The distribution of the elastic strain-energy density at the crack tip for fracture modes I and II

1982 ◽  
Vol 18 (2) ◽  
pp. 81-112 ◽  
Author(s):  
P. S. Theocaris ◽  
G. Papadopoulos
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Crack Tip ◽  
Fracture Modes ◽  
Elastic Strain Energy Density

scholarly journals A Modified Bursting Energy Index for Evaluating Coal Burst Proneness and Its Application in Ordos Coalfield, China

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1729
Author(s):  
Xuewei Liu ◽  
Quansheng Liu ◽  
Bin Liu ◽  
Yongshui Kang
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Coal Mines ◽  
Elastic Strain Energy ◽  
Peak Strength ◽  
Energy Index ◽  
Total Input ◽  
Elastic Strain Energy Density

Coal burst is a type of dynamic geological hazard in coal mine. In this study, a modified bursting energy index, which is defined as the ratio of elastic strain energy at the peak strength to the released strain energy density at the post-peak stage, was proposed to evaluate the coal burst proneness. The calculation method for this index was also introduced. Two coal mines (PJ and TJH coal mines) located in Ordos coalfield were used to verify the validity of the proposed method. The tests results indicate that modified bursting energy index increases linearly with increasing uniaxial compressive strength. The parameter A, which is used to fit relation between total input and elastic strain energy density, has a significant effect on the modified bursting energy index. A large value of parameter A means more elastic strain energy before the peak strength while a small value indicates most of input energy was dissipated. Finally, the coal burst proneness of these two coal mines was evaluated with the modified index. The results of modified index are consistent with that of laboratory tests, and more reasonable than that from original bursting energy index because it removed the dissipated strain energy from the total input strain energy density.

On the definition of elastic strain energy density in fatigue modelling

2019 ◽  
Vol 121 ◽  
pp. 237-242 ◽  
Author(s):  
Ali A. Roostaei ◽  
Amirhossein Pahlevanpour ◽  
Seyed Behzad Behravesh ◽  
Hamid Jahed
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Definition Of ◽  
Elastic Strain Energy Density

scholarly journals Strain energy-and stress-based approaches revisited in notch fatigue of ductile steels

2018 ◽  
Vol 165 ◽  
pp. 14009 ◽  
Author(s):  
Bruno Atzori ◽  
Mauro Ricotta ◽  
Giovanni Meneghetti
Keyword(s):  
Energy Density ◽  
Plastic Strain ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Fatigue Behaviour ◽  
Strength Reduction Factor ◽  
Plastic Strain Energy ◽  
Elastic Strain Energy Density

The constant amplitude, zero-mean stress, axial-fatigue behaviour of plain and bluntly notched AISI 304 L stainless steel specimens is investigated in terms of strain energy density. Concerning plain material, it was found that at the fatigue knee the plastic strain energy density is 1.49 times higher than the elastic strain energy density. In the authors’ opinion, the presence of plasticity at the fatigue knee is responsible for the unsuitableness of classical stress - based approaches to synthesise the fatigue behaviour of this material. On the contrary, the elastic-plastic strain energy density was found an efficient parameter to rationalise in a single scatter band fatigue data of plain and bluntly notched specimens. Based on this result, the classic stress-and the point stress-based approaches were revisited taking into account the presence of plasticity at the fatigue knee, by introducing an equivalent fully elastic material having a linear elastic strain energy density at the fatigue knee equal to that of the actual material. Accordingly, a coefficient of plasticity Kp was successfully introduced to modify the classical definition of fatigue strength reduction factor, Kf.

Spectral decomposition of the linear elastic tensor for monoclinic symmetry

1999 ◽  
Vol 55 (4) ◽  
pp. 635-647 ◽  
Author(s):  
Pericles S. Theocaris ◽  
Dimitrios P. Sokolis
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Stress And Strain ◽  
Monoclinic Symmetry ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Elastic Strain Energy Density

The compliance fourth-rank tensor related to crystalline or other anisotropic media belonging to the monoclinic crystal system is spectrally decomposed for the first time, and its characteristic values and idempotent fourth-rank tensors are established. Further, it is proven that the idempotent tensors resolve the stress and strain second-rank tensors into eigentensors, thus giving rise to a decomposition of the total elastic strain-energy density into non-interacting strain-energy parts. Several examples of representative inorganic crystals of the monoclinic system illustrate the results of the theoretical analysis. It is also proven that the essential parameters required for a coordinate-invariant characterization of the elastic properties of a crystal exhibiting monoclinic symmetry are both the six characteristic values of the compliance tensor and seven dimensionless parameters. These material constants, referred to as the eigenangles, are shown to be accountable for the orientation of the stress and strain eigentensors, when represented in a stress coordinate system. Finally, the restrictions dictated by the classical thermodynamical argument on the elements of the compliance tensor, which are necessary and sufficient for the elastic strain-energy density to be positive definite, are investigated for the monoclinic symmetry.

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