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.     

Crack shielding and amplification due to multiple microcracks interacting with a macrocrack

Abatract We investigate the effect of crack shielding and amplification of various arrangements of microcracks on the stress intensity factors of a macrocrack, including large numbers of arbitrarily aligned microcracks. The extended finite element method is used for these studies. In some cases the numerical XFEM simulation provides results that are more accurate than currently available analytical approximations because the assumptions are less restrictive than those made in obtaining analytical approximations. Stress intensity factors for the tip of a macrocrack under the influence of nearby microcracks are calculated under far field mode 1 boundary conditions. For a microcrack aligned with the macrocrack the numerical results agree quite well with the analytically exact stress intensity factors. The influence of the distance to the macrocrack tip and the rotation angle is investigated for unaligned microcracks, and it is shown in several examples with many randomly distributed microcracks that the influence of those microcracks which are not in close proximity to the macrocrack tip is on the order of 5%.     

Plane problem of macro-microcrack interaction taking account of crack closure

The fracture stability of a macrocrack under the tensile and shear loading in the presence of a system of microcracks is analysed. Interaction of cracks leads to full or partial closure of the crack edges. The boundary problem is formulated and a solution is obtained by the small parameter method. Domains where microcracks are closed, and regions where microcracks cause full or partial closure of the macrocrack are found. The influence of crack contact on the stress intensity coefficient is analysed under the friction free assumption.     

Interaction of a crack with a field of microcracks

Crack propagation in brittle materials is of ten accompanied by intensive microcracking; being a major energy sink,this phenomenon can strongly affect the fracture process. A two-dimensional problem of elastic interaction of a macrocrack with a field of microcracks is considered in the article. Consideration is based on the self-consistent method, generalized with the account of strong non — uniformity of the stress field in the vicinity of the macrocrack. The technique of double layer potentials is used. A closed form solution for the effective stress field is constructed.     

Self-healing of mechanical damage of polyethylene/microcapsules electrical insulation composite material

Polyethylene (PE) cable has become an important carrier of the modern power grid due to its excellent electrical insulation performance. However, small damages can inevitably occur during the preparation and operation of the materials, which can distort electric field and trigger discharge, seriously threatening power supply safety. The self-healing of insulation materials by doping microcapsules is a new research innovation. In this paper, the self-healing PE/microcapsules insulation composite material was prepared, and the self-healing behavior of mechanical damage was emphatically analyzed by scratch damage test and crack propagation simulation. The results show that the composite material with 1 wt% microcapsule has better insulation strength. Moreover, the composite material can fill the defective structures, restore local electrical properties, and reverse the deterioration process of the material. The properties of PE/microcapsules composite material are mainly related to the characteristics of the microcapsule itself and the interface introduced by the microcapsules. The properties of the repaired product can directly affect the recovery degree of the damaged area. The stress action during damage can smoothly trigger its self-healing behavior. In conclusion, the PE composite material doped with 1 wt% microcapsules can achieve a good self-healing effect on mechanical damage.

     

Simulation of local material properties based on moving-window GMC

When analyzing the behavior of composite materials under various loading conditions, the assumption is generally made that the behavior due to randomness in the material can be represented by a homogenized, or effective, set of material properties. This assumption may be valid when considering displacement, average strain, or even average stress of structures much larger than the inclusion size. The approach is less valid, however, when considering either behavior of structures of size at the scale of the inclusions or local stress of structures in general. In this paper, Monte Carlo simulation is used to assess the effects of microstructural randomness on the local stress response of composite materials. In order to achieve these stochastic simulations, the mean, variance and spectral density functions describing the randomly varying elastic properties are required as input. These are obtained here by using a technique known as moving-window generalized method of cells (moving-window GMC). This method characterizes a digitized composite material microstructure by developing fields of local effective material properties. Once these fields are generated, it is straightforward to obtain estimates of the associated probabilistic parameters required for simulation. Based on the simulated property fields, a series of local stress fields, associated with the random material sample under uniaxial tension, is calculated using finite element analysis. An estimation of the variability in the local stress response for the given random composite is obtained from consideration of these simulations.     

Stress field interaction and strain energy distribution between a stationary main crack and its process zone

The damage process zone developed by brittle materials in front of a macrocrack is simulated by means of a distribution of microcracks. Crack mutual interactions are taken into account by means of a numerical technique, based on a displacement discontinuity boundary element method that is able of considering both the macrocrack–microcrack and microcrack–microcrack interactions inside the process zone. In the frame of linear elastic fracture mechanics the stress field at each crack tip and the related elastic strain energy are calculated. The main features of the interaction phenomena turn out to be almost independent of the microcrack density. Some considerations both on the shielding and amplification effects on the main crack and on the strain energy distribution between cracks give explanation to experimental evidence and prove that crack interaction is not such a short-range effect as sometimes expected.     

Evolution of residual stress redistribution associated with localized surface microcracking in shot-peened medium-carbon steel during fatigue test

Shot peening (SP) is a conventional method used for improving material properties, especially fatigue strength, through work hardening and the induction of compressive residual stress (CRS) near the surface by plastic deformation. However, CRS is redistributed and relaxed by the occurrence of physical discontinuities such as microcracks. In this study, the effects of residual stress redistribution and relaxation during the fatigue life associated with microdamages on the properties of a material were considered. To this end, annealed medium-carbon steel was treated with SP at three levels of peening intensity to investigate the effects on fatigue life and residual stress distributions. Rotating–bending fatigue tests were carried out to clarify the fatigue life distributions, and X-ray diffraction and scanning electron microscopy were used for residual stress and full-width at half-maximum (FWHM) values, microscopic inspections, respectively. The results indicate that microcracks at the treated surface significantly influenced stress redistribution, depending on the initial residual stress distribution at the surface. Moreover, when the induced CRS was relaxed during mechanical loading, these microcracks caused fatigue life degradation regardless of peening treatment. The effects of surface microcracks on stress redistribution and relaxation were discussed and a valuable range of peening conditions of used material was proposed.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

Microcracks size growth prediction based on microdefects nucleation number

The mechanical reason for rock and concrete failure is trans-scale fracture, which can be divided into three phases: (1) microcrack evolution, (2) macrocrack nucleation, (3) macrocrack growth and run-through. Using the idea that a microcrack could be regarded as a well-organized aggregation of nucleated microdefects, the size growth model of the largest microcrack based on the accumulated number of microdefect nucleation is established. In order to test the validity of the model, trans-scale fracture of a plate made of heterogeneous material is numerically simulated to display the microcrack’s evolution. Statistical analysis of the number and sizes of the microcracks indicates that the predicted size of the largest microcrack according to the model is in close agreement with the measured crack size prior to peak stress, but not at all close to the measured values after the peak. At the end of the paper, some remaining problems are proposed for the further work.     

导电聚噻吩薄膜材料的断裂机理分析

对用电化学方法制备的导电聚噻吩薄膜材料进行了拉伸破坏实验,并用电子散斑干涉法测量了力与变形关系同时用扫描电镜对材料的断口进行了断裂机理分析.研究结果表明;不同厚度的导电聚噻吩薄膜材料对其强度有较大的影响.引起薄膜材料力学特性变化的主要原因是其微结构生成机理不同,在较厚的薄膜自由表面上聚积有比较多的颗粒或大分子团结构,在干燥成型中形成一些微裂纹,这些微缺陷的存在严重影响了薄膜材料的承载能力,导致薄膜强度随厚度增加而降低.     

Error controlled adaptive multiscale XFEM simulation of cracks

The accurate and efficient prediction of the interaction of microcracks with macrocracks has been a challenge for many years. In this paper a discretization error controlled adaptive multiscale technique for the accurate simulation of microstructural effects within a macroscopic component is presented. The simulation of cracks is achieved using the corrected XFEM. The error estimation procedure is based on the well known Zienkiewicz and Zhu method extended to the XFEM for cracks such that physically meaningful stress irregularities and non-smoothnesses are accurately reflected. The incorporation of microstructural features such as microcracks is achieved by means of the multiscale projection method. In this context an error controlled adaptive mesh refinement is performed on the fine scale where microstructural effects may lead to highly complex mechanical behavior. The presented method is applied to a few examples showing its validity and applicability to arbitrary problems within fracture mechanics.     

Macrocrack Extension by Connecting Statistically Distributed Microcracks

The present paper explores the extension of a macrocrack by connecting statistically distributed microcracks. Two issues are discussed: (1) how long a semi-infinite crack can extend by connecting collinear microcracks of equal length but distributed ligament sizes; (2) how far the crack tip can shift vertically from the original crack extension line by connecting randomly positioned and oriented microcracks. Statistical analysis is employed to calculate the expected crack extension length and the vertical shift of the crack tip. The implication of the present study for the problem of a macrocrack linking to a parallel fault is addressed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mechanical properties of Bi(x)Sb(2-x)Te3 nanostructured thermoelectric material

Research on thermoelectric (TE) materials has been focused on their transport properties in order to maximize their overall performance. Mechanical properties, which are crucial for system reliability, are often overlooked. The recent development of a new class of high-performance, low-dimension thermoelectric materials calls for a better understanding of their mechanical behavior to achieve the desired system reliability. In the present study we investigate the mechanical behavior of nanostructure bulk TE material p-type Bi(x)Sb(2-x)Te(3) by means of nanoindentation and 3D finite element analysis. The Young's modulus of the material was estimated by the Oliver-Pharr (OP) method and by means of numerically assisted nanoindentation analysis yielding comparable values about 40 GPa. Enhanced hardness and yield strength can be predicted for this nanostructured material. Microstructure is studied and correlation with mechanical properties is discussed.     

Investigation of macrocrack-microcrack interaction problems in anisotropic elastic solids – Part I: General solution to the problem and application of the J-integral

A general solution is derived for the plane problem of multiple microcracks near the tip in process zone of a semi-infinite macrocrack in an anisotropic elastic solid. The pseudo-traction method, addressed thoroughly in isotropic cases, is extended to anisotropic cases. A system of Fredholm integral equations, with difficulty in evaluation of the singular integrals, is solved by invoking the asymptotic behavior of the pseudo-tractions on the macrocrack faces. The interaction effect of the release of residual stresses due to near-tip microcracking is then evaluated. The J-integral analysis is also performed to give a consistency check of the solution and some useful conclusions. This revised version was published online in July 2006 with corrections to the Cover Date.     

The influence of microcrack nucleation on dynamic crack growth––a numerical study

The study deals with the numerical investigation of microcrack nucleation in front of a fast running macrocrack. The computations are based on a time-domain boundary integral equation method. The influence of the microcracks on different parameters such as the stress intensity factor, energy release rate or crack speed are investigated. Results obtained from numerical simulations are discussed with respect to experimental findings.     

Damage tolerance of thick hybrid composite plate containing a local hemispherical damage

Three dimensional (3-D) stress and failure analysis of thick hybrid composite plate containing a local impact damage is presented. The impact damage is modelled in the present study by an artificial hemispherical flaw. The research involves a combination of theoretical study, based on the 3-D finite strip method for fiber reinforced material, and experimental investigation. Numerical results are compared with experimental results, and found to be in good agreement. This follows by a study of the effects of the damage geometry and materials properties on the mechanical behavior of the damaged plate. Theoretical and experimental failure analysis is developed, toward computer aided assessment of the residual strength of damaged plate.     

A dilatancy model of tensile macrocracks in compressed rock

A model is developed for tensile fracture under compression for a brittle material with microcracks. The final stage of failure with the formation of macroscopic-splitting cracks is considered. Pre-existing microcracks act as a converter of compression into tension in one direction. This results in the nucleation of other tensile microcracks. Rupture of spacings between the microcracks generates a mode I macrocrack parallel to the direction of maximum compression. Crack propagation is due to sliding along planes that are inclined to the compression microcrack surfaces and is stimulated by the forces distributed along the interacting macrocrack surfaces. Equilibrium, stability and growth of cracks are studied on the basis of the theory of fracture mechanics under the assumption of the plane strain state. The behaviour of both short and long macrocracks are analysed. Parameters of the model are evaluated with the help of data from fracture experiments on some rocks.     

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.