Separation of Energies in Elastic-Plastic Fracture

Abstract

The area under load versus the load-line displacement record represents the sum of the stored potential energy, the released elastic energy, and the dissipated plastic energy necessary to grow a crack through a test specimen. When partitioned as presented in this paper, these energy components can be evaluated in terms of current elastic-plastic fracture parameters. The authors show that the elastic energy release rate, G, as calculated by measuring the appropriate component from the test record, is identical to G calculated from Kq. The plastic energy dissipated, as measured directly from the load-displacement record, represents a much higher value than would be indicated by current J-type calculations. In all cases examined, it is further shown that energy released or dissipated is strongly dependent on the size of the test specimen and the size of the initial crack length. Further, while the rolling orientation and prestraining of the steels investigated affect the plastic energy dissipation rate, there seems to be little effect on the elastic energy release rate.

Geometry Independent R‐curves in a Titanium Alloy Using a Normalised Axis for Crack Growth

“…4 show a sequence with the larger a / W ratio giving the higher curve. Similar results for deep notch compact tests on A533B were noted [16] where the original data from [18] showed scattered J curves whereas curves reconstituted from dUp,/Bda given in [17] and using a common J, showed the trend with a / W of deepest notch giving the highest curve (although that reconstitution omitted the elastic component from all of the curves and neither [17] nor [l8] used J,). For HY130 steel with two values of a / W = 0.5 and 0.8 in [24], the deep notch case clearly gives a higher R-curve.…”

“…If plotted as a direct measure of toughness following the Griffith concept of toughness as a d/da rate then a falling R-curve against crack growth is found. Such a concept was in vogue prior to 1961 (see for example, [30] p. 155) and is now being re-examined not only in [8] but also in [17]. As remarked previously a further analysis of the present data in terms of these decremental rates will be given [19] where, as in [17], it will again be seen that some scaling trends emerge consistent with the present treatment.…”

“…No doubt some of the variation seen here is due to too few experimental points in the initiation region for the present analysis but the argument that much of the scatter is in local variability seems worth pursuing. One case in support of making an adjustment has already been quoted in connection with the variable a / W data in [16] and [17] from [18]. Another case quoted in [22] finds coherent trends in R-curves with size by using data from f23] adjusted to a common initiation toughness from the chart of scatter itself given in [23] for the tests in question.…”

“…There is also evidence from infiltration studies [12], that although the fracture behaviour is bimodal in the sense of either oblique for plane stress or flat for plane strain, the fracture parameters such as COD and COA are not bimodal but vary rather smoothly through the thickness as might be anticipated from the variation of triaxiality so that in this transitional stage a whole range of factors come into play. A recent analysis [16], showed scaling of data for dU,,/Bda from [17] itself using A533B data from [18]. The present data for titanium are here examined in terms of J,.…”

Fracture behaviour of an anisotropic polygranular graphite (PGA)

“…If the second derivative of strain energy release with respect to crack length is non-zero, the averaged value obtained by the direct method over significant increments of crack length may overestimate, or underestimate, the true strain energy release rate. Convergence between the two methods would be obtained only if the normalised energy release is calculated for sufficiently small crack growth increments (see for example [40]), or if the R-curve is independent of crack length (i.e. a plateau) where the second derivative of strain energy release with respect to crack length is close to zero.…”