Kawai Kwok

Folding, Stowage, and Deployment of Viscoelastic Tape Springs

This paper presents an experimental and numerical study of the folding, stowage, and deployment behavior of viscoelastic tape springs. Experiments show that during folding the relationship between load and displacement is nonlinear and varies with rate and temperature. In particular, the limit and propagation loads increase with the folding rate but decrease with temperature. During stowage, relaxation behavior leads to a reduction in internal forces that significantly impacts the subsequent deployment dynamics. The deployment behavior starts with a short, dynamic transient that is followed by a steady deployment and ends with a slow creep recovery. Unlike elastic tape springs, localized folds in viscoelastic tape springs do not move during deployment. Finite-element simulations based on a linear viscoelastic constitutive model with an experimentally determined relaxation modulus are shown to accurately reproduce the experimentally observed behavior, and to capture the effects of geometric nonlinearity, time and temperature dependence.

Micromechanical modeling of deployment and shape recovery of thin-walled viscoelastic composite space structures

The first part of the paper presents an experimental study of the deployment and shape recovery of composite tape-springs after stowage at an elevated temperature. It is found that tape-springs deploy quickly and with a slight overshoot, but complete recovery takes place asymptotically over time. Stowage has the effect of slowing down both the shortterm deployment and long-term shape recovery. The second part of the paper presents a micromechanical finite element homogenization scheme to determine the effective viscoelastic properties of woven composite laminas. This solution scheme is employed in numerical simulations of deployment and shape recovery of composite tape-springs. The proposed micromechanical model predicts both the short-term deployment and long-term shape recovery response with close agreement to the experimental measurements.

Visco elastic Effects in Tape-Springs

Following recent interest in constructing large self-deployable structures made of reinforced polymer materials, this paper presents a detailed study of viscoelastic effects in folding, stowage, and deployment of tape-springs which often act as deployment actuators in space structures. Folding and stowage behavior at different temperatures and rates are studied. It is found that the peak load increases with the folding rate but reduces with temperature. It is also shown that a load reduction of as much as 60% is possible during stowage due to relaxation behavior. Deployment behavior after significant load relaxation demonstrates features distinct from elastic tape-springs. It starts with a short dynamic response, followed by a quasi-static deployment, and ends with a slow creep recovery process. A key feature is that the localized fold stays stationary throughout deployment. Finite element simulations that incorporate an experimentally characterized viscoelastic material model are presented and found to capture the folding and stowage behavior accurately. The general features of deployment response are also predicted, but with larger discrepancy.

Shap e Recovery of Viscoelastic Deployable Structures

The paper investigates the shape recovery behavior of a simple beam and a tape spring made of LDPE under prescribed deformation history at room temperature. The linear viscoelastic material properties of LDPE were measured via creep tests. An analysis of a LDPE beam under four-point bending with an imposed history of vertical deflection and reaction force was performed. A theoretical solution was constructed by employing the Alfrey’s Correspondence Principle to the Euler-Bernoulli beam equation. The result was validated against a four-point bending experiment and a detailed nonlinear finite element simulation. Excellent agreement was obtained between theory, experiments and numerical simulations. A LDPE tape spring was fabricated and tested to provide an example of a simple deployable structure that recovers its deployed shape through a viscoelastic process for both equal sense and opposite sense folding.

Micromechanics Models for Viscoelastic Plain-Weave Composite Tape Springs

The viscoelastic behavior of polymer composites decreases the deployment force and the postdeployment shape accuracy of composite deployable space structures. This paper presents a viscoelastic model for single-ply cylindrical shells (tape springs) that are deployed after being held folded for a given period of time. The model is derived from a representative unit cell of the composite material, based on the microstructure geometry. Key ingredients are the fiber volume density in the composite tows and the constitutive behavior of the fibers (assumed to be linear elastic and transversely isotropic) and of the matrix (assumed to be linear viscoelastic). Finite-element-based homogenizations at two scales are conducted to obtain the Prony series that characterize the orthotropic behavior of the composite tow, using the measured relaxation modulus of the matrix as an input. A further homogenization leads to the lamina relaxation ABDABD matrix. The accuracy of the proposed model is verified against the experimentally measured time-dependent compliance of single lamina in either pure tension or pure bending. Finite element simulations of single-ply tape springs based on the proposed model are compared to experimental measurements that were also obtained during this study.

Large Strain Viscoelastic Model for Balloon Film

This paper presents a constitutive model capable of predicting the anisotropic viscoelastic behavior of balloon film subject to large strains and cyclic loading. The model is based on the free volume theory of nonlinear viscoelasticity enhanced with a switching rule for treating loading and unloading differently. The model has been implemented in the finite element analysis program Abaqus/Standard and the results have been compared with experiments on the balloon film StratoFilm 420 under biaxial tension and shear.

Shape Recovery of Viscoelastic Beams After Stowage

The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions for the load relaxation and shape recovery of a linear viscoelastic beam subject to such time-varying constraints. It is shown that a viscoelastic beam recovers to its original shape asymptotically over time. The analytical solutions are employed to investigate the effect of temperature and stowage time on the time required to achieve recovery with a specified precision. Based on the time-temperature equivalence principle, the relationship between recovery time and holding duration is concisely presented on a single plot. It is found that recovery time increases with holding duration but with a diminishing effect.

Development of High Temperature Mechanical Rig for Characterizing the Viscoplastic Properties of Alloys Used in Solid Oxide Cells

Analyzing the thermomechanical reliability of the solid oxide cell (SOC) stack requires precise measurement of the mechanical properties of the different components in the stack at operating conditions of the SOC. It is challenging to precisely characterize the time-dependent deformational properties of metallic components in the SOC stacks at the required level of stress and operational conditions (high temperature and controlled atmosphere). This work presents an improved methodology for characterizing the time-dependent, or viscoplastic, properties of metallic alloys used in the SOC stacks at a high temperature and in a controlled atmosphere. The methodology uses a mechanical loading rig designed to apply variable and constant loads on samples within a gas-tight high temperature furnace. In addition, a unique, remotely installed length measuring setup involving a laser micrometer is used to monitor deformations in the sample. Application of the methodology is exemplified by measurement of stress relaxation, creep, and constant strain rate behaviors of a high-temperature alloy used in the construction of SOC metallic interconnects at different temperatures. Furthermore, measurements using the proposed methodology are also verified by the literature and experiments conducted using other machines.

Large-Strain Viscoelastic Constitutive Models for Thin Polyethylene Films

This paper presents a constitutive model capable of predicting the thermoviscoelastic behavior of the balloon thin film StratoFilm subject to large strains up to yielding. The model is based on the free volume theory of nonlinear thermoviscoelasticity and extended to orthotropic membranes. An ingredient of the present approach is that the experimentally inaccessible out-of-plane material properties are determined by fitting the model predictions to the measured non-linear behavior of the film. Creep tests, uniaxial tension tests, and biaxial bubble tests are used to determine the material parameters. The model has been validated experimentally, against data obtained from uniaxial tension tests and biaxial cylindrical tests at a wide range of temperatures and strain rates spanning two orders of magnitude (0.01%/s ~ 1%/s).

Structural and Control Concepts for Variable Geometry Planetary Entry Systems

The results presented in this paper apply to a generic vehicle that makes use of geometry changes to modulate the heat, drag, and acceleration loads while entering a planetary atmosphere. Two structural concepts for implementing the cone angle variation, namely a segmented shell and a corrugated shell, are presented. A structural analysis of the corrugated shell configuration shows that the stress levels are tolerable during entry. The analytic expressions of the longitudinal aerodynamic coefficients are also derived, and guidance laws that track reference heat flux, drag, and aerodynamic acceleration loads are also proposed. These guidance laws have been tested in an integrated simulation environment, and the results indicate that use of variable geometry is feasible to track specific profiles of dynamic load conditions during reentry.