Mode I,mode II,and mixed-mode I/II interlaminar fracture toughness of GFRP influenced by fiber surface treatment

The interlaminar fracture behavior of unidirectional glass fiber reinforced composites with fiber surface treatment has been investigated in modes I and II and for fixed mode I to mode II ratio of 1.33. The data obtained from these tests have been analyzed by using different analytical approaches. The present investigation is focused on the influence of the glass fiber surface treatment on the interlaminar fracture toughness of unidirectional laminates. Glass fibers with two different fiber surface treatments have been investigated. fiber surface treatment was carried out by using a polyethylene or silane coupling agent in combination with modifying agents. The glass fibers were embedded in the brittle epoxy matrix. Mode I, mode II, and mixed-mode I/II tests were performed in order to determine critical strain energy release rates. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode flexure (MMF) specimens were used. For both types of fiber surface treatment about the same values of mode I initiation fracture toughness G_IC ^init were obtained. It was observed that in mode I interlaminar crack growth in the DCB test for the composite sized by polyethylene, the crack propagation is accompanied by extensive fiber bridging. For both fiber surface treatments interlaminar fracture toughness increases considerably with increasing of crack length. For the fiber surface treatment with the silane coupling agent, the value of mode II initiation fracture toughness G_IIC ^init was about 2.5-times higher in comparison with that of a composite sized by polyethylene. For both types of fiber surface treatments the mixed-mode I/II test has shown a similar behavior to the mode I DCB test.     

Interlaminar fracture of multidirectional glass/epoxy laminates under mixed-mode I + II loading

The mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated. Mixed-mode bending (MMB) tests were performed on specimens with delaminations in 0/θ-type interfaces, with θ varying from 0 to 90°. Preliminary three-dimensional finite-element analyses validated the beam theory model (BTM) used for analysing experimental data. The compliances measured are in a good agreement with BTM predictions. The total critical energy release rate G_c varies linearly with the mode II ratio G_II/G, although some discrepancies are observed in the high-mode II results for the 0/45 and 0/90 specimens. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 349–366, May–June, 2007.     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Carbon-Fiber-Reinforced Plastics Based on an Imide Polymerizing Oligomer Binder with a Semi-Interpenetrating Structure

Semi-interpenetrating polymer networks (SIPNs) are synthesized based on a polyimide binder (imide polymerizing oligomer) with addition of polyamide acid. As acylating agents, they include derivatives of benzophenone-tetracarboxylic and diphenyloxide-tetracarboxylic acids and as aminocomponents - diaminodiphenylmethane, diaminodiphenyloxide, and metaphenylene diamine. It is shown that these systems form SIPNs of the snake-in-the-cage type. Uncured compositions forming melts at 300-330°C are used as binders for carbon-fiber-reinforced plastics (CFRP). The homophase structure of the SIPNs in CFRP is shown by dynamic mechanical tests. The interlaminar fracture toughness (G _1c) is measured by the method of a double cantilever beam. It is found that G _1c, as a function of the content (wt.%) of polyamid acid (PAA) in the initial composition used for obtaining CFRP, is of linear character, which is another confirmation of the homophase structure of the SIPNs. The interlaminar fracture toughness achieved for CFRP is 340 J/m² at a 30% PAA content in the initial composition, and the glass transition temperature, which determines the thermal stability of the composites, reaches 320°C. The prospects of employing these plastics in tribotechnics are discussed.     

Fracture mechanics analysis of debond growth in a single-fiber composite under cyclic loading

A model is developed to analyze the growth of a fiber/matrix debond along a broken fiber interface in a single-fiber composite subjected to tension-tension fatigue. The Paris law expressed in terms of debond growth and strain energy release rates is used. An analytical solution for the Mode II energy release rate G _II is obtained for long debonds, where the interface crack growth is self-similar. For short debonds, the interface crack interacts with the fiber break, and therefore a FEM modeling in combination with the virtual crack closure technique was performed to calculate the increase in G _II . Finally, the calculated G _II dependences are summarized in simple expressions that are used to simulate the debond growth in fatigue. A parametric study of the effect of Paris law parameters on the debond growth is performed.     

<Emphasis Type="Italic">p</Emphasis>-Geodesic transformations and their groups in second-order tangent bundles induced by concircular transformations of bases

We investigate the flattening properties of the Lie group G _r ^II of transformations of a second-order tangent bundle T ²(M) equipped with the lift ∇ ^II of an affine connection ∇ and the lift g ^II of a metric g on the base of M induced by the Lie group G _r of concircular transformations of the base of M. The obtained results reveal certain geometric features of the induced group G _r ^II within the framework of the theory of p-geodesic mappings.     

Mixed ramsey numbers: Chromatic numbers versus graphs

For positive integers n₁, n₂, …, n_I and graphs G_I+1, G_I+2, …, G_k, 1 ≤ / < k, the mixed Ramsey number _χ(n₁, …, n₁, G_I+1, …, G_k) is define as the least positive integer p such that for each factorization K_p = F₁⊕ … ⊕ F_⊕ F_I+1⊕ … ⊕ F_k, it it follows that χ(F_i) ≥ n_i for some i, 1 ? i ? l, or G_i is a subgraph of F_i for some i, l < i ? k. Formulas are presented for maxed Ramsey numbers in which the graphs G_I+1, G_I+2, …, G_k are connected, and in which k = I+1 and G_I+1 is arbitray.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

AlgebraicK-theory of von Neumann algebras

To every von Neumann algebra, one can associate a (multiplicative) determinant defined on the invertible elements of the algebra with range a subgroup of the Abelian group of the invertible elements of the center of the von Neumann algebra. This determinant is a normalization of the usual determinant for finite von Neumann algebras of type I, for the type II₁-case it is the Fuglede-Kadison determinant, and for properly infinite von Neumann algebras the determinant is constant equal to 1. It is proved that every invertible element of determinant 1 is a product of a finite number of commutators. This extends a result of T. Fack and P. de la Harpe for II₁-factors. As a corollary, it follows that the determinant induces an injection from the algebraicK ₁-group of the von Neumann algebra into the Abelian group of the invertible elements of the center. Its image is described. Another group,K ₁ ^w (A), which is generated by elements in matrix algebras overA that induce injective right multiplication maps, is also computed. We use the Fuglede-Kadison determinant to detect elements in the Whitehead group Wh(G).Partially supported by NSF Grant DMS-9103327.     

On Edge Singularity and Eigenvectors of Mixed Graphs

Let G be a mixed glaph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L（G） of G. As L（G） is positive semidefinite, the singularity of L（G） is determined by its least eigenvalue λ1 （G）. This paper introduces a new parameter edge singularity εs（G） that reflects the singularity of L（G）, which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs（G） and λ1 （G） （and other parameters） of G. In the case of εs（G） = 1, we obtain a property on the structure of the eigenvectors of G corresponding to λ1 （G）, which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.     

An inner amenable group whose von Neumann algebra does not have property Gamma

We construct inner amenable groups G with infinite conjugacy classes and such that the associated II₁ factor has no non-trivial asymptotically central elements, i.e. does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.     

Fractal materials, beams, and fracture mechanics

Continuing in the vein of a recently developed generalization of continuum thermomechanics, in this paper we extend fracture mechanics and beam mechanics to materials described by fractional integrals involving D, d and R. By introducing a product measure instead of a Riesz measure, so as to ensure that the mechanical approach to continuum mechanics is consistent with the energetic approach, specific forms of continuum-type equations are derived. On this basis we study the energy aspects of fracture and, as an example, a Timoshenko beam made of a fractal material; the local form of elastodynamic equations of that beam is derived. In particular, we review the crack driving force G stemming from the Griffith fracture criterion in fractal media, considering either dead-load or fixed-grip conditions and the effects of ensemble averaging over random fractal materials.     

Relatively thin and sparse subsets of groups

Let G be a group with identity e and let I \mathcal{I} be a left-invariant ideal in the Boolean algebra P_G {\mathcal{P}_G} of all subsets of G. A subset A of G is called I \mathcal{I} -thin if gA ?A ? I gA \cap A \in \mathcal{I} for every g ∈ G\{e}. A subset A of G is called I \mathcal{I} -sparse if, for T every infinite subset S of G, there exists a finite subset F ⊂ S such that ?_{g ? F} gA ? F \bigcap\nolimits_{g \in F} {gA \in \mathcal{F}} . An ideal I \mathcal{I} is said to be thin-complete (sparse-complete) if every I \mathcal{I} -thin (I \mathcal{I} -sparse) subset of G belongs to I \mathcal{I} . We define and describe the thin-completion and the sparse-completion of an ideal in P_G {\mathcal{P}_G} .     

A note on the monotonicity of mixed Ramsey numbers

For two graphs, G and H, an edge coloring of a complete graph is (G,H)-good if there is no monochromatic subgraph isomorphic to G and no rainbow subgraph isomorphic to H in this coloring. The set of numbers of colors used by (G,H)-good colorings of K_n is called a mixed Ramsey spectrum. This note addresses a fundamental question of whether the spectrum is an interval. It is shown that the answer is “yes” if G is not a star and H does not contain a pendant edge.     

Cohen-macaulay bipartite graphs

Let G be a graph on the vertex set V={x ₁, ..., x _n}. Let k be a field and let R be the polynomial ring k[x ₁, ..., x _n]. The graph ideal I(G), associated to G, is the ideal of R generated by the set of square-free monomials x _ix_j so that x _i, is adjacent to x _j. The graph G is Cohen-Macaulay over k if R/I(G) is a Cohen-Macaulay ring. Let G be a Cohen-Macaulay bipartite graph. The main result of this paper shows that G{v} is Cohen-Macaulay for some vertex v in G. Then as a consequence it is shown that the Reisner-Stanley simplicial complex of I(G) is shellable. An example of N. Terai is presented showing these results fail for Cohen-Macaulay non bipartite graphs. Partially supported by COFAA-IPN, CONACyT and SNI, México.     

G-Identities of Nilpotent Groups. I

The structure of a group V _n,red(G) of reduced G-identities of rank n is treated subject to the condition that G is a nilpotent group of class 1 or 2. The results obtained allow us to settle the question of whether a G-variety G-var(G) generated by a nilpotent group G of class 2 is finitely based. Moreover, we introduce the concepts of a d-commutator subgroup and of a main d-group, associated with G.     

Embeddings of bipartite graphs

If G is a bipartite graph with bipartition A, B then let G_m,n(A, B) be obtained from G by replacing each vertex a of A by an independent set a₁, …, a_m, each vertex b of B by an independent set b₁,…, b_n, and each edge ab of G by the complete bipartite graph with edges a_ib_j (1 ≤ i ≤ m and 1 ≤ j ≤ n). Whenever G has certain types of spanning forests, then cellular embeddings of G in surfaces S may be lifted to embeddings of G_m,n(A, B) having faces of the same sizes as those of G in S. These results are proved by the technique of “excess-current graphs.” They include new genus embeddings for a large class of bipartite graphs.     

A New Construction for Cohen–Macaulay Graphs

Let G be a finite simple graph on a vertex set V(G) = {x ₁₁,…, x _n1}. Also let m ₁,…, m _n  ≥ 2 be integers and G ₁,…, G _n be connected simple graphs on the vertex sets V(G _i ) = {x _i1,…, x _{im i} }. In this article, we provide necessary and sufficient conditions on G ₁,…, G _n for which the graph obtained by attaching the G _i to G is unmixed or vertex decomposable. Then we characterize Cohen–Macaulay and sequentially Cohen–Macaulay graphs obtained by attaching the cycle graphs or connected chordal graphs to arbitrary graphs.