Showing papers on "Necking published in 1990"

A finite amplitude necking model of rifting in brittle lithosphere

Abstract: We formulate a mechanical model describing the formation of rifts as finite amplitude necking of an elastic-plastic layer overlying a fluid substrate. A perfectly plastic rheology is a continuum description of faulting in rift zones. Two important aspects of rift evolution are illustrated by this model: the evolution of the rift width as extension proceeds and the finite strain that occurs. A region at yield initially develops with a width determined by the thickness of the brittle layer, and the internal deformation within this yield zone is proportional to the topographic slope. As extension proceeds, the surface within the rift subsides, and the width of the subsiding yield zone decreases. At any stage of rifting, material in regions just outside the yield zone is deformed but no longer deforming. The width of these deformed regions increases with increasing extension. Vertical forces due to the mass deficit of the rift depression will flex the elastic layer outside the yield zone, creating flanking uplifts. The external force required to maintain active rifting increases with the amount of lithospheric stretching, indicating that rifting is a quasi-static, stable process. Because the yield zone will revert to elastic behavior if the external force causing extension is removed, the model predicts that the rift depression and flanking uplifts will be preserved after extension stops. Our simple mechanical model demonstrates the inherent relationship among graben formation, lithospheric thinning, and rift shoulder uplift in rift zones.

Tensile fracture and fractographic analysis of 1045 spheroidized steel under hydrostatic pressure

Abstract: Void formation in tensile test under hydrostatic pressure is characterized through quantitative metallography, and the fracture mechanism under pressure is analyzed by fractography. Transition of the fracture surface from the cup-and-cone under atmospheric pressure to a slant structure under high pressure is explained on the basis of the void development leading to fracture and the concomitant change in fracture mechanism. The concept of “shear blocks” is introduced to illustrate the features observed on the fracture surface of specimens tested under high pressure. It is postulated that shear blocks evolve to connect the central crack regions with the shear crack initiated on neck surface due to the severe necking deformation under applied pressure.

A full tangent stiffness field-boundary-element formulation for geometric and material non-linear problems of solid mechanics

Abstract: The field-boundary-element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite-element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field-boundary-element method for geometric and material non-linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post-bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field-boundary-element formulation which takes the initial stress–velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, in initially perfect elastic–plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for large strain plasticity.

Cleavage-like Fracture at Low Temperatures in an 18Mn-18Cr-0.5N Austenitic Steel

Abstract: The low temperature embrittlement in an 18Mn-18Cr-0.5N retaining ring steel has been investigated by means of tension and Charpy impact tests. The effects of grain size, strain rate and pre-deformation were examined.The ductile to brittle transition (DBT) behaviour associated with the cleavage-like fracture has been found, where the fractured plane was regarded as {111}. The traces of intense planar plastic flow which may be related with twinning, slip band, or epsilon martensite were observed on the surface of plastically deformed specimen. When the pre-deformation was applied to the specimen at room temperature, the fracture stress at 77 K was slightly increased but the fracture mode was still cleavage-like. The DBT temperature (DBTT) is scarcely influenced by grain size, although the fractured surface unit is considered as austenite grain size. This is discussed based on the experimental data on the grain size dependences of flow stress and fracture stress. When the strain rate in tension test is increased up to 2.7×10-1/s, the fracture mode at 77 K has been found to change from cleavage-like to dimple. In this case, the plastic deformation occurs very locally and heavily, so as to induce the necking of the specimen.

Dislocation Patterns and Plastic Instabilities

Abstract: Two important types of plastic instabilities occurring in crystalline materials are discussed within a phenomenologic frame They involve anomalies in the behavior of the strain hardening rate (h) or of the strain rate sensitivity (S) of the flow stress These two quantities are calculated in terms of the evolution of the densities of mobile and forest dislocations during plastic flow This approach is exemplified by a study of the critical conditions for slip line patterning and for necking (type h) and by an investigation of the critical strains for the occurrence of jerky flow (type S) Experimental features associated with dislocation patterning are reviewed and analytical approaches through reaction-transport or reaction-diffusion are discussed Because of the nonlocal character of internal stresses, these models are, for the moment, confined to the study of fatigue patterning For this reason numerical simulations have been developed The preliminary results presented here were obtained with a 3 D simulation of collective dislocation dynamics, based on a discretization of time and space

On the necking-in process in cluster decays

Abstract: Two new macroscopic models (liquid drop and Yukawa-plus-exponential) describing the decays with emission of large fragments including alpha decay are developed. The proposed shape parametrization consists of two intersecting spheres smoothly joined by a third "rolling sphere". The first two spheres describe asymptotically the charge and mass asymmetries and the third one the necking-in process. It is shown that the potential energy surfaces in the neck and the relative distance between the centers of the spheres (for a given mass and charge fragmentation) lead to different dynamical paths depending on the mass and charge of the emitted fragment. Along the path a phenomenological shell correction term and a zero point vibrational energy are introduced. It is shown that this model gives an excellent description of the present experimental data.

Adhesion of molded polyethylene using polyethylene gels by microwave heating

Abstract: Adhesive effect of polyethylene gels on the molded polyethylene by heating with microwaves has been investigated. Polyethylene gels in polar organic solvents such aso-xylene, chlorobenzene,o-dichlorobenzene,m-dichlorobenzene, 1,1,1,2-tetrachloroethane, and 1,1,2,2-tetrachloroethane were used as adhesives. All of these gels showed adhesive effect when heated with microwaves. In particular, the gels in 1,1,2,2-tetrachloroethane showed such strong adhesion that polyethylene plates of 3 mm in thickness and 20 mm in width gave rise to necking by heating for 8 min in a 500 W (2450 MHz) microwave oven.

Study of hydrogen embrittlement in aluminium alloy 2024 in the longitudinal direction

Abstract: A comparative study of the hydrogen effect on overall ductility in the rolling direction of aluminium alloy 2024 in the T351 temper condition and aluminium alloy 2024 aged at 190°C for 7 h has been conducted. Hydrogen-pre-charged and hydrogen-free sheet tensile specimens have been tested at either a constant or an alternating strain rate. It has been found that internal hydrogen caused severe degradation in overall plastic elongation of aluminium alloy 2024-T351 and that in artificially aged alloy 2024 the embrittlement was observed only after the onset of necking. It has been observed that hydrogen-induced modification of the strain rate dependence of flow stress by reducing dynamic hardening in alloy 2024-T351 aged at 190°C for 7 h and enhancing dynamic softening in alloy 2024-T351. It is suggested that hydrogen embrittlement is caused by hydrogen-induced enhancement of plastic deformation localization that mainly affects non-uniform plastic deformation.

Ductility Enhancement from Interface Dislocation Sources in a Directionally Solidified β (γ + γ′) Ni-Fe-Al Composite Alloy.

Abstract: A directionally solidified β + (γ + γ′) Ni-Fe-AI in-situ composite alloy of composition Ni 50 Fe 30 Al 20 (at.%) has been used to investigate the effect of a plastically soft second phase on the mechanical behavior of a B 2 ordered intermetallic alloy. This material exhibits extensive plasticity during compressive deformation at room temperature and fails in shear with extensive γ + γ′ lamellar or rod pull-out. The material also exhibits ∼10% tensile elongation to fracture at room temperature, with final fracture that includes substantial necking of the γ + γ′ lamellae or rods. Observation of slip lines and dislocation substructures discloses that the normally brittle β matrix undergoes extensive plasticity in order to deform compatibly with the more ductile γ phase. The plasticity of the β matrix is accomplished by the generation of glissile dislocations into the β matrix from the β/γ interface region and is enhanced because of a favorable β - γ orientation relationship for slip transfer. Ductility enhancement from interface-generated mobile dislocations generated from β-γ interfaces is compared to that observed in film-coated β-NiAl single crystals and FeAl polycrystals.

A new approach to finite deformation problems of elastoplasticity—boundary element analysis method

Abstract: A formulation and numerical implementation of boundary element methods (BEM) for the finite deformation problems of elastoplasticity is presented in this paper in updated Lagrangian description. This formulation has considered two kinds of traction rates. The velocity-gradient equation of inner point is fully deduced to meet the desire of higher order elements and cells. A scheme of iteration suitable for J 2 -flow theory is developed, too. Moreover an effective indirect quadrature is designed to overcome the diffuculty of evaluating Cauchy principal values of domain integrals; owing to this the quadratic isoparametric elements and cells are successfully introduced in the code BELEPA. Several numerical examples, including the necking of plate specimen, are presented at the end. An interesting phenomenon is observed from the results that the BEM analysis of necking is more sensitive to the initial imperfection of specimen than FEM analysis. Further investigation is needed to confirm this phenomenon.

On fracture toughness in tearing of sheet metal

Abstract: An approximate analysis is presented for predicting the specific fracture toughness,R, in the tearing fractures of ductile sheet from the stress-strain relationships. The model assumes the fracture work to be the plastic work consumed by localized necking. Predictions are compared to experimental findings.

Theoretical and computational aspects of large plastic deformations involving strain-induced anisotropy and developing voids

Abstract: The anisotropic hardening of porous material is described in terms of the combined isotropic kinematic hardening model which appears to be a combination of the hardening laws of Prager and Ziegler. The considerations are limited to the associated flow rule, what is related with the simplified assumption that the nucleation of voids during the process is neglected. The rate equation are formulated by means of substructure corotational rates involving the relation for plastic spin

Embrittlement by liquid U in some group VB and VIB metals and alloys during tensile loading at 1473 K

Abstract: An investigation was conducted to determine the effect on tensile behavior of Ta, W, V, Nb, and a Ta-2.5 wt pct W alloy when they were exposed to liquid U. Tantalum, wolfram, and the Ta-2.5 wt pct W alloy were embrittled with a negligible reduction of cross section at failure, whereas V and Nb showed ductile behavior, with the samples necking down to a point. Tensile deformation of Ta in liquid U was also investigated at different displacement rates. It was found that ductility and strength increased with increasing displacement rate. The embrittlement in Ta, W, and the Ta-2.5 wt pct W alloy was associated with intergranular penetration of U, and the fracture surfaces showed evidence of grain boundary dissolution. At higher displacement rates, however, this evidence was less obvious. These results indicate that intergranular penetration of liquid U and tensile embrittlement in some of the Group VB and VIB metals correlate with low mutual solubility between the solid and liquid elements. It was also found that the thermo-dynamic criterion for intergranular penetration of liquid into a solid (grain boundary energy > 2 × liquid/solid interfacial energy) only applies to these systems.

Fracture mechanisms of metals

Abstract: Publisher Summary This chapter discusses the fracture mechanisms of metals. At the atomic scale, three types of fractures can be considered. One can find a separation of the atoms along a crystallographic plane, either in a direction normal to that plane (mode I according to fracture mechanics) or in a direction parallel to that plane (modes II and III) or by the coalescence of vacancies, a mechanism that can occur at high enough temperatures. The first type of separation is cleavage, while the second one is a slip mechanism. Cleavage cracks are considered to be brittle at the microscopic level because they involve little plastic deformation. Attention must be drawn, however, to the fact that sometimes they are triggered only when strain hardening has raised the stress to a level at which the macroscopic strain is not negligible. Due to stress concentrations from localized slips, cleavage is more likely when the grain size is large, when the temperature is low, or when the strain rate is high. Single crystals of a hexagonal metal, such as zinc, can slip on a single plane until complete separation of the two parts. More often, however, multiple slip occurs in single crystals, inducing a neck in the specimen loaded under tension. The section of the crystal can then reduce dramatically. In polycrystalline metals, necking takes place in a more diffuse fashion but can also lead to the complete separation of the two halves of the sample when the cross-section of the neck reduces to zero.

Apparatus for preparing label carrier strip

Abstract: PURPOSE:To eliminate the necessity for replacing a raw sheet roll according to the presence of necking by releasing printing paper and release paper from the raw sheet delivered from the raw sheet roll to apply necking and again laminating the printing paper and the release paper. CONSTITUTION:The raw sheet 30 delivered from a raw sheet roll holding means 4 is released into front printing paper 14 and back release paper 1 at the part of the first roll 68 by a draw-down roll 62 as a release means for drawing down only the release paper 1. The release paper 1 is passed between the cutter 74 arranged on the downstream side of the roll 68 and the annular groove 71 of the guide roller 72 corresponding to the cutter to be subjected to notching (necking) processing and again superposed on the printing paper 14 at the part of a press roll 8. That is, a label carrier strip A to which necking is applied by a cutter 7 is prepared.

A new analytical method for the optimization of thermomechanical conditions in zone drawing and its application to polyethylene

Abstract: An original method of zone drawing of polymers at constant load and a procedure for the optimization of thermomechanical conditions (stress, temperature) are suggested, allowing high draw ratios and favorable strength values to be obtained. The temperature (or stress) range of necking has been determined in a nonisothermal and in an isothermal regime. The advantage of the method consists in that the increasing orientation in the neck starting from the initiation point and up to fracture allows the morphology and properties to be quickly examined, depending on the varying thermomechanical conditions in different regions of the neck. At a high temperature and low load the mechanism of oriented crystallization from melt becomes operative; in opposite cases, orientation of the solid state takes place. It is shown that in the nonisothermal regime an increased rate of heating allows extreme draw ratios (up to ca. 150) to be obtained, approximately twice as high as those obtained in the isothermal regim...

Superplastic Deformation of an Al-Li-Cu-Zr Alloy under Uniaxial and Biaxial Tension

Abstract: The superplasticity of an Al-Li-Cu-Zr alloy has been studied under uniaxial tension and biaxial bulging conditions using hydrostatic pressure. An optimum tensile elongation of 850% at a strain rate of 3×10−4 /sec was obtained at 758 K. The maximum true thickness strain was 1.22 for a biaxially deformed specimen under the same conditions. It was shown that strain rate dependent flow hardening was related to necking profile. It was observed that cavity growth during superplastic deformation depended on the type of loading. Under biaxial bulging conditions, the cavities grew by forming cavity fissure networks along the grain boundaries. It was found that, by the superimposition of hydrostatic pressure, cavitation was retarded and the superplastic ductility was increased in both tensile and biaxial deformation.

High strain rate superplasticity and strength properties of two-phase. alpha. -titanium - intermetallic Ti-12Co-5Al and Ti-12Ni-5Al alloys

Abstract: The present paper describes the microstructures and the mechanical properties of quasi eutectoid Ti-12Co-5Al and Ti-12Ni-5Al alloys exhibiting large superplastic elongations without local necking at relatively low deformation temperatures and high strain rates. The investigations includes the determination of the temperature and strain-rate dependent m values as well as the Young's moduli and the strength properties from room temperature up to 800deg C. The superplastic behaviour will be discussed under consideration of power law creep equations and of rate controlling transport phenomena. (orig.).

Forming Limit of Sheet Metals

Abstract: The forming limit of sheet metals is examined in terms of the uniqueness of the solution. There are two cases indicating multiplicity, one is statically admissible and another is kinematically admissible. The multiplicities are considered to correspond to plastic instabilities. The necking plane is studied as the plane admitting the existence of velocity discontinuity, and in sheet forming it cannot take any mode except perpendicular necking. After statical instability appears, the strain path cannot be controlled as freely as we would like. Finally, localized necking occurs, when the process satisfies the condition of the second kinematical instability, the mode of which is consistent with the mode of perpendicular necking. Several strain paths are assumed, and their formabilities are discussed.

Prevention method for necking in hot rolling

Abstract: PURPOSE:To control generating positions of necking by providing a cooling device on the outlet side of an rolling mill to control the cooling rate of steel stock in a prevention method for necking to change the dimension of the sectional area corresponding to the position of change and variation in the dimension of a sectional area by necking. CONSTITUTION:A water cooling device 6 is provided on the upper side of a runout table 4 on the outlet side of a stand 1 to cool a rolled strip 3 and to transform it from phase gamma to phase alpha. Between rollers on the runout table 4 are provided (n) transformation rate sensors 7 to detect the transformation rate of steel. The supply of cooled water to the cooling device 6 is carried out through a flow rate control valve 8 to control the quantity of water. The output of each transformation rate sensor 7 is given to a computer 9 and the rolling mill given in the same way outputs a control signal CS and an aperture signal PS to control the width rolling reduction of an edger 2 by the cooling information. In this way, it is possible to control the terminal position of transformation, control necked positions and improve the yield of the product by the control of cooling rate.

Method of producing biaxially oriented polyether ether ketone film

Abstract: A biaxially oriented film of a polyether ether ketone (PEEK) having excellent accuracy, insulating properties and thermal shrinkage resistance is easily obtained from a noncrystalline PEEK film by roll stretching the film 1.5- to 3.5-fold in the machine direction while causing the necking of the film in the temperature range from 50 °C to Tg minus 10 °C, stretching the monoaxially stretched film 1.5- to 3.5-fold in the direction perpendicular to that of the first stretching in the temperature range from Tg to 170 °C, and heat setting the film thus stretched in two stages in the temperature ranges from 210 to 330° and from 180 to 210 °C.