Abstract

In this work we compare two frameworks for thermodynamically consistent hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming. The second, formulated by Wallin et al. (2003), has been used to model large shear strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this paper we show that these frameworks can result in equivalent models for certain choices of free energies. Furthermore, it is shown that the choices of free energy found in the literature only result in minor differences. These differences are discussed theoretically and investigated numerically.

Abstract

This paper presents the results of finite element simulations made on a bent pipe subjected to an in-plane variable cyclic displacement combined with internal pressure. Special emphasis is put on the capacity of the model to illustrate different failure modes depending on the internal pressure applied on the pipe. The results of the numerical analyses will be compared to experimental ones. The constitutive model used for the simulation of Ultra Low Cycle Fatigue (ULCF) loading and the hardening–softening law used are only briefly touched upon. The monotonic behavior of a large diameter pipe, as obtained from the constitutive model proposed, is also shown and compared to experimental results under two different loading conditions. The total axial load at failure for this case resulted in less than 10% error as compared to the experiments. Regarding the ULCF in-plane bending simulations conducted on a 16-in. 90º elbow, the results were in good agreement with the experimental test in terms of force–displacement hysteresis loops and total fatigue life of the specimen. An analysis of the dependence of the failure mode to the internal pressure applied has been conducted, showing that the formulation is capable of obtaining both habitual failure types.

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. (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 o n 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.

Abstract

In this work an anisotropic material model at finite strains with nonlinear mixed (isotropic and kinematic) hardening is used for the identification of the hardening parameters of sheet steel. The algorithmic system is thereby reduced to a single equation return mapping. For the identification, a cruciform specimen is loaded biaxially in an alternating shear test to provoke the kinematic hardening behavior and prevent the sheet from buckling. The material parameters are found through an optimization strategy by comparing the deformation field from the experiment to that from a finite element (FE) simulation. The resulting cost function is minimized by means of a gradient-based method.

Abstract

Abstract