J. W. Spretnak

Instability of plastic flow in the directions of pure shear: I. Theory

The localization of plastic flow (plastic instability) is a prelude to fracture initiation. Prior treatments are based mainly on the phenomenon of necking (load maximum) which has for its basis fluctuations in cross-sectional area. A second basic mode of localization has been confirmed experimentally. This is the localization of flow within a plastic zone along characteristic directions (direction of pure shear or zero extensional strain). The localization is effected by the activation of tangential velocity discontinuities along the characteristics. A necessary condition is that the material simulate the ideal plastic state. The conditions for this second mode of localization are formulated. A general condition for instability involving both modes is derived. In situations in which both modes are possible, necking is always expected to precede the localization along characteristics.

The Oxidation of Molybdenum

Abstract Scale formed upon molybdenum consists of either two or three oxide layers., depending upon temperature and time. The outermost layer is the volatile MoO3. The inner layers of oxide have a ...

Instability of plastic flow in the directions of pure shear: II. Experimental

Two aspects of the phenomenon of plastic instability in direction of pure shear are examined, namely that the condition dσ = 0 (maximum in true flow stress) is necessary for localization of flow along characteristics as defined in continuum plasticity, and that fracture is initiated and propagates along characteristics. Two types of sheet specimens were employed, the standard-type flat sheet specimens, and specimens simulating both plane stress and plane strain. Grids were placed on gage sections and photographs were taken successively in the plastic range to enable strains to be calculated and instabilities to be observed and recorded. The principal variable in the flat specimen test was theW/T ratio (width to thickness). In the plane* strain specimens, both the gage length (constantW/T) and the strength level of the material (quenched and tempered AISI 4340 steel) were varied. A maximum in true flow stress is found consistently at the onset of instabilities. Fracture propagated consistently along the instability band-matrix interface. Variations in specimen geometry produces significant changes in stress state, directions of characteristics, and ductility. For a given specimen geometry, plane strain is more closely approached the higher the strength level of the material. In mixed mode fracture paths slant fracture is associated with the more embrittling stress state.

An analysis of plastic instability in pure shear in high strength AISI 4340 steel

The phenomenon of plastic instability in pure shear was studied at room temperature in heat treated high-strength AISI 4340 steels, employing the torsion test. The instability occurs after saturation of strain hardening by the dispersed carbide particles. The strain at onset of instability is sensitively dependent on rate of straining. The effective stress (total stress minus the stress resulting from dispersion hardening) may be a result of Snoek relaxation or the Cottrell drag, depending on strain rate; the magnitude of this stress is linearly proportional to the dissolved carbon content. Experimental observations indicate that instability interfaces advance spirally in the axial direction of the specimen. It is proposed that the interface is stable in a thermodynamic sense and that the driving force for migration depends only on ratio of the speed of the front to the macroscopic strain rate. When the interface becomes stationary, fracture is nucleated at an axial distortion in the interface. Fracture by the instability occurs by a translatory motion of one now rigid body with respect to a second rigid body along the characteristic (slip) surface. Pores may be found in the fracture surface, but these are incidental to the intense flow along the characteristic, and are not the cause of the instability.

The role of pure shear strain on the site of crack initiation in notches

The states of stress and strain at the root of V and U-notches were examined through the use of an elastic-plastic finite element computer program in an effort to develop a criterion for predicting the site of crack initiation. Using simple bending under conditions approximating plane stress, the sites of initiation were determined experimentally to be well removed from the notch centerline. Furthermore, the paths of crack propagation followed the directions of pure shear strain,i.e. the “characteristic” directions. The slip line fields,i.e. the directions of pure shear strain, produced from the results of the finite element program agreed well with results expected from classical plasticity solutions. Examinations of numerous stress and strain quantities along and between the slip lines were conducted in an effort to evolve a selectivity rule that could be used to predict along which slip line a velocity discontinuity would be activated to form a crack. A rapid decrease in the average value of pure shear strain along the contour of the notch near the initiation site provided the sought predictive capability.

Distribution of boron in gamma iron grains

SpretnakThe distribution of boron in γ iron grains as a function of temperature is studied, employing three experimental techniques: a) grain growth in high purity Fe-C and Fe-C-B alloys, b) X-ray parameter measurements on Fe-B alloys as a function of temperature, and c) the metallographic test for the boron constituent. It is concluded that boron undergoes positive adsorption to γiron grain boundaries and that the temperature coefficient of adsorption is positive.

Effect of Hydrogen on Alpha Titanium Alloy

The effect of up to 200 ppm hydrogen on the microstructure and mechanical properties of high-purity titanium containing oxygen, nitrogen, tin, and aluminum was investigated. Increasing the hydrogen content resulted in precipitation of a hydride phase and decreased the notch-bend impact strength of the alloys containing oxygen, nitrogen, and tin, similar to the hydrogen embrittlement of unalloyed high-purity titanium. No hydride precipitation or significant embrittlement of the Ti-5AI alloy was found with up to 180 ppm hydrogen.

Influence of Carbon on The Lattice Parameter of Molybdenum

At very low concentrations, carbon dissolves interstitially in molybdenum resulting in a linear expansion of lattice parameter with increase of carbon in solid solution. Geometrical consideration of the relative size of carbon atom to size of interstice approximately predicts the observed volume expansion.