Yield strength anomaly

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In materials science, the yield strength anomaly refers to materials wherein the yield strength (i.e., the stress necessary to initiate plastic yielding) increases with temperature. [1] [2] [3] For the majority of materials, the yield strength decreases with increasing temperature. In metals, this decrease in yield strength is due to the thermal activation of dislocation motion, resulting in easier plastic deformation at higher temperatures. [4]

Contents

In some cases, a yield strength anomaly refers to a decrease in the ductility of a material with increasing temperature, which is also opposite the trend in the majority of materials. Anomalies in ductility can be more clear, as an anomalous effect on yield strength can be obscured by its typical decrease with temperature. [5] In concert with yield strength or ductility anomalies, some materials demonstrate extrema in other temperature dependent properties, such as a minimum in ultrasonic damping, or a maximum in electrical conductivity. [6]

The yield strength anomaly in β-brass was one of the earliest discoveries such a phenomenon, [7] and several other ordered intermetallic alloys demonstrate this effect. Precipitation-hardened superalloys exhibit a yield strength anomaly over a considerable temperature range. For these materials, the yield strength shows little variation between room temperature and several hundred degrees Celsius. Eventually, a maximum yield strength is reached. For even higher temperatures, the yield strength decreases and, eventually, drops to zero when reaching the melting temperature, where the solid material transforms into a liquid. For ordered intermetallics, the temperature of the yield strength peak is roughly 50% of the absolute melting temperature. [8]

Mechanisms

Thermally Activated Cross Slip

A number of alloys with the L12 structure (e.g., Ni3Al, Ni3Ga, Ni3Ge, Ni3Si), show yield strength anomalies. [9] The L12 structure is a derivative of the face-centered cubic crystal structure. For these alloys, the active slip system below the peak is ⟨110⟩{111} while the active system at higher temperatures is ⟨110⟩{010}. The hardening mechanism in these alloys is the cross slip of screw dislocations from (111) to (010) crystallographic planes. [10] This cross slip is thermally activated, and the screw dislocations are much less mobile on the (010) planes, so the material is strengthened as temperatures increases and more screw dislocations are in the (010) plane. A similar mechanism has been proposed for some B2 alloys that have yield strength anomalies (e.g., CuZn, FeCo, NiTi, CoHf, CoTi, CoZr). [8]

The yield strength anomaly mechanism in Ni-based superalloys is similar. [11] In these alloys, screw superdislocations undergo thermally activated cross slip onto {100} planes from {111} planes. This prevents motion of the remaining parts of the dislocations on the (111)[-101] slip system. Again, with increasing temperature, more cross-slip occurs, so dislocation motion is more hindered and yield strength increases.

Grain Boundary Precipitation

In superalloys strengthened by metal carbides, increasingly large carbide particles form preferentially at grain boundaries, preventing grain boundary sliding at high temperatures. This leads to an increase in the yield strength, and thus a yield strength anomaly. [5]

Vacancy Activated Strengthening

While FeAl is a B2 alloy, the observed yield strength anomaly in FeAl is due to another mechanism. If cross-slip were the mechanism, then the yield strength anomaly would be rate dependent, as expected for a thermally activated process. Instead, yield strength anomaly is state dependent, which is a property that is dependent on the state of the material. As a result, vacancy activated strengthening is the most widely-accepted mechanism. [12] The vacancy formation energy is low for FeAl, allowing for an unusually high concentration of vacancies in FeAl at high temperatures (2.5% at 1000C for Fe-50Al). The vacancy formed in either aluminum-rich FeAl or through heating is an aluminum vacancy. [13]

At low temperatures around 300K, the yield strength either decreases or does not change with temperature. At moderate temperatures (0.35-0.45 Tm), yield strength has been observed to increase with an increased vacancy concentration, providing further evidence for a vacancy driven strengthening mechanism. [13] [8] The increase in yield strength from increased vacancy concentration is believed to be the result of dislocations being pinned by vacancies on the slip plane, causing the dislocations to bow. Then, above the peak stress temperature, vacancies can migrate as vacancy migration is easier with elevated temperatures. At those temperatures, vacancies no longer hinder dislocation motion but rather aid climb. In the vacancy strengthening model, the increased strength below the peak stress temperature is approximated as proportional to the vacancy concentration to the one-half with the vacancy concentration estimated using Maxwell-Boltzmann statistics. Thus, the strength can be estimated as , with being the vacancy formation energy and T being the absolute temperature. Above the peak stress temperature, a diffusion-assisted deformation mechanism can be used to describe strength since vacancies are now mobile and assist dislocation motion. Above the peak, the yield strength is strain rate dependent and thus, the peak yield strength is rate dependent. As a result, the peak stress temperature increases with an increased strain rate. Note, this is different than the yield strength anomaly, which is the yield strength below the peak, being rate dependent. The peak yield strength is also dependent on percent aluminum in the FeAl alloy. As the percent aluminum increases, the peak yield strength occurs at lower temperatures. [8]

The yield strength anomaly in FeAl alloys can be hidden if thermal vacancies are not minimized through a slow anneal at a relatively low temperature (~400 °C for ~5 days). [14] Further, the yield strength anomaly is not present in systems that use a very low strain rate as the peak yield strength is strain rate dependent and thus, would occur at temperatures too low to observe the yield strength anomaly. Additionally, since the formation of vacancies requires time, the peak yield strength magnitude is dependent on how long the material is held at the peak stress temperature. Also, the peak yield strength has been found not to be dependent on crystal orientation. [8]

Other mechanisms have been proposed including a cross slip mechanism similar to that for L12, dislocation decomposition into less mobile segments at jogs, dislocation pinning, climb-lock mechanism, and slip vector transition. The slip vector transition from <111> to <100>. At the peak stress temperature, the slip system changes from <111> to <100>. The change is believed to be a result of glide in <111> becoming more difficult as temperature increases due to a friction mechanism. Then, dislocations in <100> have easier movement in comparison. [15] Another mechanism combines the vacancy strengthening mechanism with dislocation decomposition. FeAl with the addition of a tertiary additive such as Mn has been shown to also exhibit the yield stress anomaly. In contrast to FeAl, however, the peak yield strength or peak stress temperature of Fe2MnAl is not dependent on strain rate and thus, may not follow the vacancy activated strengthening mechanism. Instead, there an order-strengthening mechanism has been proposed. [8]

Applications

Turbines and Jet Engines

The yield strength anomaly is exploited in the design of gas turbines and jet engines that operate at high temperatures, where the materials used are selected based on their paramount yield and creep resistance. Superalloys can withstand high temperature loads far beyond the capabilities of steels and other alloys, and allow operation at higher temperatures, which improves efficiency. [16]

Nuclear Reactors

Materials with yield strength anomalies are used in nuclear reactors due to their high temperature mechanical properties and good corrosion resistance. [5]

Related Research Articles

In metallurgy, a shape-memory alloy (SMA) is an alloy that can be deformed when cold but returns to its pre-deformed ("remembered") shape when heated. It may also be called memory metal, memory alloy, smart metal, smart alloy, or muscle wire.

Creep (deformation) Tendency of a solid material to move slowly or deform permanently under mechanical stress

In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.

Work hardening Strengthening a material through plastic deformation

In materials science, work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.

Precipitation hardening, also called age hardening or particle hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel, titanium, and some steels and stainless steels. In superalloys, it is known to cause yield strength anomaly providing excellent high-temperature strength.

Superalloy Alloy with higher durability than normal metals

A superalloy, or high-performance alloy, is an alloy with the ability to operate at a high fraction of its melting point. Several key characteristics of a superalloy are excellent mechanical strength, resistance to thermal creep deformation, good surface stability, and resistance to corrosion or oxidation.

The Portevin–Le Chatelier (PLC) effect describes a serrated stress–strain curve or jerky flow, which some materials exhibit as they undergo plastic deformation, specifically inhomogeneous deformation. This effect has been long associated with dynamic strain aging or the competition between diffusing solutes pinning dislocations and dislocations breaking free of this stoppage.

Heusler compound

Heusler compounds are magnetic intermetallics with face-centered cubic crystal structure and a composition of XYZ (half-Heuslers) or X2YZ (full-Heuslers), where X and Y are transition metals and Z is in the p-block. The term derives from the name of German mining engineer and chemist Friedrich Heusler, who studied such a compound (Cu2MnAl) in 1903. Many of these compounds exhibit properties relevant to spintronics, such as magnetoresistance, variations of the Hall effect, ferro-, antiferro-, and ferrimagnetism, half- and semimetallicity, semiconductivity with spin filter ability, superconductivity, topological band structure and are actively studied as Thermoelectric materials. Their magnetism results from a double-exchange mechanism between neighboring magnetic ions. Manganese, which sits at the body centers of the cubic structure, was the magnetic ion in the first Heusler compound discovered. (See the Bethe–Slater curve for details of why this happens.)

Titanium aluminide, TiAl, commonly gamma titanium, is an intermetallic chemical compound. It is lightweight and resistant to oxidation and heat, but has low ductility. The density of γ-TiAl is about 4.0 g/cm3. It finds use in several applications including aircraft, jet engines, sporting equipment and automobiles. The development of TiAl based alloys began circa 1970. The alloys have been used in these applications only since about 2000.

Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element, forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms.

Nickel aluminide typically refers to the one of the two most widely used compounds, Ni3Al or NiAl, however is generally any aluminide from the Ni-Al system. These alloys are widely used due to their corrosion resistance, low-density and easy production. Ni3Al is of specific interest as the strengthening γ' phase precipitate in nickel-based superalloys allowing for high temperature strength up to 0.7-0.8 of its melting temperature. Meanwhile, NiAl displays excellent properties such as low-density (lower than that of Ni3Al), good thermal conductivity, oxidation resistance and high melting temperature. These properties, make it ideal for special high temperature applications like coatings on blades in gas turbines and jet engines. However, both these alloys do have the disadvantage of being quite brittle at room temperature while Ni3Al remains brittle at high temperatures as well. Although, it has been shown that Ni3Al can be made ductile when manufactured as a single crystal as opposed to polycrystalline. Another application was demonstrated in 2005, when the most abrasion-resistant material was reportedly created by embedding diamonds in a matrix of nickel aluminide.

Directional solidification

Directional solidification(DS) and progressive solidification are types of solidification within castings. Directional solidification is solidification that occurs from farthest end of the casting and works its way towards the sprue. Progressive solidification, also known as parallel solidification, is solidification that starts at the walls of the casting and progresses perpendicularly from that surface.

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.

Grain boundary strengthening

Grain-boundary strengthening is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain has an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain, too. So, by changing grain size one can influence the number of dislocations piled up at the grain boundary and yield strength. For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size.

Oxide dispersion strengthened alloys (ODS) are alloys that consist of a metal matrix with small oxide particles dispersed within it. They have high heat resistance, strength, and ductility. Alloys of nickel are the most common but includes iron aluminum alloys.

Low hydrogen annealing, commonly known as "baking" is a heat treatment in metallurgy for the reduction or elimination of hydrogen in a material to prevent hydrogen embrittlement. Hydrogen embrittlement is the hydrogen-induced cracking of metals, particularly steel which results in degraded mechanical properties such as plasticity, ductility and fracture toughness at low temperature. Low hydrogen annealing is called a de-embrittlement process. Low hydrogen annealing is an effective method compared to alternatives such as electroplating the material with zinc to provide a barrier for hydrogen ingress which results in coating defects.

The R-phase is a phase found in nitinol, a shape-memory alloy. It is a martensitic phase in nature, but is not the martensite that is responsible for the shape memory and superelastic effect.

Dynamic strain aging (DSA) for materials science is an instability in plastic flow of materials, associated with interaction between moving dislocations and diffusing solutes. Although sometimes dynamic strain aging is used interchangeably with the Portevin–Le Chatelier effect, dynamic strain aging refers specifically to the microscopic mechanism that induces the Portevin–Le Chatelier effect. This strengthening mechanism is related to solid-solution strengthening and has been observed in a variety of fcc and bcc substitutional and interstitial alloys, metalloids like silicon, and ordered intermetallics within specific ranges of temperature and strain rate.

Grain boundary sliding Material deformation mechanism

Grain boundary sliding (GBS) is a material deformation mechanism where grains slide against each other. This occurs in polycrystalline material under external stress at high homologous temperature and low strain rate and is intertwined with creep. Homologous temperature describes the operating temperature relative to the melting temperature of the material. There are mainly two types of grain boundary sliding: Rachinger sliding, and Lifshitz sliding. Grain boundary sliding usually occurs as a combination of both types of sliding. Boundary shape often determines the rate and extent of grain boundary sliding.

High-entropy alloys Alloys with high proportions of several metals

High-entropy alloys (HEAs) are alloys that are formed by mixing equal or relatively large proportions of (usually) five or more elements. Prior to the synthesis of these substances, typical metal alloys comprised one or two major components with smaller amounts of other elements. For example, additional elements can be added to iron to improve its properties, thereby creating an iron-based alloy, but typically in fairly low proportions, such as the proportions of carbon, manganese, and others in various steels. Hence, high-entropy alloys are a novel class of materials. The term "high-entropy alloys" was coined because the entropy increase of mixing is substantially higher when there is a larger number of elements in the mix, and their proportions are more nearly equal.

Iron aluminides are intermetallic compounds of iron and aluminium - they typically contain ~18% Al or more.

References

  1. ↑ Liu, J.B.; Johnson, D.D.; Smirnov, A.V. (24 May 2005), "Predicting yield-stress anomalies in L12 alloys: Ni3Ge–Fe3Ge pseudo-binaries", Acta Materialia, 53 (13): 3601–3612, Bibcode:2005AcMat..53.3601L, doi:10.1016/j.actamat.2005.04.011
  2. ↑ Wua, D.; Baker, I.; Munroe, P.R.; George, E.P. (February 2007), "The yield strength anomaly of single-slip-oriented Fe–Al single crystals", Intermetallics, 15 (2): 103–107, doi:10.1016/j.intermet.2006.03.007
  3. ↑ Gornostyrev, Yu. N.; A. F. Maksyutov; O. Yu. Kontsevoi; A. J. Freeman; M. I. Katsnelson; A. V. Trefilov (3 March 2003), "Negative yield stress temperature anomaly and structural stability of Pt3Al", American Physical Society March Meeting 2003, American Physical Society, vol. 2003, pp. D17.009, Bibcode:2003APS..MARD17009G
  4. ↑ Smallman, R. E. (4 September 2013). Modern physical metallurgy. Ngan, A. H. W. (Eighth ed.). Oxford. ISBN   978-0-08-098223-6. OCLC   858948359.
  5. 1 2 3 Han, F. F.; Zhou, B. M.; Huang, H. F.; Leng, B.; Lu, Y. L.; Dong, J. S.; Li, Z. J.; Zhou, X. T. (2016-10-01). "The tensile behavior of GH3535 superalloy at elevated temperature". Materials Chemistry and Physics. 182: 22–31. doi:10.1016/j.matchemphys.2016.07.001. ISSN   0254-0584.
  6. ↑ Chu, Zhaokuang; Yu, Jinjiang; Sun, Xiaofeng; Guan, Hengrong; Hu, Zhuangqi (2010-05-15). "Tensile property and deformation behavior of a directionally solidified Ni-base superalloy". Materials Science and Engineering: A. 527 (12): 3010–3014. doi:10.1016/j.msea.2010.01.051. ISSN   0921-5093.
  7. ↑ Ardley, G. W.; Cottrell, Alan Howard; Mott, Nevill Francis (1953-09-22). "Yield points in brass crystals". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 219 (1138): 328–340. Bibcode:1953RSPSA.219..328A. doi:10.1098/rspa.1953.0150. S2CID   137118204.
  8. 1 2 3 4 5 6 George, E.P.; Baker, I. (1998). "A model for the yield strength anomaly of Fe—Al". Philosophical Magazine A. 77 (3): 737–750. Bibcode:1998PMagA..77..737G. doi:10.1080/01418619808224080.
  9. ↑ Paidar, V; Pope, D. P; Vitek, V (1984-03-01). "A theory of the anomalous yield behavior in L12 ordered alloys". Acta Metallurgica. 32 (3): 435–448. doi:10.1016/0001-6160(84)90117-2. ISSN   0001-6160.
  10. ↑ Thornton, P. H.; Davies, R. G.; Johnston, T. L. (1970-01-01). "The temperature dependence of the flow stress of the γ′ phase based upon Ni3Al". Metallurgical Transactions. 1 (1): 207–218. doi:10.1007/BF02819263. ISSN   1543-1916. S2CID   137348369.
  11. ↑ Geng, Peiji; Li, Weiguo; Zhang, Xianhe; Deng, Yong; Kou, Haibo; Ma, Jianzuo; Shao, Jiaxing; Chen, Liming; Wu, Xiaozhi (2017-06-05). "A theoretical model for yield strength anomaly of Ni-base superalloys at elevated temperature". Journal of Alloys and Compounds. 706: 340–343. doi:10.1016/j.jallcom.2017.02.262. ISSN   0925-8388.
  12. ↑ Morris, D.G.; Muñoz-Morris, M.A. (2010-07-01). "A re-examination of the pinning mechanisms responsible for the stress anomaly in FeAl intermetallics". FEAL 2009 - 5th Discussion Meeting on the Development of Innovative Iron Aluminium Alloys. 18 (7): 1279–1284. doi:10.1016/j.intermet.2009.12.021. ISSN   0966-9795.
  13. 1 2 Jordan, J.L.; Deevi, S.C. (2003-06-01). "Vacancy formation and effects in FeAl". Intermetallics. 11 (6): 507–528. doi:10.1016/S0966-9795(03)00027-X. ISSN   0966-9795.
  14. ↑ Carleton, R.; George, E. P.; Zee, R. H. (1995-01-01). "Effects of deviations from stoichiometry on the strength anomaly and fracture behavior of B-doped FeAl". Intermetallics. 3 (6): 433–441. doi:10.1016/0966-9795(94)00041-I. ISSN   0966-9795.
  15. ↑ Premkumar, M.; Singh, A.K. (2011-07-01). "Strength anomaly of the B2 phase in Ti–25Al–25Zr alloy". Intermetallics. 19 (7): 1085–1088. doi:10.1016/j.intermet.2011.03.010. ISSN   0966-9795.
  16. ↑ Sheng, Li-yuan; Yang, Fang; Guo, Jian-ting; Xi, Ting-fei (2014-03-01). "Anomalous yield and intermediate temperature brittleness behaviors of directionally solidified nickel-based superalloy". Transactions of Nonferrous Metals Society of China. 24 (3): 673–681. doi:10.1016/S1003-6326(14)63110-1. ISSN   1003-6326.
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