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At least 271 records · Page 15

A Review of the Mechanical Properties of Materials Used in Nb 3 Sn Magnets for Particle Accelerators

Superconducting magnets experience significant thermo-mechanical loads throughout their life cycle. These are introduced by the electro-magnetic forces during powering, but also by the prestress applied in many magnet designs. Further to this, the large thermal excursion that components of different materials experience can generate significant internal forces. The loads are also experienced by the superconducting coils, whose critical current can decrease as a consequence of the applied strain. It is then crucial to predict the overall mechanical behavior and conservatively design a magnet, avoiding failure of the mechanical components and of the superconducting coils. Finite Element Analysis (FEA) is generally used to perform these tasks, but its results rely heavily on the material properties and models used. This is in particular true for the coil composite, which is simplified to allow reasonable model sizes in full magnet models. Here we present the state-of-art knowledge of the mechanical properties of the materials mostly used in superconducting magnet construction. We review elastic and plastic properties at room and cryogenic temperature, thermal contraction, and summarize the state-of-art failure criteria for these materials. Finally, the paper summarizes the present understanding of the mechanical behavior and limits of Nb3Sn coils. For the first time, an orthotropic failure criteria is proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Steady-state heat conduction in multilayered composite plates and shells

A study is made of a predictor-corrector procedure for the accurate determination of the temperature and heat flux distributions in thick multilayered composite plates and shells. A linear through-the-thickness temperature distribution is used in the predictor phase. The functional dependence of temperature on the thickness coordinate is then calculated a posteriori and used in the corrector phase. Extensive numerical results are presented for linear steady-state heat conduction problems, showing the effects of variation in the geometric and lamination parameters on the accuracy of the thermal response predictions of the predictor-corrector approach. Both antisymmetrically laminated anisotropic plates and multilayered orthotropic cylinders are considered. The solutions are assumed to be periodic in the surface coordinates. For each problem the standard of comparison is taken to be the analytic three-dimensional solution based on treating each layer as a homogeneous anisotropic medium. The potential of the predictor-corrector approach for predicting the thermal response of multilayered plates and shells with complicated geometry is discussed.

Noor, A. K.↗

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.↗

Structural analysis and sizing of stiffened, metal matrix composite panels for hypersonic vehicles

The present method for strength and stability analyses of stiffened, fiber-reinforced composite panels to be used in hypersonic vehicle structures is of great generality, and can be linked with planar finite-element analysis (FEA). Nonlinear temperature and load-dependent material data for each laminate are used to 'build-up' the stiffened panel's membrane, bending, and membrane-bending coupling stiffness terms, as well as thermal coefficients. The resulting, FEA-solved thermomechanical forces and moments are used to calculate strain at any location in the panel; this allows an effective ply-by-ply orthotropic strength analysis to be conducted, together with orthotropic instability checks for each laminated segment of the cross-section.

Collier, Craig S.↗

Modeling creep behavior of fiber composites

A micromechanical model for the creep behavior of fiber composites is developed based on a typical cell consisting of a fiber and the surrounding matrix. The fiber is assumed to be linearly elastic and the matrix nonlinearly viscous. The creep strain rate in the matrix is assumed to be a function of stress. The nominal stress-strain relations are derived in the form of differential equations which are solved numerically for off-axis specimens under uniaxial loading. A potential function and the associated effective stress and effective creep strain rates are introduced to simplify the orthotropic relations.

Chen, J. L.↗

Mechanical property characterization and impact resistance of selected graphite/PEEK composite materials

To use graphite/PEEK material on highly curved surfaces requires that the material be drapable and easily conformable to the surface. The mechanical property characterization and impact resistance results are presented for laminates made from two types of graphite/PEEK materials that will conform to a curved surface. These laminates were made from two different material forms. These forms are: (1) a fabric where each yarn is a co-mingled Celion G30-500 3K graphite fiber and PEEK fiber; and (2) an interleaved material of Celion G30-500 3K graphite fiber interleaved with PEEK film. The experimental results from the fabric laminates are compared with results for laminates made from AS4/PEEK unidirectional tape. The results indicate that the tension and compression moduli for quasi-isotropic and orthotropic laminates made from fabric materials are at least 98 pct. of the modulus of equivalent laminates made from tape materials. The strength of fabric material laminates is at least 80 pct. of laminates made from tape material. The evaluation of the fabric material for shear stiffness indicates that a tape material laminate could be replaced by a fabric material laminate and still maintain 89 pct. of the shear stiffness of the tape material laminate.

Baker, Donald J.↗

Postbuckling of flat unstiffened graphite-epoxy plates loaded in shear

An experimental and analytical study was conducted of the postbuckling response and failure characteristics of 8-, 16-, and 24-ply unstiffened graphite/epoxy plates under shear loading, including orthotropic, quasi-orthotropic, entirely +, -45 deg ply, and (0/90)s-class plates. Postbuckling stiffness is noted to be influenced by the stacking sequence and by the inplane boundary condition imposed on the test section by a picture frame test fixture. The ratio of failure load to buckling load was higher for specimens that had higher width-to-thickness ratios. It is noted that high displacement gradients may induce transverse shear stresses, and that delamination was the failure mechanism for many of the 8-ply specimens. An adhesive failure between the composite specimen and metal edge reinforcements initiated failure of the 16- and 24-ply specimens.

Rouse, M.↗

An experimental study of the fracture behavior of laminated graphite/epoxy composites

The results of an experimental investigation on the fracture behavior of unidirectional and multidirectional laminated graphite/epoxy composites is reported. Critical tensile fracture stresses for constant head rate uniaxial specimens containing single-edge notches, double-edge notches, and centrally located circular holes are presented. Results are reported for loads and notches at various angles to the fiber direction. Evidence of notch sensitivity and stable crack growth is presented. Self-similar crack growth is shown to occur for only a limited set of circumstances. Critical stresses are compared to the theories of Waddoups et al and Whitney et al. These comparisons are presented using isotropic and orthotropic stress concentration factors together with a finite width correction factor. The results tend to show that use of only isotropic correction factors allow good correlation between theory and experiment.

Brinson, H. F.↗

Mechanical property characterization and impact resistance of selected graphite/PEEK composite materials

To use graphite polyetheretherketone (PEEK) material on highly curved surfaces requires that the material be drapable and easily conformable to the surface. This paper presents the mechanical property characterization and impact resistance results for laminates made from two types of graphite/PEEK materials that will conform to a curved surface. These laminates were made from two different material forms. These forms are: (1) a fabric where each yarn is a co-mingled Celion G30-500 3K graphite fiber and PEEK thermoplastic fiber; and (2) an interleaved material of Celion G30-500 3K graphite fabric interleaved with PEEK thermoplastic film. The experimental results from the fabric laminates are compared with results for laminates made from AS4/PEEK unidirectional tape. The results indicate that the tension and compression moduli for quasi-isotropic and orthotropic laminates made from fabric materials are at least 79 percent of the modulus of equivalent laminates made from tape material. The strength of fabric material laminates is at least 80 percent of laminates made from tape material. The evaluation of fabric material for shear stiffness indicates that a tape material laminate could be replaced by a fabric material laminate and still maintain 89 percent of the shear stiffness of the tape material laminate. The notched quasi-isotropic compression panel failure strength is 42 to 46 percent of the unnotched quasi-isotropic laminate strength. Damage area after impact with 20 ft-lbs of impact energy is larger for the co-mingled panels than for the interleaved panels. The inerleaved panels have less damage than panels made from tape material. Residual compression strength of quasi-isotropic panels after impact of 20 ft-lbs of energy varies between 33 percent of the undamaged quasi-isotropic material strength for the tape material and 38 percent of the undamaged quasi-isotropic material strength for the co-mingled fabric material.

Baker, Donald J.↗

A Selection of Composites Simulation Practices at NASA Langley Research Center

One of the major areas of study at NASA Langley Research Center is the development of technologies that support the use of advanced composite materials in aerospace applications. Amongst the supporting technologies are analysis tools used to simulate the behavior of these materials. This presentation will discuss a number of examples of analysis tools and simulation practices conducted at NASA Langley. The presentation will include examples of damage tolerance analyses for both interlaminar and intralaminar failure modes. Tools for modeling interlaminar failure modes include fracture mechanics and cohesive methods, whilst tools for modeling intralaminar failure involve the development of various progressive failure analyses. Other examples of analyses developed at NASA Langley include a thermo-mechanical model of an orthotropic material and the simulation of delamination growth in z-pin reinforced laminates.

Ratcliffe, James G.↗

Parameter identification of material constants in a composite shell structure

One of the basic requirements in engineering analysis is the development of a mathematical model describing the system. Frequently comparisons with test data are used as a measurement of the adequacy of the model. An attempt is typically made to update or improve the model to provide a test verified analysis tool. System identification provides a systematic procedure for accomplishing this task. The terms system identification, parameter estimation, and model correlation all refer to techniques that use test information to update or verify mathematical models. The goal of system identification is to improve the correlation of model predictions with measured test data, and produce accurate, predictive models. For nonmetallic structures the modeling task is often difficult due to uncertainties in the elastic constants. A finite element model of the shell was created, which included uncertain orthotropic elastic constants. A modal survey test was then performed on the shell. The resulting modal data, along with the finite element model of the shell, were used in a Bayes estimation algorithm. This permitted the use of covariance matrices to weight the confidence in the initial parameter values as well as confidence in the measured test data. The estimation procedure also employed the concept of successive linearization to obtain an approximate solution to the original nonlinear estimation problem.

Martinez, David R.↗

Verification and Regression Testing of a Physically Stabilized Layered Solid Element Formulation in DYNA3D/Paradyn

Recent modeling of filament-wound composite structures drove the need for a new element type within the finite element code DYNA3D/Paradyn. This new layered solid element was implemented and designed to capture the kinematics and constitutive be havior of various lamina layers defined with arbitrary orientations and volume fractions within the element to accurately model a laminated composite material. The new el ement uses a single integration point in each of the lamina layers defined to capture the constitutive behavior, and a novel physical stabilization routine is used to prevent hourglassing while mitigating shear and volumetric locking. This report documents the verification testing and the regression tests added to the DYNA3D/Paradyn software quality assurance test suite to assess the proper implementation of the new layered solid element. There were a total of 27 tests added the DYNA3D test suite, which consist of problems using the layered solid element with a single layer or multiple layers for isotropic and orthotropic material models. These tests are a combination of simple kinematically driven patch tests, beam bending tests, plate bending tests, and more complicated problems. Ultimately, the testing done verifies that the element behaves as expected and is implemented correctly.

42 ENGINEERING↗

Variable Stiffness Panel Structural Analyses With Material Nonlinearity and Correlation With Tests

Results from structural analyses of three tow-placed AS4/977-3 composite panels with both geometric and material nonlinearities are presented. Two of the panels have variable stiffness layups where the fiber orientation angle varies as a continuous function of location on the panel planform. One variable stiffness panel has overlapping tow bands of varying thickness, while the other has a theoretically uniform thickness. The third panel has a conventional uniform-thickness [plus or minus 45](sub 5s) layup with straight fibers, providing a baseline for comparing the performance of the variable stiffness panels. Parametric finite element analyses including nonlinear material shear are first compared with material characterization test results for two orthotropic layups. This nonlinear material model is incorporated into structural analysis models of the variable stiffness and baseline panels with applied end shortenings. Measured geometric imperfections and mechanical prestresses, generated by forcing the variable stiffness panels from their cured anticlastic shapes into their flatter test configurations, are also modeled. Results of these structural analyses are then compared to the measured panel structural response. Good correlation is observed between the analysis results and displacement test data throughout deep postbuckling up to global failure, suggesting that nonlinear material behavior is an important component of the actual panel structural response.

Wu, K. Chauncey↗

Composite laminate optimization program suitable for microcomputers

The design of a composite panel requires some way of finding the minimum thickness laminate which will withstand the load requirements without failure. The mathematical complexity of this problem dictates the use of nonlinear optimization techniques. Specialized laminate optimization programs were developed which are compact and efficient enough to run on microcomputers. Only stresses at a point and inplane loads and deflections are considered. The programs are simple to use and require no knowledge of optimization. Techniques are developed which find minimum thickness laminates with either ply ratios or ply angles as design variables. A method is presented for finding the optimum orientation for the axis of symmetry of an orthotropic laminate. The orthotropic laminate program uses an approximate failure theory, which speed up computations dramatically.

Flanagan, G. V.↗

Assessment of computational models for multilayered composite cylinders

A study is made of the effects of variation in the lamination and geometric parameters of multilayered composite cylinders on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation shell theories. The standard of comparison is taken to be the exact three-dimensional elasticity solutions, and the quantities compared include both the gross response characteristics and detailed, through-the-thickness, distributions of displacements, stresses and strain energy densities. Based on the numerical studies conducted, a predictor-corrector approach, used in conjunction with the first-order shear-deformation theory (with five displacement parameters in the predictor phase), appears to be the most effective among the eight modeling approaches considered. For multilayered orthotropic cylinders the response quantities obtained by the predictor-corrector approach are shown to be in close agreement with the exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters.

Noor, A. K.↗

Separation of crack extension modes in composite delamination problems

This work concerns fracture mechanics modeling of composite delamination problems. In order to predict delamination resistance, an applied stress intensity factor, K, or energy release rate, G, must be compared to a mode-dependent critical value of K or G from experiment. In the interfacial fracture analysis of most applications and some tests, the mode of crack extension is not uniquely defined. It is instead a function of distance from the crack tip due to the oscillating singularity existing at the tip. In this work, a consistent method is presented of extracting crack extension modes in such cases. In particular, use of the virtual crack closure technique (VCCT) to extract modes of crack extension is studied for cases of a crack along the interface between two in-plane orthotropic materials. Modes of crack extension extracted from oscillatory analyses using VCCT are a function of the virtual crack extension length, delta. Most existing efforts to obtain delta-independent modes of crack extension involve changing the analysis in order to eliminate its oscillatory nature. One such method involves changing one or more properties of the layers to make the oscillatory exponent parameter, epsilon, equal zero. Standardized application of this method would require consistent criteria for identifying which properties can be altered without changing the physical aspects of the problem. Another method involves inserting a thin homogeneous layer (typically referred to as a resin interlayer) along the interface and placing the crack within it. The drawbacks of this method are that it requires increased modeling effort and introduces the thickness of the interlayer as an additional length parameter. The approach presented here does not attempt to alter the interfacial fracture analysis to eliminate its oscillatory behavior. Instead, the argument is made that the oscillatory behavior is non-physical and that if its effects were separated from VCCT quantities, then consistent, delta-independent modes of crack extension could be defined. Knowledge of the near-tip fields in a planar orthotropic material interfacial fracture analysis is used to determine the explicit delta dependence of VCCT parameters. Once this delta dependence is determined, energy release rates are defined with this delta dependence factored out. This modified VCCT method is applied to results from two finite element test cases. It is shown that, as predicted, delta-independent modes of crack extension result. The modified VCCT approach shows potential as a consistent method of extracting crack extension modes. It uses the same information from a finite element analysis (i.e., nodal forces and displacements) as the traditional VCCT method does. The A-independent modes extracted using the modified VCCT approach can also be used as guides to test the convergence of finite element solutions.

Beuth, Jack L.↗

The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

Nemeth, Michael P.↗

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗