Fracture Formation in Axisymmetrical Layered Materials

2016 ◽  
Vol 83 (7) ◽  
Author(s):  
Jérôme Colin
Keyword(s):  
Layered Materials ◽  
Critical Distance ◽  
Cylindrical Inclusion ◽  
Infinite Length ◽  
Periodic Distribution ◽  
Fracture Formation ◽  
Intrinsic Strain ◽  
Elastic Coefficients ◽  
Circular Cracks

A stress-based criterion for the formation of a periodic distribution of cracks in an infinite-length cylindrical inclusion of radius R embedded in an infinite-size matrix has been established when the inclusion undergoes intrinsic strain. In agreement with previous studies, it is found that the distance separating two consecutive circular cracks of the same radius than that of inclusion does not depend on stress nor elastic coefficients of the material. This critical distance has been found to be of the order of 1.67 R.

Numerical Simulation on Fracture Formation on Surfaces of Bi-Layered Materials

2007 ◽  
Vol 353-358 ◽  
pp. 993-996
Author(s):  
Tian Hui Ma ◽  
Ju Ying Yang ◽  
Zheng Zhao Liang ◽  
Yong Bin Zhang ◽  
Tao Xu
Keyword(s):  
Numerical Simulation ◽  
Numerical Solutions ◽  
Process Analysis ◽  
Failure Process ◽  
Layered Materials ◽  
Numerical Code ◽  
Material Layer ◽  
Fracture Formation ◽  
Constant State ◽  
The Individual

Fracture formation on surfaces of bi-layered materials is studied numerically. A simplified two-layered materials model like growing tree trunk is present. This work is focused on patterns of fractures and fracture saturation. We consider the formation of crack pattern in bark as an example of pattern formation due to expansion of one material layer with respect to another. As a result of this expansion, the bark stretches until it reaches its limit of deformation and cracks. A novel numerical code, 3D Realistic Failure Process Analysis code (abbreviated as RFPA3D) is used to obtain numerical solutions. In this numerical code, the heterogeneity of materials is taken into account by assigning different properties to the individual elements according to statistical distribution function. Elastic-brittle constitutive relation with residual strength for elements and a Mohr-Coulomb criterion with a tensile cut-off are adopted so that the elements may fail either in shear or in tension. The discontinuity feature of the initiated crack is automatically induced by using degraded stiffness approach when the tensile strain of the failed elements reaching a certain value. The different patterns are obtained by varying simulation parameters, the thickness of the material layer. Numerical simulation clearly demonstrates that the stress state transition precludes further infilling of fractures and the fracture spacing reaches constant state,i.e. the socalled fracture saturation. It also indicates that RFPA code is a viable tool for modeling fracture formation and studying fracture patterns.

Dynamic characteristics of infinite-length and finite-length rods with high-wave-number periodic parameters

2017 ◽  
Vol 24 (11) ◽  
pp. 2344-2358 ◽  
Author(s):  
Zu-Guang Ying ◽  
Yi-Qing Ni
Keyword(s):  
Finite Length ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Wave Number ◽  
Infinite Length ◽  
Characteristic Wave ◽  
Periodic Distribution ◽  
The Matrix ◽  
Distribution Parameters ◽  
Matrix Eigenvalues

The dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters are studied. The differential equation of longitudinal motion of the period-parametric rod is given. The algebraic matrix equation for the wave motion characteristics of the infinite-length periodic rod is derived based on the Bloch theorem and Fourier series. The characteristic frequencies are determined by the matrix eigenvalues which depend on the characteristic wave number and parametric wave number. Then the algebraic matrix equation for the dynamic characteristics of the finite-length periodic rod is derived based on the Galerkin method. The natural frequencies are determined by the matrix eigenvalues which depend on only the parametric wave number. An improving approach algorithm for solving the eigenvalue problem of high degree-of-freedom systems is developed based on the Rayleigh quotient. Finally, the circular cross-section rod with period-varying diameter is considered and numerical results on the dynamic characteristics are given. Large characteristic wave number and parametric wave number are considered for the infinite-length and finite-length periodic rods. The characteristic frequencies varying with the characteristic wave number and parametric wave number are shown, and the band gaps vanishing are revealed for increasing characteristic wave number. The finite-length periodic rod has the dynamic characteristics different from the infinite-length periodic rod. The effect of the term number of the displacement expansion on the natural frequencies and the natural frequencies varying with the parametric wave number and wave amplitude are shown for the finite-length periodic rod. The local resonance and periodical short descent of the natural frequencies with the increase of the parametric wave number and the different changes of the natural frequencies with the parametric wave amplitude are revealed. The above new dynamic characteristics of the infinite-length and finite-length rods with periodic distribution parameters have a potential application to period-structural design and optimization.

High Resolution Electron Microscopy of internal interfaces in layered materials

1990 ◽  
Vol 48 (4) ◽  
pp. 320-321
Author(s):  
Yoichi Ishida ◽  
Hideki Ichinose ◽  
Yutaka Takahashi ◽  
Jin-yeh Wang
Keyword(s):  
Grain Boundaries ◽  
Mirror Symmetry ◽  
Functional Materials ◽  
High Resolution Electron Microscopy ◽  
Layered Materials ◽  
Plane Boundary ◽  
Chemical Information ◽  
Layer Plane ◽  
High Tc ◽  
Cubic Metals

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

Antonio Negri

2018 ◽  
Author(s):  
Ingrid Diran
Keyword(s):  
Critical Distance ◽  
Middle Voice ◽  
The Subject ◽  
Definition Of ◽  
Antonio Negri

Agamben describes his posture as a reader as one of seeking a text’s Entwicklungsfähigkeit, or capacity for elaboration.1 In examining Agamben’s practices of reading, we can attend to the opposite phenomenon: the counter-elaboration that a text, in having being read by the philosopher, performs upon Agamben’s own thought. This reciprocal elaboration might constitute a paradigm for Agamben’s use of reading, according to his own idiosyncratic definition of use as an event in the middle voice, in which (according to a definition of Benveniste) the subject ‘effects an action only in affecting itself (il effectue en s’affectant)’ (UB 28). With this definition in mind, we could say that Agamben effects a text (he writes) only to the extent that he is also affected by another text (he reads). This is why Agamben’s position as a reader proves particularly important to any assessment of his work, quite aside from the problem of influence or intellectual genealogy. For this same reason, however, assessing Agamben’s relation to Antonio Negri – a figure with whom, by most measures, he is at odds – poses an unexpected challenge: how can Agamben’s thought be a use of Negri? Answering this question means not only assessing the critical distance between the two thinkers, but also taking this distance as a measure, in the Spinozan sense, of mutual affection.

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