount of stress in the crystal. Results show that the crystal-ampoule interaction is the most important parameter in dislocation generation. In addition, for the same sticking boundary conditions, concave interfaces have lower stress than convex interfaces.

Rosch, William↗

NASA NTRS1991

Micromechanical analysis of filamentary metal matrix composites under longitudinal loading

A two-material composite cylinder model (CCM) was considered for the study of the mechanical behavior at different temperatures of a fiber-reinforced silicon carbide/aluminum (SiC/Al) composite. An elastoplastic analysis of the model was performed in which the fiber was assumed to be linear elastic and the matrix elastoplastic with work-hardening. The analysis was based on the deformation theory of plasticity in conjunction with the von-Mises yield criterion. Experimental stress-strain curves of an SiC/Al composite were obtained at 24 and 288 C (75 and 550 F). The complete three-dimensional stress distribution in the composite using the CCM was determined. It was found that, in addition to longitudinal stresses, transverse stresses in both the fiber and the matrix were developed as a result of the different Poisson's ratios of the two materials. The transverse stresses, although much smaller than the longitudinal stresses, contributed to the plastic deformation of the matrix. The experimental stress-strain curves were favorably compared with the theoretical predictions.

Gdoutos, Emmanuel E.↗

NASA NTRS1991

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of an elasto-plastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗

NASA NTRS1991

Analysis and design of transonic airfoils using streamwise coordinates

A new approach is developed for analysis and design of transonic airfoils. A set of full potential equivalent equations in von Mises coordinates is formulated from the Euler equations under the irrotationality and isentropic assumptions. This set is composed of a main equation for the main variable, y, and a secondary equations for the secondary variable, R. The main equation is solved by type dependent differencing combined with a shock point operator. The secondary equation is solved by marching from a non-characteristic boundary. Sample computations on NACA 0012 and biconvex airfoils show that, for the analysis problem, the present approach achieves good agreement with experimental C sub p distributions. For the design problem, the approach leads to a simple numerical algorithm in which the airfoil contour is calculated as part of the flow field solution.

Barron, R. M.↗

NASA NTRS1991

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Henry, Donald P., Jr.↗

NASA NTRS1992

The influence of chromium on structure and mechanical properties of B2 nickel aluminide alloys

Major obstacles to the use of NiAl-based alloys and composites are low ductility and toughness. These shortcomings result in part from a lack of sufficient slip systems to accommodate plastic deformation of polycrystalline material (von Mises Criterion). It has been reported that minor additions of chromium to polycrystalline NiAl cause the predominant slip system to shift from the usual. If true, then a major step toward increasing ductility in this compound may be realized. The purpose of the present study was to verify this phenomenon, characterize it with respect to chromium level and Ni to Al ratio, and correlate any change in slip system with microstructure and mechanical properties. Compression and tensile specimens were prepared from alloys containing 0 to 5 percent chromium and 45 to 55 percent aluminum. Following about one percent strain, transmission electron microscopy foils were produced and the slip systems determined using the g x b = 0 invisibility criterion. Contrary to previous results, chromium was found to have no effect on the preferred slip system of any of the alloys studied. Possible reasons for the inconsistency of the current results with previous work are considered. Composition-structure-property relationships are discerned for the alloys, and good correlation are demonstrated in terms of conventional strengthening models for metallic systems.

Cotton, James Dean↗

NASA NTRS1992

Effects of fiber and interfacial layer architectures on the thermoplastic response of metal matrix composites

Examined here is the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs). A micromechanics model based on an arbitrarily layered concentric cylinder configuration is used to calculate thermal stress fields in MMCs subjected to spatially uniform temperature changes. The fiber is modelled as a layered material with isotropic or orthotropic elastic layers, whereas the surrounding matrix, including interfacial layers, is treated as a strain-hardening, elastoplastic, von Mises solid with temperature-dependent parameters. The solution to the boundary-value problem of an arbitrarily layered concentric cylinder under the prescribed thermal loading is obtained using the local/global stiffness matrix formulation originally developed for stress analysis of multilayered elastic media. Examples are provided that illustrate how the morphology of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface affect the evolution of residual stresses in SiC/Ti composites during fabrication cool-down.

Pindera, Marek-Jerzy↗

NASA NTRS1992

Improving the low temperature ductility of NiAl

The intermetallic NiAl exhibits excellent potential as a structural material for application in air-breathing and single-stage-to-orbit engines. Unfortunately NiAl is brittle at ambient temperature, which is partly attributed to the lack of five independent slip systems as required by von Mises criterion for uniform, volume conserving deformation since the operative group of zone axes (100) slip offers only three independent slip systems. Isostructural FeAl, however, deforms by group of zone axes (111) slip at room temperature which provides five independent slip systems. Thus, it was decided to macroalloy NiAl with Fe to promote group of zone axes (111) slip thereby possibly improving the ductility. For Ni - 30 at. (percent) Al - 20 at. (percent) Fe having essentially bcc microstructure indicated up to 6 percent tensile elongation combined with high yield strength (about 800 MPa). The results compare favorably with those of stoichiometric Ni - 50 at. (percent) Al which, however, deforms by group of zone axes (100) slip at room temperature. The multi-phase alloy approach has proven even more successful for Ni - 20 at. (percent) Al - 30 at. (percent) Fe. The high temperature ductility of the multi-phase alloy was attributed to deformation transfer across interphase boundaries and the crack stopping action of the constituent gamma/gamma' phase. While the constituent phase became increasingly brittle, the beta' phase became more ductile at elevated temperatures. Thus the multi-phase alloy did not exhibit any elevated temperature embrittlement. Similarly, while the beta' phase became weak at high temperatures, the gamma/gamma' phase exhibited better strength retention leading to the improved elevated temperature strength of the multi-phase alloy. Thus, the multi-phase alloy benefits from both its constituent phases, with each phase alleviating the disadvantages associated with the other phase over any temperature range. The multi-phase alloy approach is suggested as a possible approach to designing intermetallic-based alloys.

Guha, Sumit↗

NASA NTRS1992

Boundary formulations for sensitivities of three-dimensional stress invariants

The direct, singular, boundary element analysis (BEA) formulation has been shown to provide a basis for a computationally efficient and accurate shape structural design sensitivity analysis (DSA) approach for three-dimensional solid objects. Within the boundary element analysis context, the theoretical formulation for sensitivities of important stress-related quantities including principal and deviatoric stresses, von Mises, maximum shear, and other stress invariants are presented, both for the surface as well as the interior of a continuum structure. Numerical results are given to demonstrate the accuracy of this approach.

Guru Prasad, K.↗

NASA NTRS1923

Determination of climbing ability

The vertical distribution of the pressure, temperature, and density of the atmosphere varies from day to day. Thus, rates of climb on different days cannot be compared directly, but must be corrected with reference to a standard rate of diminution of air density with increasing altitude. The following problem, therefore, has to be solved. An airplane has climbed on a certain day under prevailing atmospheric conditions as shown by the barograph. How would the same airplane climb in a standard atmosphere? This problem has already been dealt with by Everling, using the monthly and yearly mean of the vertical temperature distribution. Von Mises solved the problem by arithmetical methods. Here, conditions are examined which shorten or lengthen the climbing time. In establishing the corrected barogram, computation seems more practical than graphical treatment. The basis of the answer to the question answered here is summed up in the remark that lift, drag, propeller thrust, and torque and engine power depend only on the density of the air and do not change with the pressure and temperature, provided that the density remains constant.

Blasius, H↗