Nonlinear deformation of laminated fiber-reinforced composites

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 6, pp. 49–56, June, 1995.     

The effect of brittle interfacial compounds on deformation and fracture of molybdenum-aluminum fiber composites

The effect of brittle intermetallic compounds at the fiber-matrix interface on the deformation characteristics of molybdenum-aluminum fiber composites was investigated. If the filament is ductile and notch-insensitive, then composite strength degradation is relatively minor and composite strength can be predicted by a modified mixture-rule which neglects the strength contribution of the brittle compound. For the case of notch-sensitive filaments, severe filament degradation occurs upon compound formation. The degradation was shown to result from cracks formed during deformation at the roots of compound nodules. The presence of 10 per cent compound by volume results in a 50 per cent decrease in tensile strength, but larger amounts of compound cause little additional strength reduction. At filament volume fractions of 25 and 34 per cent and compound volume fractions less than 10 per cent, composite fracture occurs by the statistical accumulation of fiber necks or fractures depending on the notch sensitivity of the fiber. At high fiber or compound volume fractions, composite failure occurs upon the first or the second filament fracture.     

Nonlinear deformation of thin-walled shells with local loads

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 10, pp. 50–55, October, 1994.     

Folding of fiber composites with a hyperelastic matrix

This paper presents an experimental and numerical study of the folding behavior of thin composite materials consisting of carbon fibers embedded in a silicone matrix. The soft matrix allows the fibers to microbuckle without breaking and this acts as a stress relief mechanism during folding, which allows the material to reach very high curvatures. The experiments show a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. A finite element model has been created to study the micromechanics of the problem. The fibers are modeled as linear-elastic solid elements distributed in a hyperelastic matrix according to a random arrangement based on experimental observations. The simulations obtained from this model capture the detailed micromechanics of the problem and the experimentally observed non-linear response. The proposed model is in good quantitative agreement with the experimental results for the case of lower fiber volume fractions but in the case of higher volume fractions the predicted response is overly stiff.     

On the effect of fiber creep-compliance in the high-temperature deformation of continuous fiber-reinforced ceramic matrix composites

Creep models for unidirectional ceramic matrix composites reinforced by long creeping fibers with weak interfaces are presented. These models extend the work of Du and McMeeking (1995) [Du, Z., McMeeking, R. 1995. Creep models for metal matrix composites with long brittle fibers. J. Mech. Phys. Solids 43, 701–726] to include the effect of fiber primary creep present in the required operational temperatures for ceramic matrix composites (CMCs). The effects of fiber breaks and the consequential stress relaxation around the breaks are incorporated in the models under the assumption of global load sharing and time-independent stochastics for fiber failure. From the set of problems analyzed, it is found that the high-temperature deformation of CMCs is sensitive to the creep-compliance of the fibers. High fiber creep-compliance drives the composite to creep faster, leading however to greater lifetimes and greater overall strains at rupture. This behavior is attributed to the fact that the greater the creep-compliance of the fibers, the higher the creep rate but the slower the matrix stress relaxation – since the matrix must deform with a rate compatible with the more creep-resistant fibers – and therefore the less the load carried by the main load-bearing phase, the fibers. As a result, fewer fibers fail and less damage is accumulated in the system. Moreover, the greater the creep-compliance of the fibers, the slower the matrix shear stress relaxation – and thus the lower the levels of applied stress for which this effect becomes important. The slower the shear stress relaxes, the slower the “slip” length increases. Due to the Weibull nature of the fibers, the fiber strengths at the smaller gauge length of the slip length are stronger; therefore fewer fibers undergo damage. Hence, high fiber creep-compliance is desirable (in the absence of any explicit creep-damage mechanism) in terms of composite lifetime but not in terms of overall strain. These results are considered of importance for composite design and optimization.     

Nonlinear deformation of elastomeric foams

The nonlinear deformation of a porous foam-type elastomeric material is studied, both theoretically and experimentally. The elastomer is modeled by the neo-Hookean material. The one-dimensional compressive behavior of the foam is analysed by using certain kinematic assumptions. The stress required to compress the foam is predicted by the model in terms of the porosity of the foam and the single constant in the neo-Hookean stress-strain form. A particular silicone foam is used as a test of the theory. The neo-Hookean constant is evaluated from a test of the homogeneous elastomer. Hence the behavior of the corresponding foam is predicted theoretically and compared with experimental results. The general results are applicable to closed-cells foams of intermediate density.     

Load-dependent constitutive response of fiber composites with compliant interphases

I , the influence of applied load on the overall transverse mechanical properties of fiberreinforced composites with compliant interphases is examined from a micromechanical perspective. The composite is modeled by a regular hexagonal array of circular fibers in an infinite matrix. It is assumed that a thin reaction zone (intermolecular bonding at the fiber/matrix interface) establishes the bond between the fiber and matrix phases. The model of the present paper allows us to derive expressions for the overall elastic constants in the transverse plane as a function of applied load. The finite element method is used to evaluate these expressions, and the results are discussed.     

Analysis of elastoplastic deformation in metal-matrix composites with particulate reinforcements

In this paper, elastoplastic stress-strain behavior during tensile deformation of an aluminum alloy matrix composite containing alumina circular and non-circular particles is analyzed. In terms of cell models in conjunction with continuum plasticity theory, various periodic arrays of particles are assumed in a three-dimensional finite element simulation. The geometrical effects of particle volume fraction, shape, aspect ratio, array and distribution, as well as non-circular particle orientation on the overall elastoplastic stress-strain behavior are examined in view to design optimum microstructures of the composites. The project supported by the National Natural Science Foundation of China and the State Education Commission of China     

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation. The project supported by the National Natural Science Foundation of China (10472066, 10372057). The English text was polished by Yunming Chen.     

Nonlinear effects in deformation of filled elastomers with nanodimensional fillers

Various nonlinear effects manifesting themselves in the deformation of filled elastomers are analyzed, and the advantages and restrictions in the use of several constitutive relations proposed to describe the nonlinear viscoelastic behavior of the materials under study are discussed. We also note that further development of models of nonlinear deformation of filled elastomers under finite strains, which would permit describing their deformation properties more completely, is highly desirable.