Visco-plastic and Damage Characterization of Sheet Metals for Railway Crash Applications 37 particular, engineering uniaxial stress-strain curves were obtained for different strain rates using the P1 and P2 geometries; then, the average strain computed in the necking section from DIC analyses was used to convert the engineering data into first-attempt true stress-strain curves. A mixed analytical-numerical procedure was implemented: FEM simulations were repeated varying material parameters according to an optimization scheme, where deviations between numerical and experimental load-displacement curves are minimized. Figure 2 shows the 3D meshed models developed in Abaqus/Explicit R⃝ software; the mesh size of all models was 0.25mm in the gauge area. Fig. 2 FE models in Abaqus/Explicit; a) P1 geometry, b) P2 geometry, c) P3 notched geometry, d) D10 geometry The adopted visco-plastic law is given by the Voce’s hardening law, combined with the Johnson-Cook strain rate dependency term [13], which was input in tabular form as material mechanical properties. The equation is: σ ={σ0 +R0 · εpl +R∞[1−exp(−b · εpl)]} · [1+q · ln( ˙ε/ ˙ε0)] (1) After the visco-plastic model was calibrated, the same simulations were used to extract the characteristic parameters such as stress triaxiality and effective strain rate at the core of the samples; these data were used for the definition of a fracture locus in the (T, ˙ε, εf) space; in particular, the Bao-Wierzbicki model was first calibrated based on quasi-static results. The equation is divided into three regions, the first corresponding to shear cracking, the third to void growth, and the second corresponding to a mixed failure mode: regionI : εf =a(T +1/3) b regionII : εf =cT 2 +dT +e regionIII : εf =fT−1 (2) Then, the strain rate dependency was considered by a polynomial law of second and third-order, thus to define a 3D fracture surface: f(T, log( ˙ε))=c1 +c2T +c3 log( ˙ε)+c4T 2 +c 5T log( ˙ε)+c6 log( ˙ε) 2 (3a) f(T, log( ˙ε))=c1 +c2T +c3 log( ˙ε)+c4T 2 +c 5T log( ˙ε)+c6 log( ˙ε) 2 (3b) +c7T 3 +c 8T 2 log( ˙ε)+c 9T log( ˙ε) 2 +c 10 log( ˙ε) 3 The coefficients were found by minimizing the distance between the points and the surface.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==