Energy release rate and stress field calculation for debonding crack extension at the fibre-matrix interface during single-fibre pull-out

For the micromechanical modelling of the macroscopic failure of fibre-reinforced composites the formulation of a critical parameter for initiation and extension of debonding cracks at the fibre-matrix interface is essential. This point is discussed for the 'fibre pull-out' specimen, a test commonly used to measure the adhesion quality of fibre-matrix systems. Some of the simplifying assumptions fundamental to shear lag theory-based models of the fibre pull-out test are compared with results from a detailed finite element (FE) model to examine their validity. The FE model strongly contradicts assumptions made with the shear lag theory that the axial stress gradient in the matrix can be neglected from the equilibrium equation. A critical interface shear strength is commonly used as a measure of adhesion quality. But for elastic materials the nature of the stress concentrations at the fibre end and interface crack-tip are singular. Therefore a fracture mechanic approach is better suited for a debonding criterion than a simple finite shear strength. The energy release rate shows a minimum for short crack lengths and may stabilize the moving crack.     

Coupled mixed-mode cohesive zone modeling of interfacial debonding in simply supported plated beams

The development of predictive models for plate end debonding failures in beams strengthened with thin soffit plates is a topic of great practical relevance. After the early stress-based formulations, fracture mechanics approaches have become increasingly established. More recently, the cohesive zone (CZ) model has been successfully adopted as a bridge between the stress- and fracture mechanics-based treatments. However, the few studies of this nature propose complex formulations which can only be implemented numerically. To date, the only available analytical solution based on CZ modeling for the prediction of interfacial stresses/debonding in plated beams is limited to the determination of interfacial shear stresses and thus neglects the mixed-mode effects generated by the presence of interfacial normal stresses at the plate end. This paper presents a new analytical formulation based on the CZ modeling approach for the prediction of plate end debonding in plated beams. A key enhancement with respect to the previous solution is the use of a coupled mixed-mode CZ model, which enables a full account of mixed-mode effects at the plate end. The model describes the evolution of the interface after the end of the elastic regime, and predicts the value of the load at incipient debonding. The achievement of a closed-form solution for this quite complex case entails the introduction of a crucial simplifying assumption, as well as the ad hoc modeling of an effective cohesive interfacial response. The paper presents the analytical theory and compares its predictions with numerical and experimental results.     

Multiscale modeling of strain-hardening cementitious composites

This research involves the multiscale characterization of strain-hardening cementitious composites under tensile loading. The sensitivity of cracking behavior to fiber dispersion is studied using a special form of lattice model, in which each fiber is explicitly represented. It is shown that the nonlocal modeling of fiber bridging forces is essential for obtaining realistic patterns of crack development and strain-hardening behavior. Crack count and crack size are simulated for progressively larger levels of tensile strain. The influence of fiber dispersion is clearly evident: regions with significantly fewer fibers act as defects, reducing strength and strain capacity of the material.     

Numerical study of transitional brittle-to-ductile debonding of a capsule embedded in a matrix

This work presents a numerical study that addresses the role of the interfacial fracture energy on the debonding process of a capsule embedded in an elastic matrix, which undergoes a uniaxial far-field stress. The motivation of this work is to analyze and to understand the effects of this energy in the framework of the so-called encapsulation-based self-healing cementitious materials, where glass capsules filled with a fluid healing agent are embedded in a cement-based matrix. A two-dimensional plane strain model based on a combination of the classical finite element method and cohesive surface techniques implemented in the commercial code Abaqus^® has been used. It has been found that there exist three types of debonding regimes, ranging from a perfect brittle response up to a ductile-limited response, and whose range of validity is governed by a straightforward dimensionless number able to predict the type of debonding as a function of flexural properties of the capsule and the interface strength.     

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.     

Interfacial Debonding Around Rectangular Features in Multilayer Structures

This article describes a numerical approach for predicting debonding in multi-layers comprised of rectangular features of different sizes. A single global meshing strategy for finite element analysis is described that includes focused radial meshes at every material junction to accurately capture crack tip and material junction singularities. The strategy is designed to allow straightforward yet accurate calculations of energy release rates for steady-state interfacial debonding in complex architectures. Guidelines for meshing parameters (such as element density and distribution) are discussed on the basis of convergence studies of stress distributions along interface junctions, crack opening displacements and crack driving forces along interfaces. The utility of the approach is demonstrated via a study of debonding around rectangular inclusions, which illustrates relationships between energy release rates, inclusion aspect ratio and elastic mismatch. The paper concludes with an illustration of how interfacial debonding along finite-sized features can promote cracking in adjacent layers.     

Micromechanical analysis of transverse damage of fibre-reinforced composites

The mechanical behaviour of fibre-reinforced composites under transverse tension, compression and shear is studied using computational micromechanics. The representative volume element is constructed for fibre’s random distribution. The Drucker–Prager model and cohesive zone model are used to simulate the matrix damage and interfacial debonding, respectively. The stress distribution along the interface is studied using the model with only one fibre embedded in the matrix. It is found that the interface tensile failure at the equators of fibre firstly occurs under transverse tension; the interface shear failure firstly occurs under transverse compression; both the interface tensile failure and shear failure occur under transverse shear. The direction of fracture plane is perpendicular to the loading direction under transverse tension, 52.5° with the perpendicular direction under compression and 7.5° with the perpendicular or vertical direction under shear, respectively.     

Analysis of a partially debonded elliptic inhomogeneity in piezoelectric materials

A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroeiastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity , totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Conditions for Cracking and Debond Development at Partially Bonded Bimaterial Half-Planes

Fracture phenomena at the debond tip of partially bonded bimaterial half-planes subjected to concentrated normal forces, couples, and uniform tension are considered. The crack initiation conditions are described by the stress distribution before the initiation and the energy release rate of the crack immediately after the initiation. The debond development conditions are described by the stress distribution and the energy release rate of the debond before its initiation. When both the crack and the debond have chances to occur, or when cracks can arise in both the materials, the fracture phenomena are predicted by comparing the ratio of energy release rates and the ratio of fracture toughnesses.