Unified Continuum Damage Model for Matrix Cracking in Composite Rotor Blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

Analysis of Kic and its temperature dependence of metals by a simplified dislocation model

The relative Kic values of metals are calculated with a simplified dislocation model. It is found that the ratio of KIIc to KIc and the temperature dependence of fracture toughness of some metals estimated with this model are consistent with the experimental results.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

An economic air pollution control model-application : photochemical smog in Los Angeles County in 1975

An economic air pollution control model, which determines the least cost of reaching various air quality levels, is formulated. The model takes the form of a general, nonlinear, mathematical programming problem. Primary contaminant emission levels are the independent variables. The objective function is the cost of attaining various emission levels and is to be minimized subject to constraints that given air quality levels be attained.

The model is applied to a simplified statement of the photochemical smog problem in Los Angeles County in 1975 with emissions specified by a two-dimensional vector, total reactive hydrocarbon, (RHC), and nitrogen oxide, (NO_x), emissions. Air quality, also two-dimensional, is measured by the expected number of days per year that nitrogen dioxide, (NO₂), and mid-day ozone, (O₃), exceed standards in Central Los Angeles.

The minimum cost of reaching various emission levels is found by a linear programming model. The base or "uncontrolled" emission levels are those that will exist in 1975 with the present new car control program and with the degree of stationary source control existing in 1971. Controls, basically "add-on devices", are considered here for used cars, aircraft, and existing stationary sources. It is found that with these added controls, Los Angeles County emission levels [(1300 tons/day RHC, 1000 tons /day NO_x) in 1969] and [(670 tons/day RHC, 790 tons/day NO_x) at the base 1975 level], can be reduced to 260 tons/day RHC (minimum RHC program) and 460 tons/day NO_x (minimum NO_x program).

"Phenomenological" or statistical air quality models provide the relationship between air quality and emissions. These models estimate the relationship by using atmospheric monitoring data taken at one (yearly) emission level and by using certain simple physical assumptions, (e. g., that emissions are reduced proportionately at all points in space and time). For NO₂, (concentrations assumed proportional to NO_x emissions), it is found that standard violations in Central Los Angeles, (55 in 1969), can be reduced to 25, 5, and 0 days per year by controlling emissions to 800, 550, and 300 tons /day, respectively. A probabilistic model reveals that RHC control is much more effective than NO_x control in reducing Central Los Angeles ozone. The 150 days per year ozone violations in 1969 can be reduced to 75, 30, 10, and 0 days per year by abating RHC emissions to 700, 450, 300, and 150 tons/day, respectively, (at the 1969 NO_x emission level).

The control cost-emission level and air quality-emission level relationships are combined in a graphical solution of the complete model to find the cost of various air quality levels. Best possible air quality levels with the controls considered here are 8 O₃ and 10 NO₂ violations per year (minimum ozone program) or 25 O₃ and 3 NO₂ violations per year (minimum NO₂ program) with an annualized cost of $230,000,000 (above the estimated $150,000,000 per year for the new car control program for Los Angeles County motor vehicles in 1975).