Multi-Axial Cyclic and Monotonic Behavior of a 63Sn-37Pb Solder Alloy

2001 ◽  
Author(s):  
T. Jesse Lim ◽  
Wei-Yang Lu
Keyword(s):  
Uniaxial Tension ◽  
Solder Alloy ◽  
Axial Stress ◽  
Equivalent Stress ◽  
Equivalent Strain ◽  
Monotonic Loading ◽  
Uniaxial Tensile ◽  
Pure Torsion ◽  
Strain Space ◽  
Equivalent Strain Amplitude

Abstract In this work, the cyclic and monotonic loading of both pure torsion and uniaxial behavior of 63Sn-37Pb solder alloy are compared. By comparing the monotonic loading, it is shown that the ultimate equivalent stress of both torsion and uniaxial tensile behavior is comparable; and the failure strain in uniaxial tension is considerably less than that of pure torsion. The fatigue life of this solder alloy under the same equivalent strain amplitude for both uniaxial tension-compression and pure torsion are also comparable. These data provide a baseline for investigating the behavior of the solder alloy in the multi-axial stress-strain space.

Elasto-plastic and creep behaviour of axially loaded, shouldered tubes

1980 ◽  
Vol 15 (1) ◽  
pp. 21-29 ◽  
Author(s):  
R J Dawson ◽  
H Fessler ◽  
T H Hyde ◽  
J J Webster
Keyword(s):  
Finite Element ◽  
Creep Behaviour ◽  
Equivalent Stress ◽  
Strain Curve ◽  
Equivalent Strain ◽  
Uniaxial Tensile ◽  
Plastic Strain Increment ◽  
Axially Loaded ◽  
Initial Strains ◽  
Creep Strains

This paper compares the finite element predictions of elasto-plastic and creep behaviour with experimental data for axially loaded, shouldered tube models. Four shouldered tube models were made of a lead alloy and tested at 61°C, using strain gauges to measure the elasto-plastic and creep strains in the plain tube and fillet regions of the models. Instantaneous stress-strain and creep data were obtained from strain-gauged, uniaxial tensile specimens. The finite element solutions are based on the incremental Prandtl-Reuss equations. The elasto-plastic iterative solutions use a ‘negative gradient’ from the calculated point to the equivalent stress-equivalent strain curve to get the next estimate of the plastic strain increment. A time incremental method is used to obtain the creep solutions. Tests with the mean tube stress below, at and above the yield stress showed very good agreement between prediction and measurement of initial strains in the fillets. Differences between predictions and measurements of creep strains are attributable to cast-to-cast variations.

Influence of Lode Angle on the ASME Local Strain Failure Criterion

2016 ◽  
Author(s):  
Kumarswamy Karpanan ◽  
William Thomas
Keyword(s):  
Experimental Data ◽  
Stress State ◽  
Tensile Testing ◽  
Failure Strain ◽  
Axial Stress ◽  
Equivalent Stress ◽  
Ductile Material ◽  
Uniaxial Tensile ◽  
Lode Angle ◽  
Triaxiality Factor

Failure strain at any point on a structure is not a constant but is a function of several factors, such as stress state, strain rate, and temperature. Failure strain predicted from the uniaxial tensile testing cannot be applied to the bi-axial or tri-axial stress state. ASME Sec VIII-Div-2, and −3 codes give methods to predict the failure strain for multi-axial stress state by considering the triaxiality factor, which is defined as the ratio of mean stress to the equivalent stress. Failure strain predicted by the ASME method (based on the Rice-Tracey ductile failure model) is an exponential curve that relates the failure strain to the triaxiality factor. The ASME VIII-3 method also gives procedures to calculate failure strain for various material types: ferritic, stainless steel, nickel alloy, aluminum, etc. Experimental results of failure strain at various stress states show that the failure strain is not only a function of the triaxiality factor, but also a function of the Lode angle. The Lode angle takes on the value of 1, 0, and −1 for tension, pure shear, and compression stress state, respectively. Experimental data shows that the failure strain is a 3D surface which has an exponential relation with triaxiality and a parabolic relation with the Lode angle. To validate the ASME failure strain prediction, this paper compares experimental failure strain test data from literature with the ASME predictions. The ASME predictions are non-conservative especially for moderately ductile materials such as aluminum and high strength carbon steel. A reduction factor on failure strain for low ductile material is presented using the relation between the R (yield/ultimate) and the stress ratio (shear/tensile stress). The ASME method does not account for the environmental effects while calculating the failure strain. High pressure, high temperature (HPHT) subsea components designed using ASME VIII-3 code are subjected to various environments in subsea, such as seawater, seawater with cathodic protection (CP) and production fluid (crude oil). Experimental data shows that the Elongation (EL) and/or Reduction in Area (RA) from tensile testing decrease in these environments. Therefore, to account for any environment effect on the failure strain, reduced EL and RA can be used to predict the failure strain.

Research on NX-Based Progressive Die Design

2012 ◽  
Vol 602-604 ◽  
pp. 1818-1821
Author(s):  
Jun Liu ◽  
Cong Dong Ji
Keyword(s):  
Design Method ◽  
Equivalent Stress ◽  
Equivalent Strain ◽  
Die Design ◽  
Support Design ◽  
Stress Resilience ◽  
Progressive Die ◽  
Key Technology ◽  
Product Manufacturing ◽  
Progressive Die Design

Progressive die has been widely used in product manufacturing field. This paper proposed a NX-based computer server support design method. The equivalent stress, resilience, equivalent strain, attenuation, and forming were analyzed in detail. The key technology of confirming blank dimension and stock layout of server support were explicated clearly.

A State Variable Modeling of Plasticity and Necking Under Uniaxial Tension

1992 ◽  
Vol 114 (4) ◽  
pp. 378-383 ◽  
Author(s):  
G. Ferron ◽  
H. Karmaoui Idrissi ◽  
A. Zeghloul
Keyword(s):  
Strain Rate ◽  
Uniaxial Tension ◽  
Plastic Flow ◽  
Constitutive Equations ◽  
Growth Process ◽  
Constant Strain Rate ◽  
Uniaxial Tensile ◽  
Long Wavelength ◽  
State Variable ◽  
Diffusion Controlled

Constitutive equations based on a state variable modeling of the thermo-viscoplastic behavior of metals are discussed, and incorporated in an exact, long-wavelength analysis of the neck-growth process in uniaxial tension. The general formalism is specialized to the case of f.c.c. metals in the range of intragranular, diffusion controlled plastic flow. The model is shown to provide a consistent account of aluminum behavior both under constant strain-rate and creep. Calculated uniaxial tensile ductilities and rupture lives in creep are also compared with experiments.

scholarly journals White-light speckle image correlation applied to large-strain material characterization

2009 ◽  
pp. 377-392
Author(s):  
Giovanni B. Broggiato ◽  
Luca Cortese
Keyword(s):  
Material Characterization ◽  
Plastic Material ◽  
Large Strain ◽  
Equivalent Stress ◽  
Tensile Tests ◽  
Equivalent Strain ◽  
Image Correlation ◽  
Plastic Behavior ◽  
Full Field ◽  
Measurement Devices

In experimental mechanics, the possibility of tracking on component surfaces the full-field stress and strain states during deformation can be utilized for many purposes such as formability limits determination, quantification of stress intensification factors, material characterization and so on. Concerning the last topic, an interesting application could be a direct identification of the elasto-plastic material response up to large deformation. It is well known, in fact, that with traditional measurement devices it is possible to retrieve the true equivalent stress versus true equivalent strain data from tensile tests only up to the onset of necking, where localization starts to occur. This work aims to show how from the knowledge of a tensile test full-field strain and of load data it will be possible to obtain the full-stress field as well as the complete material elasto-plastic behavior.

Cyclic Deformation Behavior and Dislocation Substructures of Hexagonal Zircaloy-4 Under Out-of-Phase Loading

1999 ◽  
Vol 122 (1) ◽  
pp. 42-48 ◽  
Author(s):  
Xiao Lin
Keyword(s):  
Phase Angle ◽  
Maximum Shear Stress ◽  
Equivalent Stress ◽  
Strain Range ◽  
Equivalent Strain ◽  
Mean Value ◽  
Shear Stresses ◽  
Phase Cycling ◽  
Variation Range ◽  
Additional Hardening

Macroscopic response and microscopic dislocation structures of Zr-4 subjected to biaxial fatigue under different phase angles of 30°, 60°, 90° and different equivalent strain ranges of 0.8%, 0.6%, 0.4% were studied. The testing results show that the delay angle between the stress deviators and strain increment tensors is strongly dependent on phase angle and the equivalent strain range. When phase angle equals 60°, the delay angle has the minimum variation range for all specimens. The mean value of the delay angle decreases with increasing phase angle or the equivalent strain range. The variation range and average value of the Mises equivalent stress have the maximum in S3 with the phase angle of 90°. They decrease as the equivalent strain range decreases. Zr-4 displays a pronounced initial hardening followed by a continuous softening for all specimens during out-of-phase cycling. The stabilized saturation stresses of Zr-4 under out-of-phase cycling are much higher than that under uniaxial cycling. It indicates that Zr-4 displays an obvious additional hardening. As the phase angle increases, the typical dislocation structure changes from dislocation cells to tangles. The dislocation-dislocation interactions increase resulting in an additional hardening. In essence, the degree of additional hardening depends, among other factors, on the maximum shear stress ratio of resolved shear stresses and critical resolved shear stresses (RSS/CRSS). [S0094-4289(00)00601-0]

Experimental and Numerical Investigation of High-Temperature Multi-Axial Fatigue

2021 ◽  
Author(s):  
Harish Ramesh Babu ◽  
Marco Böcker ◽  
Mario Raddatz ◽  
Sebastian Henkel ◽  
Horst Biermann ◽  
...  
Keyword(s):  
Gas Turbines ◽  
Biaxial Loading ◽  
Complex Geometry ◽  
Low Cycle Fatigue ◽  
Axial Stress ◽  
Equivalent Stress ◽  
Turbine Blades ◽  
Damage Development ◽  
Simulation Results ◽  
Axial Fatigue

Abstract Gas turbines and aircraft engines are dominated by cyclic operating modes with fatigue-related loads. This may result in the acceleration of damage development on the components. Critical components of turbine blades and discs are exposed to cyclic thermal and mechanical multi-axial fatigue. In the current work, planar-biaxial Low-Cycle-Fatigue tests are conducted using cruciform specimens at different test temperatures. The influence on the deformation and lifetime behaviour of the nickel-base disk alloy IN718 is investigated at selected cyclic proportional loading cases. The calculation of the stress and strain distribution of the cruciform specimens from the experimental data is difficult to obtain due to complex geometry and temperature gradients. Therefore, there is a need for Finite Element Simulations. A viscoplastic material model is considered to simulate the material behaviour subjected to uniaxial and the selected planar-biaxial loading conditions. At first, uniaxial simulation results are compared with the uniaxial experiment results for both batches of IN718. Then, the same material parameters are used for simulating the biaxial loading cases. The prediction of FE simulation results is in good agreement with the experimental LCF test for proportional loadings. The equivalent stress amplitude results of the biaxial simulation are compared with the uniaxial results. Furthermore, the lifetime is calculated from the simulation and by using Crossland and Sines multi-axial stress-based approaches. The Crossland model predicts fatigue life significantly better than the Sines model. Finally, the simulated lifetime results are compared with the experimental lifetime

scholarly journals The generalized criterion of multiaxial random fatigue based on conception proposed by prof. Macha

2019 ◽  
Vol 300 ◽  
pp. 15001
Author(s):  
Tadeusz Łagoda ◽  
Marta Kurek ◽  
Karolina Łagoda
Keyword(s):  
Shear Stress ◽  
Complex Number ◽  
Mathematical Problem ◽  
Equivalent Stress ◽  
Complex Stress ◽  
Complex Numbers ◽  
Pure Bending ◽  
Pure Torsion ◽  
Special Cases ◽  
Random Fatigue

This criterion has been repeatedly verified, analyzed and special cases of this criterion reducing complex stress to equivalent uniaxial were taken into account. Since both normal and shear stress are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to understand the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it was proposed to adopt a system of complex numbers. Normal stress was defined as the real part and shear stress as imaginary part. As a result, on the basis of the defined complex number and basing on pure bending and pure torsion after transformations, the expression for equivalent stress was identical to the previously proposed criteria defined on the basis of the concept of prof. Macha.

scholarly journals Efficiency of Plasticity Correction in the Hole-Drilling Residual Stress Measurement

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3396
Author(s):  
Tomáš Návrat ◽  
Dávid Halabuk ◽  
Petr Vosynek
Keyword(s):  
Residual Stress ◽  
Stress State ◽  
Uniaxial Tension ◽  
Relative Error ◽  
Computational Simulation ◽  
Equivalent Stress ◽  
Biaxial Stress ◽  
Hole Drilling ◽  
Plane Shear ◽  
Plasticity Effect

This paper focuses on the analysis of the plasticity effect in the measurement of the residual stress by the hole-drilling method. Relaxed strains were evaluated by the computational simulation of the hole-drilling experiment using the finite element method. Errors induced by the yielding were estimated for uniaxial tension, plane shear stress state and equi-biaxial stress state at various magnitudes of residual stress uniformly distributed along the depth. The correction of the plasticity effect in the evaluation of residual stress was realized according to the method proposed by authors from the University in Pisa, which was coded in MATLAB. Results obtained from the MATLAB script were compared to the original input data of the hole-drilling simulation and discussed. The analyses suggested that the plasticity effect is negligible at the ratio of applied equivalent stress to yield stress, being 0.6, and that the correction of the plasticity effect is very successful at the previous ratio, being 0.9. Failing to comply with the condition of the strain gauge rosette orientation according to the principal stresses directions causes an increase in the relative error of corrected stresses only for the case of uniaxial tension. It affects the relative error negligibly for the plane shear and equi-biaxial stress states.

Numerical Simulation of Double Rollers Clamping Spinning Process for Flanging

2010 ◽  
Vol 97-101 ◽  
pp. 2987-2990 ◽  
Author(s):  
Sheng Dun Zhao ◽  
S.Q. Fan ◽  
Q. Zhang ◽  
C.H. Wang
Keyword(s):  
Wall Thickness ◽  
Feed Rate ◽  
Equivalent Stress ◽  
Equivalent Strain ◽  
Simulation Code ◽  
New Process ◽  
3D Simulation Model ◽  
Spinning Process ◽  
Simulated Distribution ◽  
Wall Thickness Increase

Double rollers clamping spinning (DRCS) is a new process to form thin-walled rotary shell parts with complex flange, which adopts two rollers to clamp the workpiece in the forming. Using FE simulation code ABAQUS/Explicit, the 3D simulation model of DRCS process for flanging is established, and the whole DRCS process and material deformation have been simulated. Distribution of equivalent stress, equivalent strain and wall thickness of flange in the DRCS process are obtained. And then, the effects of roller feed rate and flange length on the formed flange part are studied. Results show that equivalent stress, equivalent strain and reduction in wall thickness increase with the decrease of roller feed rate, while increase with the increase of flange length. The results obtained in this paper can provide the references to determine and optimize the new spinning process parameters.

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