Accounting for strain hardening and strain rate effects in fluid-to-fluid /hydrostatic/ extrusion
Strain hardening and strain rate effects in fluid to fluid hydrostatic extrusion
GAS FLOW↗
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Stress and strain distributions in a thick- walled cylinder of strain-hardening material, elastic-plastically strained by internal pressure
Stress-strain distributions in thick walled cylinder of strain-hardening material, elastic- plastically strained by internal pressure
STRESS-STRAIN DISTRIBUTION↗
Extraordinary Strain Hardening from Dislocation Loops in Defect-Free Al Nanocubes
The complex interaction of crystalline defects leads to strain hardening in bulk metals. Metals with high stacking fault energy (SFE), such as aluminum, tend to have low strain hardening rates due to an inability to form stacking faults and deformation twins. Here, we use in situ SEM mechanical compressions to find that colloidally synthesized defect-free 114 nm Al nanocubes combine a high linear strain hardening rate of 4.1 GPa with a high strength of 1.1 GPa. These nanocubes have a 3 nm self-passivating oxide layer that has a large influence on mechanical behavior and the accumulation of dislocation structures. Post-compression TEM imaging reveals stable prismatic dislocation loops and the absence of stacking faults. MD simulations relate the formation of dislocation loops and strain hardening to the surface oxide. These results indicate that slight modifications to surface and interfacial properties can induce enormous changes to mechanical properties in high SFE metals.
36 MATERIALS SCIENCE↗
Atomic faulting induced exceptional cryogenic strain hardening in gradient cell–structured alloy
Coarse-grained materials are widely accepted to display the highest strain hardening and the best tensile ductility. We experimentally report an attractive strain hardening rate throughout the deformation stage at 77 kelvin in a stable single-phase alloy with gradient dislocation cells that even surpasses its coarse-grained counterparts. Contrary to conventional understanding, the exceptional strain hardening arises from a distinctive dynamic structural refinement mechanism facilitated by the emission and motion of massive multiorientational tiny stacking faults (planar defects), which are fundamentally distinct from the traditional linear dislocation–mediated deformation. In conclusion, the dominance of atomic-scale planar deformation faulting in plastic deformation introduces a different approach for strengthening and hardening metallic materials, offering promising properties and potential applications.
Gradient dislocation structure↗
Link statistics of dislocation network during strain hardening
Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.
Crystal plasticity↗
Bending of rectangular plates with nonlinear strain-hardening creep.
Metal rectangular plate bending analysis with nonlinear strain hardening, creep yielding stress and deflection expressions as functions of position and time
RECTANGULAR PLATE↗
Crystallographic orientation-dependent strain hardening in a precipitation-strengthened Al-Cu alloy
While the strengthening of Al-Cu alloys due to precipitation has been extensively studied, the effect of crystallographic orientation of the matrix and precipitates, as well as precipitate morphology, on the strain hardening behavior is not well understood. In this paper, we investigate this effect with in situ neutron diffraction during deformation of an Al-Cu alloy (206) after multiple aging treatments. Precipitate-dislocation interactions were found to change from precipitate shearing for microstructures predominantly containing GPI and θ" precipitates to Orowan looping for microstructures with primarily θ' and θ precipitates. Notably, significant anisotropy in strain hardening behavior was observed when θ' precipitates were present, which was attributed to crystallographic orientation dependent load transfer from the Al matrix to the θ' precipitates. The anisotropic load transfer is hypothesized to be caused by the extent of rotation of high aspect-ratio θ' precipitates, owing to dislocations looping around them during plastic deformation of the matrix. Predictions from an analytical model describing the anisotropic magnitude of load transfer from precipitate rotation agree well with experimental results, successfully validating the precipitate rotation hypothesis and explaining the anisotropic strain hardening behavior. This model allows for the prediction of stresses separately in the precipitate and matrix phases as a function of crystallographic orientation, only given the bulk mechanical properties.
36 MATERIALS SCIENCE↗
Strain hardening magnesium-silicate-hydrate composites (SHMSHC) reinforced with short and randomly oriented polyvinyl alcohol microfibers
Magnesium-silicate-hydrate (M-S-H) cement has emerged as an alternative binder with potentially lower energy requirements and emissions. Due to the intrinsically low pH values of its matrix, however, normal steel reinforcement is not appropriate for M-S-H system. To toughen the matrix and to overcome the brittle nature of the material, a new strain hardening magnesium-silicate-hydrate composite (SHMSHC) is developed for the first time by incorporating 2 vol% short and randomly oriented polyvinyl alcohol (PVA) microfibers. The resulting SHMSHC exhibits significant strain hardening with a tensile strain capacity of more than 3%, a compressive strength beyond 50 MPa and a tensile strength of around 3 MPa. Remarkably, saturated multiple cracking with a tight crack width less than 10 μm invisible to the human naked eyes was observed. The newly developed SHMSHC addresses the fundamental challenge of M-S-H binder and is expected to widen possible application areas of M-S-H system.
36 MATERIALS SCIENCE↗
Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels
Exact solutions of burst pressure for defect-free, thick-walled cylindrical pressure vessels with capped ends are developed using the flow theory of plasticity in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. The material is assumed to obey a power-law strain hardening rule, and the finite strain theory is adopted to describe large plastic deformation. On this basis, internal pressure is obtained as a complex polynomial function of effective strains on the inside and outside surfaces of the pressure vessel with the use of the Bernoulli numbers. At burst failure, the effective strains and stresses on the inside and outside surfaces are first determined, and then three flow solutions of burst pressure are obtained as a power series function of the diameter ratio (D o /D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). The power series solution is confirmed to agree well with the exact flow solution of burst pressure in a closed-form for each yield criterion, and the results show that the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction of burst pressure. In conclusion, two sets of full-scale burst test data are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin-walled pipes and thick-walled cylindrical pressure vessels.
36 MATERIALS SCIENCE↗
The influence of temperature on the strain-hardening behavior of Fe-22/25/28Mn-3Al-3Si TRIP/TWIP steels
In this work, the influence of temperature and stacking fault energy (SFE) on the strain-hardening behavior and critical resolved shear stress for twinning was investigated for three Fe–22/25/28Mn–3Al–3Si wt.% transformation- and twinning-induced plasticity (TRIP/TWIP) steels. The SFEs were calculated by two different methods, density functional theory and statistical thermodynamic modeling. The dislocation structure, observed at low levels of plastic deformation, transitions from “planar” to “wavy” dislocation glide with an increase in temperature, Mn content, and/or SFE. The change in dislocation glide mechanisms from planar to wavy reduces the strain hardening rate, in part due to fewer planar obstacles and greater cross slip activity. Additionally, the alloys exhibit a large decrease in strength and ductility with increasing temperature from 25 to 200 °C, attributed to a substantial reduction in the thermally activated component of the flow stress, predominate suppression of TRIP and TWIP, and a significant increase in the critical resolved shear stress for mechanical twinning. Interestingly, the increase in SFE with temperature had a rather minor influence on the critical resolved shear stress for mechanical twinning, and other temperature dependent factors which likely play a more dominant role are discussed.
36 MATERIALS SCIENCE↗
A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening
A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.
42 ENGINEERING↗
Ordering effects on deformation substructures and strain hardening behavior of a CrCoNi based medium entropy alloy
Here, a CrCoNi based medium entropy alloy with small additions of Ti, Al and Nb (denoted as (CrCoNi) 93 Al 4 Ti 2 Nb) in the as-quenched condition, exhibits tensile properties comparable to those of the equiatomic CrCoNi alloy at room temperature. Dark field transmission electron microscopy (TEM), atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) together with atom probe tomography (APT) show that spatially-localized long range ordering (LRO) L1 2 domains exist in this alloy. The evolution of deformation substructure with plastic deformation in this alloy was characterized using electron backscatter diffraction (EBSD), electron channeling contrast imaging (ECCI) and STEM based techniques including the recently developed weak beam dark field STEM imaging. Plastic deformation occurs by the slip of a/2<110>dislocations, which are narrowly dissociated into Shockley partial dislocations on {111} slip planes. Their dissociation distances in the (CrCoNi) 93 Al 4 Ti 2 Nb alloy are much smaller than the widths of the corresponding partials in the equiatomic CrCoNi alloy due to one or more of the minor alloying elements (Al, Ti, Nb). Dislocation slip in this alloy has a pronounced planar character. The leading dislocations in slip bands glide as pairs due to the existence of LRO domains. Multipoles were formed through the slip of dislocations with opposite signs on adjacent {111} slip planes. Those multipoles serve as building blocks for the formation of subgrain structures consisting of fine slip bands. The distances between slip bands were continuously refined during plastic deformation and dynamic refinement of slip bands plays a crucial role in strain hardening. The effects of LRO domains on planar dislocation slip, the deactivation of deformation twinning and strain hardening of this alloy are discussed.
36 MATERIALS SCIENCE↗
Analysis of plane-plastic stress problems with axial symmetry in strain-hardening range
A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.
Wu, M H Lee↗
Elastic-plastic torsion problem for strain-hardening materials
Successive approximation procedure for solving elastic-plastic problem for torsion of solid prismatic bar made of strain hardening material
Mendelson, A.↗
Taming Metal–Solid Electrolyte Interface Instability via Metal Strain Hardening
Abstract Solid-state lithium metal batteries have emerged as a promising technology for electric vehicles due to their high specific energy and safety potential. Obtaining intimate contact between Li and electrolyte during cell fabrication, however, remains challenging. Adequate fabrication pressure is required to promote close contact, but this pressure can cause Li deformation and penetration into the electrolyte, resulting in poor battery performance. Here, a strategy for addressing this problem is presented by incorporating 3 at% Mg into Li. Unlike pure Li which obeys the Voce hardening law and allows unconstrained deformation, Li–Mg alloy follows the Swift hardening law and strengthens with strain under compression stress. Because of the constrained deformation of Li–Mg, intimate contact with solid electrolytes is possible even at high fabrication pressure (50–65 MPa), resulting in high critical current densities. These findings underscore the importance of understanding Li metal deformation properties to improve solid-state battery performance.
25 ENERGY STORAGE↗
Optimizing Earthquake Nowcasting With Machine Learning: The Role of Strain Hardening in the Earthquake Cycle
Abstract Nowcasting is a term originating from economics, finance, and meteorology. It refers to the process of determining the uncertain state of the economy, markets or the weather at the current time by indirect means. In this paper, we describe a simple two‐parameter data analysis that reveals hidden order in otherwise seemingly chaotic earthquake seismicity. One of these parameters relates to a mechanism of seismic quiescence arising from the physics of strain‐hardening of the crust prior to major events. We observe an earthquake cycle associated with major earthquakes in California, similar to what has long been postulated. An estimate of the earthquake hazard revealed by this state variable time series can be optimized by the use of machine learning in the form of the Receiver Operating Characteristic skill score. The ROC skill is used here as a loss function in a supervised learning mode. Our analysis is conducted in the region of 5° × 5° in latitude‐longitude centered on Los Angeles, a region which we used in previous papers to build similar time series using more involved methods (Rundle & Donnellan, 2020, https://doi.org/10.1029/2020EA001097 ; Rundle, Donnellan et al., 2021, https://doi.org/10.1029/2021EA001757 ; Rundle, Stein et al., 2021, https://doi.org/10.1088/1361-6633/abf893 ). Here we show that not only does the state variable time series have forecast skill, the associated spatial probability densities have skill as well. In addition, use of the standard ROC and Precision (PPV) metrics allow probabilities of current earthquake hazard to be defined in a simple, straightforward, and rigorous way.
58 GEOSCIENCES↗
On the use of limestone calcined clay cement (LC3) in high-strength strain-hardening cement-based composites (HS-SHCC)
Highlights: • Use of LC{sup 3} slightly reduces flowability and shortens the setting time of fresh matrices. • Highly polymerized C-A-S-H gel and abundant ettringite benefit flexural strength of LC{sup 3}-matrices. • Use of LC{sup 3} enhances the bond strength between fiber and high-strength matrix. • LC{sup 3}-based HS-SHCC yields similar flexural performance as the composite with Portland cement. High-strength strain-hardening cement-based composites (HS-SHCC) demonstrate excellent mechanical and durability properties. However, high cement content typical to HS-SHCC results not only in high carbon footprint, but also in excessive hydration heat and severe autogenous shrinkage. In this investigation, Limestone Calcined Clay Cement (LC{sup 3}) was used to produce sustainable HS-SHCC. The LC{sup 3} substitution resulted in higher energy consumption during mixing and in shorter setting times of the fresh, plain matrices. Although the LC{sup 3} substitution slightly reduced the compressive strength, the formation of highly polymerized C-A-S-H gel and abundant ettringite benefited the flexural strength of the plain matrices. Additionally, single-fiber pullout experiments showed that the use of LC{sup 3} led to increased fiber-matrix bond strength and pullout energy. Finally, the replacement of Portland cement by LC{sup 3} resulted in HS-SHCC with similar mechanical performance to the reference composite, indicating a high potential for using LC{sup 3} in high-performance cement-based composites.
36 MATERIALS SCIENCE↗
In-situ investigation of strengthening and strain hardening mechanisms of Cu-added medium-Mn steels by synchrotron-based high-energy X-ray diffraction
A novel Cu-added medium-Mn steel with a chemical composition of Fe–0.27C–9.1Mn–1.86Al–3.3Cu (wt.%) was designed and subjected to intercritical annealing (IA) temperature range from 620 °C to 680 °C for 1 h. The ultimate tensile strength (UTS) increases and the yielding strength (YS) decreases with the IA temperature increasing. The YS of 824 MPa, UTS of 1222 MPa, total elongation (TE) of 55%, and product of strength and elongation (PSE) of 67.2 GPa·% are achieved after IA at 660 °C. Transmission electron microscopy confirmed that Cu-rich nanoparticles precipitate in the ferrite. The in-situ high-energy X-ray diffraction (HE-XRD) experiments show that at the beginning of plastic deformation, both austenite and ferrite bear the applied load. The load is mainly undertaken by martensite with effective transformation-induced plasticity (TRIP) effect triggered. The YS of ferrite is significantly higher than that of austenite. The individual contribution of solid solution strengthening, grain refinement strengthening, dislocation strengthening, and precipitation strengthening in ferrite and austenite is analyzed. The discrepancy between the YS of ferrite and austenite is mainly attributed to the precipitation strengthening due to the Cu-rich nanoparticles precipitation. The moderate mechanical stability and the collaboration of TRIP and twinning-induced plasticity (TWIP) effects of austenite contributed to the enhanced strain hardening capability and resulted in large ductility.
36 MATERIALS SCIENCE↗