Showing papers on "Stress–strain curve published in 1993"

Micromechanical modeling of large plastic deformation and texture evolution in semi-crystalline polymers

Abstract: A micromechanically-based composite model is proposed to study large plastic deformation and texture evolution in semi-crystalline polymers. The microstructure of many semi-crystalline polymers consists of co-existing crystalline and amorphous phases locally associated with each other in a fine plate-like morphological structure. An aggregate of two-phase composite inclusions is used to model these materials. Special consideration is given to molecular chain inextensibility within the crystalline phase. The introduction of a back stress tensor in the constitutive model of the amorphous phase accounts for hardening due to deformation-induced molecular alignment. Interface compatibility and traction equilibrium are enforced within each composite inclusion. A Sachs-like model and two newly-developed self-consistent-like hybrid models are proposed to relate volume-average deformation and stress within the two-phase composite inclusion to the remote (macroscopic) fields. Applications of these composite models arc made to predict stress strain behavior and texture evolution in initially isolropic high density polyethylene (HOPE) under different modes of straining.

Finite element analysis of thermal residual stresses at graded ceramic‐metal interfaces. Part II. Interface optimization for residual stress reduction

Abstract: An elastic‐plastic finite element method numerical model previously developed (see Part I of this article) for predicting thermal residual stresses at graded ceramic‐metal interfaces has been applied to determine interface conditions favorable for achieving residual stress reductions. Using Al2O3‐Ni as a model system, and for a fixed specimen geometry, a study was performed to investigate the effects of different interlayer thicknesses and nonlinear composition profiles on strain and stress distributions established during cooling from an assumed elevated bonding temperature. For each interface condition, relative stress reductions were evaluated by comparing the magnitude of specific stress and strain components important for controlling interface failure with those predicted for a sharp (nongraded) interface. For the geometry considered, stress was reduced by thick graded interlayers and nonlinear composition profiles that distributed the largest property changes over the interlayer region having low elastic modulus and high plasticity. In contrast to the Part I results for a linear composition profile, the optimized interlayer condition effectively reduced the peak near‐surface axial stress component.

Tensile properties and inhomogeneous deformation of ferrite-martensite dual-phase steels

Abstract: The tensile properties and inhomogeneous deformation of coarse ferrite-martensite dual-phase steels containing 17–50% martensite were analysed. The stress of dual-phase steels at equal strain increased with increasing volume fraction of martensite, f, but the rate of increase was reduced after f=0.3. The strain hardening rate was dependent on f at small strains (ɛ ⩽ 0.03), however, it became independent of f at larger strains. It was found that the deformation of the dual-phase steels divided into three different stages when f was less than about 0.3. The concurrent in situ stress-strain states of ferrite, martensite and their composite, and the stress ratios and strain ratios between ferrite and martensite were evaluated by means of a new stress and strain partition theory. The martensite phase deformed plastically after the uniform strain for f 0.25. The theoretical analyses for inhomogeneous deformation implied that the volume-fraction dependence of the stress and the characteristics of the strain-hardening rate were influenced by the plastic deformation of martensite. Further, the in situ stress-strain curves of ferrite and martensite and the internal stresses at respective phases were calculated from the partitioned stresses and strains.

Matrix cracking in unidirectional ceramic matrix composites under quasi-static and cyclic loading

Abstract: Experimental data associated with the development of matrix cracks in unidirectional continuous silicon carbide fibre/calcium alumino-silicate matrix laminates under quasi-static loading are presented, including crack density, residual strain and hysteresis behaviour as functions of applied stress. Simple models are developed, based on an assumption of purely frictional load transfer between the fibre and matrix, which describe reasonably well the quasi-static stress-strain behaviour in the presence of cracks. Under tension-tension mechanical fatigue cycling it is found that the crack density stabilises at a relatively early stage in the test. Based on the quasi-static model, the changes in fatigue hysteresis loops on fatigue cycling are interpreted in terms of a reduction in the effective frictional interfacial shear stress.

Atomistic modelling of plastic deformation of glassy polymers

Abstract: A detailed atomistic approach has been used to investigate the kinematics of plastic deformation in glassy atactic polypropylene to 20% strain. The microstructural stress-strain behaviour was found to consist of smooth reversible portions bounded by irreversible sharp stress drops indicating plastic rearrangement of the structure. Averaging the stress-strain behaviour over an ensemble of 1-815 nm microstructures showed a yield point in the neighbourhood of 5-7% strain. The transformation shear strain for plasticistructural rearrangements was found to be broadly distributed, averaging 1-5% shear strain with a standard deviation of 2-6% shear strain. Combining this result with the activation volume measurements of common glassy polymers showed the size of the plastically transforming region to have a diameter of about 10 nm, thus involving several thousand segments. The transformation shear strain was independent of the system size. Scrutiny of the molecular segment motions associated with plastic ...

Stress, strain, and microstructure in thin tungsten films deposited by dc magnetron sputtering

Abstract: Tungsten thin films were deposited on glass substrates by direct‐current planar magnetron sputtering. The induced thickness‐averaged film stress within the plane of the film was determined with the bending‐beam technique and changed from compressive to tensile on increasing working‐gas pressure. The microstructure of these films was investigated by cross‐sectional transmission electron microscopy. Compressively stressed films consisted of tightly packed columnar grains, whereas in films with a maximum value for the tensile stress the onset of a void network surrounding the columnar grains was observed. High‐pressure conditions resulted in dendritic‐like film growth, which brought about complete relaxation of internal stresses. The α phase was predominantly found in films under compression, while an increasing amount of β‐W coincided with the transition to the tensile stress regime. Special attention was focused on stress‐depth dependence and the development of two overlapping line profiles in x‐ray diffra...

The deformation and failure behaviour of wheat starch plasticized with water and polyols

Abstract: The mechanical properties of starch plasticized with water and glycerol or xylitol have been studied in flexure at room temperature. The addition of a polyol lowers the glassy modulus and the glass transition temperature of the starch. With the addition of polyols, the fall in modulus with increasing water content at the glass transition becomes less sharp and shifts to lower water contents. The high strain deformation shows that all samples fracture at a water content below 10% (wet weight basis), a proportion of which tears at water contents in the range 9%–10% and no fracture occurs in samples above about 10% water. Microscopy shows that there is evidence of permanent plastic deformation in fractured samples as the water content is increased to 10% water, although there is a negligible change in fracture stress and strain.

Model studies of fibre breakage and debonding in a metal reinforced by short fibres

Abstract: F or a metal reinforced by short, brittle fibres the development of damage by fibre cracking or decohesion is studied, taking into account the interaction between these two types of damage. The metal matrix composite, containing a periodic array of aligned fibres, is represented in terms of a cell model, and solutions for the stress and strain fields are determined numerically. Failure at the interface is modelled in terms of a cohesive zone model that accounts for decohesion by normal separation as well as by tangential separation, whereas fibre fracture is simply represented by a critical value of the average tensile stress on a cross-section. The effect of various material parameters and of the macroscopic stress state on the two types of damage is investigated, together with the subsequent mode of void growth.

Elastic stress and strain in jointed rock masses by means of crack tensor analysis

Abstract: An elastic stress-strain relation is formulated in terms of crack tensors which makes it possible to take into account explicitly the effect of joints on elastic behavior of rock masses. The present study is to discuss some related topics which may be encountered in its practical application. Two problems are solved by incorporating the elastic stress-strain relation into a program for three-dimensional finite element analyses; i. e., stress concentration by surface loading and displacement by excavation of an intersecting tunnel. Validity of the results is checked by comparing them with a laboratory model test and a field test, with the following conclusions: The overall distribution of stress definitely depends on a joint stiffness ratio (i. e., normal stiffness to shear stiffness). If the ratio is chosen as unity, the stress concentration occurs mainly in the direction parallel to major joints. If the ratio is high, say 10, then the stress concentrates along the perpendicular as well as the parallel directions to major joints. It can be said, on the basis of the fairly good agreement of the calculations using the high stiffness ratio with the field and laboratory measurements, that the elastic solution by crack tensors provides a practical tool for estimating the stress and strain in strongly jointed rock masses.

Numerical study of the hydromechanical behavior of two rough fracture surfaces in contact

Abstract: Flow in fractures is traditionally modeled by characterizing the aperture distribution with some deterministic function or set of stochastic parameters. Other models generate the aperture distribution by the closure of two stochastic surfaces. The objective of this research is to develop a model where the aperture distribution is determined during the closure of two random elastic surfaces with complete hydromechanical interaction. Because stress and strain conditions required to generate a given aperture distribution are calculated during closure, the model is used to couple the mechanical and hydraulic characteristics of the fracture. Stochastic realizations of clay fracture surfaces are generated by measuring one-dimensional profiles of a fracture surface. Next, the spectral representation of the profile is related to the fractal dimension of the fracture. Using the fractal dimension determined from one-dimensional clay profiles, an equivalent two-dimensional fractal surface is generated. Conceptually, each surface consists of linear elastic rectangular asperities resting upon a linear elastic half-space. During closure, asperities that come into contact deform and punch into the half space creating mechanical interaction between all the asperities on the grid. Once we determine the aperture distribution at an applied stress level, a hydraulic gradient is applied across the fracture and fluid flow is determined. Nodal pressures created by flow deform the aperture distribution coupling hydraulic to mechanical behavior. Stress versus relative closure results indicate that stress increases nonlinearly with relative closure. Fluid pressures in the aperture distribution exert a significant influence on the mechanical characteristics of a fracture. Fluid discharge through the fracture decreases exponentially with an increase in relative closure. Flow calculated in the rough walled aperture distribution deviates increasingly from the parallel plate model with the geometric mean aperture as the percent contact area increases. The deviation results from an increase in tortuosity and channelling of the flow field in the aperture distribution. We can use this model to develop stress and flow versus relative closure constitutive relationships for a single fracture as a function of fracture surface geometry.

A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery

Abstract: The Tensile Behavior of a brittle matrix composite is studied for post matrix crack saturation conditions. Scatter of fiber strength following the Weibull distribution as well as the influence of the major microstructural variables is considered. The stress in a fiber is assumed to recover linearly around a failure due to a fiber-matrix interface behavior mainly ruled by friction. The constitutive behavior for such a composite is analysed. Results are given for a simplified and a refined approximate description and compared with an analysis resulting from the exact analytical theory of fiber fragmentation. It is shown that the stress-strain relation for the refined model excellently follows the exact solution and gives the location of the maximum to within 1% in both stress and strain; for most materials the agreement is even better. Also it is shown that all relations can be normalized to depend on only two variables; a stress reference and the Weibull exponent. For systems with low scatter in fiber strength the simplified model is sufficient to determine the stress maximum but not the postcritical behavior. In addition, the simplified model gives explicit analytical expressions for the maximum stress and corresponding strain. None of the models contain any volume dependence or statistical scatter, but the maximum stress given by the stress-strain relation constitutes an upper bound for the ultimate tensile strength of the composite.

Effects of chain configurational properties on the stress-strain behavior of glassy linear polymers

Abstract: A systematic study of the relationship between polymer structure and the phenomenon of strain hardening was performed by employing controlled stress molecular dynamics computer simulation in conjunction with a simple polyethylene-like model. It is found that varying the sample preparational history produces materials which, while being chemically identical, differ profoundly in their response to an applied stress

Biaxial orientation of poly(ethylene terephthalate). Part I: Nature of the stress—strain curves

Abstract: The orientation characteristics of extruded poly(ethylene terephthalate) (homopolymer) sheets are discussed with respect to: mode of extension (simultaneous versus sequential), strain rate, stretch ratio, and temperature. The nature of the stress–strain curve recorded during the process of extension, and its dependence on the parameters of extension mentioned above, are analyzed. Results show that for specimens stretched in the biaxial simultaneous mode, the stress–strain curve is concave upward, which is typical for amorphous polymeric materials. Strain-hardening occurs at high planar extensions, and is accompanied by a steep rise in the stress measured during stretching. The magnitude of this stress increases with increasing strain rate and extension ratios, but decreases with increasing temperature of stretching. During biaxial sequential extension, the stress–strain curve is concave upward at low strain rates or at high temperatures of stretching, but becomes convex upward at higher strain rates or lower temperatures. The curve also changes from concave to convex upward at high limiting extension ratios in the first direction. The convex upward nature of the stress-strain curve is typical of semi-crystalline materials, indicating the occurrence of strain-induced crystallization during stretching in the first direction. Again, the level of stress, measured during stretching, increases with increasing strain rate and limiting extension ratio in the first direction, while it decreases with increasing temperature of stretching. © 1993 John Wiley & Sons, Inc.

Ultimate Strength of Confined Very High-Strength Concretes

Abstract: Results are presented from an experimental investigation into the ultimate strength of concrete under triaxial laoding. Several mixes are used with strength ranging from normal strength concrete to very high-strength concrete. Other parameters in the mixes were the use of silica fume and type of crushed coarse aggregate with the 3 types of aggregates studied. A 2-parameter model for the failure envelope for confined concrete was adopted. Empirical expressions for the failure envelope were derived for normal strength concrete and very high-strength concrete with and without silica fume. A simple lower bound expression for the ultimate strength of concrete under confinement is presented for any grade of concrete.

Dynamic 3D analysis of the Charpy V-notch test

Abstract: A full three-dimensional analysis of the Charpy V-notch specimen subject to impact loading is carried out, in order to study deviations from predictions of the plane strain analyses that have been used to estimate the energy absorption and the competition between brittle and ductile failure mechanisms. An elastic-viscoplastic version of the simplest plasticity flow theory is used to describe the material behavior, and the 3D transient analysis is based on twenty-node brick elements, using a data parallel numerical implementation. It is found that the stress and strain fields show strong surface effects, but near the specimen center the stress and strain quantities governing the failure mechanisms are in rather good agreement with plane strain predictions.

Singular behaviour near the tip of a sharp V-notch in a power law hardening material

Abstract: This paper presents an asymptotic analysis of the near-tip stress and strain fields of a sharp V-notch in a power law hardening material. First, the asymptotic solutions of the HRR type are obtained for the plane stress problem under symmetric loading. It is found that the angular distribution function of the radial stress σ presents rapid variation with the polar angle if the notch angle β is smaller than a critical notch angle; otherwise, there is no such phenomena. Secondly, the asymptotic solutions are developed for antisymmetric loading in the cases of plane strain and plane stress. The accurate calculation results and the detailed comparisons are given as well. All results show that the singular exponent s is changeable for various combinations of loading condition and plane problem.

The deformation behaviour of alloys comprising two ductile phases— I. Deformation theory

Abstract: A topological transformation has been proposed, which allows a two-phase microstructure with any combination of grain-size, grain-shape, and phase distribution, to be translated into a body consisting of three well-defined microstructural elements aligned along a particular direction of interest. The resultant three-element body is shown to be mechanically equivalent to the original body along this direction. The concept of contiguity and allied topological parameters have been combined with Eshelby's continuum transformation theory to determine the internal stresses and strains, the true stress strain curve, and the in situ stress and the in situ plastic strain distribution in the three microstructural elements and thus derive the mechanical properties of the aggregate. This approach incorporates the interaction between particles of the same phase and the effect of phase distribution as well as the effect of volume fraction. Applications of the theory are given in a companion paper.

Stress analysis of elastomeric materials at large extensions using the finite element method

Abstract: The finite element method is applied to stress and strain analyses around rigid spherical particles in elastomers at large extensions. The stress and strain distribution computed agree well with the classical theoretical ones at small strain. At large extension, however, the maximum stress concentration factor increases greatly and the maximum strain concentration factor decreases slightly as strain increases. These tendencies are increased more in carbon black-filled elastomers than in unfilled ones, which can be understood reasonably by considering both the geometric and material non-linearity. Reinforcement of elastomers with rigid spherical particles was also analysed through a numerical computation. The computed results agree with the Guth and Mooney equations at low volume fraction of fillers. In carbon black-filled elastomers, on the other hand, where the modulus is much higher than that given by the above equations, the computations give a good agreement with the experiments, considering the 20% increase in effective diameter of the filler.