The application of self adjusting interfaces to the design of fibrous composites

In the case of orthodox fibre composite materials the mechanical properties of the interfaces are fixed at an almost constant level by a choice of materials and manufacturing techniques. In such systems semi-continuous reinforcing elements fail when the tensile strain in the composite becomes comparable with the failing strain of the fibres. It is shown that the reinforcing elements can be prevented from failing, whatever the tensile strain in the composite material, if the shear strength of the interface between the reinforcing elements and the rest of the composite structure is self adjusting and is reduced locally as the local tensile stress carried by a reinforcing element increases. The characteristics of experimental reinforcing elements possessing these features have been investigated and the properties of composites utilizing such fibres are discussed.     

Non destructive ultrasonic evaluation of fibrous metal matrix composites

An iterative numerical elastic constants optimization method associated to a classical ultrasonic immersion device is used for the entire characterization of two kinds of metal matrix composites. The usual methods of optimization are generally based on Newton's algorithm. Sometimes this algorithm converges towards relative minima that gives elastic constants which do not correspond to the physical reality of the material. As a remedy, we have developed a numerical analysis technique based on a different algorithm allowing a better convergence to the unique global solution. Using the Levenberg-Marquard algorithm, the methodology to recover the elastic constant, consists in minimizing the square deviation between calculated velocities and the experimental ones measured under variable incidence from a computer controlled ultrasonic immersion device.     

Effective elastoplastic properties of the periodic composites

The article presented deals with the homogenization of composite materials with elastoplastic constituents. The transformation field analysis (TFA) approach is presented and applied to compute the effective nonlinear behavior of multicomponent periodic composite structure. Computational implementation of the method consists in special utilization of the program ABAQUS, which makes it possible to homogenize n-component periodic composites with relatively general configuration of the periodicity cell. Numerical example of homogenization of a three-component periodic composite shows the comparison between the nonlinear behavior of a real composite and of a homogenized one in a specific boundary problem defined on its representative volume element (RVE).     

Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects

This work deals with the computational and experimental identification of two probabilistic models. The first one was recently proposed in the literature and provides a direct stochastic representation of the mesoscopic elasticity tensor random field for anisotropic microstructures. The second one, formulated in this paper, is associated to the volume fraction random field at the mesoscale of reinforced composites. After having defined the probabilistic models, we first address the question of the identification of the experimental trajectories of the random fields. For this purpose, we introduce a new methodology relying on the combination of a non destructive ultrasonic testing with an inverse micromechanical problem. The parameters involved in the probabilistic models are then identified and allows realizations of the random fields to be simulated by using Monte Carlo numerical simulations. A comparison between simulated and experimental results is provided and demonstrates the relevance of the identification strategy for the chaos coefficients involved in the second model. Finally, we illustrate the use of the first probabilistic model by performing a probabilistic parametric analysis of the RVE size of the considered microstructure.     

On the numerical implementation of a shear modified GTN damage model and its application to small punch test

Gurson-type models have been widely used to predict failure during sheet metal forming process. However, a significant limitation of the original GTN model is that it is unable to capture fracture under relatively low stress triaxiality. This paper focused on the fracture prediction under this circumstance, which means shear-dominated stress state. Recently, a phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed by Nahshon and Hutchinson. We further calibrated new parameters based on this model in 22MnB5 tensile process and developed the corresponding numerical implementation method. Lower stress triaxiality were realized by new-designed specimens. Subsequently, the related shear parameters were calibrated by means of reverse finite element method and the influences of new introduced parameters were also discussed. Finally, this shear modified model was utilized to model the small punch test (SPT) on 22MnB5 high strength steel. It is shown that the shear modification of GTN model is able to predict failure of sheet metal forming under wide range of stress state.     

On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J₂-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms.     

On the application of moment methods to electromagneticnondestructive evaluation

The application of moment methods (MMs) to eddy-current testing problems for nondestructive evaluation (NDE) is considered. A general formulation for the MM that can be used to analyze NDE problems is derived, and calculated results and experimental data obtained from eddy-current testing of an artificially made sample are presented. Good agreement between the calculated results and the experimental data confirms the validity of the method and shows that the MM can be used as an alternative to the finite-element method (FEM) and the boundary-element method (BEM) in NDE     

Prediction of the fracture toughness of fibrous composites

A statistical/micromechanical model is developed for the prediction of the fracture toughness of fibrous composites. The fracture resistance of the material is assumed to be related to the statistical distribution of the fiber pull-out length. The distribution of the fiber pull-out length is derived from the fiber strength distribution. The R-curve behavior of the fibrous composite is predicted and interpreted based on the present model. The limiting fracture toughness is predicted to be proportional to the square root of the ineffective length, or proportional to the square root of the fiber length if the fiber length is less than the ineffective length.     

Damage-based failure theory and its application to 2D-C/SiC composites

Damage evolution is of great importance to determine the final failure of ceramic matrix composites (CMCs). In order to characterize the damage coupling behavior and its effect on failure strength of CMCs, a new methodology for damage coupling analysis was formulated. And, new kind of damage-based failure criteria were established under plane stress state, including maximum damage criterion and quadratic damage criterion. Both the criteria require investigation upon the damage evolution laws. The proposed failure theory was applied to predict the coupled damage behavior and the off-axis strength of a 2D C/SiC composite. The theoretical results agree well with the experimental data.     

A numerical study of the cavity expansion process and its application to long-rod penetration mechanics

The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.     

Influence of random bridging on the elastic and elastoplastic properties of fiber-reinforced composites

Summary The overall elastic moduli and elastoplastic stress-strain relations of a fiber-reinforced composite containing either aligned or randomly oriented spheroidal voids are derived explicitly. The results are given in terms of the void shape and concentration, and for the elastic moduli the void shape is further pushed to the limit for cracked bodies. The present theory also corresponds to the condition of random bridging, with a longitudinal Young's modulus and axial shear modulus lying between those of full bridging and no bridging. Numerical results further indicate that both elastic and elastoplastic strength of the fiber-reinforced composite can be significantly weakened by the presence of both types of distribution, but the extent of stiffness or strength reduction is highly dependent upon the void shape and loading direction.     

Averaging of the magnetic properties of fibrous ferromagnetic composites

Within the framework of the model of regular structures, we average the magnetic properties of fibrous ferromagnetic composites with biperiodic structure. For the general case of packing of the fibers in any cross section, the problem is reduced to finding certain functionals determined from the solutions of a regular integral equation of the corresponding boundary-value problem of magnetostatics for the structure. For a special case of packing of the fibers with circular cross section, the solution is constructed in the form of a series in elliptic functions. As a result, we obtain approximate formulas for the macroparameters of the composites with perfect cells.     

Statistical issues in the fracture of brittle-matrix fibrous composites

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional sliding of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. First, we review the overall statistical features of the failure process, and identify certain issues in terms of critical geometric, statistical and mechanical parameters. This leads to two interesting cases, one where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider ‘characteristic’ bundles in the composite which capture essential features of the statistics of the failure process, and develop their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arrangement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section. This scale, though not precisely quantified, depends on such things as the stiffness of the matrix relative to the fibers, the volume fraction of the matrix and the spacing of periodic cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fracture as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experimental results.     

On the numerical treatment of the delamination problem in laminated composites under cleavage loading

A method for the effective numerical treatment of the delamination problem in laminated composites under cleavage loading is herein proposed. The interlaminar interface mechanical behaviour is described by means of the so-called complete laws which are non-monotone and possibly multivalued force/ displacement laws including jumps (or in general, decreasing branches) corresponding to the discontinuous strength reduction. These complete laws that take into account the development of delamination phenomena in a quasistatic way are derived by non-convex energy functions, called delamination superpotentials which in turn, lead to the formulation of the principle of virtual work for the laminated composite in a hemivariational inequality form and to the generalisation of the principle of minimum potential energy as a substationarity principle. Applying an appropriate finite element discretisation scheme to the laminated composite, the respective discrete problem is formulated which describes the response of the structure taking into account the development of the delamination phenomenon. The numerical treatment of the latter problem is successfully performed by applying a new algorithm that approximates the nonmonotone law by a sequence of monotone ones. The performed numerical applications presented in the last part of the paper and several analogous numerical experiments exhibit very good convergence properties.