Three-dimensional modeling of ductile crack growth in thin sheet metals: computational aspects and validation

Crack Tip Opening Displacement and Angle for a Growing Crack in Carbon Steel

“…Finally, using the experimental J-R curves in Lam et al [25] and following the derivations in Kanninen and Popelar [30] and in Gullerud et al [16], the CTOD is qualitatively proportional to the slope of the J-R curve, and the initial high values of CTOD is shown to be a natural consequence of the crack growth resistance. Since the J-R curve is strongly depend on a/W, it can then be concluded that CTOD is essentially a function of crack tip in-plane constraint.…”

“…It can be seen that the CTOA distribution is not sensitive across the thickness t, where z=0 represents the mid-thickness of the plate, and z= 0.5t is the plane at the root of the side groove. These CTOA values are measured at 1 mm behind the crack tip, as commonly chosen by some researchers [5,16,31]. The result of an equivalent plane strain finite element analysis is also plotted in Figure 4.…”

“…Since CTOD and CTOA are equivalent, where appropriate, the term CTOD is understood to refer also to CTOA throughout the paper, unless it is specifically pointed out A comprehensive review of the work on CTOD can be found in Newman, et al [5]. The majority of the test data (e.g., aluminum alloys and A533B) and the numerical analyses (e.g., [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19]) seem to indicate that the values of CTOD are initially high, but progressively decrease to a nearly constant value after several millimeters of crack growth. It has been shown by several investigators (e.g., [9][10][11]15,[20][21][22][23]) that, based on three-dimensional (3D) and two-dimensional (2D) finite element analyses, a constant CTOD fracture criterion may be capable of predicting the experimental data (e.g., load versus crack extension curves).…”

Investigation of crack-tip plasticity in high volume fraction particulate metal matrix composites

“…Indeed, it has been increasingly understood in the past decade that surface measurements are affected by 3-D effects [28][29][30], and that caution must be exercised in analysis of experimental data. For instance, it has been shown that plane-stress approximations are not sufficient to fit experimental measures such as the crack-tip opening angle (CTOA) or the crack-tip opening displacement (CTOD) (which are the surface measurements of crack-tip loading that are the most commonly performed), whereas 3-D analyses yield much better agreement [20,[30][31][32].…”

“…To the best of our knowledge, such comparisons between elastic-plastic strain fields observed by experiment and numerically computed have rarely been performed. Three-dimensional constraint effects have, rather, been assessed by correlating numerical computations with other measurements, which are more directly accessible such as the CTOA, the CTOD or load-displacement curves [20,[31][32][33][34][35][36]. A second goal of this investigation is therefore to evaluate the significance of three-dimensional ''constraint'' effects with these half-metal/half-ceramic composite materials.…”