Modeling of interfacial debonding crack in particle reinforced composites using Voronoi cell finite element method

In this paper, Voronoi cell finite element method (VCFEM), introduced by Ghosh and coworkers (1993), is applied to describe the matrix-inclusion interfacial debonding for particulate reinforced composites. In proposed VCFEM, the damage initiation is simulated by partly debonding of the interface under the assumption of the critical normal stress law, and gradual matrix-inclusion separations are simulated with an interface remeshing method that a critical interfacial node at the crack tip is replaced by a node pairs along the debonded matrix-inclusion interface and a more pair of nodes are needed to be added on the crack interface near the crack tip in order to better facilitate the free-traction boundary condition and the jumps of solution. The comparison of the results of proposed VCFEM and commercial finite element packages MARC and ABAQUS. Examples have been given for a single inclusion of gradually interfacial debonding and for a complex structure with 20 inclusions to describe the interfacial damage under plane stress conditions. Good agreements are obtained between the VCFEM and the general finite element method. It appears that this method is a more efficient way to deal with the interfacial damage of composite materials. The financial support by the Special Funds for the National Major Fundamental Research Projects G19990650 and the National Natural Science Foundation of China No. 59871022 are gratefully acknowledged.     

Strain energy-based homogenization of nonlinear elastic particulate composites

The macroscopic constitutive law for a heterogeneous solid containing two dissimilar nonlinear elastic phases undergoing finite deformation is obtained. Attention is restricted to the case of spherical symmetry such that only the materials consisting of an irregular suspension of perfectly spherical particles experiencing all-round uniform loading are considered which leads to a one-dimensional modeling. For the homogenization procedure, a strain-energy based scheme which utilizes Hashin’s composite sphere is employed to obtain the macroscopic stress-deformation relation added by the initial volume fraction of the particles. As applications of the procedure, the closed-form macroscopic stress expression for a generalized Carroll composite material is derived. Then, by choosing carbon black-filled rubbers, unknown bulk modulus of the carbon black particles is calculated. Finally, the particle-reinforced flexible polyurethane foam is studied using the Ritz method. It is shown that the analytical outcome for composites filled by compressible inclusions is applicable for porous materials with the same matrix.     

A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications

Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.     

Simulation of high velocity concrete fragmentation using SPH/MLSPH

The simulation of concrete fragmentation under explosive loading by a meshfree Lagrangian method, the smooth particle hydrodynamics method (SPH) is described. Two improvements regarding the completeness of the SPH‐method are examined, first a normalization developed by Johnson and Beissel (NSPH) and second a moving least square (MLS) approach as modified by Scheffer (MLSPH). The SPH‐Code is implemented in FORTRAN 90 and parallelized with MPI. A macroscopic constitutive law with isotropic damage for fracture and fragmentation for concrete is implemented in the SPH‐Code. It is shown that the SPH‐method is able to simulate the fracture and fragmentation of concrete slabs under contact detonation. The numerical results from the different SPH‐methods are compared with the data from tests. The good agreement between calculation and experiment suggests that the SPH‐program can predict the correct maximum pressure as well as the damage of the concrete slabs. Finally the fragment distributions of the tests and the numerical calculations are compared. Copyright © 2003 John Wiley & Sons, Ltd.     

An SPH shell formulation for plasticity and fracture analysis in explicit dynamics

This paper introduces a new modeling method suitable for the simulation of shell fracture under impact. This method relies on an entirely meshless approach based on the smoothed particle hydrodynamics (SPH) method. The paper also presents the SPH shell formulation being used as well as the different test cases used for its validation. A plasticity model of the global type throughout the thickness is also proposed and validated. Finally, in order to illustrate the capabilities of the method, fracture simulations using a simplified fracture criterion are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Strain sensing ability of metallic particulate reinforced cementitious composites: Experiments and microstructure-guided finite element modeling

This paper evaluates the capability of waste iron powder-reinforced cementitious matrices as self-sensing materials in lieu of more expensive carbon fiber and nanoparticle reinforced matrices. Electrical impedance spectroscopy coupled with equivalent circuit modeling is used to determine the bulk resistance of the composite beams containing up to 40% by volume of iron particulates under flexural loading. The fractional change in resistance and the gage factor, as functions of the applied stress, increases with increasing iron particulate content, demonstrating the ability of these composites in self-sensing. A microstructure-guided electro-mechanical finite element model is used to simulate the strain sensing response of these composites. The 2D microstructure is subjected to different applied tensile stresses, and the deformed geometry subjected to an electrical potential to simulate the change in resistance. Debonding at the inclusion-paste interface under load, which is found to significantly influence the fractional change in resistance, is accounted for by using a bilinear softening model. The model is found to correlate well with the experimental data, and has the potential to facilitate microstructural design of materials to achieve desired degrees of self-sensing.     

Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

SPH with the multiple boundary tangent method

In this article, we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics (SPH) method. Benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries. As well, current SPH boundary approaches do not properly treat curved boundaries in complicated flow domains. These drawbacks have been remedied in a new boundary treatment method presented in this article, called the multiple boundary tangent (MBT) approach. In this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions. The two benchmark problems chosen are the lid‐driven cavity problem, and flow over a cylinder. The SPH solutions using the MBT approach and the results from literature are in very good agreement. These solutions involved solid boundaries, but the approach presented herein should be extendable to time‐evolving, free‐surface boundaries. Copyright © 2008 John Wiley & Sons, Ltd.     

Introduction of damage evolution in a scale transition approach for highly-filled particulate composites

The present paper deals with a non-conventional scale transition for modelling the behaviour of highly-filled particulate composites, starting from a methodology initially proposed by Christoffersen [Christoffersen J. Bonded granulates. J Mech Phys Solids 1983;31:55–83] and recently extended by Nadot et al. [Nadot C, Dragon A, Trumel H, Fanget A. Damage modelling framework for viscoelastic particulate composites via a scale transition approach. J Theor Appl Mech 2006;44(3):553–83] in presence of damage. The model thus obtained is here completed with several ingredients allowing to describe damage evolution and in particular a defect nucleation criterion as well as a closure criterion. These criteria are formulated in terms of displacement, and so as to ensure continuity in terms of macroscopic stress. They are finally introduced in an iterative numerical solving procedure which allows to follow damage evolution as a discrete sequence of interfacial debonding including also eventual closure of defects.     

Micromechanical modelling of the transverse damage behaviour in fibre reinforced composites

A micromechanics damage model is presented which examines the effect of fibre-matrix debonding and thermal residual stress on the transverse damage behaviour of a unidirectional carbon fibre reinforced epoxy composite. It is found that for a weak fibre-matrix interface, the presence of thermal residual stress can induce damage prior to mechanical loading. However, for a strong fibre-matrix interface the presence of thermal residual stress is effective in suppressing fibre-matrix debonding and improving overall transverse strength by approximately 7%. The micromechanical model is subjected to a multiple loading cycle (i.e. tension-compression-tension), where it is shown to provide novel insight into the microscopic damage accumulation that forms prior to ultimate failure, clearly highlighting the different roles that fibre-matrix debonding and matrix plasticity play in forming the macroscopic response of the composite. Such information is vital to the development of accurate continuum damage models, which often smear these effects using non-physical material parameters.     

Effect of interface debonding on the thermal conductivity of microencapsulated-paraffin filled epoxy matrix composites

Microcapsules containing phase change materials (microPCMs) can be filled in polymeric matrix forming smart temperature-controlling composites. The aim of this study was to investigate the effect of interface debonding on the thermal conductivity of microPCMs containing paraffin/epoxy composites. The shell thickness and average size of microPCMs were controlled by regulating the core/shell ratios and emulsion stirring rates. Test results indicated that the thermal conductivity (K_e) of all composites decreased after a thermal shock treatment. SEM and thermography measurements were applied to observe the interface behaviors of composites after a violent thermal treatment process. It was proved that the interface debonding was generated because of the mismatch of expansion coefficient between shell and epoxy. A modeling analysis of the relative thermal conductivity (K_r) indicated that the effective approach to decrease the debonding is to enhance the molecule tangling degree between shell and matrix.     

Crack tip shielding in elastic particulate composites undergoing damage

A simple rate-independent phenomenological constitutive model is used to model fracture behavior in elastic particulate composites undergoing damage. The constitutive model consists of two damage functions that govern the degradation of the bulk and the shear moduli. The elastic modulus is assumed to reach a saturation level under uniaxial conditions. Using the path independence of the J-integral and the concept of cracktip shielding, the remote or the applied stress intensity K_∞ is related to the cracktip stress intensity factor K_t. The results from the model are used to predict the cracktip conditions in particulate composites undergoing damage. The model compares well with experimental results in predicting the crack opening profile as well as the displacement field in the vicinity of a cracktip.     

Optimizing the design of particulate composites for maximum fracture resistance through modeling

The failure modes of particulate reinforced metallic alloys are reviewed with special emphasis on in situ intermetallic particle reinforced niobium alloys, but information derived from ceramic reinforced aluminum alloys is also included. Constraint of plastic deformation by particles is emphasized as one of two very important factors in controlling fracture behavior. The other factor is particle fracture toughness. Models are proposed for describing the fracture toughness, from which several methods of enhancing toughness are envisioned. This modeling of fracture toughness is intended to help optimize the design and processing of these materials for enhanced fracture resistance. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling hysteresis behavior of cross-ply C/SiC ceramic matrix composites

In this paper, the loading/unloading tensile behavior of cross-ply C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of cross-ply ceranic matrix composites including the effect of matrix cracking has been developed. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length of different matrix cracking modes are obtained by the fracture mechanics approach. The hysteresis loops of cross-ply C/SiC ceramic matrix composites corresponding to different peak stresses have been predicted.     

颗粒增强镁基复合材料的研究现状及发展趋势

综述了颗粒增强镁基复合材料的研究概况,着重介绍了颗粒增强镁基复合材料的制备技术,界面行为和制备热力学与动力学三大研究热点,另外,对颗粒增强镁基复合材料的增强机理及常温力学性能作了简单介绍,最后,对颗粒增强镁基复合材料的研究方向进行了一些看法和展望,指出原位颗粒增强镁基复合材料的制备技术交城为制备镁基复合材料的发展趋势,镁基复合材料由于具有高的比强度,比模量和良好的耐磨性、耐高温性能和减震性能,在航空航天,特别是汽车工业具有在的应用前景和广阔的市场。     

Numerical analysis of thermoplastic composites laser welding using ray tracing method

Laser technology is a good alternative for continuous joining of thermoplastics composites structures. Presence of continuous fibers at a high fiber volume fraction (superior to 30%) does not allow using traditional development as for pure thermoplastic materials, due to the presence of fiber clusters or polymer rich areas. Those heterogeneities induce macroscopic light scattering through the structure, reducing the resulting energy level absorbed at the welding interface. The study proposed here takes into account the real microstructure of the composite in order to evaluate changes in local energy diffusion directly linked with local fiber arrangements. The objective of this work is to develop an affordable numerical simulation of the laser welding process modeled with adapted physics mechanism and taking into account the microstructure heterogeneity of the considered materials regarding optical and thermal properties. To model the optical path of the laser beam through the composite fibrous structure, a simulation tool based on geometrical optic is developed. Weldability is considered on composites with different thicknesses, showing the non linear relationship between welding energy and substrate thickness.     

Multi-scales modelling of dynamic behaviour for discontinuous fibre SMC composites

The requirements of passive security, notably in the transport industry, impose to maximize the dissipation of the energy and to minimize the decelerations undergone by a vehicle and thus passengers due to violent shocks (crash). This paper aims at establishing efficient expected answers towards the preoccupations mainly emanating from transport industry. Currently, the behaviour laws implemented in the dynamic explicit schemes (RADIOSS, PAM-CRASH and LS-DYNA) do not integrate sufficiently the physical aspects in the material degradation, mainly the damage process, their kinetics, the variability and especially the heterogeneity of the composite materials microstructure. This paper deals with the development of a multi-scale predictive model coupling specific experimental methodologies and the micromechanical formulation of damage mechanisms in order to build constitutive laws for discontinuous fibre reinforced composites materials. The developed micromechanical modelling is based on an experimental methodology conducted over a range of strain rates from quasi static to 250 s⁻¹. The latter has enabled identifying local probabilistic damage criterion formulated through the Weibull’s statistical integrating the strain rate effect and describing the progressive interfacial debonding under rapid loading. The developed model has been validated to predict the stiffness reduction and the overall elastic visco-damage behaviour for SMC composite material. The model simulations agree well with high speed tensile tests and confirm that the damage threshold and kinetic in the SMC are mainly strain rate sensitive.