Fracture toughness of epoxy/multi-walled carbon nanotube nano-composites under bending and shear loading conditions

The effects of multi-walled carbon nanotubes (MWCNTs) on the mechanical properties of epoxy/MWCNT nano-composites were studied with emphasis on fracture toughness under bending and shear loading conditions. Several finite element (FE) analyses were performed to determine appropriate shear loading boundary conditions for a single-edge notch bend specimen (SENB) and an equation was derived for calculating the shear loading fracture toughness from the fracture load. It was seen that the increase in fracture toughness of nano-composite depends on the type of loading. That is to say, the presence of MWCNTs had a greater effect on fracture toughness of nano-composites under shear loading compared with normal loading. To study the fracture mechanisms, several scanning electron microscopy (SEM) pictures were taken from the fracture surfaces. A correlation was found between the characteristics of fracture surface and the mechanical behaviors observed in the fracture tests.     

Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

Compressive strength,modulus of elasticity,and water permeability of inorganic polymer concrete

Inorganic polymer concretes (IPCs) were produced from rice husk–bark ash (RHBA) combined with fly ash (FA) as a cementitious raw material. Six different mixtures were used to study the properties of IPC. Since RHBA is rich in silica material, varying the ratio of FA to RHBA results in differing SiO₂/Al₂O₃ ratios. To keep the SiO₂/Al₂O₃ ratio constant, the ratio of FA to RHBA was fixed at 80:20 by weight. High concentration sodium hydroxide solution and sodium silicate solution were used as a liquid component of the concrete mixture. The mixing and curing of these inorganic polymer concretes were performed under ambient conditions. Compressive strength, modulus of elasticity, and water permeability of the IPCs were investigated at specified intervals up to 90 days. The results showed that the compressive strength, modulus of elasticity, and water permeability of IPCs depend on the mix proportions, especially the solution to ash (S/A) ratio and the paste to aggregate (P/Agg) ratio. Moreover, the results showed that the water permeability and the elastic modulus of IPCs were significantly related to their compressive strength.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Fracture initiation at sharp notches under mode I, mode II, and mild mixed mode loading

In the context of linear elasticity, a stress singularity of the type Kⁿr^δ(δ<0) may exist at sharp re-entrant corners, with an intensity Kⁿ. In general the order of the stress singularity δ and the stress intensity differ for symmetric (mode I) and antisymmetric (mode II) loading. Under general mixed-mode loadings, the magnitudes of the mode I and II intensities fully characterize the stress state in the region of the corner. A failure criterion based on critical values of these intensities may be appropriate in situations where the region around the corner dominated by the singular fields is large compared to intrinsic flaw sizes, inelastic zones, and fracture process zone sizes. We determined the mode I and II stress intensities for notched mode I tensile specimens and notched mode II flexure specimens using a combination of the Williams (1952) asymptotic method, dimensional considerations, and detailed finite element analysis. We carried out a companion experimental study to extract critical values of the mode I and II stress intensities for a series of notched polymethyl methacrylate (PMMA) tensile and flexure specimens with notch angles of 90-. The data show that excellent failure correlation is obtained, in both mode I and II loading, through the use of a single parameter, the critical stress intensity. We then analyzed and tested a series of T-shaped structures containing 90- corners. The applied tensile loading results in mixed-mode loading of the 90- corners. Failure of the specimens is brittle and can be well-correlated with a critical mode I stress intensity criterion using the results of the notched mode I tensile tests. This is attributed to large difference in the strength of the stress singularities in modes I and II: δ= -0.4555 and -0.0915 for modes I and II for a 90- notch. As a result, the mode I loading dominates the failure process for the 90- corner in the T-structure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modelling the fracture of concrete under mixed loading

A simple and efficient numerical procedure for mixed mode fracture of quasibrittle materials is shown: This technique predicts crack trajectories as well as load-displacement or load-CMOD responses. The model is based on the cohesive crack concept and uses the local mode I approach. Numerical results agree quite well with three experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, another from García, Gettu and Carol and from a nonproportional loading by the authors. In constrast to more sophisticated models, this method offers two major advantages: it requires only material properties measured by standardized methods and it can easily be implemented with general multipurpose finite element codes.     

Fracture behaviour of PC/ABS resin under mixed-mode loading

Fracture behaviour of polycarbonate (PC)/acrylonitrile-butadiene-styrene (ABS) under mixed-mode loading conditions was studied for several weight fractions of PC and ABS. Mode I and mixed-mode fracture tests were carried out by using compact–tension–shear specimens. At a certain value of mixed-mode loading ratio K _II / K _I a crack of the shear type will initiates at the initial crack tip. Fracture toughness increases under mixed-mode loading with an increase in the mode II component, whereas it reduces with the appearance of a shear-type fracture. Fracture toughness and the appearance of a shear-type fracture depends on the blending ratio of PC and ABS. The transition to shear-type fracture occurs at lower value of K _II / K _I for resins with higher fracture toughness.     

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length (a_e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy (G_Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength (σ_u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.     

A new fixture for fracture tests under mixed mode I/II/III loading

In this paper, a new loading device for general mixed mode I/II/III fracture tests is designed and recommended. Finite element analyses are conducted on the proposed apparatus to evaluate the fracture parameters of the tested samples under various mixed mode loading conditions. The numerical results revealed that the designed loading fixture can generate wide varieties of mode mixities from pure tensile mode to pure in‐plane and out‐of‐plane shear modes. The accuracy of the proposed fixture is evaluated by conducting a wide range of fracture tests on compact tension shear (CTS) specimens made of polymethyl methacrylate (PMMA). The experimental results are then compared with the theoretical predictions obtained by the Richard criterion. A good consistency is observed between the experimental results and theoretical predictions.     

Buckling and fracture behaviour of cracked thin plates under shear loading

Thin-walled structural components are widely used in several engineering applications such as in aerospace, naval, nuclear power plant, pressure vessel, mechanical and civil fields. Since they are frequently characterised by a high slenderness, the safety assessment of such structural components requires to carefully consider the buckling collapse which can heavily limit their allowable bearing capacity. For very thin plates, buckling collapse can occur under compression, shear, or even under tension. In the present paper, the buckling and fracture collapse mechanisms in an elastic rectangular thin-plate with a central straight crack under shear loading are analysed. Different boundary conditions, crack length and orientation are considered. Through a parametric finite elements (FE) numerical analysis, the crack sensitivity of the collapse load of such a structural component is examined. The obtained results are discussed, and some interesting and useful conclusions are drawn. The collapse mechanism occurring earlier (buckling or fracture) is found by varying the fracture toughness of the material, and some failure-type maps depending on the geometrical parameters of the crack are determined.     

Fracture toughness of Ti-15Al-8Nb alloy under mixed mode I/III loading

The effect of mixed mode I/III loading on fracture toughness of Ti-15 at.% Al-8 at.% Nb alloy, which undergoes stress-induced martensitic transformation, was investigated for four different grain sizes. The fracture toughness under mixed mode I/III loading was found to be significantly higher than that under mode I loading in all cases. The results were explained on the basis of the stress and strain fields ahead of a mixed mode crack and its influence on the martensitic transformation zone.     

Fracture behavior and toughening mechanism in Zanchor reinforced composites under mode II loading

The mode II interlaminar fracture behavior and the toughening mechanism of Zanchor reinforced composite laminates were investigated by using the End Notched Flexure (ENF) and Interlaminar Shear (ILS) specimens. The ENF test results demonstrated that the Zanchor process was highly effective to improve the mode II fracture toughness of composite laminates, where the fracture toughness increased almost linearly with the Zanchor density. The R-curves of Zanchor composites were roughly divided into the transition and stable regions, where the width of the transition region became larger as the Zanchor density increased. The macroscopic fracture behavior of the Zanchor composites was still brittle under mode II loading like that of the base composite, where the crack tip process zone was estimated to be rather small regardless of the Zanchor density. The ILS test results demonstrated that the square of the normalized shear strength increased linearly with the Zanchor density and agreed quantitatively with the normalized fracture toughness. The wedge effect was supposed to be the dominant toughening mechanism against the mode II fracture, where the entangled fiber bundles partly sustained the shear stress in the vicinity of the crack tip. The entangled fiber bundles played an important role to form the mode II fracture surface, where the microscopic fracture pattern of the entangled fiber bundles was mainly the breakage of the fiber bundles rather than the pull-out or debonding of the fiber bundles.     

Two parameter approach for elastic-plastic fracture of short cracked specimens under mixed mode loading

For mode-I loading, in order to describe the near-tip stress field in a specimen under large scaled yielding, two parameter approaches such as J-T, J-Q and J-A₂ theories have been developed and proved well for their validity and limit. In this work elastic-plastic finite element analysis were performed to investigate the effects of mode mixity and T-stress upon near-tip stress distribution for a small-scale-yield model with the modified boundary layer and CTS (Compact Tension-Shear) configuration under large-scale-yield state. As the results, some peculiar characteristics were found as follows; As the mode mixity increases, normal stresses _rr and near the crack tip in the small-scale-yield model get significantly affected by the positive T-stress as well as the negative T-stress, while the shear stress _r is little affected by T-stress. Also, the near-tip stress distribution of short cracked CTS specimens under the large-scale-yield state agree fairly well with that of the small-scale-yield model with an appropriate positive T-stress. The two parameters approach with J-integral and T-stress seems to be a good tool for describing the near-tip stress field under a mixed mode loading and large-scale-yield state.     

Linear micropolar elastic crack-tip fields under mixed mode loading conditions

Micropolar elasticity laws provide a possibility to describe constitutive properties of materials for which internal length scales may become important. They are characterized by the presence of couple stresses and nonsymmetric Cauchy stress tensor. Beyond the classical displacement field, the kinematical variables are augmented by a so-called microrotation field and its gradient, the latter introducing an internal length scale in the theory. For an isotropic, linear micropolar elastic material, the near-tip asymptotic field solutions for mode I and mode II cracks are derived. It is shown that these solutions behave similar to those according to the so-called couple stress theory, which has been investigated by Huang et al. (1997a), or similar to those derived for cellular materials by Chen et al. (1998). In particular, the singular fields have an order of singularity r ^–1/2 and are governed by some amplitude factors, having the meaning of stress intensity factors as in the classical linear elastic theory. The effect of material parameters on the stress intensity factors is studied by applying the finite element method to calculate the values of the stress intensity factors for an edge-cracked specimen of finite width.     

Fracture and fatigue study of unidirectional glass/epoxy laminate under different mode of loading

Interlaminar fracture is the dominant failure mechanism in most advanced composite materials. The delaminating behaviour of materials is quantified in terms of the strain energy release rate G. In this paper, the experimental measurements of the fatigue delaminating growth for some combinations of energy release rate mode ratio have been carried out on unidirectional glass/epoxy laminates. On this base the constants in the Paris equation have been determined for each G_II/G_T considered modal ratio. The fatigue threshold strain energy release rate Δ G_Tth , below which delaminating doesn't occur, were measured. Three type specimens were tested, namely: double cantilever beam (DCB), end‐loaded split (ELS) and mixed‐mode bending (MMB) under mode I, mode II and mixed‐mode (I + II) loading, respectively. Scanning electron microscopy techniques were used to identify the fatigue delamination growth mechanisms and to define the differences between the various modes of fracture.     

Fracture behaviour and stress fields of cracked bend specimens subjected to mixed mode loading

An elastic-plastic finite element analysis of the stress fields at the tips of cracks subjected to mixed mode loading is presented. The paper concludes with a fracture analysis using several current fracture criteria and compares these theoretical results with experiment results on several materials. The three criteria based on a linear elastic theory, i.e. maximum tensile stress, strain energy density, and maximum energy release rate do not give correct predictions for mixed mode loading. The experiment data best fits the $\text{G}{}^{\mathrm{\Delta }}$ theory for crack separation energy rates that accounts for plasticity effects. This theory gives lower and upper bound solutions respectively for the CCP and the SENB specimen configurations.     

Fracture toughness of polycrystalline tungsten under mode I and mixed mode I/II loading

The fracture toughness of swaged polycrystalline tungsten was tested parallel and perpendicular to the swaging direction and under mixed mode I/mode II loading. The fracture mode is dominated by the microstructure and changed from all-transgranular cleavage in mode I to almost all-intergranular fracture in mode II. The mixed mode results can be related to two common failure criteria, the maximum tensile stress criterion (Maximum σ) and the maximum energy release rate criterion (Maximum G), but the large scatter in the data prohibits a clear distinction between the two criteria. Tests at 77 K show that the polycrystal is significantly tougher than the single crystal at this temperature. This is a consequence of the deflection of the crack into the grain boundaries and the imperfect texture (as compared to a single crystal) of the polycrystalline material.     

Mixed Mode Fracture of Concrete under Proportional and Nonproportional Loading

A novel testing procedure for mixed mode crack propagation in concrete is presented: four point bend of notched beams under the action of two independent force actuators. In contrast to classical procedures, this method allows nonproportional loading and crack trajectory modifications by changing the action of one actuator. Different experimental crack trajectories, under mixed mode and nonproportional loading, are presented together with the corresponding curves of load-CMOD and load-displacement. The tests were performed for three homotetic specimen sizes and two mixed mode loading conditions. The results are useful for checking the accuracy of mixed mode fracture analytical and numerical models. The models should predict the crack trajectory and a complete group of experimental records of load and displacements on several control points in the specimen. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture Resistance of a Cracked Concrete Beam Post-strengthened with FRP Sheets

Fibre-reinforced plastic (FRP) composites have been increasingly used in rehabilitation and strengthening of concrete structures. Significant increases in stiffness and strength have been achieved by applying this technique. However, there is concern about the ductility or toughness performance of FRP/concrete hybrid structures, which is critical in the application of this technology. This paper presents a new theoretical method to predict the fracture resistance behaviour of FRP post-strengthened concrete flexural beams. No slip between the FRP and plain concrete matrix is assumed and Mode I fracture propagation is considered. The model is valid for a wide range of span-to-depth ratios and any crack length. The influence of the bridging stresses provided by the fracture process zone (FPZ) at the tip of a fictitious fracture is examined. The effect of various material and geometric parameters on the resistance curve and toughness of the hybrid structure is discussed, based on the numerical results from the developed theoretical formulae. The results provide a useful insight into the strengthening/toughening and the design of FRP sheet/concrete beam structures.     

Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’ concept

Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at − 60°C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.