A study of process-induced stress and deformation in thick-section thermosetting composite laminates is presented. A methodology is proposed for predict ing the evolution of residual stress develop...

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Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates:

An investigation into the two-dimensional cure simulation of thick thermosetting composites is presented. Temperature and degree of cure distributions within arbitrary cross-sectional geometries are predicted as a function of the autoclave temperature history. The heat conduction equation for two-dimensional, transient anisotropic heat transfer is coupled to the cure kinetics of the thermosetting composite material. A heat generation term, expressed as a function of cure rate and the total heat of reaction, is introduced to account for the heat liberated during the curing process. A generalized boundary condition formulation is employed, enabling arbitrary temperature boundary conditions to be enforced straightforwardly. An incremental, transient finite difference solution scheme is implemented to solve the pertinent governing equations and boundary conditions. The boundary-fitted coordinate system (BFCS) transformation technique is combined with the Alternating Direction Explicit (ADE) finite difference ...

Two-Dimensional Cure Simulation of Thick Thermosetting Composites

Manufacture of large composite structures presents a number o f challenges, one of the most critical o f which is prediction and control of process-induced deformation. Traditional empirical techniques for tooling and process cycle development are particularly unsuitable for large parts, especially when development costs and process variability are key issues. Thus, there is a critical need to supplement current techniques with a science-based manufacturing approach. In the present work, a two-dimensional finite element model for prediction of process-induced deformation has been developed. Integration of this model with analyses for heat transfer and resin cure and resin flow allows analysis of all major identified deformation sources. A 'virtual autoclave' concept is employed in which autoclave control algorithms and autoclave response are simulated to predict structure boundary conditions during processing. Characterization of a carbon fibre/epoxy composite is performed and models developed to describe material behaviour during processing. A n examination of autoclave heat transfer is also performed and a model developed for the observed effect of pressure on heat transfer rates. Using these data as inputs, the process model is demonstrated through application to three case studies of varying complexity. In each, model predictions are compared to experimental results and the predicted sensitivity o f processing outcomes to process parameter variation is examined. A good match between model predictions and experimental results was obtained in most cases. The developed model is expected to perform two complementary roles. First, the ability to analyse structures of practical size and complexity makes the model a potentially useful process-development tool for the industrial composites processor. Also, the integration of analyses for all major deformation sources allows examination of parameter interaction, potentially driving fundamental research into deformation mechanisms and the development of improved material behavioural models. Sommaire La fabrication de larges structures en composites comporte de nombreux defis dont l'un des plus critiques est la determination et le controle de la deformation induite durant le procede de fabrication. Dans une optique de reduction des couts de fabrication et des variations de qualite, les methodes empiriques traditionnellement utilisees pour la determination du cycle de cure et la conception de l'outillage sont particulierement inefficaces dans le cas de pieces aux dimensions importantes. Ainsi, il est necessaire de complementer les methodes actuelles par une approche scientifique aux problemes de production. Dans ce travail, un modele d'elements finis en deux dimensions calculant les deformations induites durant la fabrication a ete developpe. Ce modele permet l'analyse des principaux phenomenes contribuant aux deformations en combinant les effets du transfert de chaleur, de la polymerisation de la resine et de l'ecoulement de la resine. Un concept de "l'autoclave virtuel", dans lequel les algorythmes de controle de l'autoclave et la reponse de l'autoclave sont simules, est inclus afin de predire plus precisement les conditions frontieres de la piece durant la fabrication. Un composite fibre de carbone-epoxy est caracterise et des modeles decrivant son comportement au cours de la polymerisation sont developpes. Les caracteristiques du transfert de chaleur de l'autoclave sont determinees et un modele reliant Feffet de la pression sur le coefficient de transfert de chaleur de l'autoclave est developpe. En utilisant ces donnees, la performance du modele d'elements finis est demontree a travers trois cas ayant differents degres de complexite. Pour chacun des cas, les predictions du modele sont comparees aux resultats experimentaux. Sommaire L'effet de la variation des entrees du modele sur la stabilite des parametres du procede est egalement etudie. En general, les resultats experimentaux et numeriques concordent bien. Le modele developpe repond a deux besoins complementaires. D'une part, il est un outil pratique pour le manufacturier de pieces en composites, car il permet d'analyser des structures aux formes complexes et de grandes dimensions. D'autre part, il permet d'analyser l'interaction des parametres, car il integre les principaux mecanismes qui induisent des deformations. Ceci permettra d'encourager la progression de la recherche fondamentale sur les mecanismes causant les deformations et de developper de meilleurs modeles decrivant le comportement du materiau.

An integrated model of the development of process-induced deformation in autoclave processing of composite structures

Epoxy resins and other thermosetting polymers change from liquids to solids during cure. A precise process model of these materials requires a constitutive model that is able to describe this transformation in its entirety. In this study the viscoelastic properties of a commercial epoxy resin were characterized using a dynamic mechanical analyzer (DMA). Specimens were tested at several different cure states to develop master curves of stress relaxation behavior during cure. Using this experimental data, the relaxation modulus was then modeled in a thermorheologically complex manner. A Prony (exponential) series was used to describe the relaxation modulus. An original model was developed for the stress relaxation times based on similar work by Scherer (16) on the relaxation of glass. Shift functions used to obtain reduced times are empirically derived based on curve fits to the data. The data show that the cure state has a profound effect on the stress relaxation of epoxy. More important, the relaxation behavior above gelation is shown to be quite sensitive to degree of cure.

Stress relaxation behavior of 3501-6 epoxy resin during cure

The significance of (an)isotropic viscoelastic Poisson ratio stress and time dependencies

Expressions are developed for the residual thermal stresses in a solid sphere cast from a chemically hardening thermosetting material in a rigid spherical mold. The description of the heat generation rate and temperature variation is derived from a first-order chemical reaction. Solidification is described by the continuous transformation of the material from an inviscid liquidlike state into an elastic solid, with intermediate properties determined by the degree of chemical reaction. Residual stress components are obtained as functions of the parameters of the hardening process and the properties of the hardening material. Variation of the residual stresses with a nondimensionalized reaction rate parameter and the relative compressibility of the hardened material is discussed in detail.

Residual Thermal Stresses in a Solid Sphere Cast From a Thermosetting Material

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

Thermoelastic constitutive equations for chemically hardening materials

: Equations are presented for the temperature distribution in a case bonded propellant grain when the environmental temperature is suddenly changed It is found that whenever the Biot modulus is relatively small, the temperature distribution is essentially independent of the radial coordinate but varies with the time coordinate only, at a rate which is dependent upon the geometry and the physical properties of the propellant grain as well as the heat transfer coefficients (Author)

Temperature distribution in a case - bonded cylindrical rocket assembly

A method is formulated for determining the transient thermal stresses that evolve during the molding process within a material hardening as the result of an exothermic chemical reaction. The formulation is applied to the restricted case in which the shear-to-bulk-modulus ratio for the fully hardened material is small, and where the material is cast in the form of an infinitely long solid cylinder in a thermally thin elastic mold. The heat-generation rate and temperature variation are derived from a first-order chemical reaction. The solidification of the material is described by a transformation from an initial liquidlike state to an elastic solid, with thermoelastic constitutive rate equations during the hardening process based upon a two-component mixture model whose composition is related to the degree of reaction. Graphs for transient stresses and residual stress distributions are shown in terms of dimensionless variables, with hardening rate related to thermochemical constants, and with the ...

Myron Levitsky

Papers

Residual Thermal Stresses in a Solid Sphere Cast From a Thermosetting Material

Thermoelastic constitutive equations for chemically hardening materials

Temperature distribution in a case - bonded cylindrical rocket assembly

Transient thermal stresses in a chemically hardening material cast within an elastic cylindrical mold