Fracture toughness characteristics of laminated composites

Parameters characterizing the resistance of laminated composites to interlaminar fracture are discussed. The properties of the specific interlaminar fracture work, i.e., the amount of work spent on the formation of a unit of new surface of interlaminar crack, were examined. Taking account of the anisotropy of the material, this work may be characterized using a matrix. Upon change in the direction of crack growth, the matrix elements are transformed similarly to the components of a symmetrical second rank tensor. An interpretation is offered for the matrix elements. The proposed theoretical model was in accord with our experimental results.Moscow Engineering Institute. Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–31, January–February, 1996.     

Strength of fibrous composites

Research on the effect of various factors on the strength of fibrous composites in tension, compression, shear, bending and plane stress, published in the journal Polymer Mechanics, is reviewed. The more important future trends are outlined.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 553–562, May–June, 1972.     

Interlaminar fracture toughness of graphite fiber-reinforced polyimide composites

Conclusion The present study has proved the effectiveness of the application of viscoelastic polymers with increased fracture toughness to graphite/polyimide composites interlaminar fracture toughness improvement. Thermoplastic polysulphone film and thermoresistant structural adhesive have proved to be inherently more effective for composites' delamination resistance growth than maleimide resin toughening and structural modification. The former inevitably results in increase of the honeycomb delamination resistance (Fig. 1) and its durability.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 6, pp. 848–852, November–December, 1994.     

Investigations of interlaminar fracture toughness of laminated polymeric composites

The behavior of interlaminar fracture of fiber reinforced laminated polymeric composites has been investigated in modes I, II, and different mixed mode I/II ratios. The experimental investigations were carried out by using conventional beam specimens and the compound version of the CTS (compact tension shear) specimen. In this study, a compound version of the CTS specimen is used for the first time to determine the interlaminar fracture toughness of composites. In order to verify the results obtained by the CTS tests, conventional beam tests were also carried out. In the beam tests, specimens of double cantilever beam (DCB) and end notched flexure (ENF) were used to obtain the critical rates of the energy release for failure modes I and II. The CTS specimen is used to obtain different mixed mode ratios, from pure mode I to pure mode II, by varying the loading conditions. The highest mixed mode ratio obtained in the experiment was G _I /G _II =60. The data obtained from these tests were analyzed by the finite element method. The separated critical rates G _I and G _II of the energy release were calculated by using the modified virtual crack closure integral (MVCCI) method. The experimental investigations were performed on a unidirectional glass/epoxy composite. The results obtained by the beam and CTS tests were compared. It was found that the interlaminar fracture toughness G _IC ^init of mode I at crack initiation and the corresponding value G _II ^Cinit of mode II obtained by the conventional beam and the CTS tests were in rather good agreement. The experimental results of interlaminar fracture of mixed mode were used to obtain the parameters required for the failure criterion. The two different failure criteria were compared. The best correlation with the experimental data was obtained by using the failure criterion proposed by Wu in 1967 containing linear and quadratic terms of the rates of the energy release.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 307–322, May–June, 1998.     

Nonlinear rescaling vs. smoothing technique in convex optimization

We introduce an alternative to the smoothing technique approach for constrained optimization. As it turns out for any given smoothing function there exists a modification with particular properties. We use the modification for Nonlinear Rescaling (NR) the constraints of a given constrained optimization problem into an equivalent set of constraints.?The constraints transformation is scaled by a vector of positive parameters. The Lagrangian for the equivalent problems is to the correspondent Smoothing Penalty functions as Augmented Lagrangian to the Classical Penalty function or MBFs to the Barrier Functions. Moreover the Lagrangians for the equivalent problems combine the best properties of Quadratic and Nonquadratic Augmented Lagrangians and at the same time are free from their main drawbacks.?Sequential unconstrained minimization of the Lagrangian for the equivalent problem in primal space followed by both Lagrange multipliers and scaling parameters update leads to a new class of NR multipliers methods, which are equivalent to the Interior Quadratic Prox methods for the dual problem.?We proved convergence and estimate the rate of convergence of the NR multipliers method under very mild assumptions on the input data. We also estimate the rate of convergence under various assumptions on the input data.?In particular, under the standard second order optimality conditions the NR method converges with Q-linear rate without unbounded increase of the scaling parameters, which correspond to the active constraints.?We also established global quadratic convergence of the NR methods for Linear Programming with unique dual solution.?We provide numerical results, which strongly support the theory. Received: September 2000 / Accepted: October 2001?Published online April 12, 2002     

Strength properties of unidirectionally reinforced hybrid composites

Conclusions Experiments were carried out with several types of unidirectionally reinforced hybrid composites (organic fiberglass plastic, organic carbon-reinforced plastic, organic boron-reinforced plastic, and carbon fiberglass plastic) with various ratios of the volume content of the fibers in various modes of simple quasistatic loading. It is shown that the strength of the examined materials in the plane stress state can be described phenomenologically by the polynomial criterion of strength with the components of the tensors of the strength surface depending on the structural parameters. The result can be used to predict (carry out interpolation calculations) the strength of the above-mentioned composites within the examined ranges of the volume content of the reinforcing fibers to optimize the selection of the type and ratio of the content of various fibers in the hybrid composite taking into account specific requirements on the strength properties of the material in the structures.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 35–41, January–February, 1984.     

Strength of cylindrical shells of laminar composites under dynamic loading

Conclusion The methods described in the present review paper for the computation of cylindrical shells of laminar composites under various types of dynamic loads make it possible to calculate the stress-strain state at any point of the body of the shell at an arbitrary time and to determine the time of the first failure of a layer (including fatigue failure) using strength criterion of an anisotropic body for the case of a plane stressed state, and also the location of the first flaw in the shell. This makes it possible to determine the magnitude of the applied pulse (the amplitude of a pulsed loading), or the amplitude of a vibratory loading for which the first centers of failure appear in the design.Presented at the Second Soviet-American Symposium on the Problem Failure of Composite Materials (Bethlehem, Pa., USA, March, 1981).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 460–467, May–June, 1982.     

SPSA vs Simplex in statistical machine translation optimization

Most statistical machine translation systems are combinations of various models and tuning scaling factors is an important step. However, this optimisation problem is hard because the objective function has many local minima and the available algorithms cannot achieve a global optimum. Consequently, optimisations starting from different initial settings can converge to fairly different solutions. We present tuning experiments with the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, and compare them with the widely used downhill simplex method. With IWSLT 2005 Chinese-English data, both methods showed similar performance, but SPSA was more robust to the choice of initial settings. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling composites on graphs,with parameter optimization

Composites have been modeled by means of graph theory and the concept of a dynamic interfacial layer on both sides of the filler-matrix boundary. Certain assumptions were made in order to eliminate the indeterminacy created by the use of models. The magnitude of the dynamic interfacial layer has been estimated for the fillers and the epoxy matrix. The calculations have been compared with experimental data.Moscow State Open University, Center for Composite Materials, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 467–479, July–August, 1996.     

Pre-commitment vs. time-consistent strategies for the generalized multi-period portfolio optimization with stochastic cash flows

In this paper, we propose a multi-period portfolio optimization model with stochastic cash flows. Under the mean–variance preference, we derive the pre-commitment and time-consistent investment strategies by applying the embedding scheme and backward induction approach, respectively. We show that the time-consistent strategy is identical to the optimal open-loop strategy. Also, under the exponential utility preference, we develop the optimal strategy for multi-period investment, which is time-consistent. We show that the above two time-consistent strategies are equivalent in some cases. We compare the pre-commitment and time-consistent strategies under different situations with some numerical simulations. The results indicate that the time-consistent strategy is more stable and secure than pre-commitment strategy under the generalized mean–variance criterion.