Effect of elastic–plastic matrix on thermo-mechanical response of continuous anisotropic fiber-reinforced composites

Based on a concentric cylinder model, the analytical elastic–plastic solution of deformations and stresses for the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers subjected to axisymmetric thermo-mechanical loading is developed. How the plasticity, volume fraction, physical and mechanical properties of the matrix affect the elastic–plastic thermo-mechanical response of the composites is investigated. The plasticity of the matrix decreases greatly the axial compressive stress in the matrix, but more noticeably increases the axial compressive stress in the fiber. For the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers, decreasing the volume fraction, thermal expansion coefficient and Young's modulus, and increasing the yield stress and hardening parameter of the matrix can lower the maximum equivalent stress of the fiber. However, increasing the yield stress and hardening parameter of the matrix raises the maximum equivalent stress of the matrix.     

Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression

The mechanical behavior of unidirectional fiber-reinforced polymer composites subjected to tension and compression perpendicular to the fibers is studied using computational micromechanics. The representative volume element of the composite microstructure with random fiber distribution is generated, and the two dominant damage mechanisms experimentally observed – matrix plastic deformation and interfacial debonding – are included in the simulation by the extended Drucker–Prager model and cohesive zone model respectively. Progressive failure procedure for both the matrix and interface is incorporated in the simulation, and ductile criterion is used to predict the damage initiation of the matrix taking into account its sensitivity to triaxial stress state. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the tension fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation, while the compression failure is dominated by matrix plastic damage. And then the effects of interfacial properties on the damage behavior of the composites are assessed. It is found that the interfacial stiffness and fracture energy have relatively smaller influence on the mechanical behavior of composites, while the influence of interfacial strength is significant.     

A continuum elastic–plastic model for woven-fabric/polymer-matrix composite materials under biaxial stresses

In this study a simple continuum model for the macro-mechanical prediction of the elastic–plastic behavior of woven-fabric/polymer-matrix composites has been proposed. This model uses a scalar hardening parameter (which is a function of the current applied stress state) instead of an effective stress-strain relation to determine plastic strain increments. For simplicity, the stresses are expressed as invariants based on the material symmetry. It has been shown, by the use of experimental data for two different woven-fabric/polymer-matrix composite materials, that the newly proposed model accurately describes the non-linear mechanical behavior for different in-plane biaxial stress states ranging from pure shear to pure tension.     

Thermomechanical analysis of elastic–plastic fibrous composites comprising an inhomogeneous interphase

An analytical approach is presented to investigate thermomechanical response of composites consisting of a transversely isotropic fiber, an inhomogeneous interphase and an elastic–plastic matrix. Using the existing cubic variation to describe the continuous change of the material properties of the interphase and dividing the interphase into a number of subdomains, the continuously varying material properties of the interphase are approximated by the constant ones of these subdomains, and the deformations and stresses of the interphase are described with the same formulae as those of transversely isotropic fibers. The analytical expressions of elastic–plastic deformations and stresses of the matrix are obtained from the basic equations of axisymmetric problems in elasticity, the assumption of generalized plane strain, the linear strain–hardening stress–plastic strain relation, Tresca’s yield condition, the associated flow rule and impressibility of plastic deformation. The boundary conditions of the composites and the continuities of the radial displacement and stress between different components are used to determine all the unknown constants and the obtained analytical solution is applied to thermomechanical analysis of the composites. The effects of the inhomogeneity of the interphase, and the plasticity and material properties of the matrix on the thermomechanical response of the composites are investigated.     

Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments

A combined experimental and numerical study has been carried out in order to study the mechanism of initial failure in transversely loaded CF/epoxy composites. Two composites with a high and a low temperature-curing matrix were investigated. Three point bending experiments on macroscopic composite specimen with special laminate lay-ups were carried out in a scanning electron microscope (SEM). The in-situ experiments allow observing the onset of microscopic composite failure under transverse loading and measurement of the macroscopic applied load at onset of failure. The experimental results show that interfacial failure was the dominating failure mechanism for both materials. For the same carbon fiber with the same treatment the interfacial failure was adhesive (weak interface) or cohesive (strong interface), depending on the matrix system. The interfacial stresses at initiation of failure were determined successfully by a non-linear micro/macro FE-analysis and compared with experimental results obtained from micro composite test. The results show that the interfacial normal strength (INS) governs failure under transverse loads.     

An enhanced FEM model for particle size dependent flow strengthening and interface damage in particle reinforced metal matrix composites

By incorporating the dislocation punched zone model, the Taylor-based nonlocal theory of plasticity, and the cohesive zone model into the axisymmetric unit cell model, an enhanced FEM model is proposed in this paper to investigate the particle size dependent flow strengthening and interface damage in the particle reinforced metal matrix composites. The dislocation punched zone around a particle in the composite matrix is defined to consider the effect of geometrically necessary dislocations developed through a mismatch in the coefficients of the thermal expansion. The Taylor-based nonlocal theory of plasticity is applied to account for the effect of plastic strain gradient which produces geometrically necessary dislocations due to the geometrical mismatch between the matrix and the particle. The cohesive zone model is used to consider the effect of interfacial debonding. Lloyd’s experimental data are used to verify this enhanced FEM model. In order to demonstrate flow strengthening mechanisms of the present model, we present the computational results of other different models and evaluate the strengthening effects of those models by comparison. Finally, the limitations of present model are pointed out for further development.     

Mechanical properties and toughening mechanisms of polypropylene/barium sulfate composites

The effect of interfacial interaction on the mechanical performance of a group of polypropylene (PP)/barium sulfate (BaSO₄) composites were studied. It was found that PP can be toughened with specially treated BaSO₄ particles. The interfacial modification contributes to the toughening in two aspects. The first is to provide a proper interfacial adhesion and control the interfacial debonding occurs at well-timed stages. This ensures the inorganic particles transfer the stress and stabilizes the cracks at the initial stage of the deformation, and satisfy the stress conditions for plastic deformation of matrix ligaments subsequently via debonding. The second is that the modified interface between PP matrix and filler particles increases the nucleating ability of the fillers and retards the motion of the PP chains. This leads to the formation of PP crystals with less perfection and smaller size in the matrix and promotes plastic deformation of the matrix after the debonding occurs.     

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.     

Finite element analysis of the stress distribution in a thermally and transversely loaded Ti–6Al–4V/SiC fibre composite

The load transfer between fibre and matrix in a metal matrix composite (MMC) depends on the properties and conditions of the fibre/matrix interfacial region. The objective of this investigation is to gain a better understanding of the stresses generated within a continuously reinforced MMC, particularly at this interface. Finite element analysis is used to investigate the effect of thermal and transverse mechanical loading on the SiC/Ti–6Al–4V composite system. The effect on the stress field of a carbon coating on the SiC fibres is also investigated. The results indicate that the interfacial region affects the stress distribution, with the presence of the carbon coating significantly altering the stress profiles generated. It is also found that the residual stresses generated as a result of cooling down the composite from processing temperature, has a marked effect on the stress profile and the behaviour of the composite when subsequent mechanical loading is applied.     

Discrete element modelling of unidirectional fibre-reinforced polymers under transverse tension

The mechanical behaviour of unidirectional fibre-reinforced polymer composites subjected to transverse tension was studied using a two dimensional discrete element method. The Representative Volume Element (RVE) of the composite was idealised as a polymer matrix reinforced with randomly distributed parallel fibres. The matrix and fibres were constructed using disc particles bonded together using parallel bonds, while the fibre/matrix interfaces were represented by a displacement-softening model. The prevailing damage mechanisms observed from the model were interfacial debonding and matrix plastic deformation. Numerical simulations have shown that the magnitude of stress is significantly higher at the interfaces, especially in the areas with high fibre densities. Interface fracture energy, stiffness and strength all played important roles in the overall mechanical performance of the composite. It was also observed that tension cracks normally began with interfacial debonding. The merge of the interfacial and matrix micro-cracks resulted in the final catastrophic fracture.     

Interfacial shear strength estimates of NiTi–Al matrix composites fabricated via ultrasonic additive manufacturing

The purpose of this study is to understand and improve the interfacial shear strength of metal matrix composites fabricated via ultrasonic additive manufacturing (UAM). NiTi–Al composites can exhibit dramatically lower thermal expansion compared to aluminum, yet blocking stresses developed during thermal cycling have been found to degrade and eventually cause interface failure in these composites. In this study, the strength of the interface was characterized with pullout tests. Since adhered aluminum was consistently observed on all pullout samples, the matrix yielded prior to the interface breaking. Measured pullout loads were utilized as an input to a finite element model for stress and shear lag analysis. The aluminum matrix experiences a calculated peak shear stress near 230 MPa, which is above its ultimate shear strength of 150–200 MPa thus corroborating the experimentally-observed matrix failure. The influence of various fiber surface treatments and consolidation characteristics on bond mechanisms was studied with scanning electron microscopy, energy dispersive X-ray spectroscopy, optical microscopy, and focused ion beam microscopy.     

Effect of damage levels and curing stresses on delamination growth behaviour emanating from circular holes in laminated FRP composites

This paper deals with the study of the effect of drilling induced delamination damage levels and residual thermal stresses (developed during manufacturing process of cooling the laminate form curing temperature to room temperature) on delamination growth behaviour emanating form circular holes in graphite/epoxy laminated FRP composites. Two sets of full three dimensional finite element analyses (one with the residual thermal stresses developed while curing the laminate and the other without residual thermal stresses i.e. with mechanical loading only) have been performed to calculate the displacements and interlaminar stresses along the delaminated interfaces responsible for the delamination onset and propagation. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of SERR obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply orientation, drilling induced damage levels and material heterogeneity at the delaminated interface dictate the interlaminar fracture behaviour of laminated FRP composites.     

Thermisch‐mechanisches Ermüdungsverhalten der partikelverstärkten Aluminiumknetlegierung EN AW‐6061‐T6 und die Entwicklung von Eigenspannungen im Matrixwerkstoff unter thermisch‐mechanischer Beanspruchung

Thermal mechanical fatigue behaviour of particle reinforced EN AW‐6061‐T6 and development of residual stresses in the matrix material by thermal mechanical loading The behaviour of non reinforced and 15 Vol.‐% α‐alumina particle reinforced wrought aluminium alloy EN AW‐6061‐T6 in thermal mechanical fatigue loading was investigated at different maximum temperatures. The tests were performed in strain controlled mode by means of an electro‐mechanical testing machine. Alternating load deformation and life cycle behaviour either materials were compared. It came out, that the reinforcement leads to an decreasing thermal mechanical fatigue life cycle while keeping constant the maximum temperature and mechanical loading. The two materials showed softening behaviour due to high maximum temperatures of 573 K to 673 K. However, there is an intense scatter of the number of cycles to failure of the non reinforced alloy aggravating the interpretation of the results. On the other hand the thermal mechanical life cycle increases in combination with increasing maximum temperatures. Simultaneously the part of plastic deformation in mechanical loading increases for both materials, while for a constant total strain range the effective maximum and minimum stresses are decreasing. Furthermore, the development of residual stresses in the matrix of the reinforced alloy by thermal mechanical fatigue loading was analysed. It was observed that only small absolute values of residual stresses will be obtained for these loads. Nevertheless, tendencies of mounting tensile residual stresses can be identified in the direction of thermal mechanical fatigue loading and subsequently reduction of the residual stresses.     

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.     

Thermal stress distributions in axisymmetrically orthotropic fiber-reinforced composites with multilayered interfaces

Treating fibrous composites with multilayered interfaces as a cylindrical assemblage consisting of multiple coaxial circular cylinders, a model has been developed with which the thermal stresses in such composites reinforced with axisymmetrically orthotropic fibers, can be analytically calculated. The developed model is employed to examine the influences of the volume fractions of the constituents as well as mechanical and physical properties of the interfacial layers on the thermal stresses in the composites. For the composites reinforced with different types of axisymmetrically orthotropic fibers, the effects of the volume fractions of the constituents on the stresses in the composites are different. The variety of mechanical and physical properties of the interfacial layers can greatly change the stress distributions in the composites. Therefore, reasonable design of the volume fractions of the constituents as well as mechanical and physical properties of the interfacial layers can help reduce the thermal stresses in the composites and improve the thermal mismatch of the composites under the thermal loading.     

Interface stress relaxation in magnesium matrix composites studied by mechanical spectroscopy

Abstract

Mechanical spectroscopy has been used to study magnesium matrix composites reinforced either by long SiC fibres or randomly distributed Al₂O₃ (Saffil) short fibres. It is well known that, in metal matrix composites, thermal stresses can be built up at the interface due to the mismatch between the thermal expansion coefficients of matrix and reinforcements. In magnesium matrix composites, these thermal stresses are relaxed by dislocation motion in the matrix. This mechanism of thermal stress relaxation yields an extra transient component in the mechanical loss spectrum, which depends on the heating/cooling rate and disappears in isothermal condition in the behaviour of the shear modulus G with temperature has been observed during thermal cycling between 100 K and 500 K. The intensity of this phenomenondepends on the spatial distribution of the reinforcements in the matrix. In particular, composites reinforced with long fibres exhibit a more pronounced anomaly. This is interpreted by the modification of the interface strength when temperature is changed.     

Fracture mechanics approach for a partially debonded cylindrical fibre

The mechanical behaviour of the fibre-reinforced composites depends on the properties of the matrix, the fibres and their reciprocal bonding. Degrading effects occurring in such materials under service – such as matrix–fibre detaching (debonding), fibre breaking, matrix cracking – must be taken into account in the safety assessments. In the present paper, the fibre–matrix debonding phenomenon at the fibre–matrix interface is examined through fracture mechanics concepts, since a geometric discontinuity arises at the edge of the debonded zone (between two dissimilar materials) producing a stress singularity. The mixed mode stress-intensity factors are determined, and the effects of the geometrical and mechanical parameters related to matrix and fibres are discussed.     

Microstructure effects on transverse cracking in composite laminae by DEM

A particle discrete element method (DEM) was employed to simulate transverse cracking in laminated fiber reinforced composites. The microstructure of the laminates was modeled by a DEM model using different mechanical constitutive laws and materials parameters for different constituents, i.e. fiber, matrix and fiber/matrix interface. Rectangular, hexagonal and random fiber distributions were simulated to study the effect of fiber distribution on the transverse cracking. The initiation and dynamic propagation of transverse cracking and interfacial debonding were all captured by the DEM simulation, which showed similar patterns to those observed from experiments. The effect of fiber volume fraction was also studied for laminae with randomly distributed fibers. It was found that the distribution and volume fraction of fibers affected not only the transverse cracking path, but also the behavior of matrix plastic deformation and fiber/matrix interface yielding in the material.     

Single-fibre Broutman test: fibre–matrix interface transverse debonding

The single-fibre Broutman test was used to study the fibre–matrix interface debonding behaviour when subjected to a transverse tensile stress. During testing, damage was detected using both visual observation under polarized light and acoustic emission (AE) monitoring. Separation of failure mechanisms, based on AE events, was performed using time domain parameters (amplitude and event width) and fast Fourier transform (FFT) frequency spectra of the AE waveforms. The latter can be considered as a fingerprint allowing to discriminate fibre failure, matrix cracking, fibre–matrix interface debonding, friction and ‘parasite noise’. Stresses in the specimens were evaluated using a two-dimensional finite element model (FEM) and monochromatic photoelasticity was used to verify the simulated stress distribution.Two failure mechanisms appeared to be in competition in the Broutman test: fibre failure under compressive stresses and fibre–matrix interface debonding under transverse tensile stresses. For systems in which the interfacial adhesion is not so ‘good’, like glass fibre–polyester systems for instance, fibre–matrix debonding was observed, and the progression of the debonding front with the interfacial transverse stress was recorded. Thermal stresses are also discussed, and a FEM simulation shows that they encourage fibre failure under compressive stresses.     

Can carbon nanotubes grown on fibers fundamentally change stress distribution in a composite?

In carbon fiber reinforced polymer composites the onset of damage occurs at the fiber/matrix interface, where stress concentrations are the highest due to the property mismatch of the two materials. This article reports results of a modelling study indicating that carbon nanotubes (CNTs) grown on fibers are effective in suppressing stress concentrations at the fiber/matrix interface. In the case of high density CNT forests, they can even fundamentally change a profile of the interfacial stress. The study is performed using a novel two-scale finite element model of a nano-engineered composite based on the embedded regions technique.