By Li, Chen, Wu.
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3. 6 Time Dependent Effects 43 Fig. 7 Modelling of crack path deviation at a material interface (welded joint) allowing the crack to propagate away from the bond line; from  versatile method of including this dependency is to make the cohesive parameters, T0 or C0, dependent on these quantities. 1 Rate Dependent Formulations Three types of rate dependent formulations are often distinguished: • Explicit rate dependency. • Viscoplastic behaviour. • Viscoelastic behaviour. The explicit rate dependency is the simplest approach, in which the TSL is usually written with two terms, one of which depends on the separation itself, and the other on the separation rate: T ¼ f1 ðdÞ þ f2 d_ or T ¼ g1 ðdÞg2 d_ ð4:1Þ A cohesive law with a very simple form of this type, namely T ¼ T0 þ gd_ has been proposed by .
If this is not available either, however, a KIc value instead, the equation C0 ¼ KIc2 E (actually valid for linear elastic materials only) serves as a (very rough) first estimate The cohesive strength should initially always be taken from an experiment according to Sect. 1. If such an experiment is not available, then a starting value can be set equal to the stress at failure of the tensile bar, as long as no localised necking occurs in the specimen during the test. g. 5 and 5 rY. 1 Trial and Error Although time consuming, this is probably the most frequently used procedure for identifying the cohesive parameters.
G. by [29, 32]. Damage accumulation Saturation occurs easily during cyclic loading, if the load history contains identical cycles, due to the unloading/reloading path, which in general is also equal. If the load does not increase from one cycle to the other, the loading path of the cohesive element will only follow this unloading/reloading path and material degradation does not increase anymore. Two ways to overcome this non-physical behaviour can be found in the literature: 46 Fig. 9 Cyclic loading of cohesive elements following a separation law with different paths for loading (solid line) and unloading (dashed line) 4 Applications T(δ) damage locus for monotonous loading δ One possibility is to define different paths for unloading and reloading, see Fig.
Generalized difference methods for differential equations. numerical analysis of finite volume methods by Li, Chen, Wu.