scholarly journals An Experimental Method for Estimating the Tearing Energy in Rubber-like Materials Using the True Stored Energy

2021 ◽  
Author(s):  
Elsiddig Elmukashfi
Keyword(s):  
Elastic Energy ◽  
Classical Method ◽  
Pure Shear ◽  
Loading Path ◽  
Dissipated Energy ◽  
Stored Energy ◽  
Total Strain Energy ◽  
Unloading Rate ◽  
Tearing Energy ◽  
Stored Elastic Energy

Abstract A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of the recovered elastic energy. Hence, the dissipated energy due to different inelastic processes is deducted from the total strain energy applied to the system. Therefore, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The elastically stored energy in a pure shear is determined experimentally using cyclic loading under quasi-static loading rate of 0.01 s-1 for different unloading rates, i.e. 0.01, 0.1 and 1.0 s-1. The experimental results show that the classical method overestimates the critical tearing energy by approximately 18% and the unloading rate is minimal which suggests that the dissipation depends only on the loading path.

scholarly journals An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Elsiddig Elmukashfi
Keyword(s):  
Crack Propagation ◽  
Viscous Dissipation ◽  
Simple Shear ◽  
Elastic Energy ◽  
Classical Method ◽  
Pure Shear ◽  
Dissipated Energy ◽  
Dynamic Experiments ◽  
Unloading Rate ◽  
Tearing Energy

AbstractA method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 -$$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 -$$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .

Determination of stored elastic energy in plastically deformed copper

2008 ◽  
Vol 2008 (27) ◽  
pp. 65-72
Author(s):  
A. Baczmanski ◽  
N. Hfaiedh ◽  
M. Francois ◽  
K. Saanouni ◽  
K. Wierzbanowski
Keyword(s):  
Elastic Energy ◽  
Stored Elastic Energy

Analysis the characteristic of energy and damage of coal-rock composite structure under cycle loading

2021 ◽  
Author(s):  
Tan Li ◽  
Guangbo Chen ◽  
Zhongcheng Qin ◽  
Qinghai Li
Keyword(s):  
Cyclic Loading ◽  
Elastic Energy ◽  
Composite Structure ◽  
Calculation Method ◽  
Composite Structures ◽  
Damage Variable ◽  
Dissipated Energy ◽  
Height Ratio ◽  
Coal Rock ◽  
The Stability

Abstract The stability of coal-rock composite structures is of great significance to coal mine safety production. To study the stability and deformation failure characteristics of the coal-rock composite structure, the uniaxial cyclic loading tests of the coal-rock composite structures with different coal-rock height ratios were carried out. Lithology and coal-rock height ratio play an important role in the energy dissipation of coal-rock composite structures. The higher the coal-rock height ratio, the greater the average elastic energy and dissipated energy produced per cycle of coal-rock composite structures, the smaller the total elastic energy and dissipated energy produced in the process of cyclic loading. Based on the difference of damage variables calculated by dissipative energy method and acoustic emission method, a more sensitive joint calculation method for calculating damage variable was proposed. The joint damage variable calculation method can more accurately and sensitively reflect the damage of coal-rock composite structure under cyclic loading. The macroscopic crack first appears in the coal specimen in the coal-rock composite structure, the degree of broken coal specimens in the composite structure is inversely proportional to the coal-rock height ratio. The strength and deformation characteristics of the coal-rock composite structure are mainly affected by coal sample in the composite structure.

scholarly journals An Experimental Research on Surrounding Rock Unloading during Solid Coal Roadway Excavation

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hongjun Guo ◽  
Ming Ji ◽  
Dapeng Liu ◽  
Mengxi Liu ◽  
Gaofeng Li ◽  
...  
Keyword(s):  
Energy Storage ◽  
Deformation Energy ◽  
Surrounding Rock ◽  
Dissipated Energy ◽  
Rock Stress ◽  
Deformation And Failure ◽  
Coal Roadway ◽  
Solid Coal ◽  
Unloading Rate ◽  
Surrounding Rock Stress

In order to further explore the deformation and failure essence of the deep coal body, based on the characteristics of surrounding rock stress adjustment before and after solid coal roadway excavation, an experiment of unloading confining pressure and loading axial pressure of the coal body was designed and conducted in this study. Based on test results, the failure mechanics and energy characteristics of the coal body were analyzed through experiments. Rapid unloading is considered a key factor contributing to lateral deformation and expansion failure, which exacerbates the deterioration of coal body and reduces the deformation energy storage capacity of coal. On the other hand, the larger loading rate tends to shorten the accumulation time of microcracks and cause damage to the coal body, resulting in strengthening the coal body and improving energy storage. Under the circumstance that the coal body is destroyed, the conversion rates of the internal deformation energy and dissipated energy are more significantly affected by unloading rate. The increasing unloading rate and rapid decreases in the conversion rate of deformation energy make the coal body more vulnerable to damage. Under the same stress conditions, the excavation unloading is more likely to deform, destroy, or even throw the coal than the experiment unloading. In order to reduce or avoid the occurrence of deep roadway excavation accidents, the understanding of the excavation unloading including possible influencing factors and the monitoring of the surrounding rock stress and energy during the excavation disturbance should be strengthened. It can be used as the basis for studying the mechanism of deformation and failure of coal and rock and dynamic disasters in deep mines, as well as the prediction, early warning, prevention, and control of related dynamic disasters.

Crack Propagation Prediction Using Haensel Damage Model

2012 ◽  
Author(s):  
Piotr Bednarz ◽  
Jaroslaw Szwedowicz
Keyword(s):  
Cyclic Loading ◽  
Crack Initiation ◽  
Crack Propagation ◽  
Damage Model ◽  
Lifetime Prediction ◽  
Dissipated Energy ◽  
Mathematical Approach ◽  
Loading Conditions ◽  
Stored Energy ◽  
Tensile Stresses

The Haensel damage model correlates lifetime of a component until crack initiation to the dissipated and stored energy in the material during cyclic loading. The crack initiation is influenced by mean stresses. The Haensel damage model considers the mean stress effect by including compressive and tensile stresses in calculations of elastic strain energy during cyclic loading conditions. The goal of the paper is to extend the above model to predict crack propagation under large cyclic plasticity and non-proportional loading conditions. After voids initiation onset of necking, voids growth and linking takes place among them. During this process a mesocrack is created. This stage of fracture involves the same amount of released energy for new crack surface creation as dissipated energy for mesocrack initiation. The amount of dissipated and stored energy is related to the process zone size and to the number of cycles. Ilyushin’s postulate is used to calculate the amount of dissipated energy. In order to consider a contribution of tensile stresses only during loading to crack propagation, tensile/compressive split is performed for the stress tensor. One of the key drivers of this paper is to provide a straightforward engineering approach, which does not require explicit modelling of cracks. The proposed mathematical approach accounts for redistribution of stresses, strains and energy during crack propagation. This allows to approximate the observed effect of distribution of dissipated energy on the front of a crack tip. The developed approach is validated through FE (Finite Element) simulations of the Dowling and Begley experiment. The Haensel lifetime prediction of Dowling’s experiment is in good agreement with the experimental data and the explicit FE results. Finally, the proposed mathematical approach simplifies significantly the engineering effort for Nonlinear Fracture Mechanics lifetime prediction by avoiding the requirement to simulate real crack propagation using node base release methods, XFEM or remeshing procedures.

Plastic incompatibility stresses and stored elastic energy in plastically deformed copper

2009 ◽  
Vol 501 (1-2) ◽  
pp. 153-165 ◽  
Author(s):  
A. Baczmański ◽  
N. Hfaiedh ◽  
M. François ◽  
K. Wierzbanowski
Keyword(s):  
Elastic Energy ◽  
Stored Elastic Energy

scholarly journals An Evaluation Method of Brittleness Characteristics of Shale Based on the Unloading Experiment

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1779 ◽  
Author(s):  
Xiaogui Zhou ◽  
Haiming Liu ◽  
Yintong Guo ◽  
Lei Wang ◽  
Zhenkun Hou ◽  
...  
Keyword(s):  
Evaluation Method ◽  
Shear Failure ◽  
Confining Pressure ◽  
Shear Zones ◽  
Loading Path ◽  
Mechanical Parameters ◽  
Failure Characteristics ◽  
Unloading Rate ◽  
Uplift And Erosion ◽  
Unloading Effect

Shale reservoir has an initial unloading effect during the natural uplift and erosion process, which causes the shale brittleness to change, affecting the design of the fracturing scheme. To consider this, the axial compression loading and confining pressure unloading experiment of shale is carried out, and then the influence of unloading rate on the mechanical parameters, failure characteristics, and the brittleness of rock are analyzed. What is more, a new evaluation method of brittleness characteristics that take the unloading effect into consideration is proposed. The conclusions are as follows: (1) The unloading rate has a weakening effect on the mechanical parameters, such as the destructive confining pressure and the residual strength of the samples. (2) The failure characteristics of shale specimens are a single shear failure in an oblique section under low unloading rate, and multiple shear zones accompanied with bedding fracture under high unloading rate. (3) The brittleness of shale samples is well verified by the brittleness index B d 1 and B d 2 during the loading path; nevertheless, it has shortage at the unloading path. This paper proposes a new brittleness evaluation method which can consider the influence of the different unloading rates and unloading points. Furthermore, there is a nice characterization between the brittleness damage and this method.

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