Andrejs Krasnikovs

Cod-based simulation of transverse cracking and stiffness reduction in [S/90n]s laminates

Abstract Closed-form expressions for the thermo-elastic properties of [S/90 n ] s laminates with transverse cracks in the 90° layers are derived. Provided the normalised average crack-opening displacement (COD) is known, expressions contain only crack density, geometrical parameters and elastic constants of layers. The average COD dependence on the crack spacing and constraint effect of adjacent sub-laminates is analysed by using finite-element method in plane stress formulation. It is found that the out-of-plane elastic constants have an insignificant effect on COD. A simple power law relating average COD to elastic and geometrical parameters of constituents is derived. The obtained power law and the developed methodology are successfully used to predict the reduction of thermo-elastic properties and damage evolution of [±θ/90 4 ] s laminates. The crack-closure technique and Monte-Carlo simulations are used to model the damage development. The 90° layer is divided in to a large number of elements and G c values are assigned to each element according to a Weibull distribution. Parameters in the Weibull distribution are determined by using experimental crack density versus strain curve for glass-fibre/epoxy [0 2 /90 4 ] s cross-ply laminates. Damage development in [S/90 4 ] s laminates of the same material, containing sub-laminates with ±θ layers only, is modelled by using these Weibull parameters and the results are in good agreement with test data. The effect of the thickness of the 90° layer on damage development is discussed in strength and fracture mechanics formulation.

Experimental determination of elastic properties of impact damage in carbon fibre/epoxy laminates

This paper describes an investigation of in-plane elastic properties of impact damaged regions in composite laminates. Quasi-isotropic carbon fibre/epoxy laminates were impacted and the impact damage examined by ultrasonic C-scanning, optical microscopy and thermal deplying. After impact damage observations, specimens were cut from the laminates and tested in tension and compression. The elastic modulus of the impact damage was, in both tension and compression, mainly controlled by the amount of fibre breakage. Interestingly, layers with broken fibres could sustain some load in compression, which led to higher elastic modulus in compression than in tension. The effect of delaminations on the elastic modulus was quite small in both tension and compression. The through-the-thickness variation of in-plane stiffness was studied by successively removing plies. The variation in stiffness was negligible, probably as a result of the very uniform distribution of delaminations and fibre breakage through the thickness of the laminates.

A Synergistic Damage Mechanics Approach to Viscoelastic Response of Cracked Cross-ply Laminates

A synergistic damage mechanics approach, i.e., a combined continuum damage mechanics (CDM) and micromechanics approach, is developed to characterize the viscoelastic response of cross-ply laminates with transverse cracks. The approach relies upon a second-order tensor-based description of damage wherein the crack opening displacement appears as an explicit function. The time variation of this function is calculated by micromechanics and is inserted into the continuum damage formulation. The relaxation moduli calculated for fixed states of damage (transverse crack density) by this approach agree well with independently calculated values by a CDM approach and finite element model.

Crack Opening Geometry in Cracked Composite Laminates

Talreja and coworkers have reported brittle and tough polymer matrix composites to show different cross-ply laminate stiffness reductions due to transverse cracks, despite very similar elastic properties. Studies of crack opening displacement (COD) in [0,,,90,] laminates may help in solution of this problem. Approximate analytical models based on the variational approach pioneered by Hashin were therefore applied in addition to FEM-calculations. Approximate models were concluded not to be reliable for future analyses of this problem. Experimental COD for brittle GF/EP laminates at low crack densities was fairly well predicted by FEM-calculations. None of the models were able to predict experimental data at high crack densities. Residual plastic strains are suggested as an explanation and may also be responsible for reported matrix-related differences in stiffness reduction.

Transverse cracks in cross-ply laminates. 1. Stress analysis

During service loading of cross-ply laminates, transverse cracks occur in plies. The cracks parallel to the fiber direction are extended over the full thickness of transverse plies and often cross the entire test specimen width. It is widely recognized that the changes of laminate thermomechanical constants, caused by the transverse cracking of composite laminates, can be significant. Theoretical stress analysis in the cross-ply laminates in the vicinity of cracks is performed using numerical (FE) and analytical methods. The effect of transverse cracks on the degradation of elastic properties will be discussed in Part 2 [1]. Approximate analytical micromechanical models based on shear lag predictions, variational analysis, and numerical 2D finite element calculations were verified in their predictive abilities. The three variational models used are based on the principle of minimum complementary energy and have different degrees of accuracy with respect to the stress assumptions used (Hashins, 2D 0° and 2D 0°/90° models). Using FEM, the plane stress and strain state were analyzed. The effect of material properties and layer thickness on the stress distribution in a 90° layer was evaluated by varying the crack spacing. The crack opening displacement (COD), normalized with respect to the far field strain, is proposed as a measure of reduction of the mechanical properties. Since the CODs are rather insensitive to the crack spacing (crack density) in a wide region, they will be used in modeling the stiffness reduction in these laminates [1].

Transverse cracks in cross-ply laminates 2. Stiffness degradation

From the results of stress analysis between two transverse cracks in cross-ply laminate [1], a model for the stiffness reduction based on generalized plane strain assumptions has been developed. Simple analytical expressions are obtained for the longitudinal modulus and the Poissons ratio as a function of the transverse crack density. Apart from the crack density, these expressions depend only on the elastic and geometrical properties of constituent laminae and the average crack opening displacement (ACOD) normalized in the proper way. Calculations of the ACOD are performed and analyzed with the FEM and analytical models used for the stress analysis in [1]. The predicting capabilities of approximate models are discussed in comparison with experimental data and FEM results. In order to predict the stiffness degradation for a wide variety of laminates, a simple procedure requiring only one FEM calculation for some “average laminate” with “average crack spacing” is proposed and has been proved effective.

Investigation of influence of nano-reinforcement on the mechanical properties of composite materials

AbstractThe present work studies the possibility to decrease the formation of micro and nano cracks around short fibres in fibre-reinforced concrete (FRC) composite with the help of nano-reinforcement, which is carbon nanotubes, or micro reinforcement, which is carbon short fibres and nano-fillers. Tensile and bending strength of FRC depends on the spatial distribution of fibres inside a material, type of fibre and cement matrix, as well as an effective micromechanical work of each fibre while pulling out of the concrete matrix. Shrinkage stresses, acting in the matrix in the vicinity of a fibre, lead to the formation of micro-cracks. Such micro-cracks were observed experimentally and were investigated numerically performing broad modelling based on the finite element method (FEM). The investigation was focused on the micromechanical behaviour of a single steel fibre in a cement matrix. Numerical modelling results demonstrated a high level of shrinkage overstresses around steel fibres in concrete. The rol...

Effect of the Fibre Type on the Rheological and Mechanical Properties of Cementitious Composites for Thin Overlays

Polypropylene (PP), nylon and polyvinyl alcohol (PVA) micro-fibres with different geometries were used at 1 vol. % dosage to investigate rheological and mechanical properties of cementitious composites to be used for thin overlays. Slump-flow and visual stability index methods were used to characterise the rheological properties. Single crack tension and bending studies were carried out to evaluate the tensile and bending strength, as well as the post-cracking behaviour. The results show that fibre geometry (L/d ratio and specific surface area) has a pronounced influence on the fresh state rheological properties of the cementitious composites. The results also surprisingly indicated that the nylon fibres are able to significantly increase the pre-cracking tensile and bending strength. All tested composites showed tensile strain softening and insignificant deflection hardening after cracking and a major strength loss. The results indicate single crack tension method to be the most appropriate for evaluation of mechanical properties of cementitious composites used for thin overlays.

Effect of short fibers orientation on mechanical properties of composite material – fiber reinforced concrete

AbstractTraditional fiberconcrete structures have fibres in the mix oriented in all spatial directions, distributed in the structural element volume homogenously, what not easy to obtain in practice. In many situations, structurally more effective is the insertion of fibres into the concrete structural element body by forming layers, with a predetermined fibre concentration and orientation in every layer. In the present investigation, layered fibre concrete is under investigation. Short steel fibres were attached to flexible warps with the necessary fibres concentration and orientation. Warps were placed into the prismatic mould separating them by concrete layers without fibres. Prisms were matured and tested under four-point bending. The bending-affected mechanical behaviour of cracked fibre concrete was simulated numerically by using a developed structural model. Comparing the simulation results with experimental data, material micromechanical fracture mechanisms were analysed and evaluated.

Plastometry for the Self-Compacting Concrete Mixes

Operative determination of consistence of self-compacting concrete mixes at plant or in construction conditions is an important problem in building practice. The Abrams cone, the Vebes device, the U-box siphon, L-box or funnel tests are used in solving this problem. However, these field methods are targeted at determination of some indirect parameters of such very complicated paste-like material like concrete mix. They are not physical characteristics suitable for the rheological calculations of the coherence between the stress and strains, flow characteristics and the reaction of the concrete mix in different technological processes. A conical plastometer having higher precision and less sensitive to the inaccuracy of the tests in construction condition has been elaborated at the Concrete Mechanics Laboratory of RTU. In addition, a new method was elaborated for the calculation of plasticity limit τ0 taking into account the buoyancy force of the liquid or non-liquid concrete mix. In the present investigation rheological test of the concrete mix by use the plastometer and the method mentioned earlier was conducted for different self-compacting and not self-compacting concrete mixes.