Robert M. Hackett

Residual Thermal Stresses in Filamentary Polymer-Matrix Composites Containing an Elastomeric Interphase

A three-phase micromechanical model based on the method of cells is for mulated to characterize residual thermal stresses in filamentary composites containing an in terphase between the fiber and the matrix. This is the first such study to incorporate a true three-phase version of the method of cells. The models performance is critically evaluated using data generated from other micromechanical models. Subsequently, a parametric study is performed to quantify the residual stresses in two hypothetical graphite fiber/epoxy matrix composites: one containing an elastomeric interphase whose Youngs modulus is less than that of the fiber and the matrix and one incorporating an interphase whose Youngs modulus is intermediate with respect to the fiber and the matrix. The data correlate the residual ther mal stresses in the fiber, interphase and matrix as a function of the interphase thickness and fiber volume fraction within each model composite. The study makes a broad assessment of the stress-attenuating characteristics that each interphase imparts to the graphite/epoxy com posites. Over the range of variables considered, properly dimensioning the elastomer inter phase leads to a more favorable reduction of residual thermal stress.

Polymeric composite materials incorporating an elastomeric interphase: A mathematical assessment

Abstract A mathematical model based upon the method of cells is extended in order to describe three-phase composite materials containing an interphase. A parametric study is performed wherein the effective properties of the composites are determined as a function of interphase material properties, interphase thickness and fiber volume fraction. The simulation is designed in particular towards describing the behavior of model composites which incorporate elastomeric polymers as an interphase to bond carbon fibers chemically to a polymeric matrix. Two hypothetical interphases are considered: one whose properties are representative of elastomers (Youngs modulus less than fiber and matrix) and one whose properties are intermediate with respect to the fiber and matrix. The two cases provide a broad assessment of how the interphase properties influence the effective composite properties.

A micromechanical characterization of graphite-fiber/epoxy composites containing a heterogeneous interphase region

Abstract An improved micromechanical model based on the method of cells is introduced in order to describe three-phase, continuous-fiber composite materials containing a heterogeneous interphase region. The models capability represents a significant improvement over that of the previous version (which is applicable to a homogeneous interphase) in that additional microstress information is obtained within the interphase region. A critical assessment of the model demonstrates that the predictions are consistent with data reproduced by using other micromechanical models. The study includes a parametric simulation in which the effective properties and the mechanical stresses associated with model graphite-fiber/epoxy composites are predicted as a function of the dimensions and Youngs modulus of the interphase. Three different interphases are modeled such that the Youngs modulus varies between that of the fiber and the matrix according to a generalized parabolic function of the radial coordinate. The parabolic functions are specified such that two of the model composites possess an interphase whose effective Youngs modulus is above that of the matrix. The third interphase is specified such that its effective Youngs modulus is below that of the matrix. The data indicate that the interphase dimensions and the functional form describing the interphase Youngs modulus significantly influence the composite microstresses. These data may be used to help identify optimum material combinations during composite material synthesis.

Two-dimensional finite element model of the pultrusion process

Composite materials used in the fabrication of industrial products/compo nents are under constant development. Applications vary widely from consumer products to high-performance aerospace components. The pultrusion process is one of the impor tant methods of production of composite materials. In order to develop a fundamental understanding of this process, a computational model employing the finite element method is developed which enables a prediction of the material temperature and degree-of-cure at any time during the process. The model is comprehensive; it can readily be employed to perform parametric studies of the process and to aid in the development of efficient design procedures for this type of material system. Comparisons are made between model predic tions and experimental results and good agreement is observed.

Microstress distribution in graphite fibre/epoxy composites containing an elastomeric interphase: response to uniaxial and biaxial loading conditions

Abstract A micromechanical model based upon the method of cells is introduced to characterize three-phase composites that contain a distinct and homogeneous interphase region. Initially, the performance characteristics of the model are shown to be quite consistent with those of a concentric cylinder model formulation. Subsequently, a parametric study is performed that examines the mechanical response of model graphite/epoxy composites as a function of selected interphase properties. The micromechanical model is utilized to establish an interdependence among the interphase Youngs modulus, the interphase thickness and the average stresses within the fibre, interphase and matrix resulting from two external loading conditions: uniaxial longitudinal tension and biaxial transverse shear. Material combinations are considered wherein the interphase Youngs modulus is systematically varied above and below the matrix Youngs modulus. The simulation indicates that the selected interphase properties significantly influence the stress state within each of the three composite constituents. The manner in which the stress states are modified proves to be non-intuitive in many of the cases considered. In particular, there are material domains encountered where the model predicts that certain stress components in a constituent will exhibit (1) a maximum with respect to variations in the interphase Youngs modulus and/or (2) a minimum with respect to variations in the interphase thickness.

A micromechanical characterization of residual thermal stresses in carbon fiber/epoxy composites containing a non-uniform interphase region ☆

Abstract There is growing speculation that the interphase in polymer composites is often a region of nonuniform material properties. This is significant given the critical role of the interphase in determining overall composite behavior. The present investigation utilizes a micromechanical model based on the three-phase method of cells to examine how spatial variations in the interphase elastic properties are predicted to influence the residual thermal stresses in carbon-fiber-reinforced epoxy. This is the first such study of its kind based on a true three-phase version of the method of cells. A total of sixteen different composite configurations are considered in which the interphase Youngs modulus and/or the interphase thermal expansion coefficient may vary as a function of the radial coordinate. The interphases are specified such that their Youngs modulus and thermal expansion coefficient may be above or below that of the epoxy matrix. The residual thermal stresses, as well as the effective composite properties, are evaluated as a function of the fiber volume fraction, the interphase thickness and the spatial nonuniformity of the interphase properties. The results indicate that the introduction of interphase property gradients is predicted to primarily influence the state of stress within the interphase. Depending upon how the interphase properties are specified to vary, the residual stresses within the interphase may either be compressive or tensile.

Viscoelastic Analysis of Filament-Wound Composite Material Systems

A methodology for the viscoelastic analysis of filament-wound polymer matrix composites is developed and demonstrated. The procedure uses the elastic- viscoelastic correspondence principle with standard micromechanics models to obtain the viscoelastic properties of the composite. For global analysis, an efficient time-stepping algorithm is developed and implemented in a general purpose finite element code via a user-supplied material subroutine. The algorithm is verified by comparison to the exact analysis of a rigid inclusion in an infinite viscoelastic plate and the utility of the entire methodology is shown by analysis and testing of a composite spring.

Computational Simulation of the Creep-Rupture Process in Filamentary Composite Materials:

A computational simulation of the internal damage accumulation which causes the creep-rupture phenomenon in filamentary composite materials is developed. The creep-rupture process involves complex interactions between several damage mechanisms. A statistically-based computational simulation using a time-differencing ap proach is employed to model these progressive interactions. The finite element method is used to calculate the internal stresses. The fibers are modeled as a series of bar elements which are connected transversely by matrix elements. Flaws are distributed randomly throughout the elements in the model. Load is applied, and the properties of the individual elements are updated at the end of each time step as a function of the stress history. The simulation is continued until failure occurs. Several cases, with different initial flaw dis persions, are run to establish a statistical distribution of the time-to-failure. The calcula tions are performed on a supercomputer. The simulation results compare favorably with the results of creep-rupture experiments conducted at the Lawrence Livermore National Laboratory.

Pultrusion Process Modeling

A basic one-dimensional heat transfer model of the pultrusion process for thermosetting resin composites was formulated. The model, employing a Galerkin finite-element approach, is the basic development. It can be expanded to a general characterization of the process and extended to characterize the pultrusion process for thermoplastic resin composites. The application of the basic model is demonstrated.

Viscoelastic/Damage Modeling of Filament-Wound Spherical Pressure Vessels

A model of the viscoelastic/damage response of a filament-wound spherical vessel used for long-term pressure containment is developed. The matrix material of the composite system is assumed to be linearly viscoelastic. Internal accumulated damage based upon a quadratic relationship between transverse modulus and maximum circumferential strain is postulated. The resulting nonlinear problem is solved by an iterative routine. The elastic- viscoelastic correspondence principle is employed to produce, in the Laplace domain, the associated elastic solution for the maximum circumferential strain which is inverted by the method of collocation to yield the time-dependent solution. Results obtained with the model are compared to experimental observations.