Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Superposition Principle”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

The viscoelastic behavior of the principal compliance matrix of a unidirectional graphite/epoxy composite

The time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite was determined. It is shown that two components of the compliance matrix are time and temperature independent and that the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors which are independent of fiber orientation, for fiber angles that vary from 10 D to 90 D with respect to the load direction.

Morris, D. H.↗
NASA NTRS1979

The viscoelastic behavior of a composite in a thermal environment

A proposed method for the accelerated predictions of modulus and life times for time dependent polymer matrix composite laminates is presented. The method, based on the time temperature superposition principle and lamination theory, is described in detail. Unidirectional reciprocal of compliance master curves and the shift functions needed are presented and discussed. Master curves for arbitrarily oriented unidirectional laminates are predicted and compared with experimantal results obtained from master curves generated from 15 minute tests and with 25 hour tests. Good agreement is shown. Predicted 30 deg and 60 deg unidirectional strength master curves are presented and compared to results of creep rupture tests. Reasonable agreement is demonstrated. In addition, creep rupture results for a (90 deg + or - 60 deg/90 deg) sub 2s laminate are presented.

Morris, D. H.↗
NASA NTRS1979

Time-temperature behavior of a unidirectional graphite/epoxy composite

A testing program to determine the time-temperature response of unidirectional T300/934 graphite/epoxy materials is presented. The short-term creep test results of tension specimens with the load at various angles to the fiber direction and at various temperatures are reported, showing that the material is elastic at all temperatures when the fiber is in the load direction. However, when the load is transverse to the fibers, the viscoelastic response varies from small amounts at room temperature to large amounts at temperatures above the 180 C transition temperature. The time-temperature superposition principle or the method of reduced variables were used to determine compliance master curves for each fiber angle, and a viscoelastic analog to the elastic orthotropic transformation equation was used incrementally to predict the master curves for the tensile compliance of the off-axis specimen.

Yeow, Y. T.↗
NASA NTRS1980

Accelerated characterization of graphite/epoxy composites

A method to predict the long term compliance of unidirectional off-axis laminates from short term laboratory tests is presented. The method uses an orthotropic transformation equation and the time-stress-temperature superposition principle. Short term tests are used to construct master curves for two off-axis unidirectional laminates with fiber angles of 10 and 90 degrees. Analytical predictions of long term compliance for 30 and 60 degrees laminates are made. Comparisons with experimental data are also given.

Griffith, W. I.↗
NASA NTRS1981

Creep and creep rupture of laminated graphite/epoxy composites

An incremental numerical procedure based on lamination theory is developed to predict creep and creep rupture of general laminates. Existing unidirectional creep compliance and delayed failure data is used to develop analytical models for lamina response. The compliance model is based on a procedure proposed by Findley which incorporates the power law for creep into a nonlinear constitutive relationship. The matrix octahedral shear stress is assumed to control the stress interaction effect. A modified superposition principle is used to account for the varying stress level effect on the creep strain. The lamina failure model is based on a modification of the Tsai-Hill theory which includes the time dependent creep rupture strength. A linear cumulative damage law is used to monitor the remaining lifetime in each ply.

Dillard, D. A.↗
NASA NTRS1980

The viscoelastic behavior of the principal compliance matrix of a unidirectional graphite/epoxy composite

A testing program was conducted to determine the time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite. It was shown that the two components of the compliance matrix are time and temperature independent. In addition, the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors. It was shown that the shift factors are independent of fiber orientation for fiber angles that vary from 10 to 90 deg with respect to the load direction.

Morris, D. H.↗
NASA NTRS1980

Creep rupture behavior of unidirectional advanced composites

A 'material modeling' methodology for predicting the creep rupture behavior of unidirectional advanced composites is proposed. In this approach the parameters (obtained from short-term tests) required to make the predictions are the three principal creep compliance master curves and their corresponding quasi-static strengths tested at room temperature (22 C). Using these parameters in conjunction with a failure criterion, creep rupture envelopes can be generated for any combination of in-plane loading conditions and ambient temperature. The analysis was validated experimentally for one composite system, the T300/934 graphite-epoxy system. This was done by performing short-term creep tests (to generate the principal creep compliance master curves with the time-temperature superposition principle) and relatively long-term creep rupture tensile tests of off-axis specimens at 180 C. Good to reasonable agreement between experimental and analytical results is observed.

Yeow, Y. T.↗
NASA NTRS1980

Accelerated characterization of graphite/epoxy composites

A method to predict the long-term compliance of unidirectional off-axis laminates from short-term laboratory tests is presented. The method uses an orthotropic transformation equation and the time-stress-temperature superposition principle. Short-term tests are used to construct master curves for two off-axis unidirectional laminates with fiber angles of 10 deg and 90 deg. In addition, analytical predictions of long-term compliance for 30 deg and 60 deg laminates are made. Comparisons with experimental data are also given.

Griffith, W. I.↗
NASA NTRS1982

An equation for bolt clampup relaxation in transient environments

An equation for bolt clampup relaxation for transient temperature-moisture (T-M) conditions was derived starting with a relaxation equation for steady-state conditions, and then using an incremental time approach that exploits the superposition principle for linear viscoelasticity. The resulting equation uses the initial T-M condition (at the time of clamping), the T-M history after clamping, and elastic clampup coefficients for temperature and moisture changes. For a given material and joint configuration, the clampup coefficients are constants that can be calculated by elastic analyses. The clampup equation was used to calculate the changes in clampup occurring in a T300/5208 graphite/epoxy joint exposed to a one-year history of temperature and moisture. Two cases were considered: one was a dry joint exposed to a relatively humid environment and the other was a nearly saturated joint exposed to an arid environment.

Shivakumar, K. N.↗
NASA NTRS1979

Study of fatigue durability of advanced composite materials under conditions of accelerated loading

The effect of temperature on the tension-tension fatigue life of the T300/5208 graphite/epoxy angle-ply laminate system was investigated in an effort to develop an acceptable and reliable method of accelerated loading. Typical S log sub 10 N curves were determined experimentally at 25 C, 75 C, and 115 C. The time-temperature superposition principle was employed to find the shift factors of uniaxial fatigue strength, and a general linear equation of S log sub 10 N for shifting purpose was established. The combined techniques of cyclic creep measurements and optical microscopy upon fatigue failure allow some assessment of the possible physical basis of S log 10 N curve shifting. Before fatigue, the laminates at all test temperatures and stress levels undergo a unique damage mechanism during fatigue loading. It is concluded that an accelerated loading method is feasible.

Shih, H. M.↗
NASA NTRS1981

The viscoelastic response of a graphite/epoxy laminate

An accelerated characterization procedure has been developed for time-dependent compliances and strengths of resin-matrix composites. The procedure, which is based on a time-temperature-stress superposition principle, is applied to a graphite/epoxy laminate T300/934. Creep rupture analytical models are discussed, and model predictions are compared with experimental data. Master curves for the creep compliances are given.

Brinson, H. F.↗
NASA NTRS1983

Analysis of structural perturbations in systems via cost decomposition methods

It has long been common practice to analyze linear dynamic systems by decomposing the total response in terms of individual contributions which are easier to analyze. Examples of this philosophy include the expansion of transfer functions using: (1) the superposition principle, (2) residue theory and partial fraction expansions, (3) Markov parameters, Hankel matrices, and (4) regular and singular perturbations. This paper summarizes a new and different kind of expansion designed to decompose the norm of the response vector rather than the response vector itself. This is referred to as "cost-decomposition' of the system. The notable advantages of this type of decomposition are: (a) easy application to multi-input, multi-output systems, (b) natural compatibility with Linear Quadratic Gaussian Theory, (c) applicability to the analysis of more general types of structural perturbations involving inputs, outputs, states, parameters. Property (c) makes the method suitable for problems in model reduction, measurement/actuator selections, and sensitivity analysis.

Skelton, R. E.↗
NASA NTRS1981

The influence of environmental effects on the mechanical properties of graphite/epoxy laminates

The time dependent deformational and creep rupture processes in graphite/epoxy laminates are examined as a function of temperature and stress level. The role of accelerated characterization of design materials is discussed, and the use of a nonlinear time-temperature-stress-superposition principle in the determination of compliance master curves as a function of stress and temperature is considered. Creep rupture analytical models are discussed as applied to polymer-matrix composites, and the data is shown to be in general agreement with a logarithmic stress and temperature-dependent delayed fracture model. Comparisons between creep and rupture experiments and phenomenological models are presented.

Brinson, H. F.↗
NASA NTRS1982

The prediction of long term viscoelastic properties of fiber reinforced plastics

A method for the experimental and analytical accelerated characterization of long term viscoelastic properties is presented. The time-temperature-stress superposition principle (TTSSP) is shown to serve as the basis for determining long term compliance data from short term creep test results. Nonlinear viscoelastic theories are discussed to provide the framework for the mathematically modeling of such a process. A time dependent Tsai-Hill-Zhurkov failure theory is used to determine long term failure properties from short term data. Compliance and failure data are incorporated in an incremental lamination theory to make long term laminate predictions. Comparisons are made between theory and experiment.

Brinson, H. F.↗
NASA NTRS1983

Environmental effects and viscoelastic behavior of laminated graphite/epoxy composites

Primarily because of the polymeric matrix, graphite/epoxy composites are viscoelastic materials which exhibit creep and delayed failures. Guided by the time-temperature superposition principle, the authors are developing accelerated characterization techniques to predict the long term compliance behavior and creep rupture strength of composite materials based on short term tests at elevated temperatures. The effect of a post-cure cycle on the compliance and creep rupture strength of composite materials is discussed. The Zhurkov type failure law is applied to experimental creep rupture data of a typical laminate and is shown to correlate the data. A beneficial mechanical strengthening effect is described which significantly affects the failure strengths of specimens which have been under creep loading for a period of time. This aging effect is reversible if the specimen is allowed to recover before being loaded to failure. Other environmental aspects of composite materials are also reviewed.

Dillard, D. A.↗
NASA NTRS1983

A non-linear viscoelastic characterisation method for matrix resin composites

Lifetime prediction of matrix resin composites is an important problem because of their viscoelastic character. If the Time-Temperature-Stress-Superposition principle is valid, results from short time tests at high stress levels can give the necessary information for the prediction of long time behavior. At such stress levels the viscoelastic response is nonlinear. In this contribution the basis of a computer routine is presented starting from a thermodynamical formulation given by Schapery. This method gives in an accurate way the different material parameters in that nonlinear constitutive equation for different stresses and temperatures.

Hiel, C. C.↗
NASA NTRS1985

Viscoelastic behavior and life-time predictions

Fiber reinforced plastics were considered for many structural applications in automotive, aerospace and other industries. A major concern was and remains the failure modes associated with the polymer matrix which serves to bind the fibers together and transfer the load through connections, from fiber to fiber and ply to ply. An accelerated characterization procedure for prediction of delayed failures was developed. This method utilizes time-temperature-stress-moisture superposition principles in conjunction with laminated plate theory. Because failures are inherently nonlinear, the testing and analytic modeling for both moduli and strength is based upon nonlinear viscoelastic concepts.

Dillard, D. A.↗
NASA NTRS1985

Viscoelastic behavior and lifetime (durability) predictions

A method for lifetime or durability predictions for laminated fiber reinforced plastics is given. The procedure is similar to but not the same as the well known time-temperature-superposition principle for polymers. The method is better described as an analytical adaptation of time-stress-super-position methods. The analytical constitutive modeling is based upon a nonlinear viscoelastic constitutive model developed by Schapery. Time dependent failure models are discussed and are related to the constitutive models. Finally, results of an incremental lamination analysis using the constitutive and failure model are compared to experimental results. Favorable results between theory and predictions are presented using data from creep tests of about two months duration.

Brinson, R. F.↗