13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 4. Application to a notched tensile test Six notched tensile specimens of 1.5 mm thick AA5182 sheet with a notch radius, R, of 3 mm, gage length, L, of 12.5 mm, width, w, of 18 mm, and total sample length of 80 mm were tested to failure under quasi-static conditions. The notch ligament length is characterized using the notch ratio defined as 2 / 0.25 R w ρ= = in this study. Fracture is characterized using both the ligament strain and axial or elongation strains. The ligament strain is representative of deformation in the region where fracture originates whereas the axial strain provides a metric for fracture based upon the bulk elongation of the material. The axial and ligament strains at fracture are defined as a ln f f o L L ε = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ lig lig ln lig f f o ε = ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (13,14) where the initial ligament length is: ligo = wo – 2R = 12 mm. The axial strain at failure is recorded at the appearance of a macro-crack at the notch root and not final failure since the objective of the finite-element models is to predict the formation of a macro-crack and not the subsequent tearing process. Tensile specimens with notch ratios smaller than 1/3 exhibit visible cracking at the notch root prior to fracture and the appearance of a macro crack corresponds to a sharp drop in the experimental load displacement curve [15]. 4.1 Material characterization Three tensile specimens were evaluated to characterize a Voce hardening law for AA5182 as: ( ) p 0.905 (MPa) 398.1 275.4exp 7.631 σ ε ⎡ ⎤ = − − ⎢ ⎥ ⎣ ⎦ p p d n d ε σ σ ε = (15a, b) with a yield stress of 122.7 MPa, and elastic moduli, E = 65.33 GPa and v = 0.33. Void nucleation in the AA5182 alloy is attributed to the iron-rich intermetallics and not the Mg2Si particles based upon the micro-tomography study by Orlov [14]. The elastic constants of the Fe-rich particles are taken as those of steel with an elastic modulus of 200 GPa and a Poisson ratio of 0.28. It is assumed that the Fe-rich particles nucleate penny-shaped voids with an aspect ratio of 0.01 via particle cracking. The fracture toughness of the Fe-rich particles in Eq. (12) is taken as 2.15 MPa-m1/2 based upon the measurements of Rathod and Katsuna [16]. 4.2 Finite-element model A one-eighth finite-element model of the notched specimen containing 24000 constant stress brick elements is shown in Figure 5a. For computational efficiency, only percolation elements are placed at the notch root (Figure 5b) to capture the initiation of the macro-crack while the remaining elements obey J2 plasticity using the hardening rule in Eq. (15). The percolation model is computationally expensive and the size of the global particle field in this specific model is limited to a size of 4000 particles split into four elements. The placement of only several percolation elements at the notch root is acceptable for this specific notch geometry because deformation is
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