Transverse Bundles Research Articles

Effect of nanoparticles on interfacial properties of carbon fibre–epoxy composites

This study assessed the effect of rigid nanoparticles on fibre–matrix adhesion in fibre-reinforced polymer composites by means of a transverse fibre bundle (TFB) test method with the fibre bundle transversely embedded in the middle of the TFB specimens. Fracture surfaces of the TFB specimens were examined by scanning electron microscopy and transmitting electron microscopy to identify dispersion and morphologies of nanoparticles on and near the fibre–matrix interfaces. A finite element analysis was conducted to identify the distribution and magnitude of the thermal residual stresses within the TFB specimen to correlate the TFB tensile strength with the fibre/matrix interfacial strength. The coefficient of thermal expansion and cure volume shrinkage of matrices with different amounts of nanosilca particles were experimentally evaluated and were included in the FE simulation. Results showed that the addition of nanosilica particles in the epoxy matrix did not noticeably affect the interfacial bonding behaviour between fibres and matrix.

Higher Order Transverse Bundles and Riemannian Foliations

The purpose of this paper is to prove that each of the following conditions is equivalent to that the foliation ${\cal F}$ is riemannian: 1) the lifted foliation ${\cal F}^{r}$ on the $r$-transverse bundle $\nu ^{r}{\cal F}$ is riemannian for an $r\geq 1$; 2) the foliation ${\cal F}_{0}^{r}$ on a slashed $\nu_{\ast}^{r}{\cal F}$ is riemannian and vertically exact for an $r\geq 1$; 3) there is a positively admissible transverse lagrangian on a $\nu_{\ast}^{r}{\cal F}$, for an $r\geq 1$. Analogous results have been proved previously for normal jet vector bundles.

Stochastic analysis of fibre volume fraction and permeability in fibre bundles with random filament arrangement

For fibre bundles with non-uniformly distributed filaments, probabilities for the occurrence of defined local filament arrangements, determining geometrical constants for permeability calculation, were described as functions of the local fibre volume fraction. Because of changing inter-filament gap geometries, the local transverse permeability decreases discontinuously with increasing local fibre volume fraction, while the local axial permeability decreases continuously. Axial bundle permeabilities, derived from log-normally distributed local permeabilities, tend to be higher than predictions for uniform filament arrangements, while transverse bundle permeabilities tend to be lower. This implies that assuming uniformity of filament arrangements is inappropriate for realistic modelling of bundle properties. For fibre bundles with rectangular cross-section, the transverse permeability decreases in width-direction and increases in thickness-direction with increasing aspect ratio of the bundle cross-section, while the axial permeability is not affected. This is of high practical relevance, in particular for spread-tow reinforcements with high aspect ratios.

Intravital and In Vitro Time-Lapse Imaging Reveals Microtubule Dynamics in Skeletal Muscle Fibers

Microtubules (MTs) play an essential role in dynamic cell processes but they also play a mechanical role, buttressing cells against compressive forces. Both roles may be especially important in the very large skeletal muscle fibers; it has recently been shown that microtubules are part of the pathology of Duchenne Muscular Dystrophy. However, the organization of microtubules in muscle fibers is poorly understood. They do not resemble the microtubule asters of proliferating cells; instead they form complex three-dimensional networks without clear organizing centers (MTOC). Imunofluorescence with anti-tubulin or anti-EB3 (microtubule plus-end marker) does not suggest a dynamic behavior.To understand how muscle microtubules are organized, we have expressed GFP-tubulin and EB3-GFP in the mouse footpad Flexor Digitorum Brevis (FDB) muscle. Time-lapse sequences were recorded from single FDB fibers plated on dishes, and from the intact muscle intravitally. Both approaches showed dynamic EB3 spots (8 and 4 micrometer/min respectively, not significantly different) and a predominantly stable tubulin network. Simultaneous observation of mCherry-tubulin and EB3-GFP indicated that EB3 moves along tracks of stable microtubules. Super-resolution microscopy confirmed that muscle microtubules include longitudinal and transverse bundles. Observation of recovering microtubules after nocodazole treatment shows that they originate from nuclear membranes and from cytoplasmic Golgi elements (50%) both of which show the MTOC protein pericentrin. The tools developed have allowed us to see for the first time how microtubules form and move in live muscle fibers and provide a platform for exploring the role of microtubules in muscle and the consequences of their defects in muscle diseases.

Three-dimensional stress analysis of cracked satin woven carbon fiber reinforced/polymer composites under tension at cryogenic temperatures

We present a thermo-mechanical stress analysis for five harness satin (5HS) woven carbon fiber reinforced polymer (CFRP) composite laminates with cracks under tension at cryogenic temperatures. The three-dimensional finite element model assumes the cracks to be located in the transverse fiber bundles and to span the thickness of the fiber bundles. Numerical calculations are carried out, and the Young’s modulus and stress distributions near the crack fronts for two-layer and infinite-layer woven composite laminates are obtained and shown in graphical form. Results of this analysis demonstrate the effects of the residual thermal stresses and cracks on the mechanical behavior.

A vanishing result for the Spin c Dirac operator defined along the leaves of a foliation

In the setting of a closed Riemannian manifold endowed with a smooth, non-necessarily integrable distribution, we extend a Lichnerowicz type formula which is known to work in the particular case of a transverse bundle associated to a Riemannian foliation. Interesting settings in which non-integrable distributions appear naturally are emphasized. As an application, we consider the distribution as being even dimensional and integrable; we consider also a hermitian line bundle, with a hermitian connection, such that the induced curvature tensor is non-degenerate, and an arbitrary hermitian bundle endowed also with a hermitian connection. Taking the k power of the line bundle and canonically constructing a Spinc Dirac operator defined along the leaves of the foliation generated by the distribution, we prove a vanishing result for the half kernel of this operator.

Interlaminar Fracture Toughness of 5 Harness Satin Woven Fabric Carbon Fiber/Epoxy Composites

This paper presents experimentally obtained results of mode-I and mode-II interlaminar fracture toughness (G IC and G IIC) of unidirectional and 5 harness satin (5HS) woven fabric carbon fiber/epoxy composites (CFRPs). The mode-I delamination resistance of 5HS specimens, which was evaluated using a double cantilever beam (DCB) method, depends on the weave pattern and the ply stacking sequence at the delamination growth plane. Higher toughness was observed for crack propagation between surfaces with more transverse bundles (L–T and T–T plane) than those with more longitudinal bundles (L–L plane) because of transverse tow delamination pinning the crack and causing it to arrest. The intrinsic mode-I fracture toughness values of the 0°/0°, 0°/90° and 90°/90° fiber combinations were estimated from the G IC values obtained from three kinds of 5HS specimens which have different mid-plane stacking patterns (L–L, L–T and T–T). The G IC of 0°/0° combination corresponded to that of unidirectional specimen. The G IC of 0°/90° combination was almost identical to that of 90°/90° combination. Results suggest that the interlaminar fracture toughness of woven fabric composites can be estimated from the G IC of 0°/0° and 0°/90° (or 90°/90°) combinations.

Experimental Research on the Permanent Prestress of Transverse Prestressing Bundle for the Xiangjiang Yinpenling Bridge

In order to assess the service states of the permanent prestress of transverse prestressing bundle for the Xiangjiang Yinpenling Bridge (XYB), the permanent prestress values are measured. Appearance census of the diseases of transverse prestressing bundles for the cable-stayed part, the east and west incremental launching girder parts of the XYB are carried out. Three transverse prestressing bundles of the most serious corrosion are investigated by windowing damage inspection. The measured results and the analysis of the permanent prestress for the XYB show that the average permanent prestress of the three transverse prestressing bundles is about 300MPa to 550MPa, which do not meet the requirements of the design tension stress. It suggests that the appropriate treatment measures should be taken.

Microscale experimental investigation of failure mechanisms in off-axis woven laminates at elevated temperatures

Off-axis woven laminates fabricated from carbon fiber and a high glass transition temperature thermosetting resin were subjected to tensile static and fatigue loading at temperatures ranging from room temperature up to 205 °C. The damage mechanism prevalent to these specimens was investigated by post-mortem examination using a scanning electron microscope. During most of their life fatigue specimens had accumulated minimal damage which consisted of matrix cracks, transverse bundle cracks and intra-ply delamination. Just before failure fiber bundles began to straighten out and rotate towards the loading direction. This behavior led to large elongation and necking of the specimens before fracture. Overall, the matrix-dominated material behavior and fiber reorientation due to the off-axis configuration had a far greater influence on the fracture morphology than the gradual accumulation of damage due to fatigue loading. It was also found that damage formation was strongly influenced by the type of applied loading and the test temperature.

Divisibility of multilinear mappings with applications to affine differential geometry

For real finite-dimensional vector spaces V, W we call a bilinear symmetric mapping h : V × V → W non-degenerate if the components of h with respect to a certain basis are linearly independent and non-degenerate. We say that a symmetric trilinear mapping C : V × V × V → W is divisible by h if there exists a linear form α such that C(v, v, v) = α(v)h(v, v) for every v ∈ V. In affine differential geometry of affine immersions h is the second fundamental form and C – the cubic form of the immersion. The immersion has pointwise planar normal sections if h(v, v) ∧ C(v, v, v) = 0 for every tangent vector v. We prove that it implies that C is divisible by h if h is non-degenerate and the codimension is greater than two. For immersions with Wiehe's or Sasaki's choice of transversal bundles divisibility of C by h implies vanishing of C.

Nerve terminal distribution in the human tongue intrinsic muscles: An immunohistochemical study using midterm fetuses

Intrinsic tongue muscles, especially the transverse and vertical (T&V) muscles, regulate the shape of the tongue. However, little information is available on the nerve distribution pattern in human T&V muscles. Using S100 protein immunohistochemistry for paraffin-embedded histology, we investigated semiserial sagittal or frontal sections of eight human fetal tongues (180-240 mm crown-rump length: CRL). The height of the T&V muscle bundle showed a threefold difference between specimens with a small and a large CRL. Thus, the T&V muscles were still growing at the stages examined. In the intrinsic longitudinal muscles and all extrinsic tongue muscles, we observed the typical motor endplate band. In lower-magnification views, the T&V muscles also appeared to carry the band in the lateral part of the tongue, where the genioglossus muscle fibers did not cross these muscles. However, in higher magnification views, the nerve terminal distribution in the T&V muscles showed a unique rule: the nerve terminal for the transverse muscle bundle was located distantly from that of the adjacent vertical muscle bundle. This pattern seemed to be established during the stages examined. To provide such "distantly separated nerve terminals," thin nerve twigs took a highly curved course oblique to the T&V muscle bundles. We hypothesize that the unique nerve course and terminal distribution in the T&V muscles are a result of sorting to provide a good functional match between the nerve fiber and the muscle bundle. After sorting, the T&V muscle cells may initiate proliferation to increase the muscle bundle.

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V k to a decreasing family of k foliations F i on a manifold M . We have shown that there exists a ( 1 , 1 ) tensor J of V k such that J k ≠ 0 , J k + 1 = 0 and we defined by L J ( V k ) the Lie Algebra of vector fields X on V k such that, for each vector field Y on V k , [ X , J Y ] = J [ X , Y ] . In this note, we study the first Chevalley–Eilenberg Cohomology Group, i.e. the quotient space of derivations of L J ( V k ) by the subspace of inner derivations, denoted by H 1 ( L J ( V k ) ) .

Affine planar geodesic immersions with maximal codimension

This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given: The affine immersions with pointwise planar normal sections (with respect to the equiaffine transversal bundle) are parallel. This result is verified for surfaces in ℝ4 and for immersions with the maximal codimension.

On purely real surfaces in Kaehler surfaces

An immersion \phi colon M to \tilde M^2 of a surface M into a Kaehler surface is called purely real if the complex structure J on \tilde M^2 carries the tangent bundle of M into a transversal bundle. In the first part of this article, we prove that the equation of Ricci is a consequence of the equations of Gauss and Codazzi for purely real surfaces in any Kaehler surface. In the second part, we obtain a necessary condition for a purely real surface in a complex space form to be minimal. Several applications of this condition are provided. In the last part, we establish a general optimal inequality for purely real surfaces in complex space forms. We also obtain three classification theorems for purely real surfaces in C^2 which satisfy the equality case of the inequality.

131 極低温におけるき裂を有する多層朱子織炭素繊維強化プラスチック積層材料の特異応力場(材料力学I,一般講演)

The objective of this research is to analyze the singular stresses at the tips of cracks in multi-layer woven carbon fiber reinforced polymer (CFRP) composite laminates under tension at cryogenic temperatures. It is assumed that cracks appear in the transverse fiber bundles. We consider both cases where the tips of the cracks are located in the fiber bundles or at the interfaces between two fiber bundles. The generalized plane strain finite element analysis is carried out for the cracked woven CFRP laminates. Numerical results are expressed in terms of the stress intensity factor, and discussed in detail.

Lie algebra on the transverse bundle of a decreasing family of foliations

J. Lehmann-Lejeune in [J. Lehmann-Lejeune, Cohomologies sur le fibré transverse à un feuilletage, C.R.A.S. Paris 295 (1982), 495–498] defined on the transverse bundle V to a foliation on a manifold M, a zero-deformable structure J such that J 2 = 0 and for every pair of vector fields X , Y on M: [ J X , J Y ] − J [ J X , Y ] − J [ X , J Y ] + J 2 [ X , Y ] = 0 . For every open set Ω of V, J. Lehmann-Lejeune studied the Lie Algebra L J ( Ω ) of vector fields X defined on Ω such that the Lie derivative L ( X ) J is equal to zero i.e., for each vector field Y on Ω : [ X , J Y ] = J [ X , Y ] and showed that for every vector field X on Ω such that X ∈ K e r J , we can write X = ∑ [ Y , Z ] where ∑ is a finite sum and Y , Z belongs to L J ( Ω ) ∩ ( K e r J | Ω ) . In this note, we study a generalization for a decreasing family of foliations.

Purely Real Surfaces in Non-Flat Complex Space Forms Satisfying a Basic Equality

An isometric immersion $$\phi : M \rightarrow \tilde{M}$$ of a manifold M into a Kahler manifold is called purely real if the complex structure J on $$\tilde{M}$$ carries the tangent bundle of M into a transversal bundle. In an earlier article, the first author discovered a general optimal inequality for purely real surfaces in a complex space form $$\tilde{M}^{2}(4\varepsilon)$$ . He also studied purely real surfaces in C2 satisfying the equality case of the inequality and obtained some classification theorems. In this article, we classify three families of purely real surfaces in non-flat complex space forms $$\tilde M^{2}(4\varepsilon)$$ which satisfy the equality case of the inequality.

Assessment of interfacial bonding between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests

Two experimental approaches were employed to assess the fibre/matrix adhesion between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests. The first approach was to measure interfacial bonding strength of the fibre/matrix interface in dog-bone-shaped tensile specimens by applying normal stress until failure, simulating the Mode I failure mode. The second approach was to determine the fibre/epoxy interfacial bonding strength in shear (simulating the Mode II failure mode) by means of a V-notched beam shear testing method, i.e. a modified Iosipescu test. In both methods, polymer threads were transversely incorporated in the middle section of the specimens. It was found that both methods were simple, reliable, and sensitive to changes in the fibre/matrix adhesion conditions, though interpretation of the test results was somewhat complex. The two experimental approaches were able to produce consistent results and can thus be adopted as alternative methods for determining the interfacial bonding properties between fibres and matrix in composite systems where conventional micro-mechanical or macro-mechanical testing methods cannot be used.

Thermal-mechanical Analysis of Satin Weave CFRP Composites with Cracks at Cryogenic Temperatures

This study deals with the thermal-mechanical behavior of satin weave carbon fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties under tension at cryogenic temperatures. Cracks are assumed to be located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. Young's modulus and stress distributions near the crack tip under combined mechanical and thermal loads are predicted by finite element models that assume generalized plane strain. The effects of residual thermal stresses and cracks on the mechanical behavior of CFRP woven laminates at cryogenic temperatures are calculated, and the numerical results are presented in graphical form.

OS0621 デジタル画像処理技術を用いた複合材料の非接触ひずみ分布計測事例(先進複合材料の強度・特性評価,オーガナイズドセッション)

A non-contact strain field measurement method using advanced digital images correlation technique has been developed by modification of the classical grating method. In this study, the strain mapping method has been applied to quantify 3D deformations of the surface of woven fabric composites subjected to a tensile loading. The out-of-plane deformation was locally developed by weave pattem in a single layer woven composite. Higher strains was also located in the matrix areas between the longitudinal fiber and transverse fiber bundles and in the area occupied by the transverse fiber bundles. It was obvious that the output of this method gives us detailed information on the unit cell level of textile composites, necessary to understand their deformation behavior, stress concentrations and damage occurrence. To conclude strain filed measurement technique is very useful for understanding the failure mechanism for geometrical defects in textile based composites.