Elastic-plastic Deformation Behavior Research Articles

Finite elastic–plastic deformation behaviour of crystalline solids based on a non-associated macroscopic flow rule 1Paper presented at the Sixth International Symposium on Plasticity and Its Current Applications, Juneau, Alaska (U.S.A.), July 14–18, 1997. 1

The present paper deals with a nonlinear finite element analysis of the macroscopic elastic–plastic deformation and localization behaviour of crystalline solids. The description includes elastic strains arising from the distortion of the lattice as well as crystallographic deformations due to irreversible microscopic slip along preferred lattice planes and in corresponding lattice directions. In addition, the effect of plastic volume changes on the microstructure is taken into account. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, and the onset of plastic yielding on the microscale is described by a modified yield condition which includes appropriate microscopic stress components. To be able to compute inelastic deformations from plastic potentials, the latter are expressed in terms of work-conjugate microscopic stress and strain measures thus leading to a non-associated flow rule for the macroscopic plastic strain rate. The numerical integration of the rate formulation of the constitutive equations is performed using a plastic predictor-elastic corrector technique. Its implementation into a nonlinear finite element program is discussed, and numerical solutions of finite strain elastic-plastic boundary value problems involving highly localized deformations are presented. They demonstrate both the efficiency of the algorithm and the influence of various model parameters on the deformation and load-carrying behaviour of crystalline solids.

Effect of Relative Humidity During Tabletting on Matrix Formation of Hydrocolloids: Densification Behavior of Cellulose Ethers

ABSTRACTThe aim of this research was to investigate the elastic-plastic deformation behavior of the cellulose ethers hydroxypropylmethylcellulose (HPMC), hydroxyethylmethylcellulose (HEMC), and sodium carboxymethylcellulose (NaCMC) at relative humidities (RH) of 38, 57, and 75% and assess how the release of drugs embedded in such matrices is affected by the inner structure of the tablets formed during tabletting. Sorption and desorption isotherms and glass transition temperature were determined between 32 and 75% RH. The materials were equilibrated at 38, 57, and 75% RH and tabletted to a range of graded maximum relative densities. Pressure-time and displacement-time curves were analyzed by use of the Heckel Junction and a modified Weibull function (pressure-time only). After equilibration at the different RHs, all materials were in the glassy state. The respective degrees of polymerization had negligible effect on the absolute content of water, the sorption isotherms, and finally the densification behavior. At 38% RH, NaCMC contains the same amount of water as HPMC and HEMC, but deforms less plastically than the latter. This is attributed to tight binding of the water of hydration in the former. With increasing RH, NaCMC becomes only a little more plastic than both HPMC and HEMC, although it contains more than twice the amount of water. The binding strength of water and its molecular mobility, not the amount, seems to determine the readiness for volume reduction under load.

On effect of particle size distribution on the elastic/plastic deformation of metal matrix composites

The elastic-plastic deformation behavior of particulate reinforced metal matrix composites is strongly influenced by not only properties of the metal matrix and reinforcement but also microstructural parameters such as particle size, volume fraction, reinforcement shape and topology that are dependent on the particular processing route used to fabricate the materials. Nan and Clarke have recently developed a hybrid, analytical model by incorporating essential features of both continuum plasticity and dislocation plasticity, which is a combination of the key features of dislocation plasticity with a continuum mechanics approach based on effective medium approximations (EMA). In the present contribution, particular attention will be paid to two problems on the hybrid model. Firstly, the authors introduce a volume-weighted averaging procedure in Nan and Clarke`s methodology and then re-estimate the effect of particle size distribution on deformation in the case of both no damage and including particle fracture. For illustrative and quantitative purposes, the calculations are compared with the experimental results on particular SiC-Al composite by Lloyd. Secondly, the difference between the deformation, secant and the incremental, tangent modulus approaches chosen for EMA modeling is addressed.

Laboratory investigation of the mechanical behaviour of Tournemire shale

This paper presents laboratory investigations of the mechanical behaviour of a typical anisotropic rock: Tournemire shale. Hydrostatic compressibility tests allowed characterization of the structural anisotropy of the material. Triaxial compression tests, including unloading cycles, were performed. Anisotropic elastic response, plastic deformation and failure behaviour have been investigated. The elastic behaviour of the shale is non-linear and the shale exhibits large anisotropic plastic deformation. The failure behaviour of the shale is anisotropic and strongly depends on confining pressure and loading orientation.

Behavior of Elastic-Plastic Rough Surface Contacts as Affected by Surface Topography, Load, and Material Hardness

Surface roughness plays an important role in affecting friction, wear, and lubrication of contacting bodies. A small change in the distribution of the asperity heights and widths can have a significant effect on the performance variables which include the real area of contact, the average gap, and the average asperity contact pressure. A series of contact simulations were conducted in order to investigate the effects of the surface topography, material hardness and load on the deformation behavior of the rough surfaces. These surfaces were numerically generated by computer and varied widely in statistical roughness properties, ranging from isotropic to strongly anisotropic. The current simulations took into account the elastic-plastic deformation behavior of the asperities. Using the contact simulation results, the performance variables were curve-fitted to convenient analytical formulas as functions of the surface roughness parameters, material hardness, and load.

Parametric Description of Elastic-Plastic Deformation Behaviour of Inhomogeneous Material with Inclusions

The macroscopic elastic-plastic constitutive relation of inhomogeneous material is affected not only by the characteristics of respective constituents, but also by the microscopic distribution of stress and strain in heterogeneous regions. In order to describe the deformation behaviour of inhomogeneous material, several parameters are defined. A plane model of inhomogeneous material with inclusions is used for numerical simulation, and the changes in the parameters during elastic-plastic deformation are calculated and compared. Uniaxial loading under the plane-strain condition is assumed. It is concluded that the initial aspect ratio has a marked influence on the deformation behaviour. One of the parameters, called the constraint ratio, remains nearly constant with increase in the applied strain or the degree of inhomogeneity. This characteristic seems to be important for estimating the deformation behaviour of inhomogeneous material. The constitutive relation of inhomogeneous material may also be estimated from the value of the constraint ratio.

A Modified Miniature Disk Test for Determining Material Mechanical Properties

AbstractThis paper briefly describes the apparatus and experimental procedure for the modified miniature specimen test (MMST). The primary focus is on the thought and methodology of converting data. The accuracy and reliability of test results are emphasized. The fundamental relations for converting experimental data are established via analysis of elastic-plastic bulge deformation behavior of a middle-thick circular plate loaded at the center for which the circumference is fixed and points at the boundary can move in a radial direction. The formulas for calculating materials strength and ductility have been derived from the relation. Three types of unirradiated materials whose strengths are different and one kind of 316 SS irradiated by protons were tested with MMST. The test results along with the standard deviations are presented. The comparison of these data with that for uniaxial tension tests is also given. The evaluation of material equivalent fracture strain was also performed with the MMST.

Materials characterization and effect of purity and ion implantation on the friction and wear of sublimed fullerene films

In previous studies, sublimed C60-rich fullerene films on silicon, when slid against a 52100 steel ball under dry conditions, have exhibited low coefficient of friction (∼0.12). Films with different purities can be produced by sublimation at different substrate temperatures. In this paper, effects of purity of fullerene films and ion implantation of the films with Ar ions on the friction and wear properties of sublimed fullerene films are reported. C60-rich films (called here films with high purity) exhibit low macroscale friction. An increased amount of C70 and impurities in the fullerene film determined using Raman and Fourier transform infrared (FTIR), increases its coefficient of friction. Microscale friction measurements using friction force microscopy also exhibited similar trends. Low coefficient of friction of sublimed C60-rich films on silicon is probably due to the formation of a tenacious transfer film of C60 molecules on the mating 52100 steel ball surface. Based on scanning tunneling microscopy (STM), transmission electron microscopy (TEM), and high resolution TEM (HRTEM), we found that fullerene films primarily consisted of C60 molecules in a fcc lattice structure. Nanoindenter was used to measure hardness and elastic modulus of the as-deposited films. Ion-implantation with 1 × 1016 Ar+ cm−2 reduced macroscale friction down to about 0.10 from 0.12 with an increase in wear life by a factor of 4; however, doses of 5 × 1016 ions cm−2 gave three times higher friction and poorer wear life; higher doses disintegrated the C60 molecules. Based on STM, TEM, Raman, FTIR, and laser desorption Fourier-transform ion cyclotron resonance mass spectrometer (LD/FT/ICR) studies, we found that the ion implantation with a dose of 1 × 1016 Ar+ cm−2 resulted in smoothening of the fullerene film surface probably by compacting clusters, but without disintegrating the C60 molecules. However, a high dose of 5 × 1016 Ar+ cm−2 damaged the C60 molecules, converting it to an amorphous carbon. Nanoindentation studies show that ion implantation with a dose of 1 × 1016 Ar+ cm−2 resulted in an increase in the hardness from about 1.2 to 4.0 GPa and in elastic modulus from about 70 to 75 GPa and modified the elastic-plastic deformation behavior.

Elastic-Plastic Deformation of Inhomogeneous Material with Inclusion and Parametric Description of Deformation Behaviour.

The macroscopic elastic-plastic deformation behaviour of inhomogeneous material is affected by the microscopic distribution of stress and strain in respective heterogeneous regions of the material. Several parameters are considered to describe the deformation behaviour of inhomogeneous material, and their relationship is discussed analytically. A model of inhomogeneous material with inclusions imbedded in a matrix is adopted for the numerical simulation of the present study. The changes of the parameters during elastic-plastic deformation are calculated and compared. Among the parameters, the constraint ratio and the plastic accommodation parameter are not affected by the degree of inhomogeneity. A modified plastic accommodations parameter is also proposed, which is uniquely related to the constraint ratio. The constraint model based on the constraint ratio is extended to describe the elastic-plastic deformation behaviour of inhomogeneous material.

Approximate formulae for estimating the [formula omitted] of a circumferentially cracked round bar under tension or torsion

The approximate formulae for estimating the J contour integral by the use of a single load-displacement curve were newly derived for the circumferentially cracked round bar subjected to tensile (Mode I) or torsional (Mode II) loading, by paying attention to the elastic-plastic deformation behavior which is characterized by full yielding (net section of specimen is in yield) or general yielding (gross section of specimen is in yield). As application examples, elastic-plastic fracture toughness tests were performed at room temperature on Ni-Cr-Mo-V forged steel. The ductile crack growth resistance curves under the Mode I or the Mode III loading were measured with the multi-specimen method, and the fracture behaviors of each mode were examined.

Elastic-plastic deformation behavior of void materials with void volume fraction dependent macroscopic elasticity moduli.

A constitutive equation taking into account the effect of the void volume fraction on the macroscopic elasticity moduli has been developed. An additional strain rate is derived from the partial differentiation of the elastic stress-strain relation with respect to the void volume fraction and is added to the strain rate obtained from the original Gurson type constitutive equation. The deformation behavior of a plane strain block with both ends fixed subjected to tension has been analyzed. The comparison between the results obtained by employing the present constitutive equation and the original one clarified that the void volume fraction dependency of macroscopic elasticity moduli has a substantial effect on the residual stress, but not on global deformation behavior.

Ｊ積分簡易評価式の有限要素法による検討

The simplified equations for estimating the J contour integral by the use of a load-displacement curve have been developed to analyze various crack problems. These equations were derived by setting certain assumptions, for example, a deep crack or a shallow crack, etc.. In this paper, the distinction between the shallow crack and the deep crack was made by paying attention to the elastic-plastic deformation behavior of cracked plates. The validity of the present equations for non-liner materials were demonstrated by comparing their prediction with the available finite element analysis results, which were obtained for different shapes of various test specimens; for example, the center cracked tension plate, double edge cracked tension plate, single edge cracked tension plate, and single edge cracked bending plate. The way to use the simplified estimating equations was given. Also, the new simplified equations for estimating the J-value were derived for elastic-plastic materials by paying attention to their elastic-plastic deformation behavior which is characterized by full yielding or general yielding.

Treatment of material laws for approximate [formula omitted] estimation methods

In order to estimate the load and elastic-plastic deformation behaviour of cracked structures, methods must take into account the influence of arbitrarily shaped real material laws on the J integral and displacement behaviour, at least in an approximate form in the sense of an engineering approach. Such methods are generated and discussed in this paper. They are based on the well-known formulas in the EPRI Handbook, which are valid only for specific power laws. An extensive study has been carried out using idealised material laws with two distinct strain-hardening regions. The influence on J has been evaluated by a systematic variation of the parameters of these idealised material laws in an unambiguous way. The approximation methods generated have been compared with finite element (FE) calculations, and their accuracy with respect to load- J curves is discussed.

Elastic-Plastic Deformation Behaviour of Inhomogeneous Materials Including Polycrystals

Elastic-plastic deformation behaviour of inhomogeneous materials such as polycrystals is investigated analytically using a plane geometrical model of inhomogeneous materials and finite element calculation. The deformation behaviour is expressed quantitatively making use of constraint ratio calculated from strain distribution in the model. The change of mean constraint ratio for polycrystals during elastic-plastic deformation is obtained. It is found that deformation proceeds between the conditions under constant strain and under constant stress for the most of the calculated range of plastic strains. When elastic inhomogeneity or anisotropy is present, however, the deformation mode becomes close to the constant strain deformation in the elastic-plastic transition stage. The difference between macroscopic yield of polycrystals and microscopic yield in grains due to the presence of elastic inhomogeneity is also discussed.

Elastic-Plastic Deformation Behaviour of Inhomogeneous Materials Including Polycrystals

Elastic-plastic deformation behaviour of inhomogeneous materials such as polycrystals is investigated analytically using a plane geometrical model of inhomogeneous materials and finite element calculation. The deformation behaviour is expressed quantitatively making use of constraint ratio calculated from strain distribution in the model. The change of mean constraint ratio for polycrystals during elastic-plastic deformation is obtained. It is found that deformation proceeds between the conditions under constant strain and under constant stress for the most of the calculated range of plastic strains. When elastic inhomogeneity or anisotropy is present, however, the deformation mode becomes close to the constant strain deformation in the elastic-plastic transition stage. The difference between macroscopic yield of polycrystals and microscopic yield in grains due to the presence of elastic inhomogeneity is also discussed.