On a Screw Dislocation Interacting With Two Viscous Interfaces

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
X. Wang ◽  
E. Pan
Keyword(s):  
Screw Dislocation ◽  
Equilibrium Position ◽  
Time Moment ◽  
Early Time ◽  
Image Force ◽  
Interface Layer ◽  
Critical Value ◽  
Time Dependent ◽  
Interphase Layer ◽  
The Matrix

We investigate a screw dislocation interacting with two concentric circular linear viscous interfaces. The inner viscous interface is formed by the circular inhomogeneity and the interphase layer, and the outer viscous interface by the interphase layer and the unbounded matrix. The time-dependent stresses in the inhomogeneity, interphase layer, and unbounded matrix induced by the screw dislocation located within the interphase layer are derived. Also obtained is the time-dependent image force on the screw dislocation due to its interaction with the two viscous interfaces. It is found that when the interphase layer is more compliant than both the inhomogeneity and the matrix, three transient equilibrium positions (two are unstable and one is stable) for the dislocation can coexist at a certain early time moment. If the inhomogeneity and matrix possess the same shear modulus, and the characteristic times for the two viscous interfaces are also the same, a fixed equilibrium position always exists for the dislocation. In addition, when the interphase layer is stiffer than the inhomogeneity and matrix, the fixed equilibrium position is always an unstable one; on the other hand, when the interface layer is more compliant than the inhomogeneity and matrix, the nature of the fixed equilibrium position depends on the time: the fixed equilibrium position is a stable one if the time is below a critical value, and it is an unstable one if the time is above the critical value. In addition, a saddle point transient equilibrium position for the dislocation can also be observed under certain conditions.

A Screw Dislocation Interacting with a Lip-Shaped Crack Bonded by a Strained Reinforcement Layer under Remote Longitudinal Shear Load

2012 ◽  
Vol 490-495 ◽  
pp. 56-60
Author(s):  
Min Yu ◽  
You Wen Liu
Keyword(s):  
Screw Dislocation ◽  
Complex Function ◽  
Image Force ◽  
Longitudinal Shear ◽  
Singularity Analysis ◽  
Infinite Matrix ◽  
Shear Load ◽  
Riemann Boundary ◽  
The Matrix ◽  
Shaped Crack

The interaction between a screw dislocation and a reinforced lip-shaped crack embedded in an infinite matrix subjected to a remote longitudinal shear load is investigated in this paper. By combining the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and Riemann boundary problem, the problem is reduced to solve an elementary complex potentials equation. The general expressions of complex function in the matrix and the reinforcement layer are derived explicitly in series form for the case when the screw dislocation is located in the matrix. The image force acting on the screw dislocation and the stress intensity factor are also calculated. Some numerical results are provided to discuss the effects of dislocation position, material parameters, geometric configurations and eigenstrain on the image force.

A Magnetoelectric Screw Dislocation Interacting with an Elliptical Inhomogeneity Containing a Confocal Rigid Line

2011 ◽  
Vol 239-242 ◽  
pp. 2195-2200 ◽  
Author(s):  
Chun Zhi Jiang ◽  
You Wen Liu ◽  
Chao Xie
Keyword(s):  
Screw Dislocation ◽  
Electric Displacement ◽  
Image Force ◽  
Material Behavior ◽  
Shear Stresses ◽  
Displacement Fields ◽  
Plane Shear ◽  
Elliptical Inhomogeneity ◽  
Rigid Line ◽  
The Matrix

Based on the complex variable method, the magnetoelectroelastic interaction of a generalized screw dislocation with an elliptical inhomogeneity containing a electrically conductive confocal rigid line under remote anti-plane shear stresses, in-plane electric and magnetic loads is dealt with. The generalized screw dislocation is located inside either the inhomogeneity or the matrix. The analytical-functions of complex potentials for stresses, electric displacement fields and magnetic induction fields in both the inhomogeneity and the matrix are derived. The image force acting on the dislocation are also calculated explicitly. The results show that the influence of the rigid line on the interaction effect between a generalized screw dislocation and an elliptical inhomogeneity is significant. In addition, the material behavior also plays an important role on the image force.

Magnetoelectroelastic Interaction between a Generalized Screw Dislocation and Multiple Circular Inclusions

2010 ◽  
Vol 26 (3) ◽  
pp. 309-316
Author(s):  
M. H. Shen ◽  
F.M. Chen ◽  
S. Y. Hung ◽  
S.N. Chen
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Screw Dislocation ◽  
Analytical Solutions ◽  
Displacement Field ◽  
Complex Variable ◽  
Crack Problem ◽  
Image Force ◽  
Variable Method ◽  
The Matrix

AbstractIn this paper, the interaction of a generalized screw dislocation with multiple circular inclusions perfectly bonded to an unbounded matrix under remote magnetoelectromechanical loadings is dealt with. The analytical solutions of electric field, magnetic field and displacement field either in the inclusions or the matrix are obtained by use of the complex variable method. The image force acting on the magnetoelectric screw dislocation is calculated by using the generalized Peach-Koehler formula. Finally, the influence of material combinations on the image force is examined for several practical examples. The obtained solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.

Interaction between a Screw Dislocation Located in Strained Reinforcement Layer and a Lip-Shaped Crack

2012 ◽  
Vol 182-183 ◽  
pp. 1549-1553
Author(s):  
Min Yu ◽  
You Wen Liu
Keyword(s):  
Stress Intensity Factor ◽  
Screw Dislocation ◽  
Complex Function ◽  
Great Influence ◽  
Image Force ◽  
Longitudinal Shear ◽  
Shear Load ◽  
The Matrix ◽  
In Series ◽  
Shaped Crack

The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

2019 ◽  
Vol 24 (10) ◽  
pp. 3080-3091
Author(s):  
Xianghua Peng ◽  
Min Yu ◽  
Yuxuan Yang
Keyword(s):  
Composite Materials ◽  
Screw Dislocation ◽  
Coupling Effect ◽  
Elliptic Hole ◽  
Great Influence ◽  
Image Force ◽  
Plane Shear ◽  
Blunt Crack ◽  
The Matrix ◽  
In Series

The paper deals with the interaction of a generalized screw dislocation and an elliptic inhomogeneity containing a confocal elliptic hole in a magneto-electro-elastic composite material. Exact solutions are derived for the case where the generalized screw dislocation is located in the matrix under a remote anti-plane shear stress field, an in-plane electric field, and a magnetic field. Based on the complex variable method, the complex potentials of both the matrix and the inhomogeneity are obtained in series, and analytic expressions for the generalized stress and strain field, the image force, the generalized stress intensity factor of the blunt crack tip, and the energy release rate are derived explicitly. The presented solutions include some previous solutions, such as pure elastic, piezoelectric, piezomagnetic, and circular inclusions. Typical numerical examples are presented and the influences of the dislocation position, the volume of inhomogeneity, and the elliptic hole on these physical quantities are discussed. The results show that the magneto-electro-elastic coupling effect has a great influence on the image force and the equilibrium position of dislocation, especially when the dislocation approaches the interface; the coupling effect makes the image force on the screw dislocation follow different variation laws in piezoelectric–piezomagnetic composite materials compared with elastic materials.

Effect of temperature on matrix multicracking evolution of C/SiC fiber-reinforced ceramic-matrix composites

2020 ◽  
Vol 39 (1) ◽  
pp. 189-199
Author(s):  
Longbiao Li
Keyword(s):  
Strain Energy ◽  
Ceramic Matrix Composites ◽  
Critical Value ◽  
Matrix Cracking ◽  
Interface Debonding ◽  
Matrix Composites ◽  
Temperature Dependent ◽  
Damage State ◽  
The Matrix ◽  
Sic Composites

AbstractIn this paper, the temperature-dependent matrix multicracking evolution of carbon-fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) is investigated. The temperature-dependent composite microstress field is obtained by combining the shear-lag model and temperature-dependent material properties and damage models. The critical matrix strain energy criterion assumes that the strain energy in the matrix has a critical value. With increasing applied stress, when the matrix strain energy is higher than the critical value, more matrix cracks and interface debonding occur to dissipate the additional energy. Based on the composite damage state, the temperature-dependent matrix strain energy and its critical value are obtained. The relationships among applied stress, matrix cracking state, interface damage state, and environmental temperature are established. The effects of interfacial properties, material properties, and environmental temperature on temperature-dependent matrix multiple fracture evolution of C/SiC composites are analyzed. The experimental evolution of matrix multiple fracture and fraction of the interface debonding of C/SiC composites at elevated temperatures are predicted. When the interface shear stress increases, the debonding resistance at the interface increases, leading to the decrease of the debonding fraction at the interface, and the stress transfer capacity between the fiber and the matrix increases, leading to the higher first matrix cracking stress, saturation matrix cracking stress, and saturation matrix cracking density.

scholarly journals Expression of VEGF-A Signaling Pathway in Cartilage of ACLT-induced Osteoarthritis Mouse Model

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jia-jia Qian ◽  
Qi Xu ◽  
Wei-min Xu ◽  
Ren Cai ◽  
Gui-cheng Huang
Keyword(s):  
Signaling Pathway ◽  
Cruciate Ligament ◽  
Time Dependent ◽  
Pathological Changes ◽  
The Matrix ◽  
Vegfr2 Signaling ◽  
Cox 2 ◽  
Anterior Cruciate ◽  
A Disintegrin And Metalloproteinase ◽  
Safranin O

Abstract Background Anterior cruciate ligament transection surgery (ACLT)-induced OA model was often used to investigate the molecular mechanism of knee osteoarthritis (KOA). Researches have shown that vascular endothelial growth factor (VEGF) played an important role in OA. The present study aimed to investigate the pathological changes after ACLT surgery and reveal the expression characteristics of the VEGF-A/VEGFR2 signaling pathway in this model. Methods Moderate KOA model was established by ACLT, and 1, 2, 4, 8, and 12 weeks after surgery, hematoxylin-eosin (HE) and Safranin-O(S-O) staining were used to detect the pathological changes in mouse knee cartilage, and the matrix biomarkers A Disintegrin and Metalloproteinase with Thrombospondin Motifs 5(ADAMTS5), Collagen II (COL-II) were detected using immunohistochemistry (IHC), CD31 was detected by immunofluorescence (IF) to show the vascular invasion in cartilage, and proteins expression of VEGF-A pathway were detected by Western blot (WB). Meanwhile, the inflammatory biomarkers cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS) in cartilage were detected by WB. Results ACLT surgery can lead to degeneration of cartilage in mice, and the characteristics of the lesion were time-dependent. The ADAMTS5-positive cells increased while COL-II decreased in OA cartilage with time, and new blood vessels labeled by CD31 can be seen from 1 week in OA cartilage, and increased in 8 and 12 weeks. The expression of VEGF-A, VEGFR2, COX-2, and iNOS were higher than control groups, which were basically consistent with the degree of osteoarthritis. Conclusions The degenerative degree of articular cartilage was time-dependent; angiogenesis and inflammation were important pathological changes of cartilage in KOA. The expression of the VEGF-A/VEGFR2 signaling pathway was basically correlated with the degree of KOA.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

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