13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- due to HCF at microscale. These microdefects cause the plasticity at microscale but the mesoscale behavior remains elastic. In light of the the basic features of HCF, a two-scale damage model is developed. A schematic of the model is shown in Figure 3. All the quantities with subscript µ are defined at the microscale. Meso-scale (elasticity) ,σ ε Localization law ( ) , , , f a b D µ = ε ε Plasticity and damage , , , , p D µ µ µ µ ε ε σ X Figure 3: A schematic for the two-scale damage model. The development of the model can be described by three steps. First of all, stress-strain ( ) −σ ε data at mesoscale can be obtained using the elastic material properties such as Young’s modulus and Poisson’s ratio ( ) ,E ν . Secondly, the scale transition from the meso to micro will be described by a localization law based on the modified Eshelby-Kroner law. Localization law relates the microscale strain µ ε to the mesoscale strain ε through material parameters a, b and damage D given in the second box in Figure 3. Here a, b are functions of ν based on Eshelby’s inclusion theory. Finally we will formulate a plasticity-damage model at the microscale as shown in the third box of Figure 3. The key component of this model is the damage evolution law, which assumes that the damage rate is proportional to the effective plastic strain rate p µ , given as if or D s s d Y D p p p w w S µ µ µ µ = ≥ ≥ (8) Here ,s S are the material parameters to be calibrated from available experimental data on fatigue, Y µis the damage energy release rate and sw is the stored energy in the material, dw is the damage threshold energy, Dp µ is the threshold effective plastic strain. Threshold values act as a barrier for damage initiation. Once these conditions are met, damage accumulation begins. Threshold values depend on the material and the type of loading condition. The major advantage of employing Eq.(8) is from the fact that fatigue failure is regarded as a function of increment in strain or stress as opposed to function of the load cycles. A constitutive solver has been developed for the two-scale damage model outlined here and integrated with the space-time FEM framework. The specific algorithm will be similar to that of a standard rate-dependent plasticity-damage model. A mixed explicit-implicit scheme has been implemented.
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