PSI - Issue 28

Romanin Luca et al. / Procedia Structural Integrity 28 (2020) 162–170 Author name / Structural Integrity Procedia 00 (2019) 000–000

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A more detailed modelling has been conducted by Stoakes and Fahnestock (2014) which studied the seismic behavior of braced frames using a nonlinear response history. They observed panel drifts indicating potential ultra low cycle fatigue fracture of the braces and express the need of refinements to existing seismic design provisions of AISC. They modelled the frame with beam elements but steel connections using shell elements. Because of the hysteretic behavior encountered during a seismic event they adopted a nonlinear kinematic and isotropic hardening model. Besides including geometrical imperfections, they included also residual stresses by means of a simplified approach adopting the Lehigh residual stress pattern. The present work is a first step towards the hysteretic behavior experienced during an earthquake. On opposite of a collapse analysis in which the global model is directly coupled with the connection model, here the global forces could be directly applied on the model without updating the global model stiffness. He, Wang, and Chen (2010) conducted a numerical evaluation of residual stresses of a steel bridge girder. A relaxation of the stress field after a cyclic load is calculated but no effect on residual displacements and tolerances was investigated. For the reason that the material has already yielded in the welding region because of weld shrinkage, an appropriate material model has thus to be chosen to model accurately the behavior of the load application. A review of the material model available for cyclic loads and especially for welding has been conducted in the next section. 2. Material Models A material subjected to cyclic loading, such the case of an earthquake event, undergoes an appreciable progressive change in stress-strain curve. At the beginning of cyclic loading a transient behavior is found where changes in cyclic deformation behavior are more pronounced, afterwards the material gradually stabilizes reaching a steady-state behavior. The transient behavior is more interesting for the analyzed joint, the first loads are believed to affect geometrical tolerances. On opposite, the stabilized hysteresis is usually utilized in the low fatigue regime. The transient behavior could be characterized by cyclic softening or hardening depending on the material characteristics. The behaviors could be observed also in stress controlled tests. In stress-controlled test, as well as structures subject to seismic loads, two phenomena could occur. The first is shakedown, which is desirable, consisting in the stabilization of hysteresis loops between a fixed range of strains. The second phenomenon occurs when the hysteresis loops proceed steadily until the end of loading or rupture. The prediction of these effects is essential to asses if the ductility reserve of a joint has been completely exploited. The two most used and simple material models are isotropic and kinematic hardening. Only kinematic hardening accounts for the phenomenon of Bauschinger effect and is often more suitable for representing the real material behavior for cyclically loaded materials. Numerically the hardening rule represents the condition for establishing the subsequent yielding behavior once the initial yielding has occurred. Given that a point in stress space cannot lie outside of the yield surface, the yield surface has to change its size or position for further yielding to occur. In CWM simulations the material constitutive model is one of the most significant variable. Smith et al. (2010) provide a comparison of different modelling solution regarding both the material model and material data. Overall, the measurements were in agreement with numerical simulations. A mixed hardening constitutive behavior was the most accurate when using data from solution-treated weld metal. A pragmatic approach is suggested using the monotonic response upon multi-pass weld metal and kinematic hardening. Schenk et al. (2009) analyzed the influence of numerous variables on numerical results comparing them to a physical model of a lap-joint and a T-joint. For a T joint neglecting phase transformation has a high effect on the deformation as well as the phase volume change. Adding the fillet weld at the very beginning has also a high influence. It is interesting that employing the hardening parameters at room temperature up to 400°C and then ramping down linearly up to zero at 1000°C has only a moderate effect. Bate, Shallcross, and Stone (2016) found that the isotropic hardening model would over predict residual stresses for a multi-pass weld. From physical cyclic tests they found that material reaches stabilization within a few cycles. It is not critical to model the progressive cyclic behavior of the material, as in austenitic steels. They have not yet completed the validation of the kinematic hardening model.