Effect Of Triaxiality Research Articles

Effects of the Earth’ s triaxiality on the polar motion excitations

his study aims to evaluate the significance of the Earth’s triaxiality to the polar motion theory. First of all, we compare the polar motion theories for both the triaxial and rotationally-symmetric Earth models, which is established on the basis of the EGM2008 global gravity model and the MHB2000 Earth model. Then, we use the atmospheric and oceanic data (the NCEP/NCAR reanalyses and the ECCO assimulation products) to quantify the triaxiality effect on polar motion excitations. Numerical results imply that triaxiality only cause a small correction (about 0. 1–0.2 mas) to the geophysical excitations for the rotationally-symmetric case. The triaxiality correction is much smaller than the errors in the atmospheric and oceanic data, and thus can be neglected for recent studies on polar motion excitations.

Effect of triaxiality on void growth and coalescence in model materials investigated by X-ray tomography

Void growth and coalescence/linkage, which play significant roles during ductile fracture processes, are strongly influenced by stress triaxiality in a deforming solid. The stress state can be changed by cutting notches in a tensile sample. In the current paper, void growth and linkage of an artificial void array embedded in a notched model material was studied by X-ray computed tomography, coupled with in situ tensile deformation. The cross-sectional shape of the tensile specimens was square, and a pair of notches was cut along only one direction. Thus, the lateral principal stress does not have an isotropic distribution: the principal stress along the notch direction is considered to be higher. This technique allowed us to explore the entire process of growth and linkage events of a void array embedded in a metal matrix. The notch effect creates a marked acceleration in void growth, leading to a large reduction in the linkage strains, as compared with similarly fabricated unnotched samples. The standard models for coalescence could not provide consistent predictions of the measured notch effect.

Investigating tensile behaviour of toughened epoxy paste adhesives using circumferentially notched cylindrical bulk specimens

Toughened epoxy adhesives are frequently used to bond metals and polymer-matrix composite materials in many structural applications. The mechanical properties of adhesives are often characterised by testing either bulk adhesive specimens or bonded joints (i.e. in-situ form). In this paper, cylindrical bulk specimens with circumferential notches were manufactured and tested to investigate the tensile behaviour of an epoxy paste adhesive toughened with hollow glass microspheres. Bulk specimens were manufactured from the paste adhesive using injection moulding. Tensile tests were conducted for strain-rate and stress triaxiality effects by varying displacement rates and notch radii, respectively. Fracture surfaces were examined using optical and scanning electron microscopy to identify failure mechanisms. The results obtained from the toughened paste adhesive indicate that strain-rate and stress triaxiality influence its tensile fracture behaviour.

Numerical modeling of elasto-plastic porous materials with void shape effects at finite deformations

A new constitutive model for elasto-plastic (rate-independent) porous materials subjected to general three-dimensional finite deformations is presented. The new model results from simple modifications of an earlier model of Kailasam and Ponte Castañeda (1997, 1998) [40,41] so that it reproduces the exact spherical and cylindrical shell solution (composite sphere and composite cylinder assemblage) under purely hydrostatic loadings, while predicting (by calibration) accurately the void shape evolution according to the recent “second-order” model of Danas and Ponte Castañeda [17]. Furthermore, the present model is based on a rigorous homogenization method which is capable of predicting both the constitutive behavior and the microstructure evolution of porous materials. The microstructure is described by voids of arbitrary ellipsoidal shapes and orientations and as a result the material exhibits deformation-induced (or morphological) anisotropy at finite deformations. This is in contrast with the well-known Gurson [32] model which assumes that the voids remain spherical during the deformation process and thus the material remains always isotropic. The present model is implemented numerically in a finite element program where a three-dimensional thin-sheet (butterfly) specimen is subjected to a combination of shear and traction loading conditions in order to examine the effect of stress triaxiality and shearing upon material failure. The ability of the present model to take into account the nontrivial evolution of the microstructure and especially void shape effects leads to the prediction of material failure even at low stress triaxialities and small porosities without the use of additional phenomenological damage criteria. At high stress triaxialities, the present model gives similar predictions as the Gurson model.

Time-dependent Triaxiality Effects on Hydrogen-assisted Micro-damage Evolution in Pearlitic Steel

This paper offers a detailed analysis of the hydrogen-assisted micro-damage (HAMD) region in axisymmetric round-notched samples of high-strength eutectoid steel under hydrogen embrittlement environmental conditions. Emphasis is placed on the microscopic appearance and the evolution of such a microscopic topography from the initiation (sub-critical) to the fracture (critical) point. The use of very different notched geometries —with the subsequent various triaxial stress distributions in the vicinity of the notch tip— allows an analysis of the influence of stress state on hydrogen diffusion and micro-cracking. In all cases, the microscopic appearance of the hydrogen-affected zone resembles micro-damage, micro-cracking or micro-tearing due to hydrogen degradation.

Effect of the Stress State Triaxiality on the Value of Limit Strain of Micro-Void Development in S235JR Steel - Numerical Analysis

This paper deals with the numerical analysis of plastic deformation and damage development in S235JR steel in complex stress states. The material Gurson Tvergaard Needleman (GTN) model was applied. The analysis was performed for notched bars subjected to tension. An attempt was made to investigate the effect of stress triaxiality on the value of critical strain of voids growth in the GTN model.

Modeling the Transition between Dense Metal and Damaged (Microporous) Metal Viscoplasticity

This article presents a physically motivated approach, which has been developed in order to describe the transition of behavior between dense metal plasticity and microporous metal plasticity in the context of dynamic plasticity and adiabatic conditions. Considering that void germination requires a certain amount of plastic deformation, a ‘primary’ hole nucleation criterion as well as a statistical law governing the ‘secondary’ hole formation kinetics has been proposed. In a consistent way, the hole nucleation criterion accounts for the accelerating effects of stress triaxiality and the delaying effects of temperature and strain rate. In addition, a modification of the GTN model was proposed, allowing for describing cavity growth under shear loading. The 3D constitutive equations were implemented as user material in the engineering finite element computation code Abaqus®. Numerical simulations were conducted considering a single finite element under uniaxial tensile loading and simple shear then notched cylindrical samples under remote uniaxial tensile loading. The numerical results clearly show the influence of the hole nucleation criteria on the ductile damage and failure.

Modeling of Anisotropic Plastic Behavior of Advanced High Strength Steel Sheet TRIP 780

Anisotropic plastic behavior of advanced high strength steel sheet of grade TRIP780 (Transformation Induced Plasticity) was investigated using three different yield functions, namely, the von Mises’s isotropic, Hill’s anisotropic (Hill’48), and Barlat’s anisotropic (Yld2000-2d) criterion. Uniaxial tensile and balanced biaxial test were conducted for the examined steel in order to characterize flow behavior and plastic anisotropy for different stress states. Especially, disk compression test was performed for obtaining balanced r-value. All these data were used to determine the anisotropic coefficients. As a result, yield stresses and r-values for different directions were calculated according to these yield criteria. The results were compared with experimental data. To verify the modelling accuracy, tensile tests of various notched samples were carried out and stress-strain distributions in the critical area were characterized. By this manner, the effect of stress triaxiality due to different notched shapes on the strain localization calculated by the investigated yield criteria could be studied.

Development of a Microscopic Damage Model for Low Stress Triaxiality

This work dealsa contribution to ductile damageof High-Strength Low-Alloy (HSLA) steel under low stress triaxiality. This work is based on micrographics observations and in-situ shear tests to examine the evolution of microstructure in this kind of loading and to identify the damage process associated. Numerical simulations by finites elements has been performed to simulate the material behavior of nucleation mechanism and the interaction between cavities during the coalescence phase, as well as the effect of the relative position of the inclusions in the shear plane.The model used as a reference in this work is the Gurson-Tvergaard- Needleman (GTN) model. It has been recently improved in order to take into account the effects of low triaxiality during shearing. A new modelisunderdevelopmentto takeintoaccounttheeffects oflowtriaxiality stresses (or loading) during shearing.

Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

A set of constitutive equations for large rate-dependent elastic–plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed. Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor–elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. Numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments.

A procedure for determining the true stress–strain curve over a large range of strains using digital image correlation and finite element analysis

A procedure for determining the stress–strain curve including post-necking strain is proposed. Hourglass type specimens were used for tensile tests, and the stress–strain curves were identified through an iteration process using finite element analysis. The strain at the position of minimum diameter was measured by digital image correlation. This procedure was applied to carbon steel of various degrees of cold work. The radius of the minimum section of the hourglass type specimen was changed in order to investigate the effect of stress triaxiality on the failure strain. The procedure could derive the stress–strain curve including the post-necking strain. From the obtained curve, it was shown that the stress–strain curves for different degrees of cold work were almost identical when the plastic strain by the cold working was added to the strain. Furthermore, it was revealed that the true stress–strain curve could be approximated well by the power law equation and the curve could be estimated by using the stress–strain relation for before-necking strain.

Effect of stress triaxiality and Lode angle on the kinetics of strain-induced austenite-to-martensite transformation

The effect of the stress state on the transformation kinetics of stainless steel 301LN sheets at room temperature is investigated using newly developed experimental techniques for simple shear and large strain in-plane compression. In addition, uniaxial and equi-biaxial tension experiments are performed. Two-dimensional and stereo digital image correlation techniques are used to measure the surface strain fields. In situ magnetic permeability measurements are performed to monitor the evolution of martensite content throughout each experiment. The experimental results indicate that the martensitic transformation kinetics cannot be described solely by a monotonically increasing function of stress triaxiality: for instance, less martensite is developed under equi-biaxial tension than under uniaxial tension for the same increment in equivalent plastic strain. A stress-state-dependent transformation kinetics law is proposed that incorporates the effect of the Lode angle parameter in addition to the stress triaxiality. In the proposed model, the rate of martensite formation increases monotonically with the stress triaxiality and the Lode angle parameter. The comparison with the experimental data demonstrates that the proposed transformation kinetics law provides an accurate description of the evolution of the martensite content in stainless steel 301LN over a wide range of stress states.

LOW-LYING STATES IN 30Mg: A BEYOND RELATIVISTIC MEAN-FIELD INVESTIGATION

The recently developed model of three-dimensional angular momentum projection plus generator coordinate method on top of triaxial relativistic mean-field states has been applied to study the low-lying states of 30 Mg . The effects of triaxiality on the low-energy spectra and E 0 and E 2 transitions are examined.

Effect of Stress Triaxiality and Matrix Microstructure on Ductile Fracture in Ductile Cast Iron

Effect of Stress Triaxiality and Matrix Microstructure on Ductile Fracture in Ductile Cast Iron

New estimates of the inertia tensor and rotation of the triaxial nonrigid Earth

The Earth's rotation is perturbed by mass redistributions and relative motions within the Earth system, as well as by the torques from both the internal Earth and celestial bodies. The present study aims to establish a theory to incorporate all these factors perturbing the rotation state of the triaxial Earth, just like the traditional rotation theory of the axial‐symmetric Earth. First of all, we reestimate the Earth's inertia tensor on the basis of two new gravity models, EIGEN‐GL05C and EGM2008. Then we formulate the dynamic equations and obtain their normal modes for an Earth model with a triaxial anelastic mantle, a triaxial fluid core, and dissipative oceans. The periods of the Chandler wobble and the free core nutation are successfully recovered, being ∼433 and ∼430 mean solar days, respectively. Further, the Liouville equations and their general solutions for that triaxial nonrigid Earth are deduced. The Liouville equations are characterized by the complex frequency‐dependent transfer functions, which incorporate the effects of triaxialities and deformations of both the mantle and the core, as well as the effects of the mantle anelasticity, the equilibrium, and dissipative ocean tides. Complex transfer functions just reflect the fact that decays and phase lags exist in the Earth's response to the periodic forcing. Our theory reduces to the traditional rotation theory of the axial‐symmetric Earth when assuming rotational symmetry of the inertia tensor. Finally, the present theory is applied to the case of atmospheric‐oceanic excitation. The effective atmospheric‐oceanic angular momentum function (AMF)χeff=χeff1+iχeff2for the present theory is compared with the AMFχeffsym=χeff1sym+iχeff2symfor the traditional theory and the observed AMFχobs=χ1obs+iχ2obs; we find that the difference betweenχeffandχeffsymis of a few milliseconds of arc (mas) and can sometimes exceed 10 mas. In addition, spectrum analyses indicate thatχeffis in good agreement withχeffsymand, further, show an increase of coherency withχobsespecially in the low‐frequency band. The obvious advantage ofχeffin the low‐frequency band with respect toχeffsymis the critical support of the present theory. However, still better performance of our theory can be expected if the models of the mantle anelasticity and oceanic dynamics were improved. Thus we conclude that the traditional Earth rotation theory should be revised and upgraded to include the effects of the Earth's triaxiality, the mantle anelasticity, and oceanic dynamics. The theory presented in this study might be more appropriate to describe the rotation of the triaxial Earth (or other triaxial celestial bodies such as Mars), though further studies are needed to incorporate the effects of the solid inner core and other possible influences.

Stress‐triaxiality‐dependent modeling of ductile damage and fracture behavior

AbstractThe paper deals with the effect of stress triaxiality on the inelastic behavior of aluminum alloys. The proposed continuum model takes into account stress‐triaxiality‐dependence of the yield condition as well as of the damage criterion and the fracture condition with different branches corresponding to different micro‐mechanisms. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of Ductile Damage and Fracture Behavior Based on Different Micromechanisms

The article deals with the effect of stress triaxiality on the inelastic deformation behavior of aluminum alloys. The proposed continuum model takes into account stress triaxiality dependence of the yield condition as well as of the damage criterion and the fracture condition with different branches corresponding to various damage and failure modes depending on the stress triaxiality and the Lode parameter. Results of numerical cell simulations on the microscale are presented and corresponding identification of micromechanically motivated material parameters is discussed. Furthermore, numerical results of three-dimensional macromechanical finite element analyses are compared with experimental data obtained from smooth and pre-notched tension specimens. The analyses allow verification of the continuum model and identification of further material parameters.

Investigation of abnormal high impact toughness in simulated welding CGHAZ of a 8%Ni 980 MPa high strength steel

It is well known that the toughness in the coarse grain heat affected zone (CGHAZ) is of the lowest in the heat affected zone (HAZ) of a HSLA steel welding joint. In the present work although the grain size in the simulated CGHAZ was as large as 100–300 μm and its tensile strength and elongation were lower than those of the fine grain heat affected zone (FGHAZ), however its Charpy V impact toughness at room temperature reached 193 J, which was appreciably higher than 138 J of the simulated FGHAZ with grain size of 30 μm. This abnormal phenomenon was investigated in this paper by analyzing the micromechanism of ductile rupture in associated microstructures and taking account of the effects of stress triaxiality.

Void growth and coalescence in f.c.c. single crystals

In this study, we investigate deformation behavior of f.c.c. single crystals containing microvoids by using three-dimensional finite element methods. The unit cell analysis has been conducted to study the effect of stress triaxialities, crystallographic orientations and initial void volume fractions on the growth and coalescence of voids in f.c.c. single crystals. The locally homogeneous constitutive model for the rate-dependent single crystal plasticity is implemented into a finite element program (ABAQUS) by means of the user-defined subroutine (UMAT). To identify the effect of stress triaxiality and the crystallographic orientation on the void evolution, the stress triaxiality was kept constant during deformation. The numerical results showed that the stress triaxiality and the deformation mode specified by the crystallographic orientation have a competitive effect on the evolution of voids. For the low level of stress triaxiality, the deformation mode is mainly determined by the crystallographic orientation. For high stress triaxiality, however, the deviation from the specific deformation mode is large even for incipient void growth and the void growth rate is mainly determined by stress triaxiality and the initial void volume fraction. For the small initial void volume fraction, the growth rate of a void is rapid compared with the large one and the effect of the initial crystallographic orientation is significant.

Effects of triaxiality on the growth of crack-like cavities in soft incompressible elastic solids

We study the finite deformation of an isolated circular or penny-shaped crack in an infinite block of soft incompressible hyper-elastic solid. The crack is subjected to remote tensile true stresses that are parallel (S) and normal (T) to the undeformed crack faces. Two material models are considered, an ideal rubber (neo-Hookean solid) and a hyperelastic material that hardens exponentially. The energy release rates for different triaxiality ratios S/T from uniaxial tension (S/T = 0) to hydrostatic tension (S/T = 1) are determined using a finite element method (FEM). For small deformations, our results agree with linear elastic theory where the energy release rate is independent of S. This is not the case at finite strains; our results show that the energy release rate increases rapidly with triaxiality. For the special case of pure hydrostatic tension, the energy release rate approaches infinity for the neo-Hookean solid at a finite tension, consistent with a previous result by Lin and Hui (Y.Y. Lin and C.Y. Hui, Int. J. Fract., 2004, 126, 205–221). Our result shows that strain hardening significantly reduces the energy release rate for the same remote loading. In particular, for the case of hydrostatic tension, the energy release rate remains bounded for the exponentially hardening solid.