Analysis of micro--macro material properties and mechanical effects of damaged material containing periodically distributed elliptical microcracks

The existence of numerous microcracks causes changes in the stiffness or fracture toughness of materials. In this paper, the manifestations of mechanical properties in the damaged materials caused by the microcracks are evaluated by the present homogenization method based on the superposition method together with the VNA solution. Moreover, it is known that the stress concentration at the macrocrack tip decreases due to the stress relaxation effect caused by the existence of the microcracks. In order to evaluate the manifestations of mechanical behavior, the mechanical effects of the existence of the microcracks on the macrocrack, the component separation method for mixed-mode stress intensity factors of the macrocrack in the damaged materials is newly developed in this paper. Various numerical analyses are successfully conducted for the two topics, the mechanical properties of the damaged materials and the mechanical behavior of the macrocrack in the damaged materials.     

Characterization of 3D morphology and microcracks in composites reinforced by multi-axial multi-ply stitched preforms

The micro-structure of polymer matrix composites reinforced by multi-axial multi-ply stitched carbon preforms and manufactured by liquid resin infusion is analyzed. The stitching induces deviations in fibre placement and creates openings which become resin-rich regions after the resin infusion. Characterization of the size and shape of the resin-rich regions of composites with different stitching yarn size and tightness and various stacking sequences has been performed by 2D metallographic micrography and X-ray microtomography. The resin-rich region volume was estimated at roughly 3.0 ± 0.5% of the material volume. The resin-rich regions constitute about 9% of the resin in the entire composite, whose fibre volume fraction is close to 65%. X-ray microtomography was successfully used to characterize the 3D microcracks created by hygrothermal fatigue.     

Analysis of damaged material containing periodically distributed elliptical microcracks by using the homogenization method based on the superposition method

The presence of multiple microcracks in a structural component causes material degradation such as reduction in the stiffness or reduction in the fracture toughness of the component. In this paper, the homogenization method is used to evaluate mechanical properties of the damaged material. The adaptation of the superposition method to the homogenization method is also presented. The proposed method makes use of the finite element solution of uncracked solid and the analytical solution. The effective elastic moduli of damaged materials containing lattice-distribution microcracks are estimated by the proposed method. Furthermore, the stress fields and the stress intensity factors of the elliptical microcracks in the damaged material at a micro-mechanics scale are evaluated to illustrate microscopic behavior such as crack interaction.     

An alternating method based on the VNA solution for analysis of damaged solid containing arbitrarily distributed elliptical microcracks

This paper presents the development of an alternating method for the interaction analysis of arbitrary distributed numerous elliptical microcracks. The complete analytical solutions (VNA solutions) for a single elliptical crack in an infinite solid, subject to arbitrary crack-face tractions, are implemented in the present alternating method, together with the coordinate transformations for stress tensors. First, the present method is verified by solving the problems of two interacting cracks for which accurate numerical solutions have been obtained previously. Next, the present method demonstrates obtaining efficient and accurate solutions for the problems of many interacting elliptical cracks, which cannot be solved in a practical sense by the ordinary numerical methods such as the finite element method. Furthermore, damaged solids containing periodically distributed elliptical microcracks are analyzed by the present alternating method. The effective elastic moduli are evaluated for varying microcrack density. Detailed structures of the interactions in the damaged solids are visualized and clarified. This revised version was published online in July 2006 with corrections to the Cover Date.     

About the analysis of microcracking in concrete

This paper deals with the techniques of characterisation of cracks and microcracks in concrete and mortars. It gives an overall view of the methods of observation in relation with image analysis. Image analysis is a useful tool to extract crack patterns from samples of concrete, since many fields are necessary to be studied at high magnifications. An analysis of the procedures and of the provided 2-D data is proposed. The parameters of damage characterisation are listed and discussed. Improvements and ways of research are suggested, mainly to extend 2-D results to 3-D space by means of crack-pattern modelling.     

Effect of cryo-induced microcracks on microindentation of hydrated cortical bone tissue

Microcracks accumulate in cortical bone tissue as a consequence of everyday cyclic loading. However, it remains unclear to what extent microdamage accumulation contributes to an increase in fracture risk. A cryo-preparation technique was applied to induce microcracks in cortical bone tissue. Microcracks with lengths up to approximately 20 μm, which were initiated mainly on the boundaries of haversian canals, were observed with cryo-scanning electron microscopy. A microindentation technique was applied to study the mechanical loading effect on the microcracked hydrated bone tissue. The microindentation patterns were section-scanned using confocal laser scanning microscopy to understand the deformation and bone damage mechanisms made by mechanical loading. The results show that there was no significant difference with respect to microhardness between the original and microcracked hydrated cortical bone tissues (ANOVA, p > 0.05). The cryo-induced microcracks in the bone tissue were not propagated further under the mechanical loads applied. The deformation mechanism of the microcracked cortical bone tissue was plastic deformation, not brittle fracture.     

Fatigue and microcracking of concrete

The direct and indirect methods of examining microcracks are reviewed. It is concluded that the discontinuity stress is a fundamental property of concrete. It signifies (1) the end of the quasi-elastic behavior of concrete (2) the long time sustained strength of concrete, (3) the point at which the Poisson's ratio starts to increase, and (4) the point at which mortar cracks begin to develop extensively. However, a logical and measurable definition of discontinuity stress has not yet been found. This paper suggests a new approach to define discontinuity stress based on fatigue tests. The fatigue interactions surface is derived, which reveals a measurable “kink”. This “kink” represents the discontinuity stress. Below this “kink” in the high cycle region, microcracks are developing as bond cracks in a slow gradual process. Above the “kink” in the low cycle region, mortar cracks are forming continuous networks.     

The effect of microcracking upon the Poisson's ratio for brittle materials

Microcracking-elasticity theories typically relate a decrement in elastic moduli to the number density,N, and the mean microcrack radius 〈a〉. In this paper, four microcracking-modulus theories are rewritten in terms of the macroscopic, observable parameters of Young's modulus and Poisson's ratio, eliminating the specific dependence on the difficult to measure, microscopic quantitiesN and 〈a〉. The rewritten microcracking elasticity theories are then compared to elasticity data on a variety of microcracked, polycrystalline ceramics.     

The influence of microcracking on the mechanical behavior of cement based materials

Quantitative acoustic emission techniques were applied to basic problems of microfracture in cement based materials. Acoustic emissions in cement based materials result from microcracks and other dynamic phenomena in the fracture process zone. The goals of this research program were to characterize microcracking in various cement based materials, to track the evolution of damage in those materials, and to examine the relationships to overall mechanical behavior. Characterizations of the microcracks showed a dependence on the degree of inhomogeneity in the material. Fine-grained materials showed different microfracture characteristics than coarse-grained materials. Microcracks were characterized according to their fracture mode. The fine-grained materials tested showed primarily mixed-mode microfracture, whereas the coarse-grained materials showed primarily mode II (shear) microfracture. It is experimentally shown that there exists a relationship between the microcrack characteristics established through quantitative acoustic emission analysis and the overall fracture toughness of the material.     

Geometric probability approach to the characterization and analysis of microcracking in rocks

Microcrack statistical data required for the modelling of thermophysical properties and failure behavior of rocks have been obtained by a geometric probability approach and by direct measurement on plane sections. A comparison of the two shows that the former is efficient and provides reasonably accurate data on microcrack surface area and its orientational variation. Methods are outlined by which theoretical predictions on stress-induced anisotropy and energetic balance can be compared with quantitative electron microscopy data. The preliminary analysis shows that stress-induced anisotropy predicted by the ‘sliding crack’ model agrees with the stereological data. Energetic considerations indicate that inelastic energy in gabbro samples deformed at pressures above 250 MPa cannot be solely dissipated by tensile microcracking. Plastic energy taken up by kinking instability (involving a plastic strain of several per cents) or frictional dissipation (involving shear slip of several microns) can explain the observations.     

The effect of indentation-induced microcracks on the elastic modulus of hydroxyapatite

The presence of microcracks in materials affects a wide range of mechanical properties including elastic modulus, Poisson’s ratio, fracture strength, and fracture toughness. The microcrack-induced reductions of the Young’s modulus, E, and Poisson’s ratio, υ, are functions of the size, geometry, and number density of microcracks. In this study, an array of Vickers indentation-induced microcracks was placed on the surfaces of two hydroxyapatite (HA) specimens with totals of 391 and 513 indentations per specimen. This study tests the validity of theoretical studies of microcrack damage-induced changes in E and υ, where the changes are expressed either by (i) the volumetric crack number density, N and (ii) the crack damage parameter, ε. All elasticity measurements were done via resonant ultrasound spectroscopy. For both the HA specimens included in the study and alumina specimens indented in an earlier study [J Mater Sci 38:1910. doi: , 1], E and υ decreased approximately linearly with increasing microcrack damage. The slopes of the E and υ versus N and ε are also computed and compared to the available theoretical models.     

On the critical size of microcracks initiated in materials

We obtain an explicit expression for the potential energy of an elastic body containing a crack with prefracture zones at its tips. This expression is used to construct an analytic dependence of the critical size of a microcrack required for its transformation into a macroscopic defect by using the theory of catastrophes. The reliability of the obtained theoretical values of the critical size of a microcrack is corroborated by comparing these results with the available experimental data. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 3, pp. 79–83, May–June, 1998.     

Development and propagation of microcracks in plain concrete

An investigation to study the development and propagation of microcracks in plain concrete was conducted. Cored and sawn cylindrical specimens were strained to predetermined stress levels at different strain rates and then after unloading polished and stained sections of axially sliced specimens were analysed under a microscope at times 30 magnification. Crack orientation and the contributions of the upper and lower halves of aggregates (with respect to the direction of compaction) towards total crack density were observed.     

The stiffness and strength of transformation toughening ceramics with misoriented microcracks

Theoretical studies on misoriented transformation particles and microcracks in transformation toughening ceramics are presented using the Eshelby equivalent inclusion method. The stress field, stiffness and strength were calculated. Experiments were done by the three-point bend method using Al₂O₃/ZrO₂ ceramics and the stiffness and strength were also measured. Comparison between theoretical and test results confirmed the important role of microcracks.     

The influence of blast-furnace slag hydration products on microcracking of concrete

New hydration products of ground granulated blast-furnace slag are formed during the hydration process of Portland slag cement concrete. Spatial distribution of microcracks in concrete is related also to newly formed slag hydrates. The chemical composition of hydration products is variable and unstable. The Si/Ca ratios rise in hydration products near the unhydrated slag core significantly. There is also a certain increase of Mg and Al content in the central parts of hydration rims. The scope of the paper is to find a relation between slag hydration products and the process of microcracking. The amount of microcracks was reduced in concretes with a lower content of vitreous fraction where the slag basicity was high. Neoformation of hydration products is accompanied by volume changes, which can lead to concrete microcracking.