Analysis of the Plastic Flow of Rock Under a Lubricated Punch

1968 ◽  
Vol 35 (1) ◽  
pp. 87-94 ◽  
Author(s):  
J. B. Cheatham ◽  
P. R. Paslay ◽  
C. W. G. Fulcher
Keyword(s):  
Plastic Flow ◽  
Yield Surface ◽  
Deformation Rate ◽  
Specific Problem ◽  
Three Dimensional ◽  
Plasticity Theory ◽  
Plane Flow ◽  
Perfectly Plastic ◽  
Isotropic Rock ◽  
Rate Vector

A general three-dimensional plasticity theory is presented for describing the plastic flow of homogeneous, isotropic rock. Normality of the deformation-rate vector to the yield surface is incorporated into the stress-deformation rate law used in the theory. The rock is assumed to be perfectly plastic or nonwork-hardening with a dependence of the yield strength on the hydrostatic component of stress. A particular type of yield surface, which is representative of the behavior of rock, is assumed in an application of the theory. The specific problem considered is the solution for the incipient plane flow under a flat lubricated punch.

Plastic Flow of Rock Under a Pointed Punch in Plane Strain

1968 ◽  
Vol 35 (1) ◽  
pp. 95-101 ◽  
Author(s):  
P. R. Paslay ◽  
J. B. Cheatham ◽  
C. W. G. Fulcher
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Yield Surface ◽  
Work Hardening ◽  
Deformation Rate ◽  
Plasticity Theory ◽  
Surface Work ◽  
Rate Vector ◽  
The Mean ◽  
Elastic Strains

Solutions are presented for the plane-strain plastic flow of rock under a pointed punch for two cases. In the first problem the indentation of a half space by a pointed punch is considered, and in the second the influence of a previous indentation on the formation of the next indentation is evaluated. The plasticity theory used in this analysis was developed by the authors earlier for rock mechanics applications. This theory incorporates a yield surface which is dependent on the mean normal stress and normality of the deformation rate vector to the yield surface. Work-hardening and elastic strains are neglected in the theory. These solutions furnish the analytical basis for some elementary experiments which may help to evaluate the theory.

Small deformation rate-independent plasticity based on a postulate of maximum dissipation

2020 ◽  
pp. 429-433
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Linear Programming ◽  
Plastic Flow ◽  
Yield Surface ◽  
Deformation Rate ◽  
Optimization Problem ◽  
Flow Direction ◽  
Small Deformation ◽  
Complementarity Conditions ◽  
Programming Theory ◽  
Plastic Dissipation

This chapter introduces the concept of maximum dissipation. The elastic set is introduced, and the plastic dissipation is maximized over the elastic set using classical methods from linear programming theory. The plastic flow direction is seen to be generally normal to the yield surface when the plastic dissipation is maximized. The Kuhn-Tucker complementarity conditions are seen in this context to arise from the postulated optimization problem, and the elastic set is seen to be necessarily convex. The concept of maximum dissipation is applied to a Mises material and the models of the earlier chapters are seen to be recovered.

General Properties of Yield-Point Load Surfaces

1968 ◽  
Vol 35 (1) ◽  
pp. 107-110 ◽  
Author(s):  
P. G. Hodge ◽  
Chang-Kuei Sun
Keyword(s):  
Strain Rate ◽  
Yield Point ◽  
Yield Surface ◽  
Plastic Material ◽  
Point Load ◽  
Perfectly Plastic ◽  
Plastic Mechanism ◽  
Rate Vector ◽  
Strain Rate Vector ◽  
Interaction Surface

A structure made of a rigid perfectly plastic material and subjected to more than one independent load is considered. A mode vector is defined for any plastic mechanism and shown to have the same properties relative to the yield-point load interaction surface that the strain-rate vector has to the material yield surface. An application to a circular plate under two independent loads leads to close bounds on the interaction curve.

Construction of plastic contact deformation maps on ceramics: a case study on aluminum nitride

1996 ◽  
Vol 54 ◽  
pp. 636-637
Author(s):  
D. L. Callahan
Keyword(s):  
Plastic Deformation ◽  
Aluminum Nitride ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Bright Field Image ◽  
Perfectly Plastic ◽  
Contrast Analysis ◽  
Deformation Patterns

Modern polishing, precision machining and microindentation techniques allow the processing and mechanical characterization of ceramics at nanometric scales and within entirely plastic deformation regimes. The mechanical response of most ceramics to such highly constrained contact is not predictable from macroscopic properties and the microstructural deformation patterns have proven difficult to characterize by the application of any individual technique. In this study, TEM techniques of contrast analysis and CBED are combined with stereographic analysis to construct a three-dimensional microstructure deformation map of the surface of a perfectly plastic microindentation on macroscopically brittle aluminum nitride.The bright field image in Figure 1 shows a lg Vickers microindentation contained within a single AlN grain far from any boundaries. High densities of dislocations are evident, particularly near facet edges but are not individually resolvable. The prominent bend contours also indicate the severity of plastic deformation. Figure 2 is a selected area diffraction pattern covering the entire indentation area.

scholarly journals Numerical investigation of plastic flow and residual stresses generated in hydroformed tubes

2021 ◽  
pp. 146442072198974
Author(s):  
A Ktari ◽  
A Abdelkefi ◽  
N Guermazi ◽  
P Malecot ◽  
N Boudeau
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Finite Element Model ◽  
Plastic Flow ◽  
Tube Hydroforming ◽  
Three Dimensional ◽  
Element Model ◽  
Tube Cross Section ◽  
Straight Wall ◽  
Hydroforming Process

During tube hydroforming process, the friction conditions between the tube and the die have a great importance on the material plastic flow and the distribution of residual stresses of the final component. Indeed, a three-dimensional finite element model of a tube hydroforming process in the case of square section die has been performed, using dynamic and static approaches, to study the effect of the friction conditions on both plastic flow and residual stresses induced by the process. First, a comparative study between numerical and experimental results has been carried out to validate the finite element model. After that, various coefficients of friction were considered to study their effect on the thinning phenomenon and the residual stresses distribution. Different points have been retained from this study. The thinning is located in the transition zone cited between the straight wall and the corner zones of hydroformed tube due to the die–tube contact conditions changes during the process. In addition, it is clear that both die–tube friction conditions and the tube bending effects, which occurs respectively in the tube straight wall and corner zones, are the principal causes of the obtained residual stresses distribution along the tube cross-section.

Three-Dimensional Simulations of Plastic Flow in Crystals

1992 ◽  
pp. 413-423 ◽  
Author(s):  
B. Devincre ◽  
V. Pontikis ◽  
Y. Brechet ◽  
G. Canova ◽  
M. Condat ◽  
...  
Keyword(s):  
Plastic Flow ◽  
Three Dimensional ◽  
Three Dimensional Simulations

Validation of the Stress Predictions in Rolling EHL Contacts Having In-Line Roughness Using the Inverse Method

2006 ◽  
Vol 128 (4) ◽  
pp. 745-752 ◽  
Author(s):  
C. J. Hooke ◽  
K. Y. Li
Keyword(s):  
Fluid Flow ◽  
Inverse Method ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Plane Flow ◽  
Preliminary Results ◽  
Rolling Contacts ◽  
Out Of Plane ◽  
Transverse Roughness

Using modern EHL programs it is relatively simple to determine the pressures and clearances in rough EHL contacts. The pressures may then be used to calculate the subsurface stresses in the two contacting components. However, the results depend on the assumptions made about the fluid’s rheology. While it is possible to measure the clearances using interferometric techniques, measurement of either the pressures or stresses is extremely difficult. However it is these, rather than the clearances, that determine the life of the contact. In previous papers the authors have described how the inverse method may be used to validate the stress predictions for contacts with transverse roughness. This type of contact has fluid flow in only one plane and it remained necessary to check the results for more general rough surfaces where the flow is three-dimensional. Accordingly, the inverse method is extended, in this paper, to a situation where out-of-plane flow is significant. The paper describes the approach and presents some preliminary results for rolling contacts.

Plane-Strain Problems

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Plastic Flow ◽  
Slip Line ◽  
Field Analysis ◽  
Valuable Insight ◽  
Line Field ◽  
Slip Line Field ◽  
Perfectly Plastic ◽  
Nonsteady State ◽  
Plane Plastic

This chapter is concerned with the formulations and solutions for plane plastic flow. In plane plastic flow, velocities of all points occur in planes parallel to a certain plane, say the (x, y) plane, and are independent of the distance from that plane. The Cartesian components of the velocity vector u are ux(x, y), uy(x, y), and uz = 0. For analyzing the deformation of rigid-perfectly plastic and rate-insensitive materials, a mathematically sound slip-line field theory was established (see the books on metal forming listed in Chap. 1). The solution techniques have been well developed, and the collection of slip-line solutions now available is large. Although these slip-line solutions provide valuable insight into deformation modes and forming loads, slip-line field analysis becomes unwieldy for nonsteady-state problems where the field has to be updated as deformation proceeds to account for changes in material boundaries. Furthermore, the neglect of work-hardening, strain-rate, and temperature effects is inappropriate for certain types of problems. Many investigators, notably Oxley and his co-workers, have attempted to account for some of these effects in the construction of slip-line fields. However, by so doing, the problem becomes analytically difficult, and recourse is made to experimental determination of velocity fields, similarly to the visioplasticity method. Some of this work is summarized in Reference [2]. The applications of the finite-element method are particularly effective to the problems for which the slip-line solutions are difficult to obtain. The finite-element formulation specific to plane flow is recapitulated here.

scholarly journals Reconstruction of the Glacial Ice Covers of Greenland and the Canadian Arctic Islands by Three-Dimensional, Perfectly Plastic Ice-Sheet Modelling

1984 ◽  
Vol 5 ◽  
pp. 115-121 ◽  
Author(s):  
N. Reeh
Keyword(s):  
Flow Pattern ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Canadian Arctic ◽  
Ice Cover ◽  
Glacial Ice ◽  
North West ◽  
Ice Caps ◽  
Perfectly Plastic

A three-dimensional perfectly plastic ice-sheet model, developed for determining the surface elevations and the flow pattern of an ice sheet with given bottom topography and ice-margin positions, is applied to the reconstruction of the glacial ice covers of Greenland and the Canadian Arctic islands. In the northern regions, two different reconstructions have been performed with ice margins along the present 600 and 200 m sea-depth contours, respectively. In central Greenland, the ice margin is considered to be at the outermost ice-margin deposits on the coastal shelf to the west, and at the present 200 m sea-depth contour to the east.The main conclusions to be drawn from the reconstructions are: (1). The flow pattern of the glacial ice cover of Greenland shows a great resemblance to the present one, the central ice divide being displaced less than 50 km from its present position and being no more than 200 m higher than today. (2). The main ice divide of the ice sheet covering the Canadian Arctic islands (the Innuitian ice sheet) was located over the highlands of eastern Ellesmere Island with local domes positioned over the present ice caps, indicating that even the deep ice of Wisconsin age in these ice caps is of local origin. This is also the case for the Devon Island ice cap. (3). Even in the not very likely case of a rather extensive glacial ice cover in north-west Greenland, the ice-flow pattern upstream of the Camp Century deep drill site would not have changed radically compared to the present flow pattern. Thus it is concluded that even advanced ice margins in late-Wisconsin time could at most have resulted in an elevation of the deposition site of the late-Wisconsin ice at Camp Century 600 m higher than at present. The consequences of this conclusion are discussed.

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