Table 6.

On-axis tensile FEM results of the T composite coupons representing the modulus of elasticity E , ultimate strength , failure strain. Table 7.

## SIAM Journal on Mathematical Analysis

Experimental results of the on-axis tension of the YS90A composite coupons representing the modulus of elasticity E , ultimate strength and failure strain. Figure SEM image showing non-homogeneities in dispersion of DP marked in red in the composite.

It is stated in the literature [25] that higher filler content leads to an agglomeration of particles, which reduces the adhesion between matrix and fillers and causes a drop in the mechanical strength of composites. Agubra et al. Sobia et al. High modulus YS90A being a pitch based carbon fiber was extremely fragile to handle in terms of fabrication of the samples and the interface bonding between diamond powder-epoxy resin was not perfectly formed which can be seen from the SEM image shown in Figure From the SEM image, it can be noted that, as the content of DP increased in the matrix, the DP filler network could have trapped some portion of epoxy resin preventing it from infiltrating the reinforcing fibers properly.

The above hypothesis could be one of the reasons for the reduction in the tensile properties Figure 11 , Table 7 of the DP filled composite. To understand the above mentioned behavior further, finite element modeling was performed with and without stress concentrations in the present composite specimen. The FEM results of the on-axis tensile behavior of the YS90A woven composite without stress concentrations exhibited a delamination type failure. Delamination triggered a substantial level of load drop due to dissipation of energy Figure At the ultimate tensile strength of the composite Figure 11 just before the occurrence of massive delamination, it is worth noting that fiber failure was not detected in any of the plies Figure 12 a and that matrix damage was also not present.

After this point, the propagation of delamination Figure 12 b , Figure 13 at the interface developed further. Figure 12 a , Figure 12 b represents the damage mode occuring in the plies and demonstrates that fibers in the on-axis plies have not failed even as the load drops significantly to a level corresponding to the failure stress. Comparison between the experimental tensile testing results and FEM tensile behavior without considering stress concentrations in the laminate.

Contour plots a b showing detection of the final fracture of the YS90A composite under tension. Delamination in the interface between the plies of the YS90A composite under tension. Table 8. On-axis tensile FEM results of the YS90A composite without stress concentrations representing the modulus of elasticity E , ultimate strength , failure strain.

The results also revealed that the presence of stress concentrations would severely reduce the stiffness and strength of the DP filled composite. From the data given above, it is evident that the reduction in the elastic modulus is due to inhomogeneities in the dispersion of the DP and the presence of possible stress concentrations in the composite.

The FEM results also show that a higher content of DP causes weak adhesion in the fiber-matrix interface which reduces the the strength of the composite and also reduces the ability of the composite to resist the damage Figure 15 a , Figure 15 b , Table 9. The FEM results also show that the presence of a rigid filler reduces the elongation at the.

Development of the OHT laminate with a diameter of 6 mm a and 10 mm b for studying the behavior of stress concentrations under tensile loading.

## Mathematical modeling and numerical analysis of reinforced composite beams - IOPscience

Table 9. Comparison of the experimental tensile and FEM-OHT results of the on-axis tension of the YS90A composite representing the modulus of elasticity E , ultimate strength and failure strain. In general, the elastic and the failure properties reduce significantly with the presence of stress concentrations.

In this study, the elastic and failure characteristics of standard modulus T and high modulus YS90A woven composites filled with diamond powder were examined. A numerical homogenization technique was applied to predict the elastic properties of the diamond powder enhanced matrix. Micromechanical unit cell models were first developed to predict the elastic properties of the diamond powder filled woven composites.

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Finite element modeling was then carried out to predict the failure behavior of the composite under tension. From the on-axis FEM simulations, it was observed that with the addition of DP, elongation at break in the composite reduced drastically as the DP filled epoxy matrix became stiffer and more brittle. Fabrication of the YS90A composite through the matrix modification technique with DP led to agglomeration.

An inhomogeneous dispersion of the diamond powder in the composite was observed from SEM images. This eventually reduced the elastic properties of the YS90A composite when subjected to on-axis tensile testing. Finite element modeling of the YS90A composite was carried out with OHT coupons to investigate the effect of stress concentrations in the composite when subjected to tensile loading. Ultrasonic dispersion technique to overcome the problem of an inhomogeneous dispersion of diamond powder in the composite must be explored and investigated.

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Furthermore, experimental testing must be carried out to examine the interfacial shear strength and stiffness of the diamond powder filled woven composites. A detailed investigation of the mesh sensitivity towards the predicted damage behavior must also be carried out.

Different constitutive laws considering through the thickness mechanical properties as well as strain rate effects in the diamond powder filled composite are required and need to be developed which could be implemented through an explicit rather than implicit FEA modeling scheme. Journal of Mechanics of Composite Materials, 49, Open Journal of Composite Materials, 6, Materials, 7, Plastics, Rubber and Composites, 42, McGraw-Hill, New York, Springer, New York, Journal of Composite Materials, 46, Computers and Structures, 84, Nanomaterials, 2, Journal of Applied Polymer Science, , Nature, , Composites Part A, 42, Nanotechnology, 18, Mechanics of Materials, 32, Composites Science and Technology, 70, Nippon Steel Technical Report No.

Nippon Graphite Fiber Corporation, Mechanics of Materials, 36, Composites Science and Technology, 60, Computational Materials Science, 52, Dassault Systemes Simulia Corp. Journal of Composite Materials, 7, Acta Mechanica Solida Sinica, 22, Composites: Part A, 42, Journal of Mechanical Engineering, 61, Share This Article:. The paper is not in the journal.

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DOI: Maettig 1 , K. Glitza 1 , B. Sanny 1 , A. Schumacher 2 , M. Duhovic 3. ABSTRACT A numerical investigation was carried out to examine the role of micro-sized diamond powder filler on the on-axis tensile stiffness properties of the standard modulus T and the high modulus YS90A woven fabric composite plates by progressive damage modeling. Finite element modeling FEM results for the T composite with and without diamond powder predicted a specific case of fiber failure in all the plies showing the characteristics of brittle failure.

A higher content of diamond powder in the coupons led to agglomeration. This induced stress concentrations and subsequently reduced the mechanical properties. FEM was carried out considering specimens with and without an induced stress concentration geometry in the YS90A coupons filled with DP. The results of the on-axis tensile tests indicated a delamination type of failure in both cases with additional fiber fracture in the Open Hole Tensile OHT coupons.

Introduction Textile structural composites are a widely used class of composites finding their applications in aerospace, automotive and manufacturing industries. The objectives of this research were: 1 To predict the elastic properties of epoxy-diamond powder matrix through a homogenization method.

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Homogenization of Heterogeneous Matrix Microstructure The macro response of the epoxy-diamond powder matrix was calculated from the micro response through numerical homogenization. Generally, in order to demonstrate the homogenized effective macroscopic response of such materials, the relation between averages are described as shown in the following: 1 where C is defined as the effective property which is the elasticity tensor used in structural scale analysis.

Therefore, the stress-strain relationship of composite laminate can be expressed as:. Pressure is defined as a third of the trace of the stresses, i. Therefore, expanding Eq. From the Eq. For the composite materials, a significant conclusion can be drawn that the volumetric and deviatoric response are strongly coupled, as that deviatoric strain can result in spherical stress, while volumetric strain can lead to deviatoric stress.

The first term, on the right side of Eq. However, for orthotropic materials, it represents the volumetric thermodynamic response. To involve the nonlinear shock effects, the first term of Eq. Meanwhile, the contribution to pressure from the deviatoric strain is remained as a correction.

Thus the expression of pressure can be rewritten as:. The failure model developed in this paper is an orthotropic failure model, which includes two stages, i. Subsequent to failure initiation, stiffness and strength properties of the failed material will be updated based on the direction or modes of the failure Silva et al. In this study, the through-thickness direction of composite laminate is defined as the direction, while the in-plane principal directions are and directions.

Delamination will be caused by the excessive stresses or strains in the or plane direction. If failure is initiated in either of these two modes, the stress in the direction and the corresponding orthotropic stiffness coefficients C ij is instantaneously set to zero Tham et al. The and directions are assumed to be in the plane of the composite.

If failure is initiated in and directions, the post-failure response is similar to direction,. If all the three material directions fail simultaneously, the material stiffness and strength will become isotropic with no stress deviators and tensile material stresses, indicating that the material can withstand only hydrostatic pressure. Due to the orthogonality of composite laminates, some elements in the impact region will be more easily distorted during the simulations, which may lead to numerical instabilities or even calculation failure Deka et al.

In this study, element effective strain is used as the erosion criterion, similar approach has been adopted in the references Grujicic et al. During the impact process, the composite material will undergo non-failure and failure states and the corresponding cell strain will also undergo this two stages. At this point, the meshes will be extremely distorted and the deletion mechanism will be triggered.

The layered projectile, carried by a polymer sabot, is accelerated by means of a single stage gas gun.