A novel reformulation of the Theory of Critical Distances to design notched metals against dynamic loading

The Theory of Critical Distances to assess failure strength of notched plain concrete under static and dynamic loading

“…In other words, contrary to what we have observed in notched metallic materials subjected to dynamic loading [43], for the specific concrete material being investigated the critical distance was seen not to be affected by the rate of the applied loading. However, it is the authors' opinion that this is a particularly favourable result, so that, in the most general case, L is expected to vary as the loading rate increases (and, in particular, it is expected to increase with the increase of ∆ & ).…”

“…If these experimental findings are reinterpreted according to the TCD's modus operandi, one may argue that, since, as per Eqs (2) and (3), both the strength and the fracture toughness of concrete follow a power law as the rate of the applied loading increases, both inherent strength σ0 and length scale parameter L should vary the same way as ε & increases [43]. In particular, by using Z to denote either the loading rate, the strain rate, the displacement rate, or the stress intensity factor (SIF) rate, according to Eqs (2) and (3) the effect of the dynamic loading on both the failure stress and the fracture toughness can be expressed as follows [43]:…”

“…According to the hypotheses formed above, in the most general case, length scale parameter L as well is expected to change as dynamic variable Z varies, in fact [43]:…”

“…Unfortunately, this simplicity results in the fact that the required constants are measured in units that are obviously unconventional. Having considered this important aspect very carefully, we decided to keep using power laws in any case not only because they have proven to be very accurate in estimating the dynamic strength of other materials [43], but also because the ultimate goal of the present paper is promoting a simple design method that is suitable for performing rapid calculations in situations of practical interest.…”

A comparison of the two approaches of the theory of critical distances based on linear-elastic and elasto-plastic analyses

“…It has also been proved that the TCD can be used to predict static fracture in ductile metallic materials containing various stress raisers and subjected to both uniaxial and multiaxial loading [8]. Moreover, in papers [9,10] was shown that Theory of Critical Distances is suitable for predicting the strength of notched metallic materials subjected to dynamic loading.…”