Measurement of Monotonic Biaxial Elastoplastic Stresses at Notch Roots

1991 ◽  
Vol 58 (4) ◽  
pp. 916-922 ◽  
Author(s):  
W. N. Sharpe
Keyword(s):  
Effective Stress ◽  
Notch Root ◽  
Sheet Material ◽  
Thin Sheet ◽  
Strain Curve ◽  
Local Stress ◽  
Uniaxial Stress ◽  
Maximum Deviation ◽  
Principal Stresses ◽  
Interferometric Technique

Biaxial principal strains were measured at the roots of notches in aluminum specimens with a laser-based interferometric technique. Interference patterns from three tiny indentations spaced 150 or 200 micrometers apart in an orthogonal pattern were monitored with a microcomputer-controlled system. Elastoplastic strains up to one percent were measured in real time with a resolution of 25 microstrain. Procedures were developed for computing the two principal stresses from the incremental strain data using J2-flow theory. The validity of the computations was checked by computing the stresses in smooth tensile specimens. Anisotropy in the thin sheet material leads to errors in the computed lateral stresses (which should be zero), but the maximum deviation of the computed effective stress from the uniaxial stress is only five percent. Three kinds of double-notched specimens were prepared to vary the amount of constraint at the notch root. These were tested under monotonic tensile loading and the biaxial notch-root strains recorded. There is considerable variation among the strains once the elastic limit is passed. This is due primarily to the local inhomogeneity of plastic strain, since the gage length of the measurement is only a few times larger than the grain size of the material. Local biaxial stresses were computed from the measured strains for the three cases. The nature of the material’s stress-strain curve tends to smooth out the variations among tests, particularly when the effective stress is computed. It is discovered that the local stress predicted by the Neuber relation agrees very closely with the measured local effective stress.

Evaluation of a Modified Monotonic Neuber Relation

1991 ◽  
Vol 113 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. N. Sharpe ◽  
K. C. Wang
Keyword(s):  
Plane Strain ◽  
Notch Root ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Predictive Capability ◽  
Stress Strain Curve ◽  
Interferometric Technique ◽  
Strain Stress ◽  
Concentration Factors ◽  
Elastoplastic Strains

It has been proposed in the literature that the Neuber relation be modified to read Kε/Kt×(Kσ/Kt)m=1 in order to improve its predictive capability when plane strain loading conditions exist. Kε, Kσ, and Kt are respectively the strain, stress, and elastic concentration factors. The exponent m is proposed to be 1 for plane stress and 0 for plane strain. This paper reports the results of biaxial notch root strain measurements on three sets of double-notched aluminum specimens that have different thicknesses and root radiuses. Elastoplastic strains are measured over gage lengths as short as 150 micrometers with a laser-based in-plane interferometric technique. The measured strains are used to compute Kε directly and Kσ using the uniaxial stress-strain curve. The exponent m can then be determined for each amount of constraint. The amount of constraint is defined as the negative ratio of lateral to longitudinal strain at the notch root and determined from elastic finite element analyses. As this ratio decreases for the three cases, the values of m are found to be 0.65, 0.48, and 0.36. The modified Neuber relation is an improvement, but discrepancies still exist when plastic yielding begins at the notch root.

scholarly journals Development of Microstructures with Improved Cryogenic Toughness Through Local Variations in Stress State: Aluminum-Lithium Alloys

1990 ◽  
Vol 186 ◽  
Author(s):  
K. T. Venkateswara Rao ◽  
R. O. Ritchie
Keyword(s):  
Stress State ◽  
Sheet Material ◽  
Thin Sheet ◽  
Local Stress ◽  
Cryogenic Temperatures ◽  
Aluminum Lithium ◽  
Thin Sheet Material ◽  
Local Stress State ◽  
Crack Tip Constraint ◽  
Induced Changes

AbstractMicrostructurally-induced changes in the local stress state (triaxial constraint) and their effect on fracture-toughness behavior are examined at ambient and cryogenic temperatures in an Al-Li-Cu-Zr alloy, processed in the form of 12.7 mm-thick "naturally laminated" plate containing aligned-weak interfaces and 1.6 mm-thin unlaminated sheet. It is shown that marked improvements in long-transverse (L-T) toughness can be achieved in the plate material at cryogenic temperatures by promoting through-thickness delamination along these interfaces, which relaxes local constraint and promotes a fracture-mode transition from global plane strain to local plane stress. Conversely, in thin sheet material, the absence of such interface delamination leads to a reduction in toughness with decrease in temperature, consistent with the greater degree of crack-tip constraint.

scholarly journals A 3D finite element model for reinforced concrete structures analysis

2011 ◽  
Vol 4 (4) ◽  
pp. 548-560 ◽  
Author(s):  
G. F. F. Bono ◽  
A. Campos Filho ◽  
A. R. Pacheco
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Concrete Structures ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Element Model ◽  
Reinforced Concrete Structures ◽  
Principal Stresses ◽  
Stress Strain

This work presents a numerical model for 3D analyses through the finite element method of reinforced concrete structures subjected to monotonic loads. The proposed model for concrete is orthotropic and uses the equivalent uniaxial strain concept. The equivalent uniaxial stress-strain relation is generalized to take into account the triaxial stress conditions. The parameters used in the equivalent uniaxial stress-strain curve are determined from the failure surface defined in the principal stress space. The implementation in finite elements is based on the consideration of smeared cracks with cracks rotating according to the directions of the principal stresses. Also, an embedded reinforcement model was implemented to represent existent reinforcing bars. Finally, some results are compared with experimental data from the literature to demonstrate the validity of the numerical model developed.

Fatigue Analysis of Notched Shafts under Multiaxial Synchronous Cyclic Loading

2007 ◽  
Vol 348-349 ◽  
pp. 233-236
Author(s):  
N. Pitatzis ◽  
G. Savaidis ◽  
A. Savaidis ◽  
Chuan Zeng Zhang
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Notch Root ◽  
Strain Curve ◽  
Local Stress ◽  
Fatigue Loading ◽  
Material Behavior ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Von Mises

Parametrical elastic-plastic finite element analyses of a circumferentially notched shaft subjected to multiaxial synchronous fatigue loading are performed considering two load combinations: (1) constant tension with cyclic torsion and (2) constant torsion with cyclic tensioncompression. The load amplitudes and the mean loads are varied to investigate their influences on the local stress-strain responses. The Multilayer Plasticity Model of Besseling in conjunction with the von Mises yield criterion is applied to describe the elastic-plastic material behavior. Coarse and fine meshes as well as three different types of multilinear approximations (twenty-, five- and threesegments) of the material stress-strain curve are used. Numerical results are presented to reveal the mutual interactions between the applied normal and torsional loads and the stress-strain response at the notch-root.

To the Influence of the Deformation Speed on Hardening Process during the Cold Sheet Forming

2018 ◽  
Vol 284 ◽  
pp. 513-518 ◽  
Author(s):  
Sergey A. Tipalin ◽  
Michael A. Petrov ◽  
N.F. Shpunkin
Keyword(s):  
Sheet Metal Forming ◽  
Metal Forming ◽  
Sheet Material ◽  
Thin Sheet ◽  
Hardening Process ◽  
Deformation Speed ◽  
Thin Sheet Material ◽  
Simulation Results ◽  
Hardening Curve ◽  
Material Forming

The accuracy of the simulation results of stamping processes of thin sheet material depends on the correct properties’ specification, namely stamping ability. Experiments have been carried out and the influence of the deformation speed on the hardening exponent during cold sheet metal forming was studied. It was found out, that strain changed 100 times can influence the strain grade of the hardening curve of about 10%. This regularity has been taken into consideration prior to the calculation in any CAE-software for material forming.

The Use of Strain Energy and Fracture Correlation to Determine Life Expectancy for Notched Components

2009 ◽  
Author(s):  
Onome Scott-Emuakpor ◽  
Tommy George ◽  
Charles Cross ◽  
M.-H. Herman Shen
Keyword(s):  
Fatigue Life ◽  
Stress Concentration ◽  
Cross Section ◽  
Strain Energy ◽  
Notch Root ◽  
Stress Gradient ◽  
Strain Curve ◽  
Experimental Results ◽  
Cyclic Process ◽  
Notched Components

An energy-based method for predicting fatigue life of half-circle notched specimens, based on the nominal applied stress amplitude, has been developed. This developed method is based on the understanding that the total strain energy dissipated during a monotonic fracture and a cyclic process is the same material property, where the density of each can be determined by measuring the area underneath the monotonic true stress-strain curve and measuring the sum of the area within each Hysteresis loop in the cyclic process, respectively. Using this understanding, the criterion for determining fatigue life prediction of half-circle notched components is constructed by incorporating the stress gradient effect through the notch root cross-section. Though fatigue at a notch root is a local phenomenon, evaluation of the stress gradient through the notch root cross-section is essential for incorporating this method into finite element analysis minimum potential energy process. The validation of this method was carried out by comparison with both notched and unnnotched experimental fatigue life of Aluminum 6061-T6 (Al 6061-T6) specimens under tension/compression loading at the theoretical notch fatigue stress concentration factor of 1.75. The comparison initially showed a slight deviation between prediction and experimental results. This led to the analysis of strain energy density per cycle up to failure, and an improved Hysteresis representation for the energy-based prediction analysis. With the newly developed Hysteresis representation, the energy-based prediction comparison shows encouraging agreement with unnotched experimental results and a theoretical notch stress concentration value.

Elastomer Behavior IV. Loop Structure of Elastomer Networks

1966 ◽  
Vol 39 (5) ◽  
pp. 1489-1495
Author(s):  
L. C. Case ◽  
R. V. Wargin
Keyword(s):  
Experimental Data ◽  
Crosslink Density ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Polymer Chains ◽  
Theoretical Treatment ◽  
Loop Structure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Selection Of

Abstract A new theoretical treatment strongly indicates that an elastomer network actually consists of a system of fused, closed, interpenetrating loops of polymer chains. This interpenetrating loop structure restricts the movement of the chains and thereby affects the stress-strain behavior of the elastomer. Methods have been developed to enable the calculation of the number of effective crosslinks caused by loop interpenetrations (virtual crosslinks). The uniaxial stress-strain behavior of an elastomer predicted using our methods can be fitted almost perfectly to published experimental data by proper selection of chain parameters. Previous theoretical treatments gave only a qualitative fit to the experimental data for the stress-strain behavior of elastomers and were not capable of predicting the correct shape of the experimental stress-strain curve. The present treatment gives a nearly perfect fit for both stress as a function of strain at constant crosslink density, and stress as a function of crosslink density at constant strain, and thus represents a vast improvement.

Viscoplastic Behavior of a Notch Root at 650°C: ISDG Measurement and Finite Element Modeling

1996 ◽  
Vol 118 (1) ◽  
pp. 88-93 ◽  
Author(s):  
Keyu Li ◽  
William N. Sharpe
Keyword(s):  
Finite Element ◽  
Notch Root ◽  
Tensile Creep ◽  
Strain Gages ◽  
Controlled System ◽  
Interferometric Technique ◽  
Pure Silicon ◽  
Nickel Based Superalloy ◽  
Silicon Coating ◽  
Computer Controlled

Viscoplastic behavior of the nickel-based superalloy, Inconel 718, at a notch root has been investigated by conducting isothermal tensile, creep and cyclic elastoplastic tests at 650°C which is the working temperature of the material in aircraft engines. A laser-based interferometric technique was extended to measure biaxial strains over a gage length of 150 μm at the notch root; the computer controlled system permits real-time measurements. A thin-film pure silicon coating and an argon atmosphere were used to prevent oxidation of the reflective indentations that serve as the strain gages. The measured strains were used to evaluate the Bodner-Partom constitutive model which was incorporated into the ABAQUS finite element code. Material constants in the model were determined from uniaxial tests on smooth specimens. The predicted strains agree reasonably well with the measured ones for all three kinds of loadings.

scholarly journals Fracturing and Porosity Channeling in Fluid Overpressure Zones in the Shallow Earth’s Crust

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Daniel Koehn ◽  
Sandra Piazolo ◽  
Till Sachau ◽  
Renaud Toussaint
Keyword(s):  
Effective Stress ◽  
Fluid Pressure ◽  
Mean Stress ◽  
High Porosity ◽  
Principal Stresses ◽  
Pressure Buildup ◽  
Failure Patterns ◽  
Vertical Zone ◽  
High Fluid ◽  
Fluid Overpressures

At the time of energy transition, it is important to be able to predict the effects of fluid overpressures in different geological scenarios as these can lead to the development of hydrofractures and dilating high-porosity zones. In order to develop an understanding of the complexity of the resulting effective stress fields, fracture and failure patterns, and potential fluid drainage, we study the process with a dynamic hydromechanical numerical model. The model simulates the evolution of fluid pressure buildup, fracturing, and the dynamic interaction between solid and fluid. Three different scenarios are explored: fluid pressure buildup in a sedimentary basin, in a vertical zone, and in a horizontal layer that may be partly offset by a fault. Our results show that the geometry of the area where fluid pressure is successively increased has a first-order control on the developing pattern of porosity changes, on fracturing, and on the absolute fluid pressures that sustained without failure. If the fluid overpressure develops in the whole model, the effective differential and mean stress approach zero and the vertical and horizontal effective principal stresses flip in orientation. The resulting fractures develop under high lithostatic fluid overpressure and are aligned semihorizontally, and consequently, a hydraulic breccia forms. If the area of high fluid pressure buildup is confined in a vertical zone, the effective mean stress decreases while the differential stress remains almost constant and failure takes place in extensional and shear modes at a much lower fluid overpressure. A horizontal fluid pressurized layer that is offset shows a complex system of effective stress evolution with the layer fracturing initially at the location of the offset followed by hydraulic breccia development within the layer. All simulations show a phase transition in the porosity where an initially random porosity reduces its symmetry and forms a static porosity wave with an internal dilating zone and the presence of dynamic porosity channels within this zone. Our results show that patterns of fractures, hence fluid release, that form due to high fluid overpressures can only be successfully predicted if the geometry of the geological system is known, including the fluid overpressure source and the position of seals and faults that offset source layers and seals.

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