Abstract:Fractal, or generally a self-similar (or self-affine) structure of infinite order, has been extensively used as a nonlinear mathematical tool to describe various irregular and complex phenomena in fracture mechanics. However, there are still critical issues remaining ambiguous, leading to inherent difficulties mainly resulted from the contradiction between the integral dimension immeasurability of a fractal and the integral dimension characteristic of a physical object in nature. Here we demonstrate that conceptually a physical object in nature can never be described as a fractal, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure), and show mathematically that a ubiquitiform must be of integral dimension in Euclidean space, which is radically different from a fractal in the sense of the Hausdorff measure and makes the fractal approximation of a ubiquitiform unavailable. Our result implies that a natural object is of ubiquitiform rather than fractal, and thus, instead of the existing fractal theory, a new type of ubiquitiform theory must be established in future. We anticipate this result to be a starting point for the coming universal ubiquitiform theory in fracture mechanics. Moreover, it can be expected that the coming ubiquitiform theory will be more easy-to-use in practice than the fractal one, since it can be constructed completely on the base of "classical" mathematics, and hence some intrinsic difficulties in applied fractal science can be avoided.

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	1. ON CONCEPT OF FRACTAL IN FRACTURE MECHANICS
	OU Zhuocheng,LI Guanying,DUAN Zhuoping,HUANG Fenglei
	Mechanics 02 August 2012
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	Abstract:Fractal, or generally a self-similar (or self-affine) structure of infinite order, has been extensively used as a nonlinear mathematical tool to describe various irregular and complex phenomena in fracture mechanics. However, there are still critical issues remaining ambiguous, leading to inherent difficulties mainly resulted from the contradiction between the integral dimension immeasurability of a fractal and the integral dimension characteristic of a physical object in nature. Here we demonstrate that conceptually a physical object in nature can never be described as a fractal, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure), and show mathematically that a ubiquitiform must be of integral dimension in Euclidean space, which is radically different from a fractal in the sense of the Hausdorff measure and makes the fractal approximation of a ubiquitiform unavailable. Our result implies that a natural object is of ubiquitiform rather than fractal, and thus, instead of the existing fractal theory, a new type of ubiquitiform theory must be established in future. We anticipate this result to be a starting point for the coming universal ubiquitiform theory in fracture mechanics. Moreover, it can be expected that the coming ubiquitiform theory will be more easy-to-use in practice than the fractal one, since it can be constructed completely on the base of "classical" mathematics, and hence some intrinsic difficulties in applied fractal science can be avoided.
	TO cite this article:OU Zhuocheng,LI Guanying,DUAN Zhuoping, et al. ON CONCEPT OF FRACTAL IN FRACTURE MECHANICS[OL].[ 2 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4486167


	2. Finite Fatigue Lives of SUS 630 H900 under High Cycle Loading
	GUO Fengming,FENG Miaolin,XU Jinquan
	Mechanics 31 January 2012
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	Abstract:This paper is concerned with the finite fatigue lives of high strength steel SUS 630 H900 taking various defects under high cycle loading in two dimensions (2D) and three dimensions (3D). SUS 630 H900 steel has the extensive applications with specific fatigue features. The related defects refer to long cracks/notches as well as small cracks/notches. The small cracks/notches generally give rise to the size effect on material fatigue strengths and lives. In order to address the size effect, the characteristic fatigue length concept, accounting for the minimum representative size of polycrystalline material under cyclic loadings, is selected to correlate the fatigue lives with the average stress amplitude within the length. In this concept, the characteristic fatigue length is considered as the material intrinsic property and does not vary with the number of cycles to failure. Based on the length, The finite fatigue lives of SUS 630 H900 with various defects are predicted and partially compared with the experimental results. Through the comparison it is found that, the predicted values agree with the experimental results well.
	TO cite this article:GUO Fengming,FENG Miaolin,XU Jinquan. Finite Fatigue Lives of SUS 630 H900 under High Cycle Loading[OL].[31 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4464573

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	3. Buckling Solutions of FGM Timoshenko Beams in Terms of Those of the Homogenous Euler-Bernoulli Beams
	Shirong Li,Zeqing Wan
	Mechanics 27 January 2012
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	Abstract:Analytical relationships between the solutions of buckling of functionally graded material (FGM) Timoshenko beams and those of the homogenous Euler-Bernoulli beams subjected to axial compressive load were investigated for different boundary conditions. Based on the first order shear deformation theory, governing equation of buckling of FGM beams with the material properties changing continuously arbitrarily in the thickness direction were derived only in terms of the deflection, which has the same form as that of the homogenous Euler-Bernoulli beams. By solving the governing equation with specific boundary conditions, an analytical relationship between the critical buckling loads of the FGM Timoshenko beams and those of the corresponding Euler-Bernoulli beams were obtained which is valid for the clamped-clamped(C-C), simply supported-simply supported (S-S) and clamped-free(C-F) end constraints. Unfortunately, the above mentioned relationship is not valid for the beams with clamped-simply supported (C-S) ends. However, a simple eigenvalue equation is presented to find the critical buckling load for a C-S FGM Timoshenko beam. Consequently, buckling loads of FGM Timoshenko beams with C-C, S-S and C-F ends can be simplified as calculations of two coefficients determined by the material gradients and the geometry of the FGM beams when the critical buckling load parameters are known.)
	TO cite this article:Shirong Li,Zeqing Wan. Buckling Solutions of FGM Timoshenko Beams in Terms of Those of the Homogenous Euler-Bernoulli Beams[OL].[27 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4463997


	4. FE analysis of creep deformation of single crystal under temperature gradient
	YU Qingmin
	Mechanics 17 January 2012
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	Abstract:In this study, thin-walled cylindrical specimen was used to model air-cooled gas turbine blade. The deformation characteristic during creep under temperature gradient was investigated by finite element method. The creep parameters along [001] and elastic constants were taken from the experiment results of nickel-based single crystal superalloy DD3. The results show that the temperature gradient has notable influence on stress and strain distributions during creep. The stress of low temperature zone increases and that of high temperature zone decreases with the development of creep. The lower the temperature is, the higher the stress is. The increase of stress induces the increase of strain rate in low temperature zone. The strain rate in high temperature zone decreases due to the stress drop. The rapid changes of stress value and distribution result in the redistribution of strain in different temperature zone. The crack will appear firstly in low temperature zone for the higher stress and strain.
	TO cite this article:YU Qingmin. FE analysis of creep deformation of single crystal under temperature gradient[OL].[17 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4462846


	5. Experimental study on creep-ratcheting-fatigue interaction of SS304 stainless steel at room and high temperatures
	Zhang Juan,Kang Guozheng,Gao Qing,Liu Yujie
	Mechanics 17 January 2012
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	Abstract:The creep, ratcheting behaviour and fatigue failure, as well as their interaction were investigated by uniaxial cyclic stressing tests for SS304 stainless steel at room temperature, 100oC and 300oC. The effects of mean stress, stress amplitude, stress rate and the peak stress holds on the ratcheting strain and final failure life were discussed. Simultaneously, the variations of responded strain amplitude with the number of cycles were illustrated to discuss the interaction of creep, ratcheting behaviour and fatigue failure. The experimental results show that the creep and ratcheting behaviour for SS304 stainless steel at different temperatures are different. The fatigue life of the material at room and high temperatures all depend greatly on mean stress, stress amplitude, stress rate and the peak stress holds of uniaxial cyclic stressing. And the material show different kind of failure modes: ratcheting failure due to large ratcheting strain and fatigue failure due to low-cycle fatigue with nearly constant responded strain amplitude.
	TO cite this article:Zhang Juan,Kang Guozheng,Gao Qing, et al. Experimental study on creep-ratcheting-fatigue interaction of SS304 stainless steel at room and high temperatures[J].


	6. Microstructure in the near-tip process zone for an impermeable macrocrack in piezoelectric materials
	Liu Q D,Cui Y H,Liu M B
	Mechanics 10 January 2012
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	Abstract:The influence of microstructures e.g. microcracks on the near-tip stress-electric field for an impermeable macrocrack in piezoelectric materials was studied using the existing pseudo-traction methods. The macrocrack could be modeled as impermeable one for its surrounding insulation environment whilst the microcracks could be modeled as permeable slit cracks due to poling or other sources without the crack surface opening effect. The conservation of the J-integral holds true for the configuration with a permeable microcrack near the tip of an impermeable macrocrack. Finally, the influence of the permeable microcrack on the macrocrack tip could be modeled as the stress intensity factor (SIF), electric displacement intensity factor (EDIF), and mechanical strain energy release rate (MSERR) in comparison with the previous work. It is found that the divergences between the present permeable microcrack model and the previous study are remarkable under combined electric-mechanical loading. The disturbance of the permeable microcracks on the near-tip stress-electric field due to the positive electric field loading is always much smaller than that given in the previous impermeable model.
	TO cite this article:Liu Q D,Cui Y H,Liu M B. Microstructure in the near-tip process zone for an impermeable macrocrack in piezoelectric materials[OL].[10 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4460318


	7. Finite element analysis on the permeable and impermeable hole in ferroelectrics
	Liu Qida,Cui Yuanhu
	Mechanics 22 December 2011
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	Abstract:The finite element method is used to study the creeping polarization and strains around a circular hole in the ferroelectric ceramics under various constant levels of electric field. Two kinds of electrical boundary conditions, the permeable and impermeable boundary conditions, are applied on the rim of the hole, while the evolution of strains and polarization distribution is computed around the hole. The strain and polarization distribution around the hole are significantly different for two conditions, which is confirmed by the birefringence measurement on PLZT specimen with an impermeable hole.
	TO cite this article:Liu Qida,Cui Yuanhu. Finite element analysis on the permeable and impermeable hole in ferroelectrics[OL].[22 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4457060


	8. Acoustic emission analysis on tensile failure of air plasma-sprayed thermal barrier coatings
	Yao Wangbin,Dai Cuiying,Mao Weiguo,Lu Chunsheng,Zhou Yichun
	Mechanics 04 December 2011
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	Abstract:An acoustic emission technique was used to monitor the cracking behavior and fracture process of thermal barrier coatings subjected to tensile loading. Acoustic emission signals were extracted and preformed by fast Fourier transform, and their corresponding characteristic frequency spectrums and dominant bands were obtained to reveal fracture modes. Three different characteristic frequency bands were confirmed, corresponding to substrate deformation, surface vertical crack and interface delamination, with the aid of scanning electronic microscopy observations. A map of the tensile failure mechanism of air plasma-sprayed thermal barrier coatings was established. Using experimental data, the fracture strength and interface shear strength were estimated as 45.73 ± 3.92 MPa and 20.51 ± 1.74 MPa, respectively, which are well agreement with available results..
	TO cite this article:Yao Wangbin,Dai Cuiying,Mao Weiguo, et al. Acoustic emission analysis on tensile failure of air plasma-sprayed thermal barrier coatings[OL].[ 4 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4453646


	9. Four parallel non-symmetric permeable mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane
	ZHOU Zhengong
	Mechanics 25 November 2011
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	Abstract:The behavior of four parallel non-symmetric permeable finite length cracks in a functionally graded piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the material parameters, the lengths and spacing of cracks. It is also revealed that the crack shielding effect presents in functionally graded piezoelectric/piezomagnetic materials.
	TO cite this article:ZHOU Zhengong. Four parallel non-symmetric permeable mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane[OL].[25 November 2011] http://en.paper.edu.cn/en_releasepaper/content/4451508


	10. New Constitutive Models of Rock Under uniaxial /Triaxial Compression Based on Statistical Damage Theory
	SHANG Xiaoji,LIU Weiqun
	Mechanics 27 June 2011
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	Abstract:It is well-known that rock materials have scale effects in the character of mechanic. In this paper, according to the damage mechanics theory, the Weibull's distribution hypothesis and therandom statistical distribution hypothesis of Brittle material strength, new scale constitutive models of rock under uniaxial /Triaxial compression of considering residual stress and not are established respectively; Then, an example of four different scale samples is analyzed; finally, comparative analysis are taken between the theoretical results and the experimental results, which shows they are in good agreement. Therefore, the accuracy and reasonableness of the statistical scale damage constitutive model is verified.
	TO cite this article:SHANG Xiaoji,LIU Weiqun. New Constitutive Models of Rock Under uniaxial /Triaxial Compression Based on Statistical Damage Theory[OL].[27 June 2011] http://en.paper.edu.cn/en_releasepaper/content/4433347

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