The effect of random grain distributions on fatigue crack initiation in a notched coarse grained superalloy specimen

Coarse grained superalloys are of large interest in high temperature applications, and can be found in e.g. gas turbine components, where great care must be given with respect to high temperature fatigue. Due to the large grain size, the material behaviour at e.g. sharp notches cannot be considered homogeneous. As a consequence, the fatigue behaviour is likely to expose a large variation. In order to numerically investigate this variation, a Monte Carlo analysis has been carried out by 100 FE-simulations of notched specimens, where placements and orientations of the grains were randomised. Furthermore, each grain was modelled as a unique single-crystal, displaying both anisotropic elastic and plastic behaviour and tension/compression asymmetry. The effect of randomness was investigated by the obtained dispersion in fatigue crack initiation life. It was concluded that the fatigue life behaviour of coarse grained nickel-base superalloys may show a considerable variation, which cannot be captured by one single deterministic analysis based on data for a homogenised material. Furthermore, the dispersion is of such a magnitude that it needs to be taken into account in industrial applications where highly stressed coarse grained materials are used.     

Grain-level statistical plasticity analysis on strain cycle fatigue of a FCC metal

The micromechanical strain cycle fatigue-life is systematically investigated by the micro-level numerical simulation, compared with symmetrical strain cycle experiments of copper, focusing on the characteristics of polycrystalline aggregation and the mechanism of microscale plastic deformation. A methodology to predict the low-cycle fatigue life by micro-level simulation along with statistical analysis is proposed through the following steps: (1) A crystal plasticity model is developed based on the nonlinear kinematic hardening mechanism of crystal slipping system. This model is applied to the calculations of crystal grain interior stresses and plastic strains. (2) A statistical representative volume element (SRVE) is constructed for a pure copper as a material model which features a polycrystalline Voronoi aggregation consisting of a number of crystal grains. This SRVE can be used for statistical analysis of the material inhomogeneous stresses and strains during cycle loading. (3) The simulations are performed to model the experimental cycle evolution of strain fatigue by using the SRVE under the symmetrical tensile–compressive loading. (4) Statistical and micromechanical analyses are carried out for the inhomogeneous interior stresses and strains of the SRVE of the polycrystalline copper in the low cycle regime. The resulting analysis can render the microscale interpretation and numerical simulation for the low-cycle fatigue evolution accordingly.     

Simulation Charpy impact energy of functionally graded steels by modified stress-strain curve through mechanism-based strain gradient plasticity theory

In the present work, Charpy impact energy of functionally graded steels produced by electroslag remelting composed of graded ferritic or austenitic layers in both crack divider and crack arrester configurations has been modeled by finite element method. The yield stress of each layer was related to the density of the statistically stored dislocations of that layer and assuming by Holloman relation for the corresponding stress-strain curves, tensile strengths of the constituent layers were determined via numerical method. By using load-displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress-strain curves from uniaxial tensile tests were modified. The data used for each layer in finite element modeling were predicted modified stress-strain curves obtained from strain gradient plasticity theory. A relatively good agreement between experimental results and those obtained from simulation was observed.     

A constitutive model for saturated compacted soils under undrained shear condition

Abstract

In this paper, elasto‐plastic constitutive equations extended from theory of plasticity and based on laws of thermo‐dynamics were derived to predict the mechanical behavior of saturated geological media. Besides, these equations can also be adapted to form the stiffness matrix for finite element analysis on deformation and stress distribution in geotechnical engineering practice. The test data were obtained from compacted crushed mudstone under consolidated un‐drained triaxial tests with pore water pressure measurement. The preparation of the specimen was different from those which had usually been adopted. Hence, it is hoped that this study will throw some light on the constitutive equations applied on compacted geological media.     

Effects of Ni on austenite stability and fracture toughness in high Co-Ni secondary hardening steel

Three kinds of high Co-Ni secondary hardening steels with different Ni contents were studied.The nanoscale austenite layers formed at the interface of matensite laths were observed.Both observation and diffusion kinetic simulation results showed that both Ni and Co did not obtain enough time to get the equilibrium content in this system.The Ni content in austenite layers decreased significantly,and Co content increased slightly with the decrease of Ni content in overall composition.The austenite stability was estimated by Olson-Cohen model,in which both chemical and mechanical driving force could be calculated by equilibrium thermodynamic and Mohr′s circle methods,respectively.Simulation and mechanical test results showed that the decrease of Ni content in austenite layers would cause the change of austenite stability and decrease the fracture toughness of the steels.When the Ni content in the overall composition was lower than 7wt.%,the Ni content inγphase would be lower than 20 wt.%.And the simulation value of Mσs(stress-induced critical martensite transformation temperature)would be up to 80°C,which was about 60°C higher than room temperature.Based on the analysis,the Ni content in the overall composition of high Co-Ni secondary hardening steels should be higher than 8wt.% in order to obtain a good fracture toughness.     

State-of-the-knowledge on TWIP steel

Abstract

High Mn twinning induced plasticity (TWIP) steel is a new type of structural steel, characterised by both high strength and superior formability. TWIP steel offers an extraordinary opportunity to adjust the mechanical properties of steel by modifying the strain hardening. The use of TWIP steel may therefore lead to a considerable lightweighting of steel components, a reduction of material use and an improved press forming behaviour. These key advantages will help implement current automotive vehicle design trends which emphasise a reduction of greenhouse gas emissions and lowering of fuel consumption. In addition, high strength TWIP steel will effectively contribute to weight containment in vehicles equipped with hybrid and electric motors, as these are considerably heavier than conventional motors. The present review addresses all aspects of the physical metallurgy of the high strength TWIP steel with a special emphasis on the properties and key advantages of TWIP sheet steel products relevant to automotive applications.     

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis (SRFEA) with finite element limit analysis (FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety (FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis (1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.     

Solution for the general integral‐type nonlocal plasticity model with Tikhonov regularization

A new solution approach, based on Tikhonov regularization on the Fredholm integral equations of the first kind, is proposed to find the approximate solutions of the strain softening problems. In this approach, the consistency condition is regularized with the Tikhonov stabilizers along with a regularization parameter, and the internal variable increments are solved from the resulting Euler's equations. It is shown that, as the regularization parameter is increased, the solutions converge to a unique one. A nonlocal yield condition and a nonlocal return mapping algorithm are proposed to carry out the integration of constitutive equations in the time and spatial domains. A global plastic dissipation principle is proposed to relax the classical local plastic dissipation postulate. Numerical examples show that the proposed approach leads to objective, mesh‐independent solutions of the softening‐induced localization problems. A comparison of the results from the proposed approach with those from the gradient‐dependent plasticity model shows that the two models give close solutions.