Biaxial load effects on the crack border elastic strain energy and strain energy rate

236

For some time now the elastic T-term has been proposed as a secondary "biaxiality" parameter, to be used in conjunction with the stress intensity factor, K1, or the path independent integral J, as the primary parameter for the characterization of crack tip fracture states. At a recent conference a theorem due to Eshelby was presented [1]. The theorem provides a convenient method of calculating the T-term, obtained by evaluating appropriate J contour integrals. Examples of analytical, semi-analytical and numerical applications were included. Here, some additional finite element applications, using a fairly simple idealization, are presented in greater detail and comparisons of the results of the different independent analyses available so far are made, giving further evidence of the practical utility of Eshelby's method. New results on double-edge notched specimens are also included.

Section: Introductionmentioning

confidence: 99%

Some evaluations of the elastic T-term using Eshelby's method

Kfouri

1986

236

“…Beginning in 1977, Eftis, [17,[19][20][21][22]24], either alone or in collaboration with others, argues that stresses parallel to the crack affect the energy release rate. He produces physical evidence of some significant effects that such stresses can have on fracture.…”

Section: ~0 6amentioning

confidence: 99%

“…Griffith was the first to recognize this in his seminal paper [1] in 1920. Since [1], there have been a number of related contributions which are primarily concerned with aspects of such an energy analysis: Wolf [2] in 1923; Griffith [3] in 1924; Sneddon [4] in 1946; Eshelby [5,6,7] in 1951, 1956 and 1959; Irwin [8] in 1957; Sanders [9] in 1960; Swedlow [10] and Spencer [11] in 1965; Cherepanov [12] in 1967; Sih and Liebowitz [13] in 1967; Rice [14] in 1968; Bilby and Eshelby [15] in 1968; Eshelby [16] in 1969; Eftis, Subramonian and Liebowitz [17] in 1977; Cherepanov [18] in 1979; Eftis and Jones [19] in 1982; Eftis [20] in 1984; Eftis [21,22] in 1987; Tyson and Roy [23] in 1989; and Eftis, Jones and Liebowitz [24] in 1990. A review of the above listed papers can possibly lead to confusion with respect to some facets of the fundamental energy argument of fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

On the fundamental energy argument of elastic fracture mechanics

Keating

Sinclair

1996

Energy arguments remain, even today, as probably the most fundamental physicaUy-reasonedjustification for the application of linear elastic fracture mechanics to brittle materials. Accordingly, they have attracted and continue to attract quite a number of investigations. Not all of these studies employ the same approach. Unfortunately, nor do they all lead to the same conclusions regarding the implications of elastic fracture mechanics. Here, by examining the energy balance of fracture mechanics from a classical physics viewpoint, equivalent valid approaches are identified. This in turn enables the various contributions over the years to be placed in perspective with respect to whether or not they are correct.

“…The effects on the fracture of cracked bodies subject to biaxially applied boundary loads are gradually coming to be known as the results from recent theoretical and experimental research into this question accumulate [1][2][3][4][5][6]. The biaxial load effects on the fracture characteristics of a plane body containing a pair of collinear cracks have been analyzed, and are here reported.…”

Section: Introductionmentioning

confidence: 99%

Influence of load biaxiality on the fracture characteristics of two collinear cracks

Eftis

1984

A theoretical investigation has been performed to determine the influence of load biaxiality on quantities pertinent to the brittle (elastic) fracture of an infinite sheet containing a pair of collinear cracks. It is shown how the biaxiality of the applied load affects the stress, the displacements and the maximum shear near the ends of the cracks, as well as the angle of initial crack extension and the displacement of the crack borders. The influence of load biaxiality on the rate at which the elastic strain energy of the entire body is altered with change in the length of the cracks is also demonstrated, and is used in conjunction with Griffith's crack instability hypothesis to show the effect of load biaxiality on the fracture load. The analysis indicates that loads applied parallel to the cracks influence the value of the critical (fracture) tensile load applied perpendicular to them, and that the Poisson ratio of the material determines the characteristics of this influence. Nomenclature (x,y)(r,O) = Z tjk, ejk = T~, uk, bk = txx , txy , tyy = l=(b-a) = U = W = P,V = F = R = A k = ~, ~, e~, ~o = F(~,p), E(~,p) = V(p), E(p) = x(p) = KI, K2 = E = k = o % = ~L = p y = 0o = rectangular and polar coordinates, respectively.x + iy, complex variable. components of the stress and strain tensors, respectively. components of the surface traction, displacement and body force vectors, respectively. rectangular stress components. rectangular displacements components. crack dimension. elastic strain energy per unit thickness. work of forces applied to the body. the total potential energy of the system and the elastic potential energy, respectively. surface energy. bound region of the x-y plane. closed boundary curves of R. sectionally holomorphic functions of the complex variable z. elliptic integrals of the first and second kinds, respectively. complete elliptic integrals of the first and second kinds.