The Effect of Local Yielding on the Strain-Energy Release Rate

1969 ◽  
Vol 91 (4) ◽  
pp. 852-854
Author(s):  
P. L. Key
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Correction Factor ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Elastic Strain Energy ◽  
Strain Energy Release ◽  
Finite Width ◽  
Dugdale Model

In a recent paper in the Journal of Basic Engineering [1], Forman presented numerical results for the strain-energy release rate of a crack in a finite width plate using the Dugdale model [2] of a yielded crack to describe the effects of local plastic flow. However, there appear to be several errors in the formulation of the problem by Forman. In addition, it is believed that an analytical rather than numerical approach to this problem would be more useful for applications. In this Note, an analytical form for a correction factor due to yielding is obtained for the elastic strain-energy release rate from an exact expression for the strain-energy release rale of the Dugdale model of a yielded crack in an infinite sheet. The effect of finite sheet width is treated as a separate correction factor.

Effect of Plastic Deformation on the Strain Energy Release Rate in a Centrally Notched Plate Subjected to Uniaxial Tension

1966 ◽  
Vol 88 (1) ◽  
pp. 82-86 ◽  
Author(s):  
R. G. Forman
Keyword(s):  
Plastic Deformation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Uniaxial Tension ◽  
Correction Factor ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Linear Elastic

This paper presents theoretical studies on the effect of plastic deformation on the strain energy release rate, G, of a plate under uniaxial tension with a central propagating crack. The linear elastic fracture mechanics solution for G is improved by using the Dugdale model for the crack and yielded region to obtain the axial rigidity of the plate. The axial rigidity is then used to obtain the solution for the strain energy release rate as the crack propagates. It is found that plastic deformation has a pronounced effect on G. A correction factor is presented for correcting the linear elastic solution for the strain energy release rate. The correction factor is found to depend upon the nominal (gross) stress to material yield stress ratio and the crack length to plate width ratio.

scholarly journals A New Bursting Liability Evaluation Index for Coal –The Effective Elastic Strain Energy Release Rate

Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3734
Author(s):  
Zhiguo LU ◽  
Wenjun JU ◽  
Fuqiang GAO ◽  
Youliang FENG ◽  
Zhuoyue SUN ◽  
...  
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Elastic Strain ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Elastic Strain Energy ◽  
Strain Curve ◽  
Strain Energy Release ◽  
Stress Strain Curve

Because both faults and cleats exist in coal, sharp stress drops occur during loading when coal is deformed. These drops occur during the pre-peak stage and are accompanied by sudden energy releases. After a stress drop, the stress climbs slowly following a zigzag path and the energy accumulated during the pre-peak stage is unstable. A stress–strain curve is the basic tool used to evaluate the bursting liability of coal. Based on energy accumulation in an unsteady state, the pre-peak stress–strain curve is divided into three stages: pre-extreme, stress drop, and re-rising stage. The energy evolution of the specimen during each stage is analyzed. In this paper, an index called the effective elastic strain energy release rate (EESERR) index is proposed and used to evaluate the coal’s bursting liability. The paper shows that the propagation and coalescence of cracks is accompanied by energy release. The stress climb following a zigzag path prolongs the plastic deformation stage. This causes a significant difference between the work done by a hydraulic press during a laboratory uniaxial compression experiment and the elastic strain energy stored in the specimen during the experiment, so the evaluation result of the burst energy index would be too high. The determination of bursting liability is a comprehensive evaluation of the elastic strain energy accumulated in coal that is released when the specimen is damaged. The index proposed in this paper fully integrates the energy evolution of coal samples being damaged by loading, the amount of elastic strain energy released during the sample failure divided by the failure time is the energy release rate. The calculation method is simplified so that the uniaxial compressive strength and elastic modulus are included which makes the new index more universal and comprehensive. Theoretical analysis and physical compression experiments validate the reliability of the evaluation.

On the Axial Rigidity of a Perforated Strip and the Strain Energy Release Rate in a Centrally Notched Strip Subjected to Uniaxial Tension

1964 ◽  
Vol 86 (4) ◽  
pp. 693-697 ◽  
Author(s):  
R. G. Forman ◽  
A. S. Kobayashi
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Uniaxial Tension ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Theoretical Studies ◽  
Correction Factors ◽  
Elasticity Solutions

This paper presents theoretical studies on the axial rigidities in strips with circular and elliptical perforations and subjected to uniaxial tension. Greenspan’s original derivations on these axial rigidities [2] were improved by using the elasticity solutions by Howland [6] and Ishida [7] for infinite strips with circular and elliptical perforations, respectively. Finally, the correction factors for centrally notched strips subjected to uniaxial tension were rederived from the above results following the energy approach by Irwin and Kies [3].

Nonlinear Approach for Strain Energy Release Rate in Micro Cantilevers

2010 ◽  
Author(s):  
Arash Kheyraddini Mousavi ◽  
Seyedhamidreza Alaie ◽  
Maheshwar R. Kashamolla ◽  
Zayd Chad Leseman
Keyword(s):  
Surface Roughness ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Rigid Substrate ◽  
Micro Cantilever

An analytical Mixed Mode I & II crack propagation model is used to analyze the experimental results of stiction failed micro cantilevers on a rigid substrate and to determine the critical strain energy release rate (adhesion energy). Using nonlinear beam deflection theory, the shape of the beam being peeled off of a rigid substrate can be accurately modeled. Results show that the model can fit the experimental data with an average root mean square error of less than 5 ran even at relatively large deflections which happens in some MEMS applications. The effects of surface roughness and/or debris are also explored and contrasted with perfectly (atomically) flat surfaces. Herein it is shown that unlike the macro-scale crack propagation tests, the surface roughness and debris trapped between the micro cantilever and the substrate can drastically effect the energy associated with creating unit new surface areas and also leads to some interesting phenomena. The polysilicon micro cantilever samples used, were fabricated by SUMMIT V™ technology in Sandia National Laboratories and were 1000 μm long, 30 μm wide and 2.6 μm thick.

Influence of Loading History on Delamination in Multilayered Beam with Creep

2021 ◽  
Vol 1046 ◽  
pp. 23-28
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Time Dependent ◽  
External Loading ◽  
Loading History ◽  
Multilayered Beam

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

The Edge Delamination Test: Measuring the Critical Adhesion Energy of Thin-Film Coatings, Part II: Mode Mixity & Application

1994 ◽  
Vol 338 ◽  
Author(s):  
Edward O. Shaffer ◽  
Scott A. Sikorski ◽  
Frederick J. McGarry
Keyword(s):  
Thin Film ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Mode I ◽  
Rigid Substrate ◽  
Edge Delamination

ABSTRACTThe edge delamination test (EDT) is being developed to measure the critical energy required to cause a thin film, under biaxial tensile stress, to debond from a rigid substrate[1]. The test uses circular features etched through biaxially stressed films adhered to a rigid substrate. If the stress is large enough, a stable debond ring grows radially about the feature. We use a finite element analysis to model the test, solving for the applied strain energy release rate as a function of crack length, feature hole radius and other geometrical parameters. The model identifies both mode I and mode II components of the strain energy release rate, and agrees with previous analytical solutions for the total debond energy. However, the model predicts, with a very refined mesh at the crack tip, the fracture process is pure mode I. To explore this result, critical strain energy release rates from the EDT and the island blister test (IBT) are compared. This agreement supports the model prediction that the failure process in the EDT is modeI peeling.

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