Plastic relaxation of the transformation strain energy of a misfitting spherical precipitate: linear and power-law strain hardening

The questions of analytical calculating the beam on the base with the modulus of deformation (modulus of elasticity), which is changed by thickness of the layer by power law, was deals in the article. The purpose of work was receiving finite expressions for reactive pressure of the basе on a beam and internal efforts in a beam when using model of the base with two characteristics (coefficient of subgrade resistance). A system of differential equations second-order with respect to the displacements of points the surface of a layer with a continuously changing modulus of elasticity was obtained based on the minimum of the total potential strain energy. The calculation of the rigid beam on the base on the action of the symmetric load was performed and the formulas for the reactive pressures of the base were got. Numerical calculation is executed and the analysis of influence of change of the module of deformation of a layer by the amount of reactive pressure and the bending moment in a beam was given. It is shown that with increase in the module of deformation on layer thickness the basе with two characteristics on nature of work is approaching vinklerovsky.

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Avalanches and power law behavior in aortic dissection propagation

Science Advances ◽

10.1126/sciadv.aaz1173 ◽

2020 ◽

Vol 6 (21) ◽

pp. eaaz1173 ◽

Cited By ~ 4

Author(s):

Xunjie Yu ◽

Béla Suki ◽

Yanhang Zhang

Keyword(s):

Cardiovascular Disease ◽

Extracellular Matrix ◽

Aortic Dissection ◽

Power Law ◽

Model Prediction ◽

Strain Energy ◽

Quantitative Agreement ◽

High Morbidity ◽

Failure Mechanics ◽

Microscopic Features

Aortic dissection is a devastating cardiovascular disease known for its rapid propagation and high morbidity and mortality. The mechanisms underlying the propagation of aortic dissection are not well understood. Our study reports the discovery of avalanche-like failure of the aorta during dissection propagation that results from the local buildup of strain energy followed by a cascade failure of inhomogeneously distributed interlamellar collagen fibers. An innovative computational model was developed that successfully describes the failure mechanics of dissection propagation. Our study provides the first quantitative agreement between experiment and model prediction of the dissection propagation within the complex extracellular matrix (ECM). Our results may lead to the possibility of predicting such catastrophic events based on microscopic features of the ECM.

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Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function

Applied Mathematics and Mechanics ◽

10.1007/bf02019593 ◽

1991 ◽

Vol 12 (5) ◽

pp. 481-492 ◽

Cited By ~ 3

Author(s):

Wang Zi-kung ◽

Wei Xue-xia ◽

Gao Xin-lin

Keyword(s):

Strain Hardening ◽

Power Law ◽

Plane Stress ◽

Stress Function

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A Proposed Generalized Model for Forming Limit Diagram

Volume 6A: Materials and Fabrication ◽

10.1115/pvp2015-45990 ◽

2015 ◽

Author(s):

Aly El Domiaty ◽

Abdel-Hamid I. Mourad ◽

Abdel-Hakim Bouzid

Keyword(s):

Constitutive Equation ◽

Strain Rate ◽

Strain Hardening ◽

Power Law ◽

Yield Criterion ◽

Rate Of Change ◽

Forming Limit ◽

Strain Hardening Exponent ◽

Sensitivity Factor ◽

Generalized Model

One of the most significant approaches for predicting formability is the use of forming limit diagrams (FLDs). The development of the generalized model integrates other models. The first model is based on Von-Misses yield criterion (traditionally used for isotropic material) and power law constitutive equation considering the strain hardening exponent. The second model is also based on Von-Misses yield criterion but uses a power law constitutive equation that considers the effect of strain rate sensitivity factor. The third model is based on the modified Hill’s yield criterion (for anisotropic materials) and a power law constitutive equation that considers the strain hardening exponent. The current developed model is a generalized model which is formulated on the basis of the modified Hill yield criterion and a power law constitutive equation considering the effect of strain rate. A new controlling parameter (γ) for the limit strains was exploited. This parameter presents the rate of change of strain rate with respect to strain. As γ increases the level of the FLD raises indicating a better formability of the material.

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Subcritical crack growth along epoxy/glass interfaces

Journal of Materials Research ◽

10.1557/jmr.1992.2621 ◽

1992 ◽

Vol 7 (9) ◽

pp. 2621-2629 ◽

Cited By ~ 10

Author(s):

K.M. Conley ◽

J.E. Ritter ◽

T.J. Lardner

Keyword(s):

Energy Release Rate ◽

Energy Release ◽

Crack Growth ◽

Power Law ◽

Release Rate ◽

Strain Energy ◽

Crack Velocity ◽

Subcritical Crack Growth ◽

Strain Energy Release Rate ◽

Strain Energy Release

Subcritical crack growth behavior along polymer/glass interfaces was measured for various epoxy adhesives at different relative humidities. A four-point flexure apparatus coupled with an inverted microscope allowed for observation in situ of the subcritical crack growth at the polymer/glass interface. The specimens consisted of soda-lime glass plates bonded together with epoxy acrylate, epoxy (Devcon), or epoxy (Shell) adhesives. Above a threshold strain energy release rate, the subcritical crack velocity was dependent on the strain energy release rate via a power law relationship where the exponent was independent of the adhesive tested and the test humidity (n = 3). However, the multiplicative constant A in the power law relation varied by over three orders of magnitude between the various adhesives with epoxy (Shell) having the smallest value and the epoxy (Devcon) the greatest value; in addition, A was very sensitive to humidity, decreasing by over two orders of magnitude from 80% to 15% relative humidity. At high strain energy release rates, the subcritical crack velocity reached a plateau at approximately 10−6 m/s. The use of this subcritical crack velocity data in predicting thin film delamination is discussed.

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Total Deformation, Plane-Strain Contact Analysis of Macroscopically Homogeneous, Compositionally Graded Materials With Constant Power-Law Strain Hardening

Journal of Applied Mechanics ◽

10.1115/1.2788992 ◽

1997 ◽

Vol 64 (4) ◽

pp. 853-860 ◽

Cited By ~ 7

Author(s):

A. E. Giannakopoulos

Keyword(s):

Strain Hardening ◽

Plane Strain ◽

Power Law ◽

Protective Coatings ◽

Contact Analysis ◽

Engineering Structures ◽

Graded Materials ◽

Line Load ◽

Structural Applications ◽

Graded Material

Plane-strain contact analysis is presented for compositionally graded materials with power-law strain hardening. The half-space, y≤0, is modeled as an incompressible, nonlinear elastic material. The effective stress, σe, and the effective total strain, εe, are related through a power-law model, σe=K0εeμ;0<μ≤min(1,(1+k)). The material property K0 changes with depth, |y|, as K0=A|y|k;A>0,0≤|k|<1. This material description attempts to capture some features of the plane-strain indentation of elastoplastic or steady-state creeping materials that show monotonically increasing or decreasing hardness with depth. The analysis starts with the solution for the normal line load (Flamant’s problem) and continues with the rigid, frictionless, flat-strip problem. Finally, the general solution of normal indentation of graded material by a convex, symmetric, rigid, and frictionless two-dimensional punch is given. Applications of the present results range from surface treatments of engineering structures, protective coatings for corrosion and fretting fatigue, settling of beam type foundations in the context of soil and rock mechanics, to bioengineering as well as structural applications such as contact of railroad tracks.

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