Amplitude Equation for a Dynamic Strain Aging Model: Beyond Linear Stability Analysis of Serrated Flow in Metallic Alloys

2000 ◽  
Vol 652 ◽  
Author(s):  
Sergey N. Rashkeev ◽  
Michael V. Glazov ◽  
Frédéric Barlat ◽  
Daniel J. Lege
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Qualitative Difference ◽  
Rate Sensitivity ◽  
Sudden Onset ◽  
Dynamic Strain ◽  
Strain Rates ◽  
Serrated Flow ◽  
Negative Strain Rate Sensitivity ◽  
First Case

ABSTRACTA method for construction of “processing windows” to avoid negative strain rate sensitivity and associated serrated flow in some aluminum alloys is described. The method is based on the amplitude Ginzburg-Landau (GL) equations and analysis of bifurcation diagrams. The mathematical technique developed in the present work was applied to a specific aluminum alloy, Al-0.4%Mg-0.2%Si considered earlier in the literature [1-3], and yielded good results in terms of predicting the negative strain rate sensitivity regions in the “strain rate “temperature” parameter space. Using the GL-analysis it was demonstrated that even though the instability area is located in the region of intermediate strain rates, a qualitative difference exists between the areas of (relatively) fast and (relatively) slow strain rates. In the first case the dynamic behavior of the system is supercritical, in the second case it is subcritical. The second case is highly undesirable because it causes a sudden onset of stable stress serrations that are difficult to suppress, while in the first case the development of instability is gradual and, consequently, more easily controllable.

Stress-State, Temperature, and Strain Rate Dependence of Vintage ASTM A7 Steel

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
S. A. Brauer ◽  
W. R. Whittington ◽  
H. Rhee ◽  
P. G. Allison ◽  
D. E. Dickel ◽  
...  
Keyword(s):  
Stress State ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Rate Dependence ◽  
Maximum Strength ◽  
Strain Rate Dependence ◽  
Dynamic Strain ◽  
Strength Increase ◽  
Negative Strain Rate Sensitivity

The structure–property relationships of a vintage ASTM A7 steel is quantified in terms of stress state, temperature, and strain rate dependence. The microstructural stereology revealed primary phases to be 15.8% ± 2.6% pearlitic and 84.2% ± 2.6 ferritic with grain sizes of 13.3 μm ± 3.1 μm and 36.5 μm ± 7.0 μm, respectively. Manganese particle volume fractions represented 0.38–1.53% of the bulk material. Mechanical testing revealed a stress state dependence that showed a maximum strength increase of 85% from torsion to tension and a strain rate dependence that showed a maximum strength increase of 38% from 10−1 to 103 s−1at 20% strain. In tension, a negative strain rate sensitivity (nSRS) was observed in the quasi-static rate regime yet was positive when traversing from the quasi-static rates to high strain rates. Also, the A7 steel exhibited a significant ductility reduction as the temperature increased from ambient to 573 K (300 °C), which is uncommon for metals. The literature argues that dynamic strain aging (DSA) can induce the negative strain rate sensitivity and ductility reduction upon a temperature increase. Finally, a tension/compression stress asymmetry arises in this A7 steel, which can play a significant role since bending is prevalent in this ubiquitous structural material. Torsional softening was also observed for this A7 steel.

Incorporation of Dynamic Strain Aging Into a Viscoplastic Self-Consistent Model for Predicting the Negative Strain Rate Sensitivity of Hadfield Steel

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
B. Bal ◽  
B. Gumus ◽  
D. Canadinc
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Strain Rate Sensitivity ◽  
Strain Aging ◽  
Rate Sensitivity ◽  
Atomic Level ◽  
Hadfield Steel ◽  
Dynamic Strain ◽  
Deformation Response ◽  
Negative Strain Rate Sensitivity

A new multiscale modeling approach is proposed to predict the contributions of dynamic strain aging (DSA) and the resulting negative strain rate sensitivity (NSRS) on the unusual strain-hardening response of Hadfield steel (HS). Mechanical response of HS was obtained from monotonic and strain rate jump experiments under uniaxial tensile loading within the 10−4 to 10−1 s−1 strain rate range. Specifically, a unique strain-hardening model was proposed that incorporates the atomic-level local instabilities imposed upon by the pinning of dislocations by diffusing carbon atoms to the classical Voce hardening. The novelty of the current approach is the computation of the shear stress contribution imposed on arrested dislocations leading to DSA at the atomic level, which is then implemented to the overall strain-hardening rule at the microscopic level. The new model not only successfully predicts the role of DSA and the resulting NSRS on the macroscopic deformation response of HS but also opens the venue for accurately predicting the deformation response of rate-sensitive metallic materials under any given loading condition.

scholarly journals Effect of Aging Process on the Strain Rate Sensitivity in V-Containing TWIP Steel

Metals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 126
Author(s):  
Shaoheng Sun ◽  
Zhiyong Xue
Keyword(s):  
Tensile Strength ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Strain Aging ◽  
Aging Process ◽  
Vanadium Carbide ◽  
Twip Steel ◽  
Rate Sensitivity ◽  
Dynamic Strain ◽  
Negative Strain Rate Sensitivity

The dynamic tensile behavior of the twinning-induced plasticity (TWIP) steel with the vanadium carbide is investigated at different strain rates of 10−4, 10−3, 10−2 and 0.05 s−1. Microstructure characterization, carried out using back scatter electron diffraction (EBSD) and transmission electron microscopy (TEM), shows a homogeneous face center cubic structured matrix with uniformly dispersed vanadium carbide. The vanadium carbide is controlled by the aging temperature and time. The best comprehensive mechanical properties are achieved when the tested steel is aged at 550 °C for 5 h. With the increase of strain rate, the tensile strength and work hardening rate decrease, and the tested material shows negative strain rate sensitivity. This would be due to an increase in stacking fault energy caused by temperature rise by adiabatic heating, which must suppress the formation of twinning. On the other hand, the strain rate sensitivity is affected by dynamic strain aging (DSA). With the increase of strain rate, the DSA weakens, which causes negative strain rate sensitivity. The tensile strength and strain rate sensitivity value both increase first and then decrease with the increase of vanadium carbide size. This is because the tensile strength is mainly affected by the vanadium carbide. In addition to the vanadium carbide, the strain rate sensitivity is also affected by the amount of solute atom (V and C) during the dynamic strain aging process.

scholarly journals A New Explanation for the Effect of Dynamic Strain Aging on Negative Strain Rate Sensitivity in Fe–30Mn–9Al–1C Steel

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3426 ◽  
Author(s):  
Jia Xing ◽  
Lifeng Hou ◽  
Huayun Du ◽  
Baosheng Liu ◽  
Yinghui Wei
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Dynamic Strain Aging ◽  
Strain Aging ◽  
Rate Sensitivity ◽  
Tensile Tests ◽  
Dynamic Strain ◽  
Strain Rates ◽  
Dislocation Arrangement ◽  
Hall Plot

In this study, the evolution of the mechanical properties of Fe–30Mn–9Al–1C steel has been determined in tensile tests at strain rates of 10−4 to 102 s−1. The results show that the strain rate sensitivity becomes a negative value when the strain rate exceeds 100 s−1 and this abnormal evolution is attributed to the occurrence of dynamic strain aging. Due to the presence of intergranular κ-carbides, the fracture modes of steel include ductile fracture and intergranular fracture. The values of dislocation arrangement parameter M were obtained using a modified Williamson–Hall plot. It has been found that once the strain rate sensitivity becomes negative, the interaction of dislocations in the steel is weakened and the free movement of dislocation is enhanced. Adiabatic heating promotes the dynamic recovery of steel at a high strain rate.

scholarly journals Negative Strain Rate Sensitivity Induced by Structure Heterogeneity in Zr64.13Cu15.75Ni10.12Al10 Bulk Metallic Glass

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 339
Author(s):  
Xiang Wang ◽  
Zhi Qiang Ren ◽  
Wei Xiong ◽  
Si Nan Liu ◽  
Ying Liu ◽  
...  
Keyword(s):  
Metallic Glass ◽  
Strain Rate ◽  
Bulk Metallic Glass ◽  
Strain Rate Sensitivity ◽  
Critical Role ◽  
Rate Sensitivity ◽  
Confined Compression ◽  
Negative Strain Rate Sensitivity ◽  
Cast Specimen ◽  
Structure Heterogeneity

The negative strain rate sensitivity (SRS) of metallic glasses is frequently observed. However, the physical essence involved is still not well understood. In the present work, small-angle X-ray scattering (SAXS) and high-resolution transmission electron microscopy (HRTEM) reveal the strong structure heterogeneity at nanometer and tens of nanometer scales, respectively, in bulk metallic glass (BMG) Zr64.13Cu15.75Ni10.12Al10 subjected to fully confined compression processing. A transition of SRS of stress, from 0.012 in the as-cast specimen to −0.005 in compression processed specimen, was observed through nanoindentation. A qualitative formulation clarifies the critical role of internal stress induced by structural heterogeneity in this transition. It reveals the physical origin of this negative SRS frequently reported in structurally heterogeneous BMG alloys and its composites.

Local Investigations of the Mechanical Properties of Ultrafine Grained Metals by Nanoindentations

2006 ◽  
Vol 503-504 ◽  
pp. 31-36 ◽  
Author(s):  
Johannes Mueller ◽  
Karsten Durst ◽  
Dorothea Amberger ◽  
Matthias Göken
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Room Temperature ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Fcc Metals ◽  
Angular Pressing ◽  
Ultrafine Grained ◽  
Indentation Strain

The mechanical properties of ultrafine-grained metals processed by equal channel angular pressing is investigated by nanoindentations in comparison with measurements on nanocrystalline nickel with a grain size between 20 and 400 nm produced by pulsed electrodeposition. Besides hardness and Young’s modulus measurements, the nanoindentation method allows also controlled experiments on the strain rate sensitivity, which are discussed in detail in this paper. Nanoindentation measurements can be performed at indentation strain rates between 10-3 s-1 and 0.1 s-1. Nanocrystalline and ultrafine-grained fcc metals as Al and Ni show a significant strain rate sensitivity at room temperature in comparison with conventional grain sized materials. In ultrafine-grained bcc Fe the strain rate sensitivity does not change significantly after severe plastic deformation. Inelastic effects are found during repeated unloading-loading experiments in nanoindentations.

Strain Rate Sensitivity of Mixed SAC-SnBi Solder Joints

2019 ◽  
Vol 2019 (1) ◽  
pp. 000480-000487
Author(s):  
Luke A. Wentlent ◽  
James Wilcox ◽  
Xuanyi Ding
Keyword(s):  
Melting Point ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Solder Joints ◽  
Volume Ratio ◽  
Rate Sensitivity ◽  
Thermal Exposure ◽  
Fracture Mechanisms ◽  
Eutectic System ◽  
Strain Rates

Abstract As the electronics industry continues to evolve a concerted effort has developed to implement lower melting point solders. The ability to minimize the thermal exposure that an assembly is subjected to affords significant benefits with respect to both the reliability and the materials that can be used. One of the most popular low melt solder alloys currently being investigated by the industry is the Bi-Sn eutectic system, which has a melting point of 139°C. The BiSn system itself is not particularly novel as it was posited as a SAC alternative during the initial shift from Pb based solders. While a body of knowledge currently exists regarding this system, and the near eutectic variant BiSnAg, there are still concerns regarding its ductility, especially as a function of thermal exposure and strain rate. Bismuth is widely acknowledged as a brittle element and its presence in such quantities raises concerns of not just Cu6Sn5 embrittlement but also solder fragility in high strain rate types of environments. A challenge with regards to near term implementation is that most packages are not available with BiSn solder bumps. Therefore, it will be necessary to use components already balled with SAC 305 solder. This means that the resulting solder interconnect, reflowed below conventional SAC reflow temperatures, will form a type of mixed hybrid microstructure. This non-equilibrium microstructure will be composed of two regions, one Bi-rich region which is well past saturation and a second region which is Bi-deficient. It is of specific industrial interest then to not just investigate the BiSn solder system but also within the context of a realistic mixed interconnect. Recent work by several researchers has shown that this hybrid microstructure is unstable and quite active with respect to the movement and localized concentration of the Bismuth. The degree of mixing of these two regions has been shown to be highly dependent upon reflow temperature and the paste to ball volume ratio. Mixed SAC-BiSn solder joints were formed by placing SAC 305 spheres on BiSn paste deposits for a paste to ball volume ratio of .18. These samples were then reflowed at either 175°C or 200°C. SAC 305 control samples were also made using a conventional Pb-free reflow profile with a peak temperature of 247°C. A 22 mil Cu-OSP pad on a 1.0 mm thick FR4 substrate was used for all samples. A selection of the solder joints were then isothermally aged at 90°C for 200 hours. Using a joint level micromechanical tester, ball shear tests were conducted at a range of strain rates for samples in the as-reflowed and aged state. Using this information, the strain rate sensitivity of the interconnects was mapped and correlated with the observed failure modes. Investigations into the fracture mechanisms were conducted by examining the shear fracture surface with optical and scanning electron microscopy. Additionally, the evolution of the microstructure was characterized. Results showed a clear transition from ductile solder failure to a brittle separation failure at the higher strain rates.

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