PSI - Issue 17

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 17 (2019) 347–354 Konstantinos Kouzoumis / Structural Integrity Procedia 00 (2019) 000 – 000

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Given that the crack runs throughout the thickness of the specimen and that the specimens are thick enough to be under plane strain in the middle, two-dimensional plane strain FE models are invoked. Due to symmetry, a quarter of the specimens is modelled. The cruciform and the uniaxial quarter models comprised of 3042 and 2632 CPE8 elements respectively, a schematic of the modelled geometries ’ quarters is given in Figure 3.

Figure 3: FE mesh of quarter of (a) biaxially, (b) uniaxially loaded specimens

The limit load values correspond to global collapse, the calculated values for each specimen/biaxiality ratio are shown in Table 4.

Table 4: Global Collapse Limit loads from FEA k=0 k=0.5 k=1 k=2 ͳ͹Ǥͳʹ ͳͻǤͶ ͳͻǤͺ͹ ͻǤͻ͵

The experimental failure loads, shown in Table 1, were applied to each model to calculate J el at failure. In addition to the applied load, the equibiaxially loaded specimen ( k=1 ) experienced an inhomogeneous temperature field during testing, which was assumed in previous assessments to have resulted in a stress field of 110MPa magnitude. In order to produce a stress field of this magnitude at the centre of the specimen a stress of 164 MPa was applied at the end of the loading beams. Overall the values of L r were calculated by dividing the applied load by the FEA limit load and K r by dividing the elastic K calculated from FE, winch includes both primary and secondary loads, by K mat . The resulting Option 3 FALs with their respective assessment points are shown in Figure 4. The assessment points from the FEA provide safe results for all biaxiality ratios when the 5% probability of fracture Master Curve toughness is used, while using the 20% Master Curve toughness leads to k=0.5 lying in the safe zone Regarding the failure assessment lines, when k exceeds 1 the distribution of the load throughout the applied spectrum (0 - L r,max ) shows geometry dependence and is not applied consistently on the crack front. This means that plasticity evolves much more at the fillet of the cruciform specimen causing loads to be redistributed and J el-pl to increase in a slower rate, acquiring slightly lower values than the corresponding J el . Hence, even though for k=2 the FAL reaches values of K r higher than one, this is a reflection of geometry dependence. Disregarding the aforementioned geometry dependence, it is observed for values of L r approximately higher than 0.5, that as biaxiality increases and so do the limiting values of K r given by the FAL. This means that as the biaxiality ratio increases, the energy release rate calculated from an elastic and an elastic plastic analysis deviate less thus denoting higher constraint of plasticity. The fact that higher in plane constraint (higher k ) gives an Option 3 FAD with a larger safe zone seems counterintuitive with the perception that constrained plasticity favors brittle fracture and is expected at lower values of J . Even though this is excused by the nondimensionalization of J el with J el-pl , both of whose values decrease with increasing biaxiality, it is also due to assessing high and low constrained specimens with the use of the same lower bound fracture toughness, K mat . In order to address this, constraint corrected assessments using the guidance of BS 7910’s Annex N follow.