Ramberg-Osgood Material Model Research Articles

Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method

ABSTRACTIn the present work, the extended finite element method has been used to simulate the fatigue crack growth problems in functionally graded material in the presence of holes, inclusions, and minor cracks under plastic and plane stress conditions for both edge and center cracks. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used for modeling purposes.

Explicit modeling of damping of a single-layer latticed dome with an isolation system subjected to earthquake ground motions

The non-uniformly distributed material damping in single-layer latticed domes subjected to earthquake ground motions has been ignored in engineering practice, and the structural damping of bearings and joints has been modeled at a structural level in previous studies. In this paper, an explicit method for modeling the material damping and structural damping using a finite element method is proposed. The proposed method includes important characteristics for modeling single-layer latticed domes. The steel material damping is directly taken into account using Ramberg–Osgood material model (power-law) with hysteretic damping; the structural damping at bearings is modeled based on the bearing type. The ball joints of domes tend to be simplified as nodes in the finite element method without considering the actual geometric shapes and sizes of the balls for convenience. In this paper, the energy dissipation at joints and modeling methods for damping are proposed and discussed in terms of the joint type in domes. To illustrate the proposed method for computation, a typical single-layer latticed dome with base isolation bearings subjected to six near-fault earthquake ground motions is selected as an example. The dynamic demands of this single-layer latticed dome are analyzed using the simulation technology proposed in this paper. The effects of key parameters of the dome on the damping forces, which are of interest to many practitioners, are presented and discussed. Compared with the previous modeling methods for damping, the proposed method can model the damping effects of domes with a higher fidelity, which eliminates the unrealistically high forces generated with conventional modeling methods.

A new design method for stainless steel columns subjected to flexural buckling

The objective of this paper is to develop a design method for stainless steel columns subjected to flexural buckling. In this method, the strength curve for every type of stainless steel in common use is generated by using the base strength curves and a slenderness conversion formula. A validated finite element model is employed to generate the strength curves for different types of stainless steels. According to the strain hardening exponent n in the Ramberg-Osgood material model, cluster analysis is conducted to separate these strength curves into two groups. In each group, one type of material parameter is selected as the base material and the corresponding strength curve is expressed in the form of a modified Perry formula that serves as the base strength curve. A slenderness conversion formula is derived for any two stainless steel columns with the same section type and boundary conditions, but with different types of stainless steel. Based on the base strength curves and the slenderness conversion formula, the strength curve for every type of stainless steel in common use can be generated. The predictions of the proposed method show a good agreement with the results of the finite element analysis.

Numerical evaluation of the original “Neuber’s rule” for pure out-of-plane shear loading

Neuber’s rule has become a popular analytical tool for evaluating notch root stress and strain for fatigue life estimation. The original study was based on the geometry of prismatic bodies with hyperbolic notches under pure out-of-plane shear with a nonlinear material model. From this study, the author observed that “The geometric mean of stress and strain concentration factors is equal to theoretical elastic stress concentration factor, Kt.” Although this conclusion was based on a “special deformation law,” Neuber suggested that it can be approximately extended to any stress–strain law and to tensile and bending loads replacing shear stress and strain with equivalent von Mises stress and strain and Neuber’s rule evolved. Extensive research has been conducted to evaluate and generalize Neuber’s rule for fatigue analysis. However, the applicability of Neuber’s rule to a specific situation requires consideration of the material model utilized, in addition to the notch geometry and loading conditions. This article presents a detailed finite element analysis of Neuber’s rule using out-of-plane shear loading on prismatic bodies with hyperbolic notch geometries identical to those considered by Neuber. Neuber’s nonlinear material model (special deformation law) is compared to the Ramberg–Osgood material model, and discernable differences were observed. Neuber’s observations were approximately valid for conditions congruent with his constitutive model. For the Ramberg–Osgood model, this happens to occur only for a strain hardening exponent of about 0.2. For other values of the strain hardening exponent, Neuber’s model cannot emulate the shape of the Ramberg–Osgood curve, and notch strain predictions from Neuber’s rule are less accurate.

Numerical prediction of elasto-plastic behaviour of interpenetrating phase composites by EFGM

Interpenetrating Phase Composites (IPCs) can be defined as multiphase materials in which each phase is three-dimensionally interconnected throughout the structure. No phase can be distinguished from the other based on the states of isolation and continuity; however both the phases contribute to the strengthening and improvement of the composite. The tensile and compressive yield and ultimate strengths of IPCs are much higher than a similar particulate composite due to their interpenetrating structure. This behaviour has been numerically simulated using element free Galerkin method. Ramberg–Osgood material model has been used to model the elasto-plastic behaviour of the composite. A progressive damage model has been used to simulate the failure mechanism of each phase. Three types of models have been proposed based on the treatment of the interface. The ultimate strength and the yield strength of IPC are obtained. The ultimate strength and the yield strength of the IPC depend largely on the properties, volume fraction and interpenetration of the constituent phases. The results of the present simulations are found in good agreement with the experimental results.

Strength enhancements in cold-formed structural sections — Part I: Material testing

This paper describes a material test programme carried out as part of an extensive study into the prediction of strength enhancements in cold-formed structural sections. The experiments cover a wide range of cross-section geometries – twelve Square Hollow Sections (SHS), five Rectangular Hollow Sections (RHS) and one Circular Hollow Section (CHS), and materials – austenitic (EN 1.4301, 1.4571 and 1.4404), ferritic (EN 1.4509 and 1.4003), duplex (EN 1.4462) and lean duplex (EN 1.4162) stainless steel and grade S355J2H carbon steel. The experimental techniques implemented, the generated data and the analysis methods employed are fully described. The results from the current test programme were combined with existing measured stress–strain data on cold-formed sections from the literature and following a consistent analysis of the combined data set, revised values for Young's modulus E and the Ramberg–Osgood material model parameters n, n′0.2,u and n′0.2,1.0 are recommended. A comparison between the recommended values and the codified values provided in AS/NZS 4673 (2001) [1], SEI/ASCE-8 (2002) [2] and EN 1993-1-4 (2006) [3] is also presented. The test results are also used in a companion paper Rossi et al. (submitted for publication) [4] for developing suitable predictive models to determine the strength enhancements in cold-formed structural sections that arise during the manufacturing processes.

Nonlinear Simulation of an Embedded Crack in the Presence of Holes and Inclusions by XFEM

In this work, nonlinear analysis of an embedded cracked plate is performed by XFEM in presence of multiple discontinuities under plane stress condition. Von-Mises yield criterion is used to model the elasto-plastic behavior of the plate assuming isotropic strain hardening. The stress-strain response of the plate is modeled using Ramberg-Osgood material model. XFEM is used as a numerical tool to simulate the plate containing a major centre crack, holes and inclusions. A domain based J-integral approach is used to evaluate the stress intensity factors. The generalized Paris law is used to estimate the fatigue life of the plate under mode-I cyclic loading condition. The effect of inclusions and holes on the fatigue life of the component for linear and nonlinear material behavior is discussed in detail.