Inelastic Hysteresis Research Articles

NONLINEAR EFFECTS IN CRYSTALLINE SOLIDS WITH SATURATION OF AMPLITUDE-DEPENDENT INTERNAL FRICTION, DECREASING WITH IN-CREASING FREQUENCY

As a result of modification of quasi-static elastic and inelastic hysteresis, dynamic hysteresis equations of state of crystalline solids with frequency-dependent saturation of amplitude-dependent internal friction decreasing with increasing frequency are proposed. The nonlinear propagation of initially harmonic longitudinal elastic waves in rods made of such materials is investigated by the perturbation method. Numerical, graphical and comparative analysis of the obtained solutions is carried out and characteristic amplitude-frequency dependenc-es of nonlinear wave effects are revealed. A method for determining the type of dynamic hysteresis for crystal-line solids with frequency-dependent saturation of amplitude-dependent internal friction is proposed.

New Damage Accumulation Model for Spall Propagation Mechanism in Bearing Raceways

The aim of this study was to investigate the spall propagation mechanism in ball bearing raceways using physics-based models. Spalling is one of the most common types of bearing failures that can lead to catastrophic failure. This research takes a step forward toward developing a prognostic tool for ball bearings. It is first necessary to understand the spall progression process in order to formulate a constitutive law of spall deterioration and to estimate the amount of remaining useful life. Fragment formation in the vicinity of the spall edge was found to consist of surface and sub-surface cracks that eventually coalesce, and a fragment is released from the raceway, based on naturally-developed spalls. Here, we describe a physics-based model, integrating a dynamic model with a finite element one to simulate this process. A continuum damage mechanics (CDM) approach and fracture mechanics tools were embedded into the finite element model to simulate the damage propagation. The formation of cracks in the vicinity of the spall (surface and sub-surface cracks) were studied using this effective stress CDM model, and the propagation of the cracks was examined using two approaches: a fracture mechanics approach and an accumulated inelastic hysteresis energy CDM approach. The latter also predicts the overall process of a single fragment release. The simulation results of the spall propagation models are supported by experimental results of spalls from both laboratory experimental bearings and an in-service Sikorsky CH-53 helicopter swashplate bearing. The results obtained show that the impact of the ball on the spall edge affects the crack propagation and the appearance of the surface and sub-surface cracks. Both release the residual stresses and cause crack propagation until a fragment is released.

Finite element model for simulating entropy-based strength-degradation of carbon-fiber-reinforced plastics subjected to cyclic loadings

In this study, a novel model for simulating strength and fracture energy reductions based on the stress and strain histories of a carbon-fiber-reinforced plastic (CFRP) ply is developed, thus allowing us to comprehensively simulate the versatile failures including fatigue failure for CFRPs. The strength and fracture energy reductions are defined as functions of entropy generation. The entropy value is obtained from the absolute temperature and dissipated mechanical energy, such as the area of the inelastic hysteresis loop. Strength and fracture energy reductions are introduced into the conventional Hashin’s criterion. An algorithm for this model and some numerical validations are presented herein. Through a simplified CFRP laminate model with frequency dependence, a delayed failure of 90°layer under cyclic displacement conditions is numerically simulated.

Micromechanics based modelling of fatigue crack initiation of high strength steel

The cyclic behaviour and fatigue crack initiation in low cycle regime of dual phase (DP) steel grade 590 were characterized. Experimental strain-controlled tension–compression tests and corresponding simulations using representative volume elements were carried out. The Chaboche kinematic hardening parameters were determined for each individual phases. The damage model based on accumulated inelastic hysteresis energy was incorporated for describing crack onset mechanism in the microstructure. Damage parameters were calibrated with experimental strain-life curves for crack initiation state. Effects of pre-strain on crack occurrence of steel were studied. Observed crack initiation and its life were well predicted by the proposed modelling scheme.

A multiscale shear-transformation-zone (STZ) model and simulation of plasticity in amorphous solids

In this work, we have developed a multiscale shear-transformation-zone (STZ) model to simulate inelastic deformations in amorphous materials at macroscale without using phenomenological constitutive modeling. The main novelties of the multiscale method are two: (1) the multiscale method employs an atomistic-based representative sampling cell (RS-cell) that is embedded in every quadrature points of macroscale finite elements, and it generically contains potential shear-transformation-zones. Thus the evolution of RS-cells can naturally allow molecular clusters having irreversible microstructure rearrangements at microscale in response to applied loads, and subsequently translate the effects of the irreversible rearrangements of molecular clusters in each RS-cell to inelastic responses at the continuum scale, i.e. delineating the defect-mediated amorphous plasticity, and (2) the method uses a Parrinello-Rahman molecular mechanics based the Cauchy-Born rule to construct an atomistically-informed constitutive model at continuum level, which is able to quantitatively measure amorphous plasticity behaviors, including plastic flow stress, inelastic hysteresis loops under cyclic loading, and strain localizations at macroscale. By doing so, we have successfully simulated plastic deformation in the Lennard-Jones binary glass (LJBG) at macroscale level. Moreover, we have shown that the multiscale shear-transformation-zone can capture cyclic plasticity and the shear band formations in LJBG material.

Simulation study on thermo-fatigue failure behavior of solder joints in package-on-package structure

In this work, the simulating analysis of PoP structure under the temperature range from 0°C to 125°C is carried out using direct thermal-cycle analysis and Coffin-Manson method. The results show that the maximum accumulating inelastic hysteresis energy appears on the solder ball in the bottom fine-pitch ball grid array (FBGA) structure. The thermal-fatigue crack initiates in the two symmetrical corners of solder ball in FBGA structure. The thermal-fatigue damage evolves fast in the outer row corner's balls then slowly propagates into the inner row balls in FBGA structure. By analyzing the failure data of solder balls, a thermal-fatigue failure criterion is defined where the critical failure probability value is about 80%.

Constitutive and damage modelling of H11 subjected to low‐cycle fatigue at high temperature

AbstractHot‐work tool steel H11 is extensively applied in extrusion industries as extrusion tools. The understanding of its mechanical properties and damage evolution as well as failure is crucial for its implementation. In this paper, a finite element (FE) model employing Chaboche unified constitutive model and ductile damage rule is proposed to simulate the mechanical responses of H11 subjected to low‐cycle fatigue (LCF). Accumulated inelastic hysteresis energy is adopted to demonstrate the impact on damage initiation and evolution rules. A series of tension and LCF experiments were conducted to investigate H11's mechanical properties and its deterioration processes. In addition, to deeply understand the deformation and damage mechanism, scanning electron microscope (SEM) investigations were performed on the fracture section of gauge‐length part of the specimen after failure. Furthermore, the parameters in both constitutive model and damage rule are identified based on experimental data. The comparison of the hysteresis loop of the first cycle and stable cycle with different strain amplitudes demonstrates that the Chaboche constitutive model provides high precision to predict the evolution of mechanical properties. Based on the reliable achieved constitutive model, LCF behaviour prediction with damage rule was executed successfully using FE model and gains a good agreement with the experiments. It is believed that the proposed FE method lays the foundation of structure analysis and rapid design optimization in further applications.

The Inelastic Hierarchy: Multiscale Biomechanics of Weak Bonds

Living tissue is a mechanical chameleon. It may behave as a viscous or elastic material, depending on how fast and strong you pull on it. It also responds plastically to permanent loads, as evidenced by the Tutankhamun-style lobe-stretching ear piercings that are currently regaining popularity. To mechanistically explain and quantitatively predict how such impressive versatility and resilience is accomplished by the molecular composition and architecture of living matter is the holy grail of biomechanics.

The Wave Processes in the Media Having Inelastic Hysteresis with Saturation of The Nonlinear Loss

We study theoretically the nonlinear wave processes during excitation of a longitudinal harmonic wave in an unbounded medium and the rod resonator with inelastic hysteresis and saturation of the amplitude-dependent loss. The nonlinear-wave characteristics in such systems, namely, the amplitude-dependent loss, variation in the wave-propagation velocity, the resonant-frequency shift, and the higher-harmonic amplitudes are determined. The results of the theoretical and experimental studies of nonlinear effects in the rod resonator of annealed polycrystalline copper are compared. The effective parameters of the hysteretic nonlinearity of this metal are evaluated.

Computational study of low-cycle fatigue behaviour of lotus-type porous material

A computational study of low-cycle fatigue behaviour of lotus-type porous material subjected to uniaxial/biaxial tension and compressive loading cycles is presented in this paper. The considered computational models have different pore topology patterns. The low-cycle fatigue analysis is performed using a damage initiation and evolution law, based on the inelastic hysteresis energy for stabilized loading cycle. The direct cyclic analysis is used to obtain the stabilized response of a model subjected to periodic loading. The present study clarifies the influences of pore topology on the low-cycle fatigue behaviour under different type of transversal loading conditions with respect to the pore orientations.

Damage and failure modeling of lotus-type porous material subjected to low-cycle fatigue

The investigation of low-cycle fatigue behaviour of lotus-type porous material is presented in this paper. Porous materials exhibit some unique features which are useful for a number of various applications. This paper evaluates a numerical approach for determining of damage initiation and evolution of lotus-type porous material with computational simulations, where the considered computational models have different pore topology patterns. The low-cycle fatigue analysis was performed by using a damage evolution law. The damage state was calculated and updated based on the inelastic hysteresis energy for stabilized cycle. Degradation of the elastic stifness was modeled using scalar damage variable. In order to examine crack propagation path finite elements with severe damage were deleted and removed from the mesh during simulation. The direct cyclic analysis capability in Abaqus/Standard was used for low-cycle fatigue analysis to obtain the stabilized response of a model subjected to the periodic loading. The computational results show a qualitative understanding of pores topology influence on low-cycle fatigue under transversal loading conditions in relation to pore orientation.

Fatigue crack initiation and crystallographic growth in 316L stainless steel

A mesoscale model of fatigue crack formation and stress–strain behavior in crystalline alloys entitled Sistaninia–Niffenegger Fatigue (SNF) model is applied to AISI 316L austenitic stainless steel. An inelastic hysteresis energy criterion in conjunction with continuum damage modeling provides a strong tool for studying the behavior of the austenitic steel under cyclic loading. The model predictions are validated against fatigue experimental data. The results show that this microstructural-based modeling approach is capable for predicting the behavior of the steel even under complex loading conditions. It can reproduce and help to understand well known fatigue experimental facts, e.g. the effect of grain size and initial defects, by considering the anisotropic behavior of crystalline materials at the level of the microstructure.

Prediction of damage-growth based fatigue life of polycrystalline materials using a microstructural modeling approach

A new finite element-based mesoscale model is developed to simulate the localization of deformation and the growth of microstructurally short fatigue cracks in crystalline materials by considering the anisotropic behavior of the individual grains. The inelastic hysteresis energy is used as a criterion to predict the fatigue crack initiation and propagation. This criterion in conjunction with continuum damage modeling provides a strong tool for studying the behavior of materials under cyclic loading at the level of the microstructure. The model predictions are validated against an austenitic stainless steel alloy experimental data. The results show that a combined microstructural and continuum damage modeling approach is able to express the overall fatigue behavior of crystalline materials at the macroscale based on the microstructural features. It correctly predicts the crack initiation on slip bands and at inclusions in low-cycle and high-cycle fatigue, respectively, in agreement with experimental observations reported in the literature.

Fatigue damage behavior of a surface-mount electronic package under different cyclic applied loads

This paper studies and compares the effects of pull–pull and 3-point bending cyclic loadings on the mechanical fatigue damage behaviors of a solder joint in a surface-mount electronic package. The comparisons are based on experimental investigations using scanning electron microscopy (SEM) in-situ technology and nonlinear finite element modeling, respectively. The compared results indicate that there are different threshold levels of plastic strain for the initial damage of solder joints under two cyclic applied loads; meanwhile, fatigue crack initiation occurs at different locations, and the accumulation of equivalent plastic strain determines the trend and direction of fatigue crack propagation. In addition, simulation results of the fatigue damage process of solder joints considering a constitutive model of damage initiation criteria for ductile materials and damage evolution based on accumulating inelastic hysteresis energy are identical to the experimental results. The actual fatigue life of the solder joint is almost the same and demonstrates that the FE modeling used in this study can provide an accurate prediction of solder joint fatigue failure.

Large-scale finite element analysis of a 3D angle-interlock woven composite undergoing low-cyclic three-point bending fatigue

This paper reports the large-scale finite element analysis (FEA) of a 3D angle-interlock layer-to-layer woven composite material undergoing low-cyclic three-point bending fatigue at microstructure level. A microstructure geometrical model of the 3D woven composite material was established to model the real structure of the woven composite. The fatigue behaviors of the 3D woven composite undergoing three-point bending with sinusoidal wave-form were investigated from experimental and FEA approaches. Based on displacement-controlled bending and inelastic hysteresis energy fatigue damage criterion, the interior deformation, energy absorption, and stress distribution characteristics during the fatigue process were analyzed. The different failure mechanisms and damage patterns of yarns and resin were discussed. The influence of the 3D woven structure on the fatigue behaviors was discussed. The fatigue damage morphologies and stiffness degradation were obtained to compare with the experimental results. The results show that the most of energy was absorbed by warp yarns. Stress concentration was emerged on the inclined part of warp yarns and the interface between yarns and resin. The damage morphologies from experimental and FEA results are in good agreement. The stiffness degradation curves also show the same tendency.

지진하중의 특성과 이력모델에 따른 저층 표준학교건물의 비탄성 지진거동

The inelastic response characteristics of the standard school buildings depending on selection of hysteresis models and variable earthquakes are studied. Three earthquake records of El-centro, Santa-Monica, Taft in accordance with KBC2009 standard and four inelastic hysteresis models such as Degrading tri-linear model, Clough model, Takeda model, and Modified Takeda model are used. The inelastic response characteristics such as story shear force, story drift ratio, story displacement are reviewed. As results, El-centro earthquake shows large response in transverse direction and Santa Monica earthquake shows larger response in longitudinal direction on the contrary. Taft earthquake shows less variation of story drift ratio and story displacement for all hysteresis models and stable response.

Amplitude dependent internal friction and generation of harmonics in granite resonator

The results of experimental and theoretical studies of low-frequency effects of amplitude dependent internal friction (nonlinear losses and resonance frequency shift) and generation of second and third harmonics in an acoustic bar resonator made of Karelian granite are presented. The analytical description of the observed effects is performed within the framework of phenomenological hysteretic equations of state containing elastic and inelastic hysteresis. It was shown that elastic cubic hysteresis is manifested at small amplitudes of strains, whereas superposition of elastic and inelastic quadratic hysteresises occurs at large amplitudes of strain. Relative weights of these hysteresises and effective parameters of acoustic nonlinearity of granite are determined.

Tests of Cold-Formed Circular Tubular Braces under Cyclic Axial Loading

This paper describes a series of tests to failure of fix-ended tubular braces subjected to cyclic concentric axial loading. The braces were made from cold-formed steel grade C350L0 ~350 MPa nominal yield stress! circular hollow sections ~CHS!. Nine different diameter-to-thickness ratios in the range of 19,D/t,56 that have a moderate member slenderness in the range of 25,KL/r,41 were tested. The effects of three loading protocols on the inelastic hysteresis behavior of the CHS braces were examined. The CHS braces exhibited stable hysteresis behavior up to local buckling, and then showed considerable degradation in strength and ductility depending on KL/r and D/t ratios. First-cycle buckling loads were compared with design loads predicted using a number of steel specifications. The effects of section and member slenderness on strength, ductility, and energy absorption capacity of the braces were examined. The structure response factor ~ductility index! was determined and used to derive new section slenderness limits suitable for seismic design. CE Database subject headings: Cold-formed Steel; Bracing; Tubes; Cyclic loads.

Nanoindentation behavior of a two-dimensional carbon-carbon composite for nuclear applications

Nanoindentation tests on a carbon fiber and carbon matrix composite (C/C composite) for nuclear applications were carried out over a load range from 50 μN to 20 mN on two different crosssections, normal and parallel to the fiber axis. For reference, an isotropic nuclear graphite was also examined. Both the composite and graphite revealed a large amount of elastic recovery on the first loading-unloading indentation curves and inelastic hysteresis on the subsequent cycling curves. The analysis of mean indentation pressure data on the basis of the Weibull statistics indicates that the data on the C/C composite are separated into two groups with different Weibull moduli; the group of the lower modulus with higher mean pressure is attributed to the fiber, and the higher modulus with lower mean pressure to the matrix. The average of mean indentation pressure is obtained as 101 MPa for the fiber and 35.5 MPa for the matrix, while graphite has an intermediate value of 52.2 MPa. There is a slight dependence of mean stress p m on the applied load P in all the materials. However, the trend appears to be different between the two materials; p m decreases with increasing P for the C/C composite, while the reverse is true in graphite. Young's moduli of the graphite and the two constituents of the C/C composite are estimated from the stiffness of the unloading indentation curves at 10.7 GPa for the graphite as 6.71 GPa for the fiber and 1.97 GPa for the matrix. The values estimated for the graphite and the fiber are comparable to those of the bulk graphite and C/C composite, respectively.

Inelastic Earthquake Response of Tall Steel Frames

A procedure for evaluating the lateral response of unbraced multistory building frames subjected to a prescribed base motion was developed for use on a digital computer. A Ramberg-Osgood type moment-curvature function was used to describe the inelastic hysteresis behavior of girders, while the columns were assumed to behave elastically. Representative frames of 10, 25, and 40 stories were analyzed. Recorded accelerograms of El Centro 1940, Taft 1952, and Alameda Park, Mexico 1962 earthquakes were used with modified intensities. The results indicate that the shape and intensity of the velocity response spectrum of the earthquakes and the elastic fundamental period of the structures have a marked influence upon their inelastic response. While the elastic behavior of columns is well documented by the results, the hysteresis behavior of girders alone may be a potential source of energy dissipation during a severe earthquake.