Plastic Strain Concentrations in Ligaments

1977 ◽  
Vol 99 (2) ◽  
pp. 328-336 ◽  
Author(s):  
J. S. Porowski ◽  
W. J. O’Donnell
Keyword(s):  
Plastic Strain ◽  
Numerical Solutions ◽  
Pure Shear ◽  
Solid Material ◽  
Shear Loading ◽  
Plastic Strains ◽  
Perfectly Plastic ◽  
Circular Holes ◽  
Elastic Perfectly Plastic ◽  
Conservative Values

The sheet perforated with a uniform array of circular holes arranged in a square pattern is investigated. The plastic strains are derived for progressive in-plane loading which eventually results in gross yielding. The finite element method is used to obtain numerical solutions. Plane stress conditions and elastic perfectly plastic solid material properties are assumed. Thus the results provide conservative values of plastic strain concentrations for a considerable range of perforated materials. The plastic strain multipliers for equibiaxial and pure shear loading are given for three ligament efficiencies of the penetration pattern. The tendency of forming highly localized plastic strains with progressive yielding is observed, and the implications of the results in plastic design are discussed.

scholarly journals The Prospects for Mechanical Ratcheting of Bulk Metallic Glasses

2003 ◽  
Vol 806 ◽  
Author(s):  
Wendelin J. Wright ◽  
R. H. Dauskardt ◽  
W. D. Nix
Keyword(s):  
Plastic Strain ◽  
Metallic Glasses ◽  
Room Temperature ◽  
Tensile Axis ◽  
Uniaxial Stress ◽  
Temperature Deformation ◽  
Steel Alloys ◽  
Cyclic Torsion ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

ABSTRACTThe major mechanical shortcoming of metallic glasses is their limited ductility at room temperature. Monolithic metallic glasses sustain only a few percent plastic strain when subjected to uniaxial compression and essentially no plastic strain under tension. Here we describe a room temperature deformation process that may have the potential to overcome the limited ductility of monolithic metallic glasses and achieve large plastic strains. By subjecting a metallic glass sample to cyclic torsion, the glass is brought to the yield surface; the superposition of a small uniaxial stress (much smaller than the yield stress) should then produce increments in plastic strain along the tensile axis. This accumulation of strain during cyclic loading, commonly known as ratcheting, has been extensively investigated in stainless and carbon steel alloys, but has not been previously studied in metallic glasses. We have successfully demonstrated the application of this ratcheting technique of cyclic torsion with superimposed tension for polycrystalline Ti–6Al–4V. Our stability analyses indicate that the plastic deformation of materials exhibiting elastic–perfectly plastic constitutive behavior such as metallic glasses should be stable under cyclic torsion, however, results obtained thus far are inconclusive.

Loading History Effects for Deepwater S-Lay of Pipelines

2003 ◽  
Author(s):  
Heedo D. Yun ◽  
Ralf R. Peek ◽  
Paul P. Paslay ◽  
Frans F. Kopp
Keyword(s):  
Numerical Solutions ◽  
Loading History ◽  
Material Models ◽  
Plastic Deformations ◽  
Perfectly Plastic ◽  
History Effects ◽  
Departure Angle ◽  
Numerical Finite Element ◽  
Elastic Perfectly Plastic ◽  
The Moment

For economic reasons S-Lay is often preferred to J-Lay. However in very deep water S-Lay requires a high curvature of the stinger to achieve the required close-to-vertical departure angle. This can lead to plastic deformations of the pipe. The high top tension increases the plastic deformations in two ways: firstly it adds an overall tensile component to the strains, thereby increasing the strains at the 12 o’clock position. Secondly it increases the strain concentrations which arise due to discontinuous support of the pipe on the stinger. Typically the pipe is guided over a series of roller beds. The high top tension tends to straighten the spans between the roller beds. To accommodate this (so that the pipe can still follow the stinger), higher curvatures are required at the roller beds. Analytical and numerical solutions are provided to quantify this effect. The analytical solution is fully developed for an elastic-perfectly-plastic pipe, but can also be applied for other material models provided that: (i) the moment-curvature relation for the pipe under tension is known, and (ii) no cyclic plastic ratchetting occurs due to repeated bending of the pipe over the roller beds and straightening in the spans between roller beds. Agreement between the analytical and numerical (finite element) results is excellent, if the proper loading history is used in the numerical simulation. Otherwise the level of strain concentration can be overpredicted.

Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material

1968 ◽  
Vol 35 (2) ◽  
pp. 372-378 ◽  
Author(s):  
Chi-Hung Mok
Keyword(s):  
Spherical Cavity ◽  
High Speed ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Numerical Technique ◽  
Nonlinear Dependence ◽  
Static Approximation ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.

Plane strain distribution in perfectly plastic regions around circular holes due to unequal biaxial loads

1966 ◽  
Vol 1 (5) ◽  
pp. 394-397 ◽  
Author(s):  
I S Tuba
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Strain Distribution ◽  
Plastic Region ◽  
Secant Modulus ◽  
Compatibility Equation ◽  
Perfectly Plastic ◽  
Biaxial Loads ◽  
Circular Holes ◽  
Elastic Perfectly Plastic

The elastic-perfectly plastic solution of Galin provides only the stress distribution for the plastic region. The theory is extended and the compatibility equation is solved for the secant modulus. The unfinished problem of Galin is thus completed and the strain distribution is obtained for the perfectly plastic region around a circular hole due to unequal biaxial loads.

Some theoretical considerations relating to strain concentration in elastic-plastic bending of beams

1968 ◽  
Vol 3 (4) ◽  
pp. 304-312 ◽  
Author(s):  
M Radomski ◽  
D J White
Keyword(s):  
Strain Hardening ◽  
Numerical Solutions ◽  
Bending Moment ◽  
Rate Of Change ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Rate Of Increase ◽  
Plastic Zones ◽  
Elastic Perfectly Plastic

Theoretical derivations are presented for the relations between maximum deflection and the corresponding maximum strain for some simple beams subject to elastic-plastic bending. Both elastic-perfectly plastic and arbitrary stress-strain relations are considered. Where possible, explicit analytical solutions are given, but where this is not possible numerical solutions are obtained by means of computer programmes. The calculations show that in elastic-perfectly plastic material short plastic zones may develop and cause large strains in the beam even though the deflection corresponding to first yield is not greatly exceeded. On the other hand, strain hardening elongates the plastic zones, so producing a more favourable strain distribution along the length of the beam than would exist without it. The more pronounced the strain-hardening characteristic, i.e. the greater the rate of increase of stress with strain, the less concentrated will be the strains. The mode of loading is important in that the higher the rate of change of bending moment, in the region of ihe maximum bending moment, the more concentrated will be the local strains.

Plastic Deformation of Bulk Amorphous Alloys

2000 ◽  
Vol 644 ◽  
Author(s):  
L.Q. Xing ◽  
T.C. Hufnagel ◽  
K.T. Ramesh
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Metallic Glasses ◽  
Shear Bands ◽  
Bulk Metallic Glasses ◽  
Serrated Flow ◽  
Perfectly Plastic ◽  
Elastic Loading ◽  
The Difference ◽  
Elastic Perfectly Plastic

AbstractWe have studied plastic deformation, including “serrated flow,” of bulk metallic glasses under quasi-static uniaxial compression. The deformation response is essentially elastic-perfectly plastic, but the “plastic” deformation actually consists of sections of elastic loading separated by abrupt load drops. The load drops are due to the formation of shear bands, which represent the primary mechanism of plastic deformationIn Zr-Ti-Cu-Ni-Al bulk metallic glasses, fracture occurs after about 1-2% plastic strain, but in Zr-Ta-Cu-Ni-Al metallic glass the plastic strain to failure can be as large as 6-7%. The difference appears to be due a strong tendency for the shear bands in this alloy to branch. The branching presumably reduces the stress concentration on the shear bands, retarding the onset of fracture. No evidence is seen for the formation of crystalline phases in this alloy.

The Dynamic Hole Expansion Problem for a Plate of Elastic-Perfectly Plastic Material

1978 ◽  
Vol 45 (4) ◽  
pp. 961-963
Author(s):  
P. C. Upadhyay ◽  
V. K. Stokes
Keyword(s):  
Circular Hole ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Plastic Region ◽  
Infinite Plate ◽  
Tangential Component ◽  
Constant Acceleration ◽  
Perfectly Plastic ◽  
Hole Boundary ◽  
Elastic Perfectly Plastic

Numerical solutions have been obtained for the problem of the dynamic expansion of a circular hole in an infinite plate of elastic-perfectly plastic material, due to the imposition of a constant acceleration at the hole boundary, for three different materials. It has been shown that Freiberger’s assumption, concerning the vanishing of the tangential component of stress in the plastic region, is not valid.

Multiaxial Fatigue of 16MnR Steel

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Zengliang Gao ◽  
Tianwen Zhao ◽  
Xiaogui Wang ◽  
Yanyao Jiang
Keyword(s):  
Pure Shear ◽  
Ambient Air ◽  
Shear Loading ◽  
Multiaxial Fatigue ◽  
Experimental Results ◽  
Pressure Vessel Steel ◽  
Critical Plane ◽  
Cracking Behavior ◽  
Vessel Steel ◽  
Axial Torsion

Uniaxial, torsion, and axial-torsion fatigue experiments were conducted on a pressure vessel steel, 16MnR, in ambient air. The uniaxial experiments were conducted using solid cylindrical specimens. Axial-torsion experiments employed thin-walled tubular specimens subjected to proportional and nonproportional loading. The true fracture stress and strain were obtained by testing solid shafts under monotonic torsion. Experimental results reveal that the material under investigation does not display significant nonproportional hardening. The material was found to display shear cracking under pure shear loading but tensile cracking under tension-compression loading. Two critical plane multiaxial fatigue criteria, namely, the Fatemi–Socie criterion and the Jiang criterion, were evaluated based on the experimental results. The Fatemi–Socie criterion combines the maximum shear strain amplitude with a consideration of the normal stress on the critical plane. The Jiang criterion makes use of the plastic strain energy on a material plane as the major contributor to the fatigue damage. Both criteria were found to correlate well with the experiments in terms of fatigue life. The predicted cracking directions by the criteria were less satisfactory when comparing with the experimentally observed cracking behavior under different loading conditions.

scholarly journals A FEM analysis of the settlement of a tall building situated on loess subsoil

2020 ◽  
Vol 10 (1) ◽  
pp. 519-526
Author(s):  
Krzysztof Nepelski
Keyword(s):  
Fem Analysis ◽  
Actual Process ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Modified Cam Clay ◽  
Linear Behaviour ◽  
Subsequent Calculation ◽  
Elastic Perfectly Plastic ◽  
Subsoil Model ◽  
Storey Building

AbstractIn order to correctly model the behaviour of a building under load, it is necessary to take into account the displacement of the subsoil under the foundations. The subsoil is a material with typically non-linear behaviour. This paper presents an example of the modelling of a tall, 14-storey, building located in Lublin. The building was constructed on loess subsoil, with the use of a base slab. The subsoil lying directly beneath the foundations was described using the Modified Cam-Clay model, while the linear elastic perfectly plastic model with the Coulomb-Mohr failure criterion was used for the deeper subsoil. The parameters of the subsoil model were derived on the basis of the results of CPT soundings and laboratory oedometer tests. In numerical FEM analyses, the floors of the building were added in subsequent calculation steps, simulating the actual process of building construction. The results of the calculations involved the displacements taken in the subsequent calculation steps, which were compared with the displacements of 14 geodetic benchmarks placed in the slab.

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