Two interfacial shear strength calculations based on the single fiber composite test

The fragmentation of a single fiber embedded in a polymer matrix upon stretching (SFC test) provides valuable information on the fiber-matrix bond strength (), which determines stress transfer through the interface and, thus, significantly affects the mechanical properties of the composite material. However, the calculated bond strength appears to depend on data interpretation, i.e., on the applied theoretical model, since the direct result of the SFC test is the fiber fragment length distribution rather than the value. Two approaches are used in SFC testing for calculation of the bond strength: 1) the Kelly-Tyson model, in which the matrix is assumed to be totally elastic and 2) the Cox model using the elastic constants of the fiber and the matrix. In this paper, an attempt has been made to compare these two approaches employing theory as well as the experimental data of several authors. The dependence of the tensile stress in the fiber and the interfacial shear stress on various factors has been analyzed. For both models, the mean interfacial shear stress in the fragment of critical length (l_c) was shown to satisfy the same formula () = (_cD)/2l_c, where D is the fiber diameter and _c is the tensile strength of a fiber at gauge length equal to l_c. However, the critical lengths from the Kelly-Tyson approach and Cox model are differently related to the fragment length distribution parameters such as the mean fragment length. This discrepancy results in different () values for the same experimental data set. While the main parameter in the Kelly-Tyson model assumed constant for a given fiber-matrix pair is the interfacial shear strength, the ultimate (local) bond strength _ult may be seen as the corresponding parameter in the Cox model. Various _ult values were obtained for carbon fiber-epoxy matrix systems by analyzing the data of continuously monitored single fiber composite tests. Whereas the mean value of the interfacial shear stress calculated in the Cox approach was comparable to the interfacial shear strength from the Kelly-Tyson model, its ultimate value characterizing the true adhesional bond strength appeared to be three or four times greater.To be presented at the Ninth International Conference on the Mechanics of Composite Materials in Riga, Latvia, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 446–461, July–August, 1995.     

Fatigue strength of glass fiber/epoxy angle-ply laminates with different matrix ductility

Conclusion Angle ply laminates made up of glass fiber/epoxy plies have a good static strength for laminate angles up to about 45 °. This is due to the limitation of transverse strain in the plies due to constraints exerted by neighboring plies. At laminate angles of 50 ° and above the transverse and shear strains in the plies are not sufficiently constrained and cause failure in the matrix material. The constraint effect is present in fatigue but since the polymeric matrix material is sensitive to fatigue loading fatigue failure will occur at much lower strain levels than in static loading. This effect cannot be offset by increasing the ductility of the matrix material. Thus, strain to failure under fatigue loading will be only a small fraction of the static strain to failure for angle ply laminates with ply angles up to around 45 ° where the static strength is due to the constraint effect.Published in Mekhanika Kompozitnykh Materialov, No. 5, pp. 632–638, September–October, 1992.     

Fracture of a piezoelectric fiber/elastic matrix composite

A piezoelectric fiber/elastic matrix system subjected to axially symmetric mechanical and electric loads is considered. The fiber contains a penny-shaped crack located at its center perpendicularly to the fiber. By using the Fourier and Hankel transforms, the problem is reduced to the solution of an integral equation. Numerical solutions for the crack tip fields are obtained for various crack sizes and different fiber volume fractions. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 301–318, May–June, 2006.     

Analysis of fiber breaking in fiber/matrix composites under torsional loads

The initiation of multiple cracks in a fiber/matrix composite subjected to a torsional load is studied. The composite is made of a cylindrical fiber surrounded by a matrix of different properties. A periodic array of cracks is assumed to exist in the fiber along its central axis. A dual integral equation is formulated in terms of equivalent crack face loads. The effects of crack spacing on the crack tip field intensity factor, the stress, the torque, and the equivalent stiffness of the fiber are investigated and displayed graphically.     

Strain localization mechanism of interfacial failure in steel fiber/concrete specimens

The full strain field near the interface of steel fiber/concrete in a half-mold specimen was measured using a combined method of pullout test and digital image correlation. The strain localization mechanism of the interfacial failure is discussed. The strain distributions near the interface at a straight fiber under different loads show that the interfacial shear failure has a distinct characteristic of intervals in time and space directly related to the strain localization, which makes the interfacial failure initiate, develop and transfer successively. In particular, the local strain distributions around pores near the straight fiber interface demonstrate that the strain changes its sign at the irregular parts of the pore where the initial debonding took place and the deformation path is affected by the pore.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Influence of SiO2 in SiCp on the microstructure and impact strength of Al/SiCp composites fabricated by pressureless infiltration

The effect of SiO₂ in SiC_p and the following processing parameters on the microstructure and impact strength of Al/SiC_p composites fabricated by pressureless infiltration was investigated: Mg content in the aluminum alloy, SiC particle size, and holding time. Preforms of SiC_p in the form of rectangular bars (10 × 1 × 1 cm) were infiltrated at 1150°C in an argon→nitrogen atmosphere for 45 and 60 min by utilizing two aluminum alloys (Al-6 Mg-11 Si and Al-9 Mg-11 Si, wt.%). The results obtained show that the presence of SiO₂ in SiC affects the microstructure and impact strength of the composites significantly. When Al₄C₃ is formed, the impact strength decreases. However, a high proportion of SiC to SiO₂ limits the formation of the unwanted Al₄C₃ phase in the composites. Also, a higher content of Mg in the Al alloy lowers the residual porosity and, consequently, increases the composite strength. The impact strength grows with decrease in SiC particle size and increases considerably when the residual porosity is less than 1%. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 401–418, May–June, 2006.     

Symmetrization of matrix technique in a finite element context

A finite element Galerkin-based formulation of the mass conservation and momentum equations can require, if convective type terms are retained in the coefficient matrix, a non-symmetric solver. The resulting increase in core storage for efficient utilization of CPU time can be considerable. The current paper advocates a simple symmetrization of matrix technique, at element level which results in a considerable reduction in core requirement. The increase in CPU time required when solving linear systems of equations is considerable. However, for nonlinear systems the penalty can be negligible.     

Effect of surface modification of fibers with a polymer coating on the interlaminar shear strength of a composite and the translation of fiber strength in an F-12 aramid/epoxy composite vessel

The surface of aramid fibers was modified with a polymer coating — a surface treatment reagent containing epoxy resin. The resulting fibers were examined by using NOL tests, hydroburst tests, and the scanning electron microscopy. The modified fibers had a rougher surface than the untreated ones. The interlaminar shear strength of an aramid-fiber-reinforced epoxy composite was highest when the concentration of polymer coating system was 5%. The translation of fiber strength in an aramid/epoxy composite vessel was improved by 8%. The mechanism of the surface treatment of fibers in improving the mechanical properties of aramid/epoxy composites is discussed. Russian translation publeshed in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 729–738, November–December, 2006.     

Effect of fiber length on the strength and fracture properties of a fiber-filled silicone composite

The mechanism by which fillers strengthen polymers is discussed, and the effect of fiber length on static and impact bending strength and on the area of the fracture surface is studied with reference to the example of a silicone composite. A correlation is established between the strength properties and the area of the fracture surface. On the basis of the data obtained it is shown that, as the fiber length increases, the fracture mechanism changes from extraction of the ends of the fibers along the fracture path to breakage of the fibers.Moscow Lomonosov Institute of Fine Chemical Technology. Ter-Gazaryan State Scientific-Research Planning Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 445–449, May–June, 1971.     

A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix

The question of whether a real matrix is symmetrizable via multiplication by a diagonal matrix with positive diagonal entries is reduced to the corresponding question for M-matrices and related to Hadamard products. In the process, for a nonsingular M-matrix A, it is shown that tr(A^-1A^T) ? n, with equality if and only if A is symmetric, and that the minimum eigenvalue of A^-1 ° A is ? 1 with equality in the irreducible case if and only if A is positive diagonally symmetrizable.