High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.     

Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM

This paper presents the micromechanical behavior of granular materials due to different initial inherent anisotropic conditions during cyclic loading using the discrete element method (DEM). Oval particles were used to model the samples. Three samples, with three different inherent anisotropic conditions based on the particle’s bedding direction, were prepared and subjected to biaxial cyclic loading. The differences in the inherent anisotropic conditions of the samples affect the stress–strain-dilative behavior of granular materials. The width of the stress–strain cyclic loops decreases as the preferred bedding angle changes from vertical to horizontal. Contact fabric evolution is found to be dependent on the inherent anisotropic fabric of the sample during loading and unloading. The fabric anisotropy is dominant for horizontal particle bedding at the end of loading and for vertical particle bedding at the end of unloading. A change in fabric anisotropy is observed only for the first few loading–unloading cycles for the given conditions depicted in the present study.     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

Determination of large deformation and fracture behaviour of starch gels from conventional and wire cutting experiments

Large deformation and fracture properties of two types of starch gels were investigated through uniaxial compression, single edge-notched bend (SENB) and wire cutting experiments. Tests were performed at various loading rates and for various starch/powder concentrations (%w/w). It was found that starch gels exhibit rate independent stress–strain behaviour but show rate-dependent fracture behaviour, i.e. stress–strain curves at three loading rates are similar but fracture stress and fracture strain increase with increasing strain rate. This is rather unusual and interesting behaviour. SENB and wire cutting experiments also revealed rate-dependent fracture behaviour and that the true fracture toughness (G _c) values increase with loading/cutting speeds and starch powder concentration. In addition, the G _c values from wire cutting and SENB tests were in reasonable agreement. The wire cutting process was also studied numerically using finite element techniques. A non-linear elastic constitutive relationship based on Ogden was used to model the starch gels and a frictionless condition was assumed at the wire–starch gel contact interface. A fracture criterion based on maximum principal strain was assumed for the prediction of the steady state cutting force.     

Some observations of the effects of pore fluids on the triaxial behaviour of a sand

This paper describes unusual stress–strain behaviour, involving deviatoric stress, axial strain and pore pressure jumps, observed during undrained triaxial compression testing of Leighton Buzzard sand when using syrup and silicon oil pore fluids. The materials, pore fluids, specimen preparation and test methods are described, as are the results of a suite of triaxial tests in a temperature controlled cell in which deviatoric stress, pore pressure and local strain were measured. The results are compared with the some existing data showing similar effects, and possible causes of the strain jumps are postulated. The results suggest that specimen formation in the way used here, in a viscous fluid, could suppress dilatancy.     

Constitutive descriptions for hot compressed low-pressure rotor steel at elevated high temperature

The constitutive equation of the material is an essential ingredient of any structural calculation. In this article, a phenomenological constitutive model is established to describe the dynamic deformation behavior of 30Cr2Ni4MoV steel in wide strain rate, strain, and temperature ranges. Also, the mathematical models to predict peak stress and corresponding strain were obtained. The stress–strain values predicted by the developed model well agree with experimental results, which confirmed that the developed constitutive equation gives an accurate and precise estimate for the flow stress of 30Cr2Ni4MoV steel.     

Stress in particulate reinforcements and overall stress response on aluminum alloy matrix composites during straining by analytical and numerical modeling

SiC and Al₂O₃ (10–20v%) particle-reinforced Al-2618 matrix composites subjected to tensile loading were selected to simulate stress–strain curves and average stress in particles, and to examine mechanical properties experimentally in comparison. A particle-compounded mechanical model was established based on Eshelby equivalent inclusion approach to simulate stress–strain curves by introducing secant modulus and tangent modulus techniques, and to calculate stress in particles and in matrices. The same modeling work was carried out by FEM analysis based on the unit cell model using a commercial ANSYS code. The modeling and experiment were also applied to compare the mechanical behaviors between hard matrix and soft matrix, which were produced under different heat treatments. Through the comparison of the results between simulations and experiment, it is shown that Eshelby particle-compounded mechanical model can predict the stress–strain curve of the composites with both hard matrix and soft matrix, while the FEM model can match the experimental data with only hard matrix. The modeling was also carried out to study the influence of different volume fractions and aspect ratios on elastic modulus and yield strength of the composites with different reinforcing particles to get a better understanding of strengthening mechanisms of the composites.     

Comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials

This paper presents the results of a comprehensive study of the effects of rolling resistance on the stress–strain and strain localization behavior of granular materials using the discrete element method. The study used the Particle Flow Code (PFC) to simulate biaxial compression tests in granular materials. To study the effects of rolling resistance, a user-defined rolling resistance model was implemented in PFC. A series of parametric studies was performed to investigate the effects of different levels of rolling resistance on the stress–strain response and the emergence and development of shear bands in granular materials. The PFC models were also tested under a range of macro-mechanical parameters and boundary conditions. It is shown that rolling resistance affects the elastic, shear strength and dilation response of granular materials, and new relationships between rolling resistance and macroscopic elasticity, shear strength and dilation parameters are presented. It is also concluded that the rolling resistance has significant effects on the orientation, thickness and the timing of the occurrence of shear bands. The results reinforce prior conclusions by Oda et al. (Mech Mater 1:269–283, 1982) on the importance of rolling resistance in promoting shear band formation in granular materials. It is shown that increased rolling resistance results in the development of columns of particles in granular materials during strain hardening process. The buckling of these columns of particles in narrow zones then leads to the development of shear bands. High gradients of particle rotation and large voids are produced within the shear band as a result of the buckling of the columns.     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

An improved model for predicting fatigue S–N (stress–number of cycles to fail) behavior of glass fiber reinforced plastics

In a previous study a model to predict the fatigue S–N behavior of glass fiber reinforced thermoplastics by using a fracture mechanics approach was presented. Using a single flaw size model, some degree of success was observed, particularly for a reinforced polyamide. The model was not successful in predicting the S–N behavior of a reinforced polyester. The earlier study also employed flexural fatigue rather than tensile fatigue data in the calculations because the calculated flaw sizes were more nearly constant as a function of stress level. Subsequently it was shown that the flexural fatigue stress calculations were in error for these types of short glass fiber reinforced plastics owing to the nonlinearity of their stress–strain behavior. In this report we reexamine the utility of the fracture mechanics approach to predict fatigue S–N behavior for both materials using an improved model. Whereas previously a single initial surface flaw was assumed, here we assume multiple flaws growing simultaneously across the sample thickness. The new model is applied to both flexural and tensile fatigue loading. Results demonstrate that this new approach provides accurate predictions of the S–N behavior for both materials under both loading conditions. This reflects the fact that the calculated initial flaw sizes are relatively independent of stress level. No additional adjustable parameters are required if one uses the initial breaking strength of the material as part of the model calculations.     

A modified Johnson–Cook model for 30Cr2Ni4MoV rotor steel over a wide range of temperature and strain rate

The compressive behaviors of 30Cr2Ni4MoV rotor steel were investigated at the temperatures from 1223 to 1523 K and strain rates from 0.001 to 0.1 s⁻¹. A modified Johnson–Cook (JC) model was proposed to describe the compressive behaviors of the studied alloy steel. In the modified JC model, the coupling effects of strain, strain rate, and deformation temperature were considered. Comparisons between the predicted stress–strain values by the modified JC model and measured ones indicate a good agreement, which confirms that the modified JC model is valid for the predicting the flow stress of 30Cr2Ni4MoV rotor steel over a wide range of temperature and strain rate.     

A bounding surface plasticity model for cyclic loading of granular soils

A constitutive model for describing the stress–strain behaviour of granular soils subjected to cyclic loading is presented. The model is formulated using bounding surface theory within a critical state framework. A single set of material parameters is introduced for the complete characterization of the constitutive model. The shape of the bounding surface is based on experimental observations of undrained stress paths for loose samples. A mapping rule which passes through stress reversal points is introduced to depict the stress–strain behaviour during unloading and reloading. The effect of particle crushing is considered through a modified critical state line. Essential features of the model are validated using several experimental data from the literature. Both drained and undrained loading conditions are considered. The characteristic features of behaviour in granular soils subjected to cyclic loading are captured. Copyright © 2005 John Wiley & Sons, Ltd.     

FE-investigation of shear localization in granular bodies under high shear rate

Shear localization in granular materials under high shear rate is analysed with the finite element method and a micro-polar hypoplastic constitutive model enhanced by viscous terms. We consider plane strain shearing of an infinitely long and narrow granular strip of initially dense sand between two very rough walls under conditions of free dilatancy. The constitutive model can reproduce the essential features of granular materials during shear localization. The calculations are performed under quasi-static and dynamic conditions with different shear rates. In dynamic regime, the viscosity terms are formulated based on a modified Newtonian fluid and according to the formula by Stadler and Buggisch (Proceedings of the conference on Reliable flow of particulate solids, EFCE Pub. Series, vol 49. Chr. Michelsen Institute, Bergen, 1985). Emphasis is given to the influence of inertial and viscous forces on the shear zone thickness and mobilized wall friction angle.     

Experimental Study on Tensile Behavior of Carbon Fiber and Carbon Fiber Reinforced Aluminum at Different Strain Rate

In this study, dynamic and quasi-static tensile behaviors of carbon fiber and unidirectional carbon fiber reinforced aluminum composite have been investigated. The complete stress–strain curves of fiber bundles and the composite at different strain rates were obtained. The experimental results show that carbon fiber is a strain rate insensitive material, but the tensile strength and critical strain of the C_f/Al composite increased with increasing of strain rate because of the strain rate strengthening effect of aluminum matrix. Based on experimental results, a fiber bundles model has been combined with Weibull strength distribution function to establish a one-dimensional damage constitutive equation for the C_f/Al composite.     

Hot compressive deformation behavior of 7075 Al alloy under elevated temperature

The hot compression tests were conducted with wide strain rates and forming temperature ranges to study the high-temperature deformation behavior of 7075 Al alloy. The material flow behavior and microstructural evolution during hot-forming process are discussed. Based on the measured stress–strain data, a new constitutive model is proposed, considering the coupled effects of strain, strain rate, and forming temperature on the material flow behavior of 7075 Al alloy. In the proposed model, the material constants are presented as functions of forming temperature. The proposed constitutive model gives good correlations with the experimental results, which confirms that the proposed model can give an accurate and precise estimate of flow stress for 7075 Al alloy.     

Non-coaxial version of Rowe’s stress-dilatancy relation

Non-coaxiality occurs when the directions of the principal plastic strain increments and the principal stresses deviate. Extensive experimental data have now conclusively shown that plastic flow in granular soils is non-coaxial particularly during loadings involving rotation of the principal stress directions. One way to integrate the effects of non-coaxiality is by modifying the expressions for energy dissipation and stress-dilatancy used in modeling plastic deformation of granular soils. In this regard, the paper’s main objective is to derive a non-coaxial version of Rowe’s stress-dilatancy relation, thereby making it more general and applicable to loadings involving principal stress rotation. The paper also applies Rowe’s non-coaxial stress-dilatancy equation in the determination of the effects of principal stress rotation in granular soils during simple shear loading conditions. Previous experimental data from simple shear tests on sand are used to validate the proposed non-coaxial version of Rowe’s stress-dilatancy relation.     

Viscoelastic incremental formulation using creep and relaxation differential approaches

A new incremental formulation in the time domain for linear, non-ageing viscoelastic materials undergoing mechanical deformation is presented in this work. The formulation is derived from linear differential equations based on a discrete spectrum representation for the creep and relaxation tensors. The incremental constitutive equations are then obtained by finite difference integration. Thus the difficulty of retaining the stress and strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress analysis is developed in terms of increments of strains and stresses in order to establish the constitutive stress–strain relationship. The presented method is validated using numerical simulations and reliable results are obtained.     

Cyclic inelasticity and high-cycle fatigue of metals with consideration of the stress gradient effect*

Cyclic deformation behavior of metals and alloys under high-cycle loading in the nonuniform stress state is considered. A significant effect of the stress gradient on the cyclic inelastic deformation of the metal surface layers is shown. A model explaining the difference between the fatigue limits in the uniform and nonuniform stress states is proposed, which is based on accounting for the distinctions between cyclic stress–strain diagrams in the uniform and nonuniform stress states and for the fact that the fatigue limit is equal to the cyclic elasticity limit found for inelastic deformation typical of this class of materials.     

Theoretical and experimental determination of residual stresses in plane joints

We have developed a mathematical model for determining residual stresses and stress concentration in the neighborhood of a plane joint of dissimilar materials and formulated variational statements of direct and inverse problems. The parameters of the stress–strain state of the object under study measured by nondestructive methods serve as input data for the inverse problem. We carry out a numerical analysis of solutions of the direct and inverse problems of determining stress concentration in the neighborhood of a joint of materials with different moduli. Finally, we discuss the applicability of the developed approach to the monitoring of the stress–strain state of joints in the course of their operation and to the evaluation of their residual life.