Mechanics of a nanocrystalline coating and grain-size dependence of its plastic strength

From the mechanics perspective the most critical properties of a coating material are likely its yield strength, hardness, and wear resistance. These properties are intimately related to each other as a material with high yield strength usually also possesses superior hardness and strong wear resistance. Our objective in this study is to seek for the strongest material state in terms of its plastic strength, and the critical grain size at which this strength can be attained. Based on the cross-sectional morphology of a nanocrystalline coating we first conceive a composite plate model consisting of the columnar grains and the grain boundary affiliated region (broadly called the GB zone), and present a plane-stress theory to investigate its in-plane behavior. We then make use of a linear comparison composite and a field fluctuation approach to explore the competition between the grain interior and the plastically softer GB zone as the grain size decreases from the coarse grain to the nanometer range. Based on the developed model the anisotropic stress-strain relations of a ZrN coating are illustrated as a function of grain size in both in-plane and out-of-plane directions. It is demonstrated that, as the grain size decreases, the variation of plastic strength in the Hall-Petch plot undergoes a transition from a positive to a negative slope, exhibiting the Hall-Petch and the inverse Hall-Petch effects. The strength-differential effect between tension and compression is also observed. The critical grain sizes at which the maximum strength develops are found to be lower along the out-of-plane direction than along the in-plane ones, and also lower under compression than under tension. Based on Tabor’s law, our calculated critical grain size for the hardness was about 16 nm, while a recent indentation test indicated a range of 14.2-19 nm. The existence of Hall-Petch, inverse Hall-Petch, and strength-differential effects, and of an optimal grain size, is thus theoretically proven for the first time for nanocrystalline coatings.     

Mechanical properties of Fe-Co soft magnets

The tensile behavior of two magnetically soft alloys, Fe-49Co-2V and Fe-27Co, has been characterized as a function of testing temperature, grain size, and degree of long-range order. Several trends in the yield strength of the two alloys have been noted and possible mechanisms for their occurrence discussed. Ordering is found to markedly lower the yield strength of the Fe-49Co-2V. Both alloys exhibit three distinct regions in their yield strength vs. temperature curves. At lower and higher temperatures, i.e. regions I and III, the yield strength shows the normal drop with increasing temperature. In the intermediate temperature range (region II), however, Fe-49Co-2V with a B2 ordered structure demonstrates an anomalous strengthening with increasing temperature while the yield strength remains constant in the disordered Fe-27Co. Both alloys exhibit a Hall-Petch type relationship in their yield strength as a function of grain size and show a decrease in the strain hardening coefficient with increasing grain size.     

Nanomechanics of Hall-Petch relationship in nanocrystalline materials

Classical Hall-Petch relation for large grained polycrystals is usually derived using the model of dislocation pile-up first investigated mathematically by Nabarro and coworkers. In this paper the mechanical properties of nanocrystalline materials are reviewed, with emphasis on the fundamental physical mechanisms involved in determining yield stress. Special attention is paid to the abnormal or ‘inverse’ Hall-Petch relationship, which manifests itself as the softening of nanocrystalline materials of very small (less than 12 nm) mean grain sizes. It is emphasized that modeling the strength of nanocrystalline materials needs consideration of both dislocation interactions and grain-boundary sliding (presumably due to Coble creep) acting simultaneously. Such a model appears to be successful in explaining experimental results provided a realistic grain size distribution is incorporated into the analysis. Masumura et al. [Masumura RA, Hazzledine PM, Pande CS. Acta Mater 1998;46:4527] were the first to show that the Hall-Petch plot for a wide range of materials and mean grain sizes could be divided into three distinct regimes and also the first to provide a detailed mathematical model of Hall-Petch relation of plastic deformation processes for any material including fine-grained nanocrystalline materials. Later developments of this and related models are briefly reviewed.Prof. Frank Nabarro was a physicist by training, a metallurgist by profession and a genius by nature, blessed with a unique ability to treat everyone as his equal. During his later years he was very much interested in the mechanical properties of nanocrystalline materials. This review on that topic is our contribution to the special issue of Progress in Materials Science honoring him.     

Changes in texture and grain size in hot rolled magnesium and effect on yield strength

Variations in the grain size and basal texture in magnesium hot-rolled in the temperature range 570–770 K have been studied and compared with those observed in specimens hot-rolled at 570 K and annealed at different temperatures in the range 570–770 K. In specimens hot-rolled temperatures higher than 670 K, a rapid increase in grain size and a weakening in basal texture have been observed. The yield stress of the specimen is lower than that predicted by the Hall-Petch relation and this result is interpreted in terms of the reduced basal texture. The dependence of yield stress on grain size in magnesium hot-rolled at different temperatures lower than 670 K matches with that observed in specimens annealed at different temperatures.     

Effect of grain size on the tensile deformation of wrought Mg-MM-Al-Zn-Sn alloy

The effect of grain size on the tensile deformation of Mg-MM-Al-Zn-Sn (EAZT211) alloy sheet has been investigated. Specimens with grain size varying from ~ 10 to ~ 20 μm have been obtained by altering the annealing conditions after rolling. The yield strength of EAZT211 sheet exhibits grain size dependence according to Hall-Petch relationship from room temperature to 200 °C. Occurrence of yield phenomenon and decrease of Hall-Petch slope (k) with increasing strain suggest that non-basal slip system operates during deformation. In addition, deformation mechanism changes from slip mechanism to grain boundary sliding mechanism at ~ 150 °C.     

Effect of Microstructure Refinement on the Strength and Toughness of Low Alloy Martensitic Steel

Martensitic microstructure in quenched and tempered 17CrNiMo6 steel with the prior austenite grain size ranging from 6 μm to 199 μm has been characterized by optical metallography （OM）, scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. The yield strength and the toughness of the steel with various prior austenite grain sizes were tested and correlated with microstructure characteristics. Results show that both the prior austenite grain size and the martensitic packet size in the 17CrNiMo6 steel follow a HalI-Petch relation with the yield strength. When the prior austenite grain size was refined from 199 μm to 6 μm , the yield strength increased by 235 MPa, while the Charpy U-notch impact energy at 77 K improved more than 8 times, indicating that microstructure refinement is more effective in improving the resistance to cleavage fracture than in increasing the strength. The fracture surfaces implied that the unit crack path for cleavage fracture is identified as being the packet.     

Characterization of Grain Size and Yield Strength in AISI 301 Stainless Steel Using Ultrasonic Attenuation Measurements

AISI 301 stainless steel samples were annealed over the temperature range of 800?C1200°C for 60?minutes to produce different grain sizes. These samples were characterized by ultrasonic immersion technique, tensile test, and optical microscopy. The attenuation of ultrasonic waves measured at a frequency of 20?MHz showed a good correlation with average grain size, hardness, and yield strength of AISI 301 stainless steel samples. A?new equation was derived for calculation of yield strength on the basis of ultrasonic wave attenuation and Hall-Petch relation.     

纳米TiO2的Raman光谱研究进展

Raman光谱是研究纳米TiO2结构的最常用工具之一.纳米T2O2的Raman光谱研究是建立在以前对TiO2体材料的Raman光谱研究的基础之上.但是纳米TiO2与体相材料的表面性质和结构有较大的不同,其Raman光谱会产生明显变化.研究人员对纳米TiO2的Raman光谱已展开研究.本文概述了晶粒大小、结构、氧空位、退火温度、压力、相组成等因素对纳米TiO2的Raman光谱的影响.     

Structure-sensitive properties during room-temperature wire drawing at various speeds in nickel 200

The effects of drawing speed, cell size and grain size on the yield strength of nickel 200 wires drawn at room temperature up to a true strain of 2.09 have been investigated. The wire drawing speeds in the range from 17 to 140 mm s^–1 do not show any effect on the yield strength, cell size and grain size of drawn wires. However, the cell sizes as well as grain sizes decrease with increase in true wire drawing strain when their values are averaged over all the wire drawing speeds at a given strain. Even though the Hall-Petch equation is valid for all the grain diameters observed in this study, the graph suggests that two distinct linear regimes may be more appropriate to properly describe the strengthening mechanisms during wire drawing. The cell diameter has been correlated with the yield strengths of drawn wires by an inverse relationship.     

The combined influence of grain size distribution and dislocation density on hardness of interstitial free steel

Understanding the relationship between microstructure features and mechanical properties is of great significance for the improvement and specific adjustment of steel properties. The relationship between mean grain size and yield strength is established by the well-known Hall-Petch equation. But due to the complexity of the grain configuration within materials, considering only the mean value is unlikely to give a complete representation of the mechanical behavior. The classical Taylor equation is often used to account for the effect of dislocation density, but not thoroughly tested in combination with grain size influence. In the present study, systematic heat treatment routes and cold rolling followed by annealing are designed for interstitial free(IF) steel to achieve ferritic microstructures that not only vary in mean grain size, but also in grain size distribution and in dislocation density, a combination that is rarely studied in the literature. Optical microscopy is applied to determine the grain size distribution. The dislocation density is determined through XRD measurements. The hardness is analyzed on its relation with the mean grain size, as well as with the grain size distribution and the dislocation density. With the help of the variable selection tool LASSO, it is shown that dislocation density, mean grain size and kurtosis of grain size distribution are the three features which most strongly affect hardness of IF steel.     

Influence of grain size on the mechanical behaviour of some high strength materials

Combining in an additive or synergetic manner the most potent strengthening mechanisms available in an alloy is the art of the metallurgist. The various models proposed in the literature in order to interpret the Hall-Petch relation are critically reviewed by comparison with experimental data. The pile-up models and the work hardening theories must include the inner structure of the grain in the case of alloys hardened by a second phase. Similarly, the properties and structure of the grain boundaries are influenced by impurities or the presence of particles. Ultra-fine grain sizes can provide ductility to high strength materials when surface preparation eliminates microcracks.In steady-state creep equations, introducing the influence of grain size in complex alloys by incorporating the Hall-Petch stress as one component of the internal stress helps in rationalizing the existence of an optimal grain size where creep resistance is maximized. Slower crack growth rates can be obtained by controlling the grain boundary structure as well as grain size. Fatigue tests at room temperature clearly point out the interest of small grain sizes for reducing crack initiation, usually associated, however, with lower propagation threshold and somewhat faster growth rates.     

Enhanced Hall-Petch strengthening in graphene/Cu nanocomposites

Grain size dependent strength,known as Hall-Petch relation,has been approved to be valid in crystalline metals and alloys.However,softening would eventually occur as grain size reduced into nanoscale that below a critical value.Hence,it is essential to find a way to break the strength limitation by avoiding the deformation mechanism transition from dislocation-mediated to grain-boundary-mediated processes.By replacing grain boundary (GB) of nanocrystalline Cu with graphene,in the present study,molecular dynamics simulations show that graphene-boundary (GrB) embedded GrB/Cu nanocomposites exhibit enhanced enlarged Hall-Petch slope with decreasing grain size.The absence ofinverse-Hall-Petch relation and the extremely high strength derived at the GrB/Cu nanocomposites were interpreted by the high back stress and abundant dislocation activity that attributed from the high-degree of heterogeneous structure of the nanocomposites.     

Tensile strength and flux pinning force of superconducting Nb3Sn compound as a function of grain size

In order to evaluate the influence of grain size on the strength and flux pinning force of the Nb₃Sn compound, the microstructure, tensile behaviour and flux pinning force of the bronze-processed Nb₃Sn superconducting composite materials were investigated under various heat treatments. It was found that the strength of the Nb₃Sn layer has a strong dependency on the grain size and it can be expressed by the Hall-Petch type relation. The flux pinning force was roughly proportional to the inverse grain size, agreeing with the results of former investigations.     

Hall-Petch relationship in Mg alloys: A review

Grain refinement could effectively enhance yield strength of Mg alloys according to the well-known Hall-Petch theory. For decades, many studies have been devoted to the factors influencing the Hall-Petch slope (k) in Mg alloys. Understanding the factors influencing k and their mechanisms could offer guidance to design and produce high-strength Mg alloys through effective grain refinement hardening. A review and comments of the past work on the factors influencing k in Mg alloys are presented. Results of these previous investigations demonstrate that the value of k in Mg alloys varies with texture, grain size, temperature and stain. The influence of texture and grain size on k is found to be an essential result of the variation of deformation mode on k value. Without the variation of deformation modes, it is revealed that texture could also impose a significant effect on k and this is also summarized and discussed in this paper. The reason for texture effect on k is analyzed based on the mechanism of Hall-Petch relationship. In addition, it is found in face-centered cubic (fcc) or body-centered cubic (bcc) metals that boundary parameters (boundary coherence, boundary energy and boundary diffusivity) could strengthen twinning or slips to a different extent. Therefore, the role of boundary parameters is also extended into the k values in Mg alloys and discussed in this paper. In the end, we discuss the future research perspective of Hall-Petch relationship in Mg alloys.     

On the Influence of Microstructure on the Fracture Behavior of Gamma-Based Titanium Aluminides. I. Effects of Alloying with Mn

The results of a study of the effects of grain size on the tensile and fracture properties of Mn-containing gamma alloys are presented in part I of this paper. Ductility and yield/ultimate tensile strengths at room- and elevated-temperature are shown to exhibit a simple Hall-Petch dependence on the average grain/lamellar packet size. The observed Hall-Petch behavior is found to be independent of lamellar volume fraction and fracture mechanism at room - and elevated-temperature. The implications of the results are discussed for future alloy/process development.     

Influence of grain size on tensile properties of Al-Mg alloys

Abstract

Grain size refinement is an important strengthening mechanism in Al-Mg 5000 series alloys, which have a relatively large Hall-Petch slope compared with other Al alloys. In addition, the high work hardening rate exhibited by Al-Mg alloys provides excellent formability. This paper investigates the influence of grain size on the flow stress over a range of strains, and in several different Al-Mg alloys. It is found that the Hall-Petch slope decreases after yield, indicating that the large grain size effect is primarily associated with initiating plasticity in these alloys. Beyond yield the slope decreases to a value equivalent to other, non-Mg containing alloys, and shows no clear dependence on strain. The intercept stress from the Hall-Petch plots at different strains is non-linear with ? 1/2 for alloys containing up to 3 wt-%Mg, which indicates that the free slip distance is strain dependent in these alloys. In an Al-5 wt-%Mg alloy the intercept stress is linear with ? 1/2, indicating that solute atoms are controlling the free slip distance. If Mn is added to the Al-5 wt-%Mg alloy, as it is in commercial alloys, it has little influence on the grain size dependence, but it does increase the frictional stress at the highest Mn level of 0.7 wt-%.     

Effects of microstructural variables on the deformation behaviour of dual-phase steel

An expression for the stress of martensite in dual-phase steel was developed, which shows the interdependence of the stress of martensite and strain hardening in the ferrite matrix and the contribution of microstructural variables (the volume fraction of martensite f_m, ferrite grain size d_f, and martensite particle size d_m). The onset of plastic deformation of martensite in dual-phase steel was predicted to depend on its yield strength and the microstructural variables, and this was verified by the modified Crussard-Jaoul analysis. It was found that for this dual-phase steel, refining the grain size and increasing f_m increase the flow stress and raise the strain hardening rate at low strains, but little affect the strain hardening rate at high strains. The effect of the ferrite grain size on the flow stress of this dual-phase steel was found to obey the Hall-Petch relation, i.e. σ = σ₀^e + K^ed_f^−1/2, where the Hall-Petch intersection σ₀^e and slope K^e are functions of strain, f_m and d_m. The effects of the plastic deformation of martensite and the microstructural variables on the strain hardening rate and the Hall-Petch behaviour were analysed in terms of the densities of statistically stored dislocations and geometrically necessary dislocations using the previously developed theoretical model.     

Grain-refining and strengthening mechanisms of bulk ultrafine grained CP-Ti processed by L-ECAP and MDF

The microstructural evolution and mechanical properties of ultrafine-grained(UFG)CP-Ti after an inno-vative large-volume equal channel angular pressing(L-ECAP)and multi-directional forging(MDF)were systematically examined using monotonic tensile tests combined with transmission electron microscope(TEM)and electron backscatter diffraction(EBSD)techniques.Substantially refined and homogeneous microstructures were achieved after L-ECAP(8-pass and 12-pass)and MDF(2-cycle and 3-cycle),respec-tively,where the grain size distribution conformed to lognormal distribution.The grain refinement of 450℃L-ECAP is dominated by dynamic recrystallization(DRX)and dynamic recovery(DRV),while that of MDF is dominated by DRX.The iron impurities promote recrystallization by pinning-induced dislocation accumulation so that DRX is prone to occur at iron segregation regions during L-ECAP.The monotonic tensile results show that the strain hardening rate of CP-Ti increases with the decrease of grain size,while the continuous strain hardening ability decreases.The relationship between the average grain size and yield strength is in accordance with Hall-Petch relationship.Meanwhile,the individual strength-ening mechanisms were quantitatively examined by the modified model.The results indicate that the strengthening contribution of dislocation accumulation to yield strength is greater than that of grain refinement.     

On the Influence of Microstructure on the Fracture Behavior of Gamma-Based Titanium Aluminides. III. Effects of Interstitials and Microalloying with W

The results of a recent study of the effects of interstitial elements and microalloying with 0.2 at.% W on the tensile and fracture properties of Ti-48Al (compositions quoted in atomic % unless stated otherwise) base gamma alloys are presented in this paper. Lower interstitial oxygen levels are shown to promote higher levels of tensile ductility at the expense of yield/ultimate tensile strength and fracture toughness. Microalloying with W is also shown to result in microstructural instability and a concomitant degradation in tensile and fracture properties. Ductility and yield/ultimate tensile strengths in binary gamma alloys at room - and elevated-temperature are shown to exhibit a simple Hall-Petch dependence on the average grain/lamellar packet size. The observed Hall-Petch behavior is found to be independent of lamellar volume fraction and fracture mechanism at room- and elevated-temperature. The implications of the results are discussed for future alloy/process development.     

Hall-Petch relationship in two-phase TiAl alloys with fully lamellar microstructures

The dependences of the room temperature tensile properties of two-phase TiAl alloys with fully lamellar microstructures on colony size and the effects of alloying elements on the k value of Hall-Petch relationship were investigated. It is found that the ultimate tensile strength and the yield strength show Hall-Petch dependences on colony size, but the ductility does not obey a Hall-Petch dependence on colony size. The k value of Hall-Petch relationship increases when Ti-47Al (at.%) is alloyed with interstitial elements C or B, but the additions of substitutional elements Cr or Nb don’t lead to its apparent change.