Energy release rate of small cracks in hyperelastic materials

Abstract

International audienceThe energy release rate of a small crack in an infinite hyperelastic medium, and subjected to large strain multiaxial loading conditions, is derived by considering the balance of configurational stresses acting on two planes: one cutting the center of the crack face, and the other at an infinite distance in front of the crack tip. The analysis establishes that the energy release rate of a small crack is always proportional to the size of the crack, irrespective of the loading conditions and the crack orientation. The balance of configurational stresses is illustrated for several benchmark cases including simple extension, pure shear and equibiaxial extension, and for perpendicular and inclined cracks

Analytical model to predict the lifetime of concrete members externally reinforced with FRP

“…On one hand, a perusal of the literature surveyed in the references (in particular [4,8,10,29,33,36,[39][40][41][42]) reveals that debonding is the result of mixed modes I/II. On the other hand, however, the delayed debonding is induced by loads much lower than the loads that induce the debonding (contrary to the latter, the former is only due to permanent, quasi-permanent, and frequent loads).…”

“…According to fracture mechanics of brittle materials, the velocity da/dt (t denotes the time) at which the crack propagates in a given concrete depends on the ratio between K II and K IIC only [4,6,9,[18][19][20]25,29,34,35,[40][41][42]. In brittle materials there are three regimes of crack growth as K II varies from 0 to its critical value K IIC .…”

“…The literature [2,3,5,13,[21][22][23]26,28,43,47,49] also reveals that v c and N depend on humidity and temperature as well, but these dependences are not strong. Ultimately, for concrete members with a carbonation depth greater than the cover, K IIC is close to 1.0 MPa m 0.5 [31,36,[44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61], v c to 0.0015 m/s [22][23][24]31,36,41,[43][44][45][46], and N to 16 [18,24,41,43,59]. It is to note that N is the exponent and thus it is important to provide the model with a reliable value; however, N = 16 is simultaneously an accurate and preservative assumption.…”

“…In order to plug into the model the actual values that K IIC , v c , and N assume in a specific concrete, instead of a priori values, tests have to be accomplished, either on-site or in laboratory [18,[22][23][24]29,31,36,39,41,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. On the contrary to K IIC , however, v c and N are not simple to be measured; thus, it is more convenient to use the aforementioned values borrowed from literature.…”

Crack precursor size for natural rubber inferred from relaxing and non-relaxing fatigue experiments

“…Differences arise because the crack propagation approach is focused on one (or a few) crack(s), where the initiation approach is focused on the possibility of many small crack precursors. In any event, the initiation life can be computed by integration of the crack growth rate law, and assuming that the energy release rate of small cracks scales linearly with size of the crack [20]. The most common crack growth laws are the Thomas [21] model and the Lake-Lindley [22] model for fully relaxing loading conditions.…”