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.

An Experimental Study of the Structure of Constitutive Equations for Nonproportional Cyclic Plasticity

1985 ◽  
Vol 107 (4) ◽  
pp. 307-315 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Yield Surface ◽  
Hysteresis Loops ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Plastic Strain Rate ◽  
Hardening Modulus ◽  
Rate Vector ◽  
Strain Rate Vector

Three type 304 stainless steel specimens of the same geometry were subjected to complex, cyclic axial-torsional histories characterized by varying degrees of non-proportionality of straining. All tests were at room-temperature. The data from cyclically stable hysteresis loops were reduced and the direction of the plastic strain rate vector, variation of plastic hardening modulus, and direction of translation of a rate and time-independent yield surface were studied. It is shown that the independent variables in a Mroz-type formulation map the experimental results with a higher degree of uniqueness than other popular formulations studied for both the hardening modulus and direction of yield surface translation. Also, the plastic strain rate is not, in general, in the direction of the deviatoric stress or stress rate.

Nonuniqueness in Contained Plastic Deformation

1980 ◽  
Vol 47 (2) ◽  
pp. 273-277 ◽  
Author(s):  
P. G. Hodge ◽  
D. L. White
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Yield Point ◽  
Displacement Field ◽  
Point Load ◽  
Point Of View ◽  
Computational Point ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.

Linear integral analysis of bar rough rolling by strain rate vector

2010 ◽  
Vol 17 (3) ◽  
pp. 28-33 ◽  
Author(s):  
Wei Deng ◽  
De-wen Zhao ◽  
Xiao-mei Qin ◽  
Xiu-hua Gao ◽  
Lin-xiu Du ◽  
...  
Keyword(s):  
Strain Rate ◽  
Integral Analysis ◽  
Rate Vector ◽  
Linear Integral ◽  
Strain Rate Vector ◽  
Rough Rolling

Rolling With Simplified Stream Function Velocity and Strain Rate Vector Inner Product

2012 ◽  
Vol 19 (3) ◽  
pp. 20-24 ◽  
Author(s):  
De-wen Zhao ◽  
Shun-hu Zhang ◽  
Can-ming Li ◽  
Hong-yu Song ◽  
Guo-dong Wang
Keyword(s):  
Strain Rate ◽  
Stream Function ◽  
Inner Product ◽  
Rate Vector ◽  
Strain Rate Vector

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.

Interaction of Pressure, End Load, and Twisting Moment for a Rigid-Plastic Circular Tube

1963 ◽  
Vol 30 (3) ◽  
pp. 396-400 ◽  
Author(s):  
Joseph E. Panarelli ◽  
Philip G. Hodge
Keyword(s):  
Circular Cylinder ◽  
Shell Theory ◽  
Circular Tube ◽  
Plastic Material ◽  
Rigid Plastic ◽  
End Effects ◽  
Perfectly Plastic ◽  
Special Cases ◽  
Interaction Surface

A thick-walled circular cylinder acted on by pressure, axial end load, and twisting moment is analyzed under the assumption that end effects are negligible. The locus of all load points (interaction surface) for which unaccelerated flow of a perfectly plastic material can occur is found parametrically. Certain special cases are considered and the results compared with those of shell theory.

An Approach to Predicting Evolution of Material Properties Near Surfaces With High Friction in Metal Forming

2005 ◽  
Author(s):  
S. Alexandrov
Keyword(s):  
Strain Rate ◽  
Material Properties ◽  
Evolution Equations ◽  
Plastic Material ◽  
Equivalent Strain ◽  
Maximum Friction ◽  
Perfectly Plastic ◽  
Equivalent Strain Rate ◽  
Strain Rate Intensity ◽  
Friction Surfaces

In the case of rigid/perfectly plastic material, the velocity fields in the vicinity of maximum friction surfaces must be describable by nondifferentiable functions. In particular, the equivalent strain rate follows an inverse square root rule near such surfaces and, therefore, approaches infinity at the surface. Because the equivalent strain rate is involved in many evolution equations for material properties, its behavior near the maximum friction surfaces should lead to high gradients in the material properties near the surface, which is confirmed by experiment. To quantitatively describe the evolution of material properties in the vicinity of surfaces with high friction, the concept of strain rate intensity factor can be adopted.

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