Elastic-viscoplastic Constitutive Model Research Articles

An analysis of the temperature and rate dependence of Charpy V-notch energies for a high nitrogen steel

The brittle-ductile transition for a high nitrogen steel is investigated by numerical analyses of the Charpy impact test. The material is described in terms of an elastic-viscoplastic constitutive model that accounts for the nucleation and growth of micro-voids, leading to ductile fracture, as well as for cleavage failure by micro-crack nucleation. The temperature dependence of flow strength and strain hardening is included in the model, and this leads to the prediction of a transition from cleavage fracture to predominantly ductile fracture as the temperature increases. For the particular steel considered it is found that the variation of strain hardening with temperature has a strong effect on the failure mode transition. Both slow loading and impact loading of the Charpy specimen are analyzed. Most of the computations are based on a quasi-static formulation since, even at the strain rates encountered in the Charpy impact test, material strain rate sensitivity is the main time effect. The influence of material inertia is investigated in a few transient analyses.

Dynamic tensile tests with superimposed ultrasonic oscillations for stainless steel type 321 at room temperature

In recent years various containment codes for Fast Breeder Reactor accidents have been assessed by comparison with explosion tests in water-filled vessels (COVA experiments). Common to the various codes, a systematic underestimation of the circumferential vessel strains was found. In the COVA tests high frequency pressure oscillations in the ultrasonic range were observed and thus it has been conjectured that the phenomenon of “acoustic softening” might be relevant in explaining the discrepancies in the strains. To validate this conjecture a hydro-pneumatic tensile test apparatus was developed which allows dynamic tensile testing at room temperature with and without superimposed ultrasonic oscillations. The dynamic tensile tests on the COVA sheet material (stainless steel AISI 321) without ultrasonic insonation show a linear dependence of the flow stress on the logarithm of the strain rate. The results at low strain rates (10 −3 s −1) agree favourably with previous measurements but at high rates (50 s −1) at 20% lower flow stress is observed. The dynamic tensile tests with continuous and intermittent insonation show the phenomenon of “acoustic softening”: The average flow stress is reduced by an amount of about half the oscillating amplitude. At high strain rates the reduction is less. A severe “acoustic softening” observed by several authors for various metals at low strain rates was not observed. The experimental results were compared with the theory of the superposition mechanism assuming a rate-independent elastic-plastic and an elastic-viscoplastic constitutive model. Although the rate-independent model is capable to predict qualitatively some of the observed effects, a better description is obtained with the viscoplastic model. The conclusion is that the “acoustic softening” of the COVA material is far too small to explain the discrepancies between measured and computed strains found in the containment code validation studies.

Effect of material rate sensitivity on failure modes in the Charpy V-notch test

For the C harpy V-notch test the influence of strain rate on competing failure mechanisms is analyzed numerically. The nucleation and growth of micro-voids is represented in terms of an elastic-viscoplastic constitutive model, which describes the mechanism of ductile fracture by void coalescence. Failure by cleavage is assumed to occur if the maximum principal tensile stress exceeds a certain critical value. Attention is focused on the temperature regime where the transition in fracture mode between cleavage and ductile rupture takes place. In the analyses the temperature is taken as constant and the effect of inertia is neglected, so that time dependence enters only through the material strain rate sensitivity. The material model is found to reproduce the experimentally observed change in failure mode from predominantly ductile fracture at low strain rates, to cleavage fracture at high strain rates. The numerical results show that in the transition regime, the porosity in the notch tip region plays a role in the fracture process even when failure occurs by cleavage. Once the transition of failure mode from cleavage to ductile rupture has occurred, the energy absorbed at low rates is greater than that absorbed at high rates.

Interpretation of shock-wave data for beryllium and uranium with an elastic-viscoplastic constitutive model

We have developed a new elastic-viscoplastic constitutive model for metals which can easily be incorporated into a one-dimensional Lagrangian hydrodynamic computer code. Rather than the usual constant relaxation time, we have used one which is a function of temperature (i.e., thermal energy) and strain rate. This allows us to successfully calculate shock-wave profiles, including the effect of spall, in beryllium and uranium over a wide range of stress, temperature, strain, and strain rate.

Graphical analysis of accelerated life test data with a mix of failure modes : Wayne Nelson. IEEE Trans. Reliab.R-24 (4), 230 (1975)

An experimental investigation was combined with a non-linear finite element analysis using an elastic–viscoplastic constitutive model to study the effect of ball shear speed on the shear forces of BGA solder joints. Two solder compositions were examined in this work: Sn–3.5Ag and Sn–3.5Ag–0.75Cu. The Cu substrates had been surface finished electrolytically with a 7 μm thick Ni diffusion barrier followed by an 0.5 μm thick Au layer to enhance solderability. Ag3Sn and a few AuSn4 intermetallic compound (IMC) particles were found inside the two solders. Only a continuous Ni3Sn4 layer was observed at the interface between the Au/Ni plated layer and the Sn–3.5Ag, while a continuous (Ni1−xCux)3Sn4 layer and a small amount of discontinuous (Cu1−yNiy)6Sn5 particles were formed at the interface between the substrate and the Sn–3.5Ag–0.75Cu. The IMC was identified using energy dispersive spectrometer (EDS) and electron probe micro analysis (EPMA). Shear tests were carried out over a shear speed range from 10 to 700 μm/s at a shear ram height of 50 μm. The shear force was observed to linearly increase with shear speed and reach a maximum value at the highest shear speed in both the experimental and the computational results. All test specimens fractured in a ductile mode. The failure mechanisms were discussed in terms of von Mises stresses and plastic strain energy density distributions.