Homogeneous Plastic Deformation Research Articles

Напряженно-деформированное состояние континуума с очагом пластической деформации

The paper describes a method for constructing a shear plastic band in an elastic plane using the Crouch solution in the problem of a constant discontinuity of displacement on a finite segment of an unbounded plane. Analytical equations are obtained for calculating the stress-strain state (SSS) of a plane with a band of homogeneous plastic deformation for the cases of simple and pure shear. The analysis of SSS was carried out and the features of the field of internal stresses in an elastic plane with a band of plastic deformation shear were revealed. It is shown that a zone of homogeneous plastic shear deformation can be used as an element for constructing a zone of arbitrary geometric shape with a given distribution of plastic shear deformation. In the general case, the proposed approach can also be applied to construct zone with a homogeneous distribution of the normal components of plastic deformation.

Low temperature deformation mechanisms of polycrystalline CoZr and Co39Ni11Zr50 B2-type intermetallic compounds

The B2-type intermetallic compounds CoZr and Co39Ni11Zr50 were deformed in tension at low temperatures. While CoZr is ductile down to 4 K, Co39Ni11Zr50 becomes brittle below 125 K due to a martensitic phase transformation. Thermal activation analysis shows that CoZr follows the Cottrell-Stokes law indicating forest dislocation cutting as the dominant rate-controlling deformation mechanism, similar to face-centered cubic metals. The moderate ductility of both intermetallic compounds at low temperatures may qualitatively be related to a significant metallic character of bonding giving rise to a low Peierls stress estimated for primary {110}<100> slip and most likely also leads to an easier activation of secondary {110}<110> slip which was proven by transmission electron microscopy. Secondary slip is necessary for the fulfillment of the von Mises criterion for homogeneous plastic deformation of polycrystalline materials. The present results generalize the findings made on the ductile rare earth intermetallics YAg and YCu and, therefore, may help to search for other ductile systems in the broad class of intermetallic compounds.

Extracting true stresses and strains from nominal stresses and strains in tensile testing

AbstractSeemingly a simple task, the extraction of the flow curve (true stress vs. true plastic strain) from nominal stresses and strains in standard tensile testing still has its unsolved points. This study addresses two of them: (i) in materials without yield point phenomenon (or generally in the region of homogeneous plastic deformation), the true stress is typically calculated assuming constant volume, ignoring the elastic volume changes. Here, we derive a set of exact analytical solutions for true stresses and strains with remarkable simplicity and beauty that fully account for the elastic volume changes. This set of exact solutions is cross‐checked by finite element simulations as well as zeroth‐ and first‐order approximations; perfect agreement has been found. (ii) In materials with a pronounced yield point phenomenon, a complicated three‐dimensional stress state inevitably arises at the edge of the Lüders bands, which masks the real (or inherent) material behaviour. To determine the real material behaviour in the Lüders region, here we use a new macroscopic analytical approach characterised by a high true upper yield point, a typical strain hardening behaviour common for many materials, and the triaxiality of the stress state that inevitably develops at the edges of the Lüders bands and that determines the stress level at the observed lower yield point. This approach is verified by experiments (including video observations as well as digital image correlation (DIC) strain distribution measurements) and finite element simulations with very good agreement.

Cryogenic formability and deformation behavior of 2060 Al–Li alloys with water-quenched and T4 aged temper

In this study, the formability and deformation behavior of new third-generation aluminum-lithium alloys at temperatures ranging from 113 to 298 K were studied by uniaxial tension tests, Erichsen cupping tests, and microstructure observations. The results show that the water quenched 2060 alloy exhibits excellent formability at 113 K with a fracture elongation of 34.1%, and Erichsen cupping value of 10.1 mm that are 33.2% and 40.3% higher than those at 298 K. Homogeneous plastic deformation was obtained at the cryogenic temperature for the water quenched alloy, as was reflected by the following three observations: 1) homogeneous lattice rotation and fewer coarse slip bands occurred in the grains; 2) a large number of substructures (i.e., dislocation cells, subgrains) uniformly distributed in the interior grains; 3) serrated flow caused by the dynamic strain aging disappeared at the cryogenic temperature. The naturally aged 2060 alloy exhibited limited formability improvement. As temperature decreased from 298 K to 113 K, the fracture elongation increased slightly by 11.8% and the Erichsen cupping value decreased by 26.4% for the naturally aged Al–Li alloy. The δ' precipitation phase of the naturally aged Al–Li alloy gave rise to planar slip due to the low misfit with the Al matrix and induced stress concentration at the grain boundaries. Meanwhile, the planar slip resulted in a higher texture and anisotropy at the cryogenic temperature, triggering early fracture and decreasing the ductility.

Microstructural characteristics and evolution mechanisms of 90W–Ni–Fe alloy under high-strain-rate deformation

Investigations into the microstructural characteristics and evolution mechanisms of 90W–Ni–Fe alloy during deformation under high strain rates were conducted using a Split Hopkinson Pressure Bar (SHPB) system. With increasing strain rate and strain the 90W–Ni–Fe alloy deformation behavior changes from homogenous plastic deformation to localized shear deformation resulting in adiabatic shear bands (ASBs). At strain rates below 4779s−1, 90W–Ni–Fe alloy undergoes a homogenous deformation, and in the tungsten and γ- (Ni, Fe) phase the distribution of dislocations, dislocation tangles and the formation of substructures such as dislocation cell structures and subgrains appear randomly. Up to the strain rate of 6146s−1, an ASB with a width of about 50 μm is formed in the deformed specimen, and the microstructure in the ASBs undergoes significant dynamic recrystallization, which is more pronounced in the γ-(Ni, Fe) phase than in the tungsten phase. The evolution mechanism of the microstructure was determined through calculating the temperature rise of specimens during the deformation. A rotational dynamic recrystallization mechanism is proposed which provides a reasonable explanation for the development of the fine equiaxed grains in the ASBs. This study provides an important contribution to the design of self-sharpening tungsten alloy kinetic energy penetrators.

Determining deformation behaviors in a CuZr-based bulk metallic glass composite

In this work, deformation behaviors of a CuZrAlNb bulk metallic glass composite (BMGC) with different volume fractions of the crystalline phase were characterized using in-situ tensile tests in an optical microscope. For the studied composite, it was found that the volume fraction of the crystalline phase plays a significant role in shear band types. Shear bands which are not restrained by the crystalline phase, disappeared with increasing the crystallization volume fraction. There exists a critical volume fraction (~ 29.63 %) of the crystalline phase determining deformation behaviors of the studied composite. Beyond the critical value, this composite exhibits the homogeneous plastic deformation. Otherwise, the deformation of the BMGC is affected by shear bands which are not restrained by the crystalline phase, resulting in a decrease in the plasticity of the BMGC. Besides, the crystalline phase with a large-size bears more strain than that with a small-size in BMGCs, thereby improving their mechanical properties.

Flow behaviors and deformation mechanism of WQ-tempered Al–Li alloy at cryogenic temperatures

Abstract Cryogenic forming is a promising technique for fabricating complex components using high-strength aluminum alloys. In this work, the flow behaviors and microstructure evolution of a WQ-tempered (solution treatment followed by water quenching) 2195 Al–Li alloy was studied by uniaxial tension tests from −196 to 25 °C and strain rates from 2.5 × 10−4 to 1 × 10−2 s−1. The results showed that the ductility gradually increased after decreasing the deformation temperature, while the strain rate had a limited effect on the ductility. Serrated flow caused by dynamic strain aging occurred from −60 to 25 °C, which increased the flow stress due to additional pinning of mobile dislocations by solute atom clusters. Smooth flow curves were obtained from −196 to −90 °C due to the suppression of dynamic strain aging. The microstructure observations indicated that more homogeneous plastic strain and grain rotation occurred in the cryogenically-deformed sample, leading to the formation of weaker fiber texture compared with the sample deformed at room temperature. A higher work hardening rate was achieved at cryogenic temperature, which delayed local necking. The suppression of serrated flow and homogeneous plastic deformation significantly improved the ductility at −196 °C, with a uniform elongation of 35.2%, which was 84.3% higher than that at 25 °C.

Role of Glass Composition on Mechanical Properties of Shape Memory Alloy‐Metallic Glass Composites

In this work, the molecular dynamics (MD) simulation was applied to design a laminated composite structure comprised of the shape memory alloy (SMA) and Cu‐Zr metallic glasses (MGs). A wide range of MG compositions was considered to tune the mechanical features and improve the homogenous plastic deformation during the tension loading. The results indicated that the martensitic transformation in the SMA inhibited the sudden shear band propagation in the composite for all the samples. Moreover, it was revealed that the mechanism of plasticity was significantly affected by the change of MG composition. In the Cu‐rich MGs, the formation and propagation of thick shear bands occurred at the end of the tension loading; however, the increase in Zr content induced the interaction of multiple shear bands with finer configurations in the system. Nevertheless, the excessive Zr addition in the MG composition facilitated the aggregation of nanopores at the interface of SMA and MGs, which may be due to the softening effect in the Zr‐rich MGs. Finally, it is concluded that an optimized MG composition is required for the trade‐off between the plasticity and the strength in the SMA‐MG composites.

Grain size dependence of twinning behaviors and resultant cryogenic impact toughness in high manganese austenitic steel

Two high manganese austenitic steels with different grain size were prepared to comprehensively investigate size effect on twinning and resultant cryogenic impact toughness at −196 °C. The microstructure was characterized by means of electron back-scattered diffraction, transmission electron microscopy and X-ray diffraction. It is found that the Charpy impact absorbed energy can be enhanced by 36% via increasing grain size from ~11 to ~47 μm, exhibiting an inverse size effect of cryogenic impact toughness. The major difference in deformed microstructure is that the number fraction of type III grains (intense twinning in grain interior) increases from ~16% to ~56% as the grain size increases from ~11 to ~47 μm. Moreover, it has been demonstrated that the larger grain size, inducing better Charpy impact toughness at −196 °C, is due to the following aspects: (1) stronger dynamic grain refinement; (2) higher dislocation density and wider extended dislocations contributing to stronger strain hardening and better plasticity as well as (3) relatively homogeneous plastic deformation.

Phase-Specific Strain Hardening and Load Partitioning of Cold Rolled Duplex Stainless Steel X2CrNiN23-4

Multi-phase materials often times consist of constituents with high contrasts in phase-specific mechanical properties. Here, even after homogeneous plastic deformation phase-specific residual stresses develop that may affect the components behaviour in service. For numerical simulation of phase-specific residual stresses, knowledge of the particular phase-specific strain hardening behaviour is essential. In this study, the strain hardening of ferrite and austenite in cold rolled duplex stainless steel of type X2CrNiN23-4 is investigated. By means of X-ray diffraction, the phase-specific load partitioning and residual stress evolution are analysed for uniaxial load application in three directions within the sheets plane, taking into account the sheet metals phase specific anisotropy. In order to assess the necessity for experimental determination of anisotropic phase specific behaviour, the strain hardening parameters, derived from only one loading direction, are implemented in a mean-field approach for prediction of phase-specific stresses. A simplified simulation approach is applied that only considers macroscopic plastic anisotropy and results are compared to experimental findings. For all investigated loading directions, it was observed that austenite is the high-strength phase. This load partitioning behaviour was confirmed by the evolution of phase-specific residual stresses as a result of uniaxial elasto-plastic loading. With the simplified and fast numerical approach, satisfying results for prediction of anisotropic phase-specific (residual) stresses are obtained.

Ultrasonic-assisted plastic flow in a Zr-based metallic glass

Ultrasonic vibration can be used for the micro-molding of metallic glasses (MGs) due to stress-softening and fast surface-diffusion effects. However, the structural rearrangement under ultrasonic vibration and its impact on the mechanical response of metallic glasses remain a puzzle. In this work, the plastic flow of the Zr35Ti30Cu8.25Be26.75 metallic glass with the applied ultrasonic-vibration energy of 140 J was investigated by nanoindentation. Both Kelvin and Maxwell-Voigt models have been adopted to analyze the structural evolution during the creep deformation. The increase of the characteristic relaxation time and the peak intensity of relaxation spectra can be found in the sample after ultrasonic vibration. It effectively improves the activation energy of atomic diffusion during the glass transition ( E g) and the growth of the crystal nucleus ( E p). A more homogenous plastic deformation with a weak loading-rate sensitivity of stress exponent is observed in the ultrasonic-vibrated sample, which coincides with the low pile-up and penetration depth as shown in the cross profile of indents. The structural rearrangement under resonance actuation demonstrated in this work might help us better understand the defect-activation mechanism for the plastic flow of amorphous systems.

Strength and plasticity of amorphous ceramics with self-patterned nano-heterogeneities

Amorphous ceramics with superb strength and irradiation tolerance are promising candidate materials for nuclear industry. However, the brittle-like behavior extremely limits their applications. Here, we demonstrate that Fe–SiOC amorphous ceramic composites (ACCs) with self-patterned Fe-rich nanoclusters fabricated by co-sputtering Fe and amorphous SiOC ceramic not only exhibits exceptional, homogeneous plasticity at room temperature but also remains high strength and good irradiation tolerance. Flow strength of Fe–SiOC ACCs decreases but plasticity increases with the increase in Fe content. Moreover, the strength and plasticity of Fe–SiOC ACCs can be further tailored by subsequent annealing and ion irradiation associated with the change in their microstructure. High temperature annealing tunes amorphous Fe-rich nanoclusters into crystalline Fe nanoparticles, significantly enhancing flow strength of Fe–SiOC ACCs without loss of plasticity. Ion irradiation does not apparently modify the microstructure and reduce plasticity of Fe34at.%-SiOC ACC, but slightly enhances their flow stress. For instance, annealed Fe34at.%-SiOC ACC has flow true stress exceeding 4.0 GPa at a large uniform compressive strain of 55% without plastic flow instability and cracking. The spatially distributed Fe-rich heterogeneities (amorphous nanoclusters and crystalline nanoparticles) plastically co-deform with amorphous SiOC matrix and discretize shear transformation zones in amorphous ceramics, thus preventing the shear-banding instability and significantly enhancing compressive plasticity. The plastic co-deformation between Fe-rich nano-heterogeneities and amorphous SiOC ceramic matrix is achieved due to interface constraint, preventing cracking and ensuring homogeneous plastic deformation of Fe–SiOC ACCs. These findings suggest that patterning nanoscale metal-rich heterogeneities can tailor mechanical properties of amorphous ceramics.

Revisit initiation of localized plastic deformation: Shear band & necking

Localizations of plastic deformation such as shear band and necking have been investigated during past several decades. From experimental observations, microstructural details inside shear band are related to combination of re-crystallization, phase transformation, and high temperature rising. Because it happens in such a short time, e.g., a few nanoseconds, that initiation of localization can hardly be captured by current experimental methods. On the other hand, theoretical explanations of initiation of localized plastic deformation have attempted in many ways. Early investigations are based on corotational constitutive models and singular yielding surface theory. Recently different viscoplastic constitutive models are applied to understand localization. But a clear picture is still not obtained because of complex mathematical structures and phenomenological aspect of current constitutive models and yielding theories. For example, it is not clear that initiation of localized plastic deformation is from dislocation softening or thermal softening. In this paper, a new proposed physical model from the perspective of energy transmission is used to explain initiation of localization of plastic deformation. It is shown in this mathematical framework that a transition from homogenous plastic deformation to localized plastic deformation is mathematically related to a transition from hyperbolic differential system to elliptical differential system. In this transition, wave equation is changed to become Laplace equation. Initial value problem is changed to boundary value problem. Heat generated due to plastic energy is calculated by mechanical version of Joule’s law. The trigger of localization is not only initial imperfections but also can be hydrostatic pressure and grain size changes.

Mechanical behavior of metallic glasses with pressure-promoted thermal rejuvenation

The pressure-promoted thermal rejuvenation is a promising approach for improving the macroscopic plasticity of metallic glasses (MGs). Here, molecular dynamics simulations have been performed to investigate the atomic structure and mechanical behavior of the rejuvenated MGs with pressure-promoted thermal processing. The effects of annealing temperatures and pressures are investigated, with results suggesting that the pressure has a significant influence on the deformation and failure mechanism of the rejuvenated MGs. The MGs can be rejuvenated either by the application of negative pressures with the low annealing temperature, or by the application of positive pressures with the high annealing temperature. Accompanied by the rejuvenation, a transition in failure mode from localized shear banding to homogeneous plastic deformation occurs due to the higher-energy glassy state induced by the thermal-pressure loading process. The present study provides important insights into the atomic-level structures of the rejuvenated MGs, as well as useful guidelines for the design of strong and high plastic MGs.

Irradiation-induced homogeneous plasticity in amorphous/amorphous nanolaminates

Achieving homogeneous plastic deformation in metallic glasses is a long-standing goal yet to be solved in materials science. Here we investigate the effect of ion irradiation on the plastic deformation behavior of ZrCu/ZrCuNiAlSi amorphous/amorphous nanolaminates (A/ANLs) via nanoindentation testing. The experimental results indicate a dramatic change in deformation mode from multiple shear banding events to homogeneous compressive deformation before and after ion irradiation on the A/ANLs in the areas underneath the indenter. Ion irradiation-induced changes of both fraction and distribution of free volume inside each constituent layer and interfacial state in the A/ANLs may be responsible for the unusual homogeneous deformation behavior. Our results suggest that the mechanical property of A/ANLs could be modified by tuning both the inner and interfacial structure via ion irradiation.

Crack Behavior and Crystallographic Feature for TMCP690 Steel under Fatigue Loading

For a new type of thermomechanical controlled process steel, when stress intensity factor was about 32 MPa m1/2, several slip bands with different orientations occurred in cyclic plastic zone. Some slip bands had strong interaction with dominant crack, which led to crack bifurcation and aggregation. After that, electron back-scattered diffraction technique was employed to evaluate the cyclic plasticity effect on crystallographic features of kernel average misorientation (KAM), strain distribution and fraction of different categories of grains for fatigue loading sample in crack tip zone. Before fatigue loading, KAM distribution map revealed relatively homogeneous plastic deformation and few grains displayed distortion based on strain distribution map. After fatigue loading, KAM showed higher cyclic plasticity in the middle, and lower value on both sides. Strain network structure formed. Meanwhile, when fatigue loading was executed, proportion of recrystallized grains had a little variation from 3.15 to 5.58%. Ratio of substructured grains increased to 19.63%, and deformed grains reduced to 74.79%.

Simulation of Adiabatic Shear Bands in Orthogonal Machining of Ti6Al4V Using a Rigid-Viscoplastic Finite Element Analysis

Catastrophic shear instability is the dominant mechanism during orthogonal cutting of Ti6Al4V. Chip segmentation even at low speeds testifies to the emergence of some kind of instability during plastic deformation of the material. Among the theoretical models, catastrophic thermoplastic slip is proposed as a mechanism to explain the destabilization of homogeneous plastic deformation, which results in localized, band-like adiabatic shear deformation. On the other hand, fracture models which consider machining as a mechanism of ductile or brittle fracture are used to explain the segmented chip formation as a periodic crack generation mechanism. This work aims at elucidating the fundamental mechanisms of the above theoretical models using a coupled thermomechanical rigid-viscoplastic FEM analysis. Introducing an energy criterion for ductile damage, numerical results showed that failure within the adiabatic shear band (ASB) is a post-localization mechanism occurring after intense shear localization. Simulations revealed a void initiation and coalescence mechanism which resembles an array of discontinuous degraded elements of nearly ellipsoidal shapes that grows and progressively coalesces forming a macro crack inside the ASB. Several aspects of ASB formation are addressed, among others, the micro-scale spatial temperature profile, parametric studies of critical damage energies, chip segmentation frequency, etc. Experimental results of ASB formation pertaining to chip morphology and cutting forces are compiled and analyzed to evaluate the FEM model at the low speed regime.

Improvement of Microstructural and Mechanical Characteristics of Friction Stir Welded AA6061 Aluminium Alloy Joint

To improve mechanical characteristics of friction stir welded joint made of AA6061-T6, AA2024 was used as a filler material due to its high strength and compatibility with AA6061 aluminium alloy. Different filler strip thickness (1, 1.5, and 2 mm) were investigated. Homogenous plastic deformation of the mixture with soft and refined grains was observed in the stir zone due to dynamic recrystallization of the grains. Friction stir welded joints with filler strip showed high hardness and tensile strength compared with filler-free joints. Welded joint with 1 mm filler strip has the highest tensile strength among other joints due to the dynamic recrystallization of the refined grains as a result of heat concentration. In addition, using greater thickness of filler strips makes the joining process more difficult, causes joint defects and reduces the tensile strength of welded joints.

Напряженно-деформированное состояние упругой пластины с трещиной

The article considers a crack in the form of a narrow cut with a certain cfn at the cut out in an unbounded plate. The characteristics of the mechanical state of this system under uniaxial loading are determined: the stress concentration coefficient, the crack-driving force, and the energy of a solid with a crack. The elastic energy expenditure during crack propagation is determined. The general regularities of the mechanical state of a solid with a crack, not necessary having the form of an ellipse, are revealed. An important parameter of a crack is the curvature at the tip. It is shown that the Griffiths crack does not actually have a singularity at the tip. The stress strain state of the plate with an elliptical crack is identical to the same of the plate with a focus of homogeneous plastic deformation.

Void configuration-induced change in microstructure and deformation mechanisms of nano-porous materials

Void configuration plays an essential role in the deformation behavior of ductile metals; its effects on intervoid interference has not been investigated systematically until now. In the present study, molecular dynamics simulation was employed to study the void configuration-induced change in mechanical properties and deformation mechanisms during tensile loading. The results show that void configuration has a significant influence on the yield stress and yield strain, while its effect on the elastic modulus is about 3.14 ± 0.23%. The deformation mechanisms of porous materials with various void configurations at micro- and nanoscale are proposed: (i) local plastic deformation and (ii) homogeneous plastic deformation. Further analysis indicates that the difference between the above two deformation mechanisms is mainly caused by the competition and synergy between the stacking faults and dislocation. Local plastic deformation is mainly controlled by stacking faults. Homogeneous plastic deformation is dominated by dislocation motion with only a small amount of stacking shear motion, which gives material a superior plastic elongation. The result is of great value for improving the plasticity limit of nanostructures.