Equations tearing energy

Tear strength data are very limited.Tearing energy is given by the following equation ... 

The puncture force F at rupture is related to the tearing energy Ti by the equation... 

For fatigue tests a SEN tension specimen is most suitable [189], and the associated tearing energy equation is shown [190] to be... 

The best predictive equation that has been found for the tear energy f C)... 

The tearing energy of a pure shear test-piece is given by Equation (5.6) ... 

The cyclic crack growth AcjAn is related to maximum tearing energy T attained during the cycle by Equation (5.14) ... 

The tearing energy of a split tear test-piece is computed using Equation (5.7), discussed in Section 5.2. 

In formal mathematical terms, if the crack increases in length by an amount dc, an amount of work TB dc must be done, where Tis the tearing energy per unit area and B is the thickness of the sheet. Assuming that no external work is due, this can be equated to the change in elastically stored energy, giving... 

A study was made of gas decompression failures in elastomeric seals using a fracture mechanics approach with considerations of gas permeation. An equation is proposed for the tearing energy associated with crack growth from internal gas bubbles in a finite thickness elastic media. The effects of gas pressure, temperature, rate of decompression and mechanical strain were studied for a range of elastomers used in oil and gas sealing applications. A theoretical treatment is presented based on a fracture mechanics criterion for fracture from an internal disc shaped flaw in a thick elastic medium. Permeation theory provides a quantification of the amount of gas available internally to initiate failures. 21 refs. 

Compute a new set of values of the Vj tear variables one at a time, starting with V3, from an energy-balance equation that is obtained by combining Eqs. (13-72) and (13-74), ehminating Lj-i and Lj to give... 

Compute a new set of values of the T) tear variables by solving simultaneously the set of N energy-balance equations (13-72), which are nonlinear in the temperatures that determine the enthalpy values. When linearized by a Newton iterative procedure, a tridiagonal-matrix equation that is solved by the Thomas gorithm is obtained. If we set gj equal to Eq. (13-72), i.e., its residual, the hnearized equations to be solved simultaneously are... 

When rubbers eventually fracture, they do so by tearing. Fracture surface energies, using the Griffith equation, have been found to be of the order of 10 J m , whereas the true surface energies are only 0.1-1.0 J Hence, more energy is involved in fracture than is required to form new surfaces, and, as with other polymers, this extra energy is assumed to be used up in viscoelastic and flow processes that occur between the molecules immediately before the rubber breaks. 

In TPE, the hard domains can act both as filler and intermolecular tie points thus, the toughness results from the inhibition of catastrophic failure from slow crack growth. Hard domains are effective fillers above a volume fraction of 0.2 and a size <100 nm [200]. The fracture energy of TPE is characteristic of the materials and independent of the test methods as observed for rubbers. It is, however, not a single-valued property and depends on the rate of tearing and test temperature [201]. The stress-strain properties of most TPEs have been described by the empirical Mooney-Rivlin equation... 

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