Eshelby Tensor for an Elastic Inclusion With Slightly Weakened Interface

1993 ◽  
Vol 60 (4) ◽  
pp. 1048-1050 ◽  
Author(s):  
Jianmin Qu
Keyword(s):  
Integral Representation ◽  
Matrix Material ◽  
Elastic Inclusion ◽  
Ellipsoidal Inclusion ◽  
Eshelby Tensor ◽  
Matrix Interface ◽  
Infinite Extent ◽  
The Matrix ◽  
Perfect Bonding ◽  
Inclusion Matrix

The Eshelby tensor for an ellipsoidal inclusion in an elastic matrix of infinite extent is considered in this paper. Instead of assuming perfect bonding between the inclusion and the matrix, the interface between the inclusion and the matrix is modeled by a spring layer of vanishing thickness. The inclusion- matrix interface is said to be slightly weakened if the compliance of the spring layer is much smaller than that of the matrix material. By virtue of the Betti-Rayleigh reciprocal identity in linear elasticity, an integral representation for the displacement field due to an elastic inclusion with a spring layer interface is derived. Explicit expressions of the Eshelby tensor for an ellipsoidal inclusion with slightly weakened interface are obtained through an iteration procedure developed from the integral representation.

The Elastic Inclusion With a Sliding Interface

1984 ◽  
Vol 51 (2) ◽  
pp. 308-310 ◽  
Author(s):  
T. Mura ◽  
R. Furuhashi
Keyword(s):  
Stress Field ◽  
Shear Deformation ◽  
Spherical Inclusion ◽  
Elastic Inclusion ◽  
Ellipsoidal Inclusion ◽  
Spheroidal Inclusion ◽  
Sliding Interface ◽  
Shear Traction ◽  
The Matrix ◽  
Invariant Transformation

It is found that when an ellipsoidal inclusion undergoes a shear eigenstrain and the inclusion is free to slip along the interface, the stress field vanishes everywhere in the inclusion and the matrix. It is assumed in the analysis that the inclusion interface cannot sustain any shear traction. There exists a shear deformation that transforms an ellipsoid into the identical ellipsoid without changing its orientation (ellipsoid invariant transformation). This is not true, however, for a spheroidal inclusion. The amount of slip and the associated stress field are calculated for a spherical inclusion for a given uniform eigenstrain εij*.

scholarly journals Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4928
Author(s):  
Yosyf Piskozub ◽  
Heorhiy Sulym
Keyword(s):  
Dry Friction ◽  
Strain State ◽  
Complete System ◽  
Thin Inclusion ◽  
Matrix Interface ◽  
Reinforced Composite ◽  
The Matrix ◽  
Modular Method ◽  
Inclusion Matrix

A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.

Geochemistry of orbicular diorite from the Grenville Front zone, eastern Labrador

1992 ◽  
Vol 56 (385) ◽  
pp. 451-458 ◽  
Author(s):  
J. Victor Owen
Keyword(s):  
Matrix Material ◽  
Shell Structures ◽  
Core Material ◽  
Matrix Interface ◽  
Fine Grained ◽  
Fine Grain ◽  
Eu Anomaly ◽  
The Matrix ◽  
Elevated Water ◽  
Front Zone

AbstractOrbicules in diorite from the Grenville Front zone of eastern Labrador consist of biotite- and/or hornblende-studded, dioritic cores enclosed by fine-grained shell structures alternately enriched and depleted in biotite. The orbicules occur in a mesocratic, quartz-bearing matrix. Epidote of inferred magmatic origin occurs in all parts of the rock. Plagioclase in the matrix is relatively sodic, and biotite more ferroan than in the orbicules, suggesting that the matrix material has the most evolved composition, and crystallized last.The diorite is unusually aluminous (orbicules: 24.9-27.4 wt.% Al2O3; matrix: 22.4-23.6% Al2O3) and calcic (orbicules: 7.0-8.4 wt.% CaO; matrix: 6.0-6.9% CaO); it shows a positive Eu anomaly, and has elevated Sr concentrations (1800-2500 ppm Sr), demonstrating that, compositionally, it resembles a plagioclase cumulate. Mass-balance calculations suggest that the orbicule cores had a crystal/melt ratio of ≤5. This accounts for the extreme fractionation of the rock (e.g., in orbicules, Zr <5 ppm). Compared with fractional crystallization patterns, variation diagrams show counter-trends (e.g. the siliceous matrix contains elevated TiO2) or scatter for several components, suggesting that the crystal/melt ratio governed some of the geochemical characteristics of the diorite.The presence of coarse mafic clots containing primary epidote, biotite and/or hornblende testify to an elevated water content in the orbieule cores. The shell magma apparently formed as a result of the interaction of supercooled orbicule core fluids with the matrix magma, and tended to serve as a reservoir for alkalis and Fe. Alkalis and Ca diffused in opposite directions, possibly as a result of a temperature gradient at the orbicule/matrix interface. This, however, requires decoupling of the thermodiffusional behaviour of alkalis and femic components in hydrated intermediate magma, which contrasts with documented Soret diffusion in mafic systems.The solidification of the shell magma prior, to the orbicule cores and matrix is attributed to dewatering, consistent with the fine grain size of the shell structures. Except where remobilized core material has disrupted the shells, the cores crystallized in isolation from the matrix, which fractionated toward a more evolved composition.

Use of an Advanced Shear-Lag Model to Obtain the Optimum Internal Damping in Short-Fiber Composites

1989 ◽  
Vol 42 (11S) ◽  
pp. S93-S99
Author(s):  
P. Hajela ◽  
C.-J. Shih
Keyword(s):  
Stress Distribution ◽  
Matrix Material ◽  
Short Fiber ◽  
Internal Damping ◽  
Shear Lag ◽  
Shear Lag Model ◽  
Damping Characteristics ◽  
The Matrix ◽  
Lag Model ◽  
Perfect Bonding

The present paper examines a modified shear-lag model for predicting the stress distribution in short fiber reinforced composite materials. The model assumes perfect bonding between the fiber and the matrix materials, and allows for the matrix material to partially sustain axial loads. The stress distribution obtained on the basis of this model is used to predict the internal damping characteristics of the composite material. These characteristics are a function of both the material properties and the geometrical layout of the composite, and are optimized by combining the analytical model with a nonlinear programming optimization algorithm. Representative numerical results are obtained for glass–epoxy and graphite–epoxy composites

Polishing process effect on the image of dispersed precipitates

1984 ◽  
Vol 42 ◽  
pp. 534-535
Author(s):  
C.T. Hu ◽  
C.W. Allen
Keyword(s):  
Matrix Material ◽  
Specimen Preparation ◽  
Second Phase ◽  
Precipitate Particle ◽  
Polishing Process ◽  
Second Phase Particles ◽  
The Matrix ◽  
Surface Profiles ◽  
Thinning Process

One important problem in determination of precipitate particle size is the effect of preferential thinning during TEM specimen preparation. Figure 1a schematically represents the original polydispersed Ni3Al precipitates in the Ni rich matrix. The three possible type surface profiles of TEM specimens, which result after electrolytic thinning process are illustrated in Figure 1b. c. & d. These various surface profiles could be produced by using different polishing electrolytes and conditions (i.e. temperature and electric current). The matrix-preferential-etching process causes the matrix material to be attacked much more rapidly than the second phase particles. Figure 1b indicated the result. The nonpreferential and precipitate-preferential-etching results are shown in Figures 1c and 1d respectively.

Application of cross correlation to HREM images of surfaces

1987 ◽  
Vol 45 ◽  
pp. 754-755
Author(s):  
D. E. Luzzi ◽  
L. D. Marks ◽  
M. I. Buckett
Keyword(s):  
Cross Correlation ◽  
A Priori ◽  
Matrix Material ◽  
Correlation Method ◽  
Accurate Knowledge ◽  
Complex Image ◽  
Fourier Filtering ◽  
The Matrix ◽  
Low Pass ◽  
Data Reduction Technique

As the HREM becomes increasingly used for the study of dynamic localized phenomena, the development of techniques to recover the desired information from a real image is important. Often, the important features are not strongly scattering in comparison to the matrix material in addition to being masked by statistical and amorphous noise. The desired information will usually involve the accurate knowledge of the position and intensity of the contrast. In order to decipher the desired information from a complex image, cross-correlation (xcf) techniques can be utilized. Unlike other image processing methods which rely on data massaging (e.g. high/low pass filtering or Fourier filtering), the cross-correlation method is a rigorous data reduction technique with no a priori assumptions.We have examined basic cross-correlation procedures using images of discrete gaussian peaks and have developed an iterative procedure to greatly enhance the capabilities of these techniques when the contrast from the peaks overlap.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

Impact Strength, Flexural Modulus and Wear Rate of PMMA Composites Reinforced by Eggshell Powders

2020 ◽  
Vol 38 (7A) ◽  
pp. 960-966
Author(s):  
Aseel M. Abdullah ◽  
Hussein Jaber ◽  
Hanaa A. Al-Kaisy
Keyword(s):  
Impact Strength ◽  
Wear Rate ◽  
Flexural Modulus ◽  
Matrix Material ◽  
Weight Fraction ◽  
Pure Pmma ◽  
Calcination Process ◽  
The Matrix ◽  
The Impact ◽  
Interface Bond

In the present study, the impact strength, flexural modulus, and wear rate of poly methyl methacrylate (PMMA) with eggshell powder (ESP) composites have been investigated. The PMMA used as a matrix material reinforced with ESP at two different states (including untreated eggshell powder (UTESP) and treated eggshell powder (TESP)). Both UTESP and TESP were mixed with PMMA at different weight fractions ranged from (1-5) wt.%. The results revealed that the mechanical properties of the PMMA/ESP composites were enhanced steadily with increasing eggshell contents. The samples with 5 wt.% of UTESP and TESP additions give the maximum values of impact strength, about twice the value of the pure PMMA sample. The calcination process of eggshells powders gives better properties of the PMMA samples compared with the UTESP at the same weight fraction due to improvements in the interface bond between the matrix and particles. The wear characteristics of the PMMA composites decrease by about 57% with increases the weight fraction of TESP up to 5 wt.%. The flexural modulus values are slightly enhanced by increasing of the ESP contents in the PMMA composites.

scholarly journals Self-Reinforced Nylon 6 Composite for Smart Vibration Damping

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1235
Author(s):  
Bidita Salahuddin ◽  
Rahim Mutlu ◽  
Tajwar A. Baigh ◽  
Mohammed N. Alghamdi ◽  
Shazed Aziz
Keyword(s):  
Matrix Material ◽  
Nylon 6 ◽  
Vibration Damping ◽  
Vibration Energy ◽  
Damping Factor ◽  
Passive Vibration Control ◽  
Reinforced Composite ◽  
Coiled Structure ◽  
The Matrix ◽  
3D Printed

Passive vibration control using polymer composites has been extensively investigated by the engineering community. In this paper, a new kind of vibration dampening polymer composite was developed where oriented nylon 6 fibres were used as the reinforcement, and 3D printed unoriented nylon 6 was used as the matrix material. The shape of the reinforcing fibres was modified to a coiled structure which transformed the fibres into a smart thermoresponsive actuator. This novel self-reinforced composite was of high mechanical robustness and its efficacy was demonstrated as an active dampening system for oscillatory vibration of a heated vibrating system. The blocking force generated within the reinforcing coiled actuator was responsible for dissipating vibration energy and increase the magnitude of the damping factor compared to samples made of non-reinforced nylon 6. Further study shows that the appropriate annealing of coiled actuators provides an enhanced dampening capability to the composite structure. The extent of crystallinity of the reinforcing actuators is found to directly influence the vibration dampening capacity.

Investigation on the Influence of Pressure Terms in a Volume-Averaged Energy Balance in the Modelling of Liquid Composite Moulding Processes

2019 ◽  
Vol 809 ◽  
pp. 480-486
Author(s):  
Rohit George Sebastian ◽  
Christof Obertscheider ◽  
Ewald Fauster ◽  
Ralf Schledjewski
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Energy Balance ◽  
Matrix Material ◽  
Energy Balance Equation ◽  
Manufacturing Processes ◽  
Composite Manufacturing ◽  
Liquid Composite Moulding ◽  
The Matrix ◽  
Computational Fluid Dynamics Cfd

The growing use of composite materials has generated interest in improving and optimising composite manufacturing processes such as Liquid Composite Moulding (LCM). In LCM, dry preforms are placed in a mould and impregnated with the matrix material. The efficiency of filling the moulds can be improved by using Computational Fluid Dynamics (CFD) filling simulations during the design of the mould. As part of an on-going effort to develop a CFD tool for the simulation of LCM processes, a volume averaged energy balance equation has been derived and implemented in a custom OpenFOAM solver. The energy balance is implemented in a custom OpenFOAM solver with and without the pressure terms for comparison with results from RTM experiments. It is found that the pressure terms do not significantly influence the results for LCM processes.

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