Analysis of Ultra Low Cycle Fatigue problems with the Barcelona plastic damage model and a new isotropic hardening law

Abstract

This paper presents a plastic-damage formulation and a new isotropic hardening law, based on the Barcelona plastic damage model initially proposed by Lubliner et al. in 1989 [1], which is capable of predicting steel failure due to Ultra Low Cycle Fatigue (ULCF). This failure mechanism is obtained when the material is subjected to cyclic loads and breaks after applying a very low number of cycles, usually less than hundreds. The failure is driven by the plastic response of the material, and it is often predicted based on the plastic strains applied to it. The model proposed in this work has been formulated with the objective of predicting accurately the plastic behavior of the material, as well as its failure due to ULCF. This is achieved taking into account the fracture energy dissipated during the whole loading process. This approach allows the simulation of ULCF when it takes place due to regular cyclic loads or non-regular cyclic loads, as it is the case of seismic loads. Several simulations are conducted in order to show the capabilities of the formulation to reproduce the mechanical response of steel when it is subjected to regular and non-regular cyclic loads. The formulation is validated comparing the numerical results with several experimental tests made on X52 steel specimens. The agreement between the numerical and experimental results asses the validity of the proposed model to predict the plastic behavior of steel and its failure due to Ultra Low Cycle Fatigue.

Validation on large scale tests of a new hardening–softening law for the Barcelona plastic damage model

“…Therefore, the proposal presented in Martinez et al [10] and in the current paper presents a new focus for the ULCF modelling. The complete nonlinear constitutive model is an extension of a given plasticity model to incorporate the damage effects due to cyclic action.…”

“…A new isotropic hardening law is also developed especially for steel materials, designed to reproduce their hardening and softening performance under monotonic and cyclic loading conditions. The exact expression of the constitutive law and the thermodynamic formulation of the model are presented in Martinez et al [10], [12] and Barbu et al [13].…”

“…In Sections 2 and 3 a summary of the new isotropic hardening law is presented with emphasis on small improvements made with respect to the expressions presented in [10] . In Section 4 the complete calibration procedure on small scale samples is presented step by step.…”

High cycle fatigue simulation: A new stepwise load-advancing strategy

“…A more detailed description of the code and some of its capabilities can be obtained from [35], [36], [37] and [38].…”

Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe

“…The classical constitutive model of predicting material failure due to ULCF is the Barcelona plastic damage model initially proposed by Lubliner et al [20], which is based on an internal variable-formulation of plasticity theory for the non-linear analysis of concrete. Martinez and Oller et al [21] developed a new plastic-damage formulation to simulate the mechanical response and failure due to ULCF specially for steels. It is based on the Barcelona plastic model, but provides enhancements by adding a non-linear kinematic hardening law coupled with a new isotropic hardening law.…”