A Unified Micromechanical Model for the Mechanical Properties of Two Constituent Composite Materials. Part IV: Rubber-Elastic Behavior

This series of papers reports a new, general, and unified micromechanical model for estimating the three-dimensional mechanical properties of a composite made from two constituent materials, i.e., continuous fiber and matrix. The present paper addresses the application of the model to rubber-based composites, with a focus on prediction of the entire stress-strain response characteristic of a composite having an elastomer matrix constituent material. For this purpose, an accurate constitutive theory has been developed for any incompressible rubber-like material. Its incremental stress-strain relationship at any given level is simply correlated by a load-dependent compliance matrix, similar to Hooke's law. The theory is consistent in that when the involved material parameters, i.e., the load-dependent Young's modulus and Poisson's ratio, are determined using a single type of test data such as uniaxial tension data, it is then able to predict precisely the material responses to other types of deformation conditions. Combining the incremental theory with the unified model developed in Parts I and II, an analysis procedure for the overall properties of elastomer-based composites follows. As an application, an interlock weft-knitted polyester-fiber fabric-reinforced polyurethane elastomer composite is investigated. Favorable correlation has been found between the theoretical and experimental results.

[1]  G. Dvorak,et al.  Plasticity Analysis of Fibrous Composites , 1982 .

[2]  T. G. Rogers,et al.  Plane Deformations of Incompressible Fiber-Reinforced Materials , 1971 .

[3]  Tsu-Wei Chou,et al.  Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites , 1988 .

[4]  T. Chou,et al.  Finite deformation of flexible composites , 1990, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Jacob Aboudi,et al.  Micromechanical Analysis of Composites by the Method of Cells - Update , 1996 .

[6]  G. A. V. Leaf,et al.  43—The Geometry of a Plain Knitted Loop , 1955 .

[7]  C. Chamis,et al.  Critique on Theories Predicting Thermoelastic Properties of Fibrous Composites , 1968 .

[8]  Thierry Chotard,et al.  Experimental determination of TSAI failure tensorial terms Fij for unidirectional composite materials , 1995 .

[9]  Mn Nahas,et al.  Survey of Failure and Post-Failure Theories of Laminated Fiber-Renforced Composites , 1986 .

[10]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[11]  Shankar Mall,et al.  Micromechanical Relations for Fiber-Reinforced Composites Using the Free Transverse Shear Approach , 1993 .

[12]  Z. Hashin.  Analysis of Properties of Fiber Composites With Anisotropic Constituents , 1979 .

[13]  Elastoplastic Transverse Properties of a Unidirectional Fibre Reinforced Composite , 1973 .

[14]  L. P. Isupov.  A variant of the theory of plasticity of two-phase composite media , 1996 .

[15]  Stephen W. Tsai,et al.  Nonlinear Elastic Behavior of Unidirectional Composite Laminae , 1973 .

[16]  J. Echaabi,et al.  REVIEW OF FAILURE CRITERIA OF FIBROUS COMPOSITE MATERIALS , 1996 .

[17]  K. Reifsnider,et al.  Tensile Strength of Unidirectional Composites: The Role of Efficiency and Strength of Fiber-Matrix Interface , 1995 .

[18]  C. Chamis.  Mechanics of Composite Materials: Past, Present and Future , 1989 .

[19]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials—III. self-consistent model , 1965 .

[20]  N. L. Hancox,et al.  Primer on composite materials analysis (2nd Ed) , 1992 .

[21]  D. Salinas,et al.  Initial Yield Surface of a Unidirectionally Reinforced Composite , 1972 .

[22]  T. Nicholas,et al.  Analysis of Thermomechanical Cyclic behavior of Unidirectional Metal Matrix Composites , 1993 .

[23]  R. Pipes,et al.  On the Off-Axis Strength Test for Anisotropic Materials1 , 1973 .

[24]  Jun Chen,et al.  Micromechanical characterization of nonlinear behavior of advanced polymer matrix composites , 1996 .

[25]  Donald F. Adams,et al.  Inelastic Analysis of a Unidirectional Composite Subjected to Transverse Normal Loading , 1970 .

[26]  H. S. Morgan,et al.  Analysis of Nonlinear Stress-Strain Behavior of Fiber-Reinf orced Composite Materials , 1977 .

[27]  Christos C. Chamis,et al.  Thermoviscoplastic nonlinear constitutive relationships for structural analysis of high temperature metal matrix composites , 1988 .

[28]  C. Sun,et al.  A Simple Flow Rule for Characterizing Nonlinear Behavior of Fiber Composites , 1989 .

[29]  Y. Macheret,et al.  An experimental study of elastic-plastic behavior of a fibrous boron-aluminum composite , 1988 .

[30]  L. Treloar,et al.  Stress-strain data for vulcanised rubber under various types of deformation , 1944 .

[31]  B. W. Shaffer.  Elastic-plastic stress distribution within reinforced plastics loaded normal to its internal filaments. , 1968 .

[32]  George J. Dvorak,et al.  Elastic-plastic behavior of fibrous composites , 1979 .

[33]  Jacob Aboudi,et al.  Micromechanical analysis of the strength of unidirectional fiber composites , 1988 .

[34]  S. Ramakrishna.  CHARACTERIZATION AND MODELING OF THE TENSILE PROPERTIES OF PLAIN WEFT-KNIT FABRIC-REINFORCED COMPOSITES , 1997 .

[35]  S. Peng,et al.  A compressible approach in finite element analysis of rubber-elastic materials , 1997 .

[36]  Jacob Aboudi,et al.  A continuum theory for fiber-reinforced elastic-viscoplastic composites , 1982 .

[37]  J. E. Adkins,et al.  Large elastic deformations of isotropic materials X. Reinforcement by inextensible cords , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[38]  W. W. Stinchcomb,et al.  A micromechanics model for the prediction of static strength of off-axis unidirectional laminates , 1994 .

[39]  Zheng-ming Huang,et al.  Characterization of a Knitted Fabric Reinforced Elastomer Composite , 1999 .

[40]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[41]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour , 1964 .

[42]  Steven M. Arnold,et al.  Influence of fiber architecture on the inelastic response of metal matrix composites , 1996 .

[43]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[44]  H. T. Hahn,et al.  Nonlinear Behavior of Laminated Composites , 1973 .