Plastic Strain Incompatibility Research Articles

Scan Strategy Effect on the Mechanical Properties and Microstructure of Directed Energy Deposited 18Ni300 Maraging Steel

Although the laser scan strategy does not affect the energy density of laser-based additive manufacturing, changes in laser scan direction critically influence the residual stress and microstructure of metallic components. However, only a limited number of studies have investigated the role of laser scan strategy on the microstructure and mechanical properties of additively manufactured maraging steels. Therefore, this study examines the effect of laser scan strategy on the mechanical properties of 18Ni300 maraging steel. Different laser scan strategies influence the morphologies of the molten pool, where retained austenite is concentrated in 18Ni300 maraging steel. The 45o sample exhibits a denser molten pool distribution compared to the other samples due to reduced layer overlapping. Because of the plastic strain incompatibility between martensite and austenite at the molten pool boundary, this dense molten pool distribution in the 45o sample resulted in the highest back-stress hardening. Additionally, the minimal layer overlapping in the 45o sample reduces heat exposure during laser-based additive manufacturing, leading to a finer martensite block and lath size. By combining high back-stress hardening with a fine martensite block and lath size, the 45o sample achieved the highest tensile property compared to the other samples. These results indicate that the selection of laser scan strategy is crucial for designing a heterogeneous microstructure in additively manufactured parts, which can enhance mechanical properties, even with the same energy density.

Homogenization temperature dependent microstructural evolution and mechanical properties in a Nb-stabilized cast austenitic stainless steel

A Nb-stabilized cast austenitic stainless steel is processed by homogenization treatments at 1050 °C, 1150 °C, and 1250 °C respectively to investigate microstructure dependent deformation behaviors and mechanical properties. Homogenization treatment at 1050 °C could not change the size of primary NbC, while significant dissolution of primary NbC destroys the network connectivity after homogenization treatments at temperatures above 1150 °C. Meanwhile, dissolution of NbC will increase C and Nb content in austenite matrix, leading to an increase in SFE. Nucleation of microcracks within NbC at the initial stage of deformation is caused by plastic strain incompatibility at the NbC/γ interface. Fast crack propagation along the continuous network of primary NbC leads to premature fracture at a lower stress level, and resultant lower ultimate tensile strength and elongation in as-cast and 1050-H samples. A higher SFE reduces the susceptibility to localization of deformation and crack propagation along the discrete primary NbC is suppressed, resulting in an obvious improvement in the ultimate tensile strength and elongation in 1150-H and 1250-H samples. • The dissolution and precipitation of NbC during homogenization treatments by different temperatures were revealed. • A higher SFE is responsible for the lower rate of deformation-induced α'-martensitic transformation by suppressing the planar slip. • A higher SFE reduces the susceptibility to localization deformation and the crack propagation along the primary NbC is suppressed. • A noticeable improvement in the ultimate tensile strength and elongation after homogenization treatment at temperatures above 1150 °C.

A New Stored Energy Model Based on Plastic Work of Back Stress during Cyclic Loading in Polycrystalline Metal.

Two mesomechanics models were analyzed in an attempt to reveal the relationship between stored energy and back stress. It has been indicated that the portion of elastic stored energy due to residual microstresses (ESR) is closely related to intergranular back stress (Xinter), and the stored energy of dislocations inside grains (ESD) can be estimated with the plastic work of intragranular back stress (Xintra). Then, the evolution of back stress during cyclic loading was studied, and the plastic work of back stress (WpB) was calculated with the low cycle fatigue experimental data of Ti-6Al-4V. The result shows that WpB is partially released at every reverse loading, sufficient to reproduce the evolution of stored energy correctly under cyclic loading. The study also reveals that partially released energy is related to the decrease of Xinter at the initial state of reversal loading resulting from the reduction of the plastic strain incompatibility between grains.

Elasto-viscoplastic tensile behavior of as-forged Ti-1023 alloy: Experiments and micromechanical modeling

This works focused on the mechanical behavior of an ‘as-forged’ Ti-1023 alloy used in airframe forging applications. Its microstructure, characterized by SEM and EBSD, was composed by 15% of primary αp nodules (2–5 μm in size) embedded in millimeter long β grains partially fragmented into equiaxed β subgrains of 5–10 μm. Further neutron diffraction analysis indicated an almost random β texture. Tensile tests at different strain rates were performed. A very low strain rate sensitivity was observed. The contribution of each phase to the overall mechanical behavior was numerically investigated by a two-phase elasto-viscoplastic self-consistent (EVPSC) model with affine-type linearization. Internal stresses arising from elastic and plastic strain incompatibilities were analyzed. Throughout the mechanical loading, {100}β oriented grains were more deformed than {111}β grains and all the α nodules. The onset of plasticity occurred sequentially in the β phase, initially in {110}β grains followed by {111}β and then {100}β ones. The effect of the crystallographic texture on slip activity was also studied through simulations made with a synthetic rotated cube β texture, typical of β-working, while considering α textures in Burgers Orientation Relationship (BOR) with the β phase or being random.

Tailored microstructures and strengthening mechanisms in an additively manufactured dual-phase high-entropy alloy via selective laser melting

Dual-phase high-entropy alloys (DP-HEAs) with excellent strength-ductility combinations have attracted scientific interests. In the present study, the microstructures of AlCrCuFeNi3.0 DP-HEA fabricated via selective laser melting (SLM) are rationally adjusted and controlled. The mechanisms engendering the hierarchical microstructures are revealed. It is found that the AlCrCuFeNi3.0 fabricated by SLM at the scanning speed of 400 mm s−1 falls into the eutectic coupled zone, and increasing the scanning speed will make this composition deviate away from the eutectic coupled zone due to the increased cooling rate. The enrichment of Cr and Fe solutes with large growth restriction values ahead of the solid/liquid interface can develop a constitutional supercooling zone, thus facilitating the heterogeneous nucleation and near-equiaxed grain formation. The synergy of the near-eutectic DP nano-structures and near-equiaxed grains instead of columnar ones effectively suppresses cracking for the as-built DP-HEA. During the tensile deformation, the intergranular back stress hardening similar to the grain-boundary strengthening is discovered. Meanwhile, the near-eutectic microstructures comprised of soft face-centered cubic and hard ordered body-centered cubic (B2) DP nano-structures lead to plastic strain incompatibility within grains, thus producing the intragranular back stress. The Cr-rich nano-precipitates inside the B2 phase are found to be sheared by dislocation gliding and can complement the back stress. Additionally, multiple strengthening mechanisms are physically evaluated, and the back stress strengthening contributes obviously to the high performances of the as-built DP-HEA.

Synergetic strengthening of layered steel sheet investigated using an in situ neutron diffraction tensile test

Synergetic strengthening induced by plastic strain incompatibility at the interface, and the resulting extra geometrically necessary dislocations (GNDs) generated during plastic deformation, were investigated to understand the origin of extra strength in heterogeneous structured (HS) materials. The mechanism of extra GND generation in twinning-induced plasticity (TWIP)-interstitial free (IF) steel layered sheet was quantitatively analyzed by conducting in situ neutron scattering tensile test. Load partitioning due to the different mechanical properties between the TWIP-steel core and IF-steel sheath at the TWIP/IF interface was observed during the in situ tensile testing. Because of the plastic strain incompatibility from load partitioning, extra GNDs are generated and saturate during tensile deformation. The extra GNDs can be correlated with the back-stress evolution of the HS materials, which contributes to the strength of layered materials. Because of the back-stress evolution caused by load partitioning, the strength of TWIP-IF layered steel is higher than the strength estimated by the rule-of-mixtures. This finding offers a mechanism by which extra GNDs are generated during load partitioning and shows how they contribute to the mechanical properties of HS materials.

Back-Stress Effect on the Mechanical Strength of TWIP-IF Steels Layered Sheet

Although back-stress contributes to the mechanical properties of materials, the degree of strength enhancement from back-stress is not easy to estimate. In this research, back-stress hardening of twinning-induced plasticity (TWIP) + interstitial free (IF)-layered steel sheets were estimated by implementing a non-linear combined isotropic and kinematic hardening model. High back-stress evolution occurs due to plastic strain incompatibility between a TWIP-steel core and IF-steel sheath, and the strength of TWIP + IF layered steel sheath is greater than the strength estimated by the rule-of-mixtures. A non-linear combined isotropic and kinematic hardening model was used to estimate the strength enhancement from back-stress hardening, and the simulation results were correlated with the experimental results. This result shows that the back-stress evolution in heterogeneous materials contributes to their strength, and that the non-linear combined isotropic and kinematic hardening should be included to estimate the degree of back-stress hardening.

Effect of Fe2Zr phase on the mechanical properties and fracture behavior of Fe-Cr-W-Zr ferritic alloy

Two Fe-9Cr-2W-Zr ferritic alloys with Zr contents of ~7 and ~10 wt% were designed to investigate the effect of Fe2Zr phase on the mechanical properties and fracture behavior. It is found that after hot deformation and annealing, the as-cast lamellar eutectic structures are destroyed, showing a microstructure consisting of dispersed micrometer-sized Fe2Zr phases and equiaxed α-Fe grains. The area fraction of Fe2Zr phase increases with the increase of Zr content, and the strengthening effect of dispersed Fe2Zr phases leads to a remarkable increase in the strength and a decrease in the ductility at room and elevated temperature. Compared with 9Cr2WVTa steel, Fe-Cr-W-Zr ferritic alloy with the Zr content of ~10 wt% presents a higher strength-ductility synergy at elevated temperature. Investigation on the fracture process shows that the critical event controlling fracture at room temperature is the nucleation of cracks within Fe2Zr phases due to the plastic strain incompatibility between the soft α-Fe and hard Fe2Zr phases, which further leads to the cleavage fracture of α-Fe matrix. When tensile at 973 K, ductile α-Fe matrix could retard the nucleation and propagation of cracks, resulting in the enhanced high-temperature ductility. Besides, the excellent thermal stability of α-Fe grain boundaries and Fe2Zr/matrix interfaces in the Fe-Cr-W-Zr ferritic alloy ensures better creep-rupture properties than 9Cr2WVTa steel.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: ε′f and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: εf′ and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

Superior high tensile elongation of a single-crystal CoCrFeNiAl0.3 high-entropy alloy by Bridgman solidification

The crystallographic orientation, tensile behavior, fracture mechanism, hardness, and elastic modulus of a single-crystal CoCrFeNiAl0.3 high-entropy alloy (HEA) successfully synthesized by Bridgman solidification are investigated in detail. The growth direction of the single-crystal product mainly focuses on the <001> orientation. An ultimate tensile elongation of about 80% is achieved in the single-crystal alloy, accompanied by a large work-hardening exponent and a shear-fracture mode. A quantitative Hall–Petch relationship for the current HEA can be obtained as σy=171.65+0.73/d. The single-crystal sample displays a relatively-lower elastic modulus than the as-cast counterpart, indicating the anisotropy of elastic modulus. The outstanding tensile ductility for the single-crystal product is attributed to (1) low-angle grain boundaries and thus less distance to dislocation motion; and (2) single <001> crystallographic orientation and therefore less plastic-strain incompatibility.

Grain boundary structure and intergranular stress corrosion crack initiation in high temperature water of a thermally sensitised austenitic stainless steel, observed in situ

The development of an intergranular stress corrosion crack initiation site in thermally sensitised type 304 austenitic stainless steel has been observed in situ in high temperature oxygenated water using digital image correlation of time-resolved optical observations. The grain boundary normal stresses were calculated using the Schmid-Modified Grain Boundary Stress (SMGBS) model of Was et al., applying three-dimensional data for the grain boundary planes and grain orientations. The initiation site coincided with the most highly stressed sensitised boundary, demonstrating the importance of the combined contributions to crack initiation of grain boundary structure and plastic strain incompatibility.

Deformation behavior of a statically recrystallized Mg–Zn–MM alloy sheet

For a warm rolled Mg–Zn–MM (Misch Metal) alloy sheet, the static recrystallization process is adapted to develop a weak-textured microstructure with an average grain size of 4µm. Due to the relatively low recrystallization temperature of the alloy, the sheet can be fabricated by the warm rolling process and then recrystallized at 220°C. Enhanced ductility is observed from room temperature to 350°C. In addition to the basal slips within the grains, at room temperature nano-twins actively form near the grain boundaries, accommodating the plastic strain incompatibility near the grain boundaries. Moreover, above 150°C, dynamic recrystallized grains are actively developed during deformation. In the temperature range of 100–350°C, the values of elongation to failure are approximately 40% higher than those of the AZ31 alloy sheet without the loss of tensile strength.

Modeling the interfacial plastic strain incompatibilities associated with dispersed particles in high strength aluminum alloys

A new formulation based on an eigenstrain representation of Orowan looping was developed, and was coupled with a dislocation density based crystalline plasticity formulation and a specialized finite element framework to model the unrelaxed plastic strain and interfacial behavior associated with dispersed particles in high strength aluminum alloys. This representation accounts for the increased stresses associated with Orowan looping at interfacial locations, where extra half-planes due to Orowan loops occur at opposite particle corners. Plastic relaxation of the Orowan loops was modeled using the incompatibility of the lattice rotations between the particles and the alloy matrix. The predictions indicate that the orientations and morphologies of the particles with respect to the most active slip plane are the critical factors in the relaxation of the eigenstrains associated with the loops.

Strain gradient plasticity modelling of high-pressure torsion

Gradient plasticity modelling combining a micro-structure-related constitutive description of the local material behaviour with a particular gradient plasticity frame is presented. The constitutive formulation is based on a phase mixture model in which the dislocation cell walls and the cell interiors are considered as separate ‘phases’, the respective dislocation densities entering as internal variables. Two distinct physical mechanisms, which give rise to gradient plasticity, are considered. The first one is associated with the occurrence of geometrically necessary dislocations leading to first-order strain gradients; the second one is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains, which lead to second-order strain gradients. These two separate variants of gradient plasticity were applied to the case of high-pressure torsion: a process known to result in a fairly uniform, ultrafine grained structure of metals. It is shown that the two complementary variants of gradient plasticity can both account for the experimental results, thus resolving a controversial issue of the occurrence of a uniform micro-structure as a result of an inherently non-uniform process.

ECCI Observation of Dislocation Structure Formed around an Intergranular Fatigue Crack in Copper

A fatigue crack growth test was conducted in a polycrystalline copper. Dislocation structure formed near an intergranular fatigue crack was investigated by electron channelling contrast imaging (ECCI) method. The ECCI method enables us to observe dislocations lying under surface using a scanning electron microscope. The fatigue crack in the copper specimen was grown along both grain boundaries and slip bands inside grain. The ECCI observations revealed that both the vein dislocation structure and the cell structures were formed near the grain boundaries. The formations of different dislocation structures near boundaries could be interpreted in terms of the plastic strain incompatibility.

Fracture behaviors of AZ80 magnesium alloy during multiple forging processes

The initiation, propagation and the accompanied dislocation structures of the cracks in AZ80 magnesium alloy during multiple forging processes were investigated. The results show that the cracks firstly initiate at the Mg/Mg 17Al 12 interface under the hoop tensile stress on equatorial free surface. On further deformation, the cracks in the Mg 17Al 12 particles tend to propagate along the grain boundaries(GBs) in a zigzag pattern and link with adjacent cracks in other Mg 17Al 12 particles to form one whole crack, leading to the fracture surface. Low deformation temperature and too many forging passes during the deformation will promote the nucleation of interfacial microcrack inside the specimens due to the strong plastic strain incompatibility and the high internal stresses near the GBs. The loading axis rotating during the process can change the stress field at the tip of cracks, leading to the change of the crack propagating path and assisting in inhabiting microcracking development.

The influence of dispersion particles on the Portevin–Le Chatelier effect: from average particle characteristics to particle arrangement

Abstract The Portevin–Le Chatelier (PLC) effect in Al–Mg alloys reinforced with second-phase particles was studied both experimentally and by computer simulation. An emphasis is placed on the understanding of the influence of the arrangement, and not just the volume fraction and average spacing of particles, on plastic instability. Statistical properties of stress jumps, sensitive to the dynamical features of plastic instability, were analyzed alongside macroscopic characteristics of stress–strain curves. The analysis provides a quantitative basis for a comparison between the observed and the simulated behavior of materials with different particle populations. The computer model comprises several principal ingredients: (i) a local feature of the negative strain rate sensitivity of stress (ii) non-local effects stemming from plastic strain incompatibilities and accounted for by an elastic-type spatial coupling and (iii) the particle distribution included in the model with the aid of the Voronoi mesh technique.

Grain-size effects on tensile behavior of nickel and AISI 316L stainless steel

The aim of this work is to provide experimental results to understand the grain-size effects on tensile hardening of fcc polycrystalline materials. The contribution of grain size on hardening rate is discussed in terms of backstress (X) and effective-stress (Σ ef) evolutions in the different hardening stages. Based on this stress partition, the origin of the classical Hall-Petch relationship is clarified at the different levels of microstructural heterogeneities. If the backstresses and effective stresses verified the Hall-Petch formulation, however, the effective stress is less dependent on grain size than the backstress. The grain-size effect on short-range internal stresses (effective stress) is well explained in terms of a mean path length using classical dislocation modeling. The backstress dependence on grain size seems to be mainly the result of intergranular plastic-strain incompatibilities in relation with the formation of a grain-boundary layer in stage I. In others stages (higher plastic strain), the interactions between intergranular and intragranular long-range internal stresses have been illustrated. The degree of these interactions remains unclear.

Cyclic stress–strain response of textured Zircaloy-4

In this paper, the cyclic stress–strain response of textured Zircaloy-4 is investigated at room temperature in an incremental step test using fully reversed tension–compression loading under strain control. The material exhibits an asymmetry of stress response in both rolling and transverse directions, and the corresponding cyclic stress–strain curves can be expressed by a power law relation. Furthermore, phenomenological friction and back stresses are derived from an analysis of hysteresis loop shapes using the Cottrell scheme. It has been shown that the magnitude of the phenomenological friction stress in compression is always higher than that in tension for either rolling or transverse direction. While the magnitude of the phenomenological back stress, being independent of the loading direction, increases much more rapidly in transverse direction than that in rolling direction with increasing the plastic strain amplitude, and the trend in both directions can be expressed by a logarithmic relation. A further discussion suggests that (i) the intergranular thermal stress in the material is responsible for the difference in the phenomenological friction stress between tension and compression, thus leading to the asymmetry of stress response; (ii) the increase of the saturated stress with the plastic strain amplitude stems from the back stress that is primarily a direct consequence of the plastic strain incompatibilities between grains; (iii) the different performance between rolling and transverse directions results from the texture effect.