Post-bifurcation behavior in the plastic range

In the first part of the paper a simple model is used to introduce some of the analytical and physical features of post-bifurcation phenomena in continuous elastic-plastic systems. An analysis is presented for the initial post-bifurcation behavior of a class of elastic-plastic solids subject to loads characterized by a single load parameter. Bifurcations which occur at the lowest possible load are singled out for attention. The theory makes connection with Hill's general theory of bifurcation and uniqueness in elastic-plastic solids and Koiter's general approach to the initial post-buckling behavior of conservative elastic systems. Buckling of an axially compressed column in the plastic range is used to illustrate the theory.     

Reduction of strain rosettes in the plastic range

In reducing strain-rosette data, it is not always possible to tell by inspection whether permanent strains are present. If permanent strains are present, the reduction of the principal strains to principle stresses, assuming perfectly elastic conditions, can be much in error. This paper gives equations for the principal stresses which can be used when purely elastic or elastic-plus-plastic strains are present. Comparisons of theoretical and experimental results are given in order to check the validity of the theory.     

The sensitivity of strain gauges when used in the plastic range

The sensitivity behaviour of three types of high elongation strain gauge has been established experimentally. The gauges were bonded to a variety of testpiece materials and calibrated in uniaxial stress fields of tension and bending. It is shown from loading and unloading cycles within the plastic range that three sensitivity factors can be identified. These relate elastic, plastic and total resistance change responses to their respective strain components. The variation in each sensitivity factor with applied strain is examined both experimentally and theoretically. Gauges operate most reliably when their separate responses are co-linear.     

Materials with elastic range and plastic change of volume

Following the lines of Lucchesi and Podio-Guidugli, Lucchesi and Šilhavý, and Lucchesi et al. we sketch a theory of materials with elastic range that, unlike the treatment in those papers, places no restrictions on plastic changes of volume or on related quantities. We then describe with some detail the constitutive behavior of two important classes of materials with elastic range that, by analogy with the terminology used in classical plasticity, we call v. Mises materials and ideally plastic materials. Finally, for a specific ideally plastic v. Mises material, we present a numerical computation that shows how, when plastic change of volume is allowed, the shear stress maintaining a simple shear flow need not have constant value.     

IMPERFECTION SENSITIVITY ANALYSIS OF A RECTANGULAR COLUMN COMPRESSED INTO THE PLASTIC RANGE

I.IntroductionSinceelasticunloadingoccursinthedeformationprocess,theimperfectionsensitivityanalysisofstructuresloadedintotheplasticrangeismuchcomplicated.TheproblemisfirststudiedintheorybyHutchinson(1973,1974)l"ZI.HeusedKoiter'stheorytoanalysethebehaviorpriortotheonsetofelasticunloadingandtoobtaintheloadandthedisplacementatwhichelasticunloadingbegins.NeedlemanandTvergaard(1982)l'jpresentedananalysisofimperfeCtionsensitivityintheplasticrangethatignoreselasticunloading,thatis,substituteshypo-…     

On transformation laws for plastic deformations of materials with elastic range

Archive for Rational Mechanics and Analysis -     

Elastic unloading,neutral loading,and plastic loading in the theory of materials with elastic range

A plasticity index is an evolution indicator that allows one to predict, in a situation of potential plastic flow, whether plastic loading, instead of elastic unloading or neutral loading, will actually occur. It is shown in this article how a notion of plasticity index arises within the theory of materials with elastic range.     

Large plastic strains in sheet-bending

Based on Hill's general theory of sheet bending, a closed form expression is derived for strain in any fiber of a sheet bent under the conditions of plane strain and negligible elastic strains. A numerical example indicates that the assumptions of the theory are plausible over a wide range of the angle of bending.     

Torsional hysteresis in plastic clay

Summary Plastic clay when subjected to symmetrical cyclic torsional strain behaves in a non-linear manner and produces a stress-strain hysteresis loop of characteristic shape. A mathematical model introducing the idea of an energy-controlled breakdown process involving the conversion of elastic elements to viscous elements is proposed and shown to be capable of representing the observed loops.

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Zusammenfassung Wenn man plastische Tone einer symmetrischen zyklischen Torsionsbeanspruchung aussetzt, so weisen sie ein nichtlineares Verhalten auf, wobei sich charakteristische Hystereseschleifen ergeben. Es wird ein mathematisches Modell vorgeschlagen, welches auf der Vorstellung eines energieabhängigen Abbauvorganges beruht, bei dem eine Umwandlung elastischer in viskose Elemente vor sich geht. Es wird gezeigt, daß sich die ermittelten Hystereseschleifen an Hand des vorgeschlagenen Modells erklären lassen.

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Paper presented at the British Society of Rheology Conference, held at Shrivenham, from 9th–12th September, 1968.     

On the relation for plastic spin

Summary Within the framework of the theory of finite elastoplasticity based on the known concept of the local, relaxed, isoclinic configuration the large plastic deformations with strain induced anisotropy and emerging plastic spin are studied. The derivation of the relation for plastic spin, based on the analysis on the simple shear problem for rigid-plastic material with kinematic hardening is provided and the experimental verification of the calculated axial elongation in the unconstrained large-strain shear problem is presented. The applicability of the proposed model is discussed.

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Zur Ermittlung der Stoffgesetze für den plastischen Spin

Übersicht Im Rahmen der Theorie endlicher elastoplastischer Formänderungen unter Verwendung des bekannten Konzepts lokaler, relaxierender, isokliner Konfigurationen werden große plastische Deformationen mit durch Dehnung hervorgerufener Anisotropie und daraus resultierendem plastischen Spin untersucht. Die Gleichung für den plastischen Spin wird mit dem Modell der einfachen Scherung hergeleitet. Dabei wird starr-plastisches, kinematisch verfestigendes Material angenommen. Das Modell des reinen Schubes wird numerisch behandelt und mit experimentellen Ergebnissen tordierter dünnwandiger Zylinder mit unbehinderter axialer Dehnung verglichen. Die Anwendbarkeit des vorgeschlagenen Modells wird diskutiert.

     

On the dead-zone formation in plastic axially-symmetric converging flow

An upper-bound analysis is used to examine dead-zone formation in rigid/plastic axially-symmetric converging flow. A quasi-stable internal shear is found to occur under certain conditions. Bounds on the geometry for quasi-stable behavior and bounds on the required power are presented. The analysis agrees favorably with experiments.     

Dissipative mesoscopic structures in plastic deformation

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 128–139, July–August, 1993.     

Oscillating plate viscometer in the Hz to kHz range

A low and audio frequency viscometer with a frequency range 2 Hz to 1 kHz and possibly up to 10 kHz is described, which shears a liquid sample (shear volume < 0.3 ml) between an oscillating glass plate and the wall of a cuvette. Alternating velocity and force exerted on the oscillating plate are measured by a mechanical impedance head, designed for the frequency range 1 Hz to 10 kHz. This device permits the determination of frequency dependent viscous liquid properties. Real and imaginary part of the complex viscosity can be obtained from the complex mechanical impedance. Inertial forces from the oscillating plate are compensated in an adjustable electronic circuit.Significant shear parameters, as the frequency, the exciting wave form and the amplitude, can be set independently. In this way viscous spectral data and also nonlinear properties can be studied, e.g., in aqueous DNA solutions. In addition, processes with time constants >0.1 s in (relaxing) viscoelastic systems, which do not obey the Boltzmann superposition principle, can be monitored by means of the (nonlinear) modulation of an LF sampling signal. Some examples of measurements will be shown. Model calculations for water and for glycerol give typical values for the complex impedances to be obtained with this oscillatory rheometric device.     

Torsion test of aluminum in the large strain range

A series of experiments was conducted on cast and extruded high purity aluminum material under monotonic large strain torsion condition. Both free-end and fixed-end torsions were studied using tubular specimens of different gage lengths (long, medium and short). The experiments used an axial–torsional extensometer. A procedure of calibration for elevated temperature test was determined. The torque versus angle of twist curves were recorded and converted into true shear stress–strain curves by use of the modified Nadai method developed previously by the authors. The axial extension for free-end torsion and the axial stress developed during fixed-end torsion were recorded. The hoop strain was also measured and was found to be approximately 0.8–0.9 times the axial strain when the shear strain is 150%. The effect of specimen geometry was studied. It was found that the long, thick-walled tubular specimen is suitable for torsion test in the large strain range.