scholarly journals The deformation model of the DCB-sample with elastoplastic properties

2021 ◽  
pp. 55-63
Author(s):  
V. V Glagolev ◽  
A. A Markin
Keyword(s):  
Layer Thickness ◽  
External Load ◽  
Plasticity Condition ◽  
Crack Model ◽  
Deformation Model ◽  
Dugdale Model ◽  
Interaction Layer ◽  
Local Plasticity ◽  
Energy Product ◽  
Elastoplastic Properties

The loading of a strip with a crack-like defect according to mode I is considered. In contrast to the classical representation of a crack in the form of a mathematical section, the proposed model defines a crack as a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer (IL). It is important that the stress-strain state of the layer at a finite value of the linear parameter does not introduce a singularity into the crack model. The process of elastoplastic deformation with a constant layer length is considered. We obtained a simplified analytical solution to the problem of deformation of two elastic bodies connected by a thin layer with elastoplastic properties. The dependence of the displacement and stress fields on the length and thickness of the interaction layer has been found. It is shown that, under the classical plasticity condition, the range of variation of the external load leading to a purely elastic behavior is possible only for a finite layer thickness. As the layer thickness tends to zero, as in the Dugdale model, the plasticity region is formed at an arbitrarily small external load. For small layer thicknesses, a local plasticity criterion is proposed, by using which it is possible to distinguish the intervals of the external load variations associated with elastic and plastic deformations. The local plasticity condition, determined by the critical value of the energy product, makes it possible to reflect the stage of elastic deformation at an arbitrarily small finite thickness of the interaction layer. An asymptotic dependence of the external load on the IL thickness and the reduced length of the plastic zone is obtained. At the same time, the separation of the external load into elastic and plastic components is preserved. From the analysis of the experimental data, an estimate of the elastic limit of the energy product for the AV138 adhesive was obtained.

scholarly journals Energy product in a crack-like defect model under loading of mode II type

2019 ◽  
pp. 48-58
Author(s):  
V V Glagolev ◽  
L V Glagolev ◽  
A A Markin
Keyword(s):  
Characteristic Equation ◽  
Linear Size ◽  
Mode Ii ◽  
Crack Model ◽  
Interaction Layer ◽  
Real Roots ◽  
Energy Product ◽  
The Face ◽  
Simplified Solution ◽  
The Relationship

The loading of a crack-like defect in mode II is considered. In contrast to the classical representation of a crack in the form of a mathematical cut, the proposed model defines a crack in the form of a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer. It is significant that the stress-strain state of the layer does not introduce a singularity to the crack model. The product of the increment of the specific free energy in the face square element of the layer by the linear size determines its energy product. The object of the study is a double-cantilever sample, and the subject of study is the energy product in the face element of the interaction layer. The external load of the cantilevers leads to their horizontal antisymmetric displacements, which form uniform shear deformations in the interaction layer. From the equilibrium conditions of the cantilevers in the variation form, taking into account the hypothesis of axial deformation homogeneity and their reduction, a system of differential equations is obtained, which relates the stress state in the layer and the cantilevers. The solution of the characteristic equation of the system is investigated for various ratios of layer thickness and cantilevers. It is shown that when the relationship is less than a certain value, depending on the Poisson's ratio, real roots take place. In the framework of the real roots of the characteristic equation, an analytical solution of the problem is obtained. Subject to the neglect of compression cantilevers found a simplified solution. The deformations in the layer are determined taking into account the compression of the consoles and without it. The analysis of the dependence of the energy product on the relationship of the thickness of the layer and cantilevers. It is shown that with a thickness ratio of 10-6 or less, the energy product practically does not change its value. Accounting for the compression of cantilevers gives a difference in the values of the energy product of the order of 20 % in relation to the simplified solution of the problem.

Exchange Spring Type Magnet Realized in FePt/Fe Multilayers Deposited by Magnetron Sputtering

2005 ◽  
Vol 872 ◽  
Author(s):  
Yousong Gu ◽  
Dayong Zhang ◽  
Xiaoyuan Zhan ◽  
Zhen Ji ◽  
Xiaolan Zhen ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Magnetron Sputtering ◽  
Layer Thickness ◽  
Lattice Constants ◽  
Si Substrates ◽  
Energy Product ◽  
Layer Deposition ◽  
Different Temperatures ◽  
Spring Type ◽  
Type Magnet

AbstractSeries of FePt/Fe multilayers with different layer thicknesses have been deposited on Si substrates by magnetron sputtering and post annealing at different temperatures and durations. The structure, surface morphology, composition, and magnetic properties of the deposited films have been characterized by XRD, SEM, EDX and VSM. It is found that after annealing at temperatures above 500°C, FePt phase undergoes a phase transition from disorder fcc into ordered fct structure, and become a hard magnetic phase. For [FePt/Fe]n multilayer with varying Fe layer thickness, lattice constants and grain sizes change with Fe layer thickness and annealing temperature. The coercivities of [FePt/Fe]n multilayers decrease with Fe layer deposition time, and the energy product (BH)max shows a maximum with Fe layer thickness. Optimization on layer thickness leads a high (BxH)max value of 15.2MGOe for [FePt(8min)/Fe(4min)]8. The effects of quick annealing and Ag underlayer on the structure and magnetic properties were also studied.

A Nonlinear Analysis of an Equilibrium Craze: Part II—Simulations of Craze and Crack Growth

1988 ◽  
Vol 55 (1) ◽  
pp. 52-58 ◽  
Author(s):  
T. Ungsuwarungsri ◽  
W. G. Knauss
Keyword(s):  
Crack Growth ◽  
Crack Tip ◽  
Energy Dissipation Rate ◽  
Crack Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Critical Crack ◽  
Dugdale Model ◽  
Nonlinear Force ◽  
Crack Tip Opening

In this study we investigate the effects of nonlinear fibril behavior on the mechanics of craze and crack growth. The effect of strain-softening cohesive material on crack stability is of particular interest and is examined via a craze and crack model developed in the first part of this work where the formulation and solution of the problem are discussed.1 In this second part, quasi-static growth of a craze with a central crack is analyzed for different nonlinear force-displacement (p-v) relations for the craze fibrils. A “critical crack tip opening displacement” (CTOD), or more precisely, “critical fibril extension” is employed as the criterion for fracture. The p-v relation is further assumed to be invariant with respect to the craze and crack lengths. The results are compared with the Dugdale model; the craze zone size and the energy dissipation rate approach asymptotic values in the limit of long cracks. The problem of craze growth from a precut crack under increasing far-field loading is then studied. In the case where the p-v relation is monotonically softening, the crack can start to grow in an unstable manner before the crack tip opening displacement reaches its critical value.

A Phase Field Approach to Fracture with Mass Transport Extension for the Simulation of Environmentally-Assisted Cracking

2017 ◽  
Vol 754 ◽  
pp. 153-156 ◽  
Author(s):  
Rainer Falkenberg
Keyword(s):  
Crack Initiation ◽  
Mass Transport ◽  
Crack Propagation ◽  
Phase Field ◽  
Isotropic Hardening ◽  
Crack Model ◽  
Deformation Model ◽  
Coupling Mechanism ◽  
Crack Patterns ◽  
Field Approach

The fracture mechanics assessment of materials exposed to harmful environments requires the understanding of the interaction between the soluted species and the affected mechanical behaviour. With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase field approach is presented with an embrittlement-based coupling mechanism showing the influence on crack patterns and fracture toughness. Within the phase field approach the modeling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies such as curvilinear crack patterns, without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations. The simulation of showcases demonstrates crack initiation and crack propagation aiming for the determination of stress-intensity factors and crack-resistance curves.

Response of Sensitive Device of Piozoresistive Accelerometer to Load

2012 ◽  
Vol 203 ◽  
pp. 252-256
Author(s):  
Jian Hong Zhang
Keyword(s):  
Mechanical Properties ◽  
External Load ◽  
Optimization Design ◽  
Dynamic Deformation ◽  
Deformation Model ◽  
Virtual Operation ◽  
Deformation Equation ◽  
Sensitive Characteristics ◽  
Micro Cantilever ◽  
Micro Structures

The sensitive characteristics of sensitive device which was closely related to the mechanical properties of its micro elastic cantilever play a role in analysing the performance of piezoresistive accelerometer. To make a research on the response of the system to load, the deformation model of micro elastic cantilever of sensitive device belongs to piezoresistive accelerometer was built based on the method of system identification in this article to analyze their mechanical properties under static external load, the deformation equation was deduced and the quasi-dynamic deformation model of micro cantilever was obtained according to the principle that displacement was directly proportional to load. The conclusion could be used for evaluating the dynamic behavior of structure on virtual operation which would provide reference for optimization design of micro structures.

Structure and Orientation of As Precipitates in LT-MBE Grown GaAs

1991 ◽  
Vol 49 ◽  
pp. 900-901 ◽  
Author(s):  
Alain Claverie ◽  
Zuzanna Liliental-Weber
Keyword(s):  
Transport Properties ◽  
Layer Thickness ◽  
Growth Temperature ◽  
Low Temperatures ◽  
Lattice Parameter ◽  
Crystalline Quality ◽  
Insulating Properties ◽  
Lt Gaas

GaAs layers grown by MBE at low temperatures (in the 200°C range, LT-GaAs) have been reported to have very interesting electronic and transport properties. Previous studies have shown that, before annealing, the crystalline quality of the layers is related to the growth temperature. Lowering the temperature or increasing the layer thickness generally results in some columnar polycrystalline growth. For the best “temperature-thickness” combinations, the layers may be very As rich (up to 1.25%) resulting in an up to 0.15% increase of the lattice parameter, consistent with the excess As. Only after annealing are the technologically important semi-insulating properties of these layers observed. When annealed in As atmosphere at about 600°C a decrease of the lattice parameter to the substrate value is observed. TEM studies show formation of precipitates which are supposed to be As related since the average As concentration remains almost unchanged upon annealing.

EM of rapidly solidified permanent magnets

1992 ◽  
Vol 50 (1) ◽  
pp. 198-199
Author(s):  
Raja K. Mishra
Keyword(s):  
Melt Spinning ◽  
Permanent Magnets ◽  
Dark Field Image ◽  
Dark Field ◽  
Maximum Energy ◽  
Quench Rate ◽  
Maximum Energy Product ◽  
Energy Product ◽  
Annular Dark Field ◽  
Rapidly Solidified

The discovery of a new class of permanent magnets based on Nd2Fe14B phase in the last decade has led to intense research and development efforts aimed at commercial exploitation of the new alloy. The material can be prepared either by rapid solidification or by powder metallurgy techniques and the resulting microstructures are very different. This paper details the microstructure of Nd-Fe-B magnets produced by melt-spinning.In melt spinning, quench rate can be varied easily by changing the rate of rotation of the quench wheel. There is an optimum quench rate when the material shows maximum magnetic hardening. For faster or slower quench rates, both coercivity and maximum energy product of the material fall off. These results can be directly related to the changes in the microstructure of the melt-spun ribbon as a function of quench rate. Figure 1 shows the microstructure of (a) an overquenched and (b) an optimally quenched ribbon. In Fig. 1(a), the material is nearly amorphous, with small nuclei of Nd2Fe14B grains visible and in Fig. 1(b) the microstructure consists of equiaxed Nd2Fe14B grains surrounded by a thin noncrystalline Nd-rich phase. Fig. 1(c) shows an annular dark field image of the intergranular phase. Nd enrichment in this phase is shown in the EDX spectra in Fig. 2.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

On the Effect of 2-Layer Thickness by High-Specific Gravity Armor Blocks on Wave Reflection

1999 ◽  
Author(s):  
Masahiro Ito ◽  
Yuitch Iwagaki ◽  
Hiroshi Murakami ◽  
Kenji Nemoto ◽  
Masato Yamamoto ◽  
...  
Keyword(s):  
Specific Gravity ◽  
Layer Thickness ◽  
Wave Reflection ◽  
High Specific Gravity
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