Physical constants, deformation twinning, and microcracking of titanium aluminides

Physical properties that are relevant to mechanical behavior of single-phase TiAl and Ti₃Al and two-phase TiAl/Ti₃Al alloys are summarized. By using planar-fault energies and temperature-dependent elastic constants, dislocation dissociation reactions applicable to twin formation in TiAl are analyzed, and a pole mechanism based on a jogged [110]/2 ordinary dislocation is proposed to explain the available experimental data on deformation twinning in γ-TiAl single crystals. The strong plastic anisotropy reported in TiAl polysynthetically twinned (PST) crystals is attributed in part to the localized slip along lamellar interfaces, thus lowering the yield stress for soft orientations. The experimental findings reported on cleavage habit planes of PST crystals are discussed in terms of the calculated ideal work of adhesion and possible extrinsic factors. This article is based on a presentation made in the symposium “Fundamentals of Gamma Titanium Aluminides,” presented at the TMS Annual Meeting, February 10–12, 1997, Orlando, Florida, under the auspices of the ASM/MSD Flow & Fracture and Phase Transformation Committees.     

Room-temperature deformation behavior of directionally solidified multiphase Ni-Fe-Al alloys

Directionally solidified (DS) β + (γ + γ′) Ni-Fe-Al alloys have been used to investigate the effect of a ductile second phase on the room-temperature mechanical behavior of a brittle 〈001〉-oriented β (B2) phase. The ductile phase in the composite consisted of a fine distribution of ordered γ′ precipitates in a γ (fcc) matrix. Three microstructures were studied: 100 pct lamellar/rod, lamellar + proeutectic β, and discontinuous γ. The β matrix in the latter two microstructures contained fine-scale bcc precipitates formed due to spinodal decomposition. Room-temperature tensile ductilities as high as 12 pct and fracture toughness (K _Q ) of 30.4 MPa √m were observed in the 100 pct lamellar/rod microstructure. Observations of slip traces and dislocation substructures indicated that a substantial portion of the ductility was a result of slip transfer from the ductile phase to the brittle matrix. This slip transfer was facilitated by the Kurdjumov-Sachs (KS) orientation relationship between the two phases and the strong interphase interface which showed no decohesion during deformation. In microstructures which show higher values of tensile ductility and fracture toughness, 〈100〉 slip was seen in the β phase, whereas 〈111〉 slip was seen in the β phase in the microstructure which showed limited ductility. The high ductility and toughness are explained in terms of increased mobile dislocation density afforded by interface constraint. The effect of extrinsic toughening mechanisms on enhancing the ductility or toughness is secondary to that of slip transfer.     

Slip transfer and dislocation nucleation processes in multiphase ordered Ni-Fe-Al alloys

Directionally solidified (DS) alloys with the nominal composition Ni-30 at. pct Fe-20 at. pct Al having eutectic microstructures were used to study slip transfer across interphase boundaries and dislocation nucleation at the interfacial steps. The slip transfer from the ductile second phase, γ(fcc) containing ordered γ′(L1₂) precipitates, to the ordered β(B2) phase and the generation of dislocations at the interface steps were interpreted using the mechanisms proposed for similar processes involving grain boundaries in polycrystalline single-phase materials. The criteria for predicting the slip systems activated as a result of slip transfer across grain boundaries were found to be applicable for interphase boundaries in the multiphase ordered Ni-Fe-Al alloys. The potential of tailoring the microstructures and interfaces to promote slip transfer and thereby enhance the intrinsic ductility of dislocation-density-limited intermetallic alloys is discussed.     

Creep deformation in near-γ TiAl: Part 1. the influence of microstructure on creep deformation in Ti-49Al-1V

The influence of microstructure on creep deformation was examined in the near-y TiAl alloy Ti-49A1-1V. Specifically, microstructures with varying volume fractions of lamellar constituent were produced through thermomechanical processing. Creep studies were conducted on these various microstructures under constant load in air at temperatures between 760 °C and 870 °C and at stresses ranging from 50 to 200 MPa. Microstructure significantly influences the creep behavior of this alloy, with a fully lamellar microstructure yielding the highest creep resistance of the microstructures examined. Creep resistance is dependent on the volume fraction of lamellar constituent, with the lowest creep resistance observed at intermediate lamellar volume fractions. Examination of the creep deformation structure revealed planar slip of dislocations in the equiaxed y microstructure, while subboundary formation was observed in the duplex microstructure. The decrease in creep resistance of the duplex microstructure, compared with the equiaxed y microstructure, is attributed to an increase in dislocation mobility within the equiaxedy constituent, that results from partitioning of oxygen from the γ phase to the α₂ phase. Dislocation motion in the fully lamellar microstructure was confined to the individual lamellae, with no evidence of shearing of γ/γ or γ/α₂ interfaces. This suggests that the high creep resistance of the fully lamellar microstructure is a result of the fine spacing of the lamellar structure, which results in a decreased effective slip length for dislocation motion over that found in the duplex and equiaxed y microstructures. BRIAN D. WORTH, formerly with the Department of Materials Science and Engineering, The University of Michigan     

Microstructural stability of fine-grained fully lamellar XD TiAl alloys by step aging

XD TiAl alloys (Ti-45 and 47Al-2Nb-2Mn+0.8 vol pct TiB₂) (at. pct) were oil quenched to produce fine-grained fully lamellar (FGFL) structures, and aging treatments at different temperatures for different durations were carried out to stabilize the FGFL structures. Microstructural examinations show that the aging treatments cause phase transformation of α ₂ to γ, resulting in stabilization of the lamellar structure, as indicated by a significant decrease in α ₂ volume fraction. However, several degradation processes are also introduced. After aging, within lamellar colonies, the α ₂ lamellae become finer due to dissolution, whereas most of the γ lamellae coarsen. The dissolution of α ₂ involves longitudinal dissolution and lateral dissolution. In addition, at lamellar colony boundaries, lamellar termination migration, nucleation and growth of γ grains, and discontinuous coarsening occur. With the exception of longitudinal dissolution, all the other transformation modes are considered as degradation processes as they result in a reduction in α ₂/γ interfaces. Different phase transformation modes are present to varying degrees in the aged FGFL structures, depending on aging conditions and Al content. A multiple step aging reduces the drive force for phase transformation at high temperature by promoting phase transformation via longitudinal dissolution at low temperatures. As a result, this aging procedure effectively stabilizes the lamellar structure and suppresses other degradation processes. Therefore, the multiple step aging is suggested to be an optimal aging condition for stabilizing FGFL XD TiAl alloys.     

Compatibility of deformation in two-phase Ti-Al alloys: Dependence on microstructure and orientation relationships

A two-phase alloy of composition Ti-47.5Al-2.5Cr has been studied under two heat-treated conditions in order to obtain different microstructures. These consisted of lamellar and equiaxed distributions of y grains in which the α₂ phase was distributed as long lamellae or smaller globules, respectively. The specific rotation relationships between γ/γ and γ/α₂ grains have been measured, and these have been used to understand their effect on the compatibility of deformation across adjacent grains. For this, detailed analysis of active slip systems has been carried out by transmission electron microscopy (TEM) observations of deformed samples. A theoretical calculation of a geometric compatibility factor characterizing the best slip transfer across adjacent grains has been used in such a way that it has been possible to deduce the role played by the type of orientation relationship between grains in producing active deformation systems that allow the maximum compatibility of deformation.     

Room-temperature deformation behavior of directionally solidified multiphase Ni−Fe−Al alloys

Directionally solidified (DS) β+(γ+γ′) Ni−Fe−Al alloys have been used to investigate the effect of a ductile second phase on the room-temperature mechanical behavior of a brittle 〈001〉-oriented β (B2) phase. The ductile phase in the composite consisted of a fine distribution of ordered γ′ precipitates in a γ (fcc) matrix. Three microstructures were studied: 100 pct lamellar/rod, lamellar+proeutectic β, and discontinuous γ. The β matrix in the latter two microstructures contained fine-scale bcc precipitates formed due to spinodal decomposition. Room-temperature tensile ductilities as high as 12 pct and fracture toughness (K _Q) of 30.4 MPa were observed in the 100 pct lamellar/rod microstructure. Observations of slip traces and dislocation substructures indicated that a substantial portion of the ductility was a result of slip transfer from the ductile phase to the brittle matrix. This slip transfer was facilitated by the Kurdjumov-Sachs (KS) orientation relationship between the two phases and the strong interphase interface which showed no decohesion during deformation. In microstructures which show higher values of tensile ductility and fracture toughness, 〈100〉 slip was seen in the β phase, whereas 〈111〉 slip was seen in the β phase in the microstructure which showed limited ductility. The high ductility and toughness are explained in terms of increased mobile dislocation density afforded by interface constraint. The effect of extrinsic toughening mechanisms on enhancing the ductility or toughness is secondary to that of slip transfer. A. MISRA, formerly Graduate Student, Department of Materials Science and Engineering, University of Michigan is Research Associate     

Precipitation strengthening in K5-series γ-TiAl alloyed with silicon and carbon

Interstitial additions and precipitation hardening in fully lamellar gamma TiAl have been investigated in recent years, with a prime objective of improving the high-temperature creep resistance. As a result of this alloy development effort, the alloy system K5 (Ti46Al-2Cr-3Nb-0.2W) was found to show remarkably improved creep resistance when reinforced with C or C+Si additions and then aged appropriately. Precipitation strengthening is the proposed mechanism accounting for the observed creep strengthening of K5SC alloys, with emphasis being paid on the effect of B2 particles, ζ-type silicides, and H-type carbide precipitates delineating γ/γ interfaces. In this study, the creep-deformed microstructures of fully lamellar K5 (S-C)-type alloys in aged and unaged conditions were characterized using detailed electron microscopy, involving high-resolution imaging techniques and in-situ heating studies. Overall, the presence of these particles and their relative distribution result in strengthening of the lamellar structure. The particular effect of each type of precipitate (silicides vs carbides) on creep has been assessed. New information about the nature of the light-element precipitation processes has been obtained by studying the nucleation and growth of the carbide and silicide precipitates at the expense of dissolving α ₂ laths during aging. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

Modeling creep deformation of a two-phase TiAI/Ti3Al alloy with a lamellar microstructure

A two-phase TiAl/Ti₃Al alloy with a lamellar microstructure has been previously shown to exhibit a lower minimum creep rate than the minimum creep rates of the constituent TiAl and Ti₃Al single-phase alloys. Fiducial-line experiments described in the present article demonstrate that the creep rates of the constituent phases within the two-phase TiAl/Ti₃Al lamellar alloy tested in compression are more than an order of magnitude lower than the creep rates of single-phase TiAl and Ti₃Al alloys tested in compression at the same stress and temperature. Additionally, the fiducial-line experiments show that no interfacial sliding of the phases in the TiAl/Ti₃Al lamellar alloy occurs during creep. The lower creep rate of the lamellar alloy is attributed to enhanced hardening of the constituent phases within the lamellar microstructure. A composite-strength model has been formulated to predict the creep rate of the lamellar alloy, taking into account the lower creep rates of the constituent phases within the lamellar micro-structure. Application of the model yields a very good correlation between predicted and experimentally observed minimum creep rates over moderate stress and temperature ranges. Formerly with the Department of Materials Science and Engineering, University of Virginia     

The role of grain size and selected microstructural parameters in strengthening fully lamellar TiAl alloys

More than 5 years ago, wrought processing was first used to produce fully lamellar (FL) microstructures in TiAl alloys having grain sizes less than ≈400 μm. These alloys exhibit an improvement in overall balance of properties, especially at high temperatures. More recently, such microstructural forms led to exceptional yield strengths (500 to 1000 MPa at low temperatures) while maintaining attractive high-temperature properties. The improvements appeared to be related to an unusually high apparent sensitivity of strength to grain size. Studies reported an apparent value for the slope of the Hall-Petch (HP) plot approaching 5 MPa√m for FL gamma alloys, while that for single-phase or duplex microstructures is near unity. The present investigations examine the slope of the HP plot for FL microstructures, paying particular attention to the lamellar microstructural variables. Results show that the α ₂ lamellar thickness and spacing and the γ lamellar thickness can vary over more than two orders of magnitude with typical process methods. These spacings influence the value of k _y in the HP (grain size) relationship. Since they often change concomitantly with grain size in processing, they can give rise to a large scatter in the HP plot. The investigations also examine the flow behavior, glide barriers, and slip multiplicity for polysynthetically twinned (PST) crystals (the single-grain analogue of FL material), and then map this behavior into an explanation of the yield behavior of high-strength FL gamma alloys. This article is based on a presentation made in the symposium “Fundamentals of Gamma Titanium Aluminides,” presented at the TMS Annual Meeting, February 10–12, 1997, Orlando, Florida, under the auspices of the ASM/MSD Flow & Fracture and Phase Transformations Committees.     

Microstructure stability during creep deformation of hard-oriented polysynthetically twinned crystal of TiAl alloy

The hard-orientated polysynthetically twinned (PST) crystal with the lamellar plates oriented parallel to the compression axis was deformed at 1150 K under the applied stress of 158 to 316 MPa. Microstructural changes were examined quantitatively for the PST crystal during creep deformation. In the as-grown PST crystal of the present study, proportions of α ₂/γ, true twin, pseudotwin, and 120 deg rotational fault interfaces were 12, 59, 12, and 17 pct, respectively. After creep deformation, lamellar coarsening by dissolution of α ₂ lamellae and migration of γ/γ interfaces were observed. The acceleration of creep rate after the minimum strain rate in the creep curve was attributed to the lamellar coarsening and destruction of lamellar structure during the creep deformation. Thirty-two percent of α ₂/γ interfaces, 51 pct of true twin interfaces, 74 pct of pseudotwin interfaces, and 80 pct of 120 deg rotational faults disappeared after 4 pct creep strain at 1150 K. The α ₂/γ interface was more stable than γ/γ interfaces during the creep deformation. The pseudotwin interface and 120 deg rotational fault were less thermally stable than the true twin interface for γ/γ interfaces. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

Effect of phase morphology on the mechanical behavior of two titanium aluminide composites

Two binary titanium aluminide alloys, Ti-43A1 and Ti-47A1 (atomic percent), were discontinuously reinforced with 6 vol pct titanium diboride, resulting in a two-phase Ti₃Al and TiAl (α₂ and γ, respectively) matrix with a dispersion of TiB₂ particulate. Cast material was successfully ex-truded and subjected to a series of single-step and duplex-step heat treatments. Thermo-mechanical processing was correlated with microstructural changes, and the ambient temperature mechanical properties were measured for the various heat-treated conditions using tensile and hardness testing. Yield stress and plastic elongation to failure and hardness were found to cor-relate well with the fraction of proeutectoid, or primary, TiAl formed during heat treatment within the α/γ phase field. Precipitation of y within proeutectoid α grains during subsequent aging treatments within the α₂ phase field was seen to increase the room-temperature ductility with negligible debits in yield stress. Enhanced ductility and decreases in yield stress and hard-ness are associated with morphologically large regions of the TiAl phase. Incompatibility of slip systems across γ/α₂ and the inherent resistance to slip in hyperstoichiometric Ti₃Al are suggested as possible explanations for the observed phenomena. Formerly with Martin Marietta Laboratories     

Tensile,creep, and low-cycle fatigue behavior of a cast γ-TiAl-based alloy for gas turbine applications

The influence of chemical composition on the microstructure of the γ-titanium aluminide alloy Ti-48Al-2W-0.5Si (at. pct) and the accompanying tensile, low-cycle fatigue, and creep properties has been evaluated. The study showed that small variations in chemical composition and casting procedures resulted in considerable variations in the microstructure, yielding vastly different mechanical properties. Low contents of aluminum and tungsten led to a coarse-grained lamellar (γ/α ₂) microstructure with high creep resistance. A composition close to the nominal one produced a duplex (γ+γ/α ₂) structure with favorable strength, ductility, and low-cycle fatigue properties. By controlling the solidification and cooling rates at casting, a pseudoduplex (PS-DP) microstructure with a unique combination of high strength and high fatigue and creep resistance can be obtained. These unique properties can be explained by the diffuse boundaries between the relatively small γ grains and the neighboring lamellar colonies, combined with semicoherent interfaces between the γ and α ₂ phases. At tensile and low-cycle fatigue loading, these boundaries act like high-angle boundaries, producing a virtually fine-grained material promoting strength, whereas at creep loading, grain-boundary sliding is hindered in the semicoherent interfaces leading to high creep resistance.     

Plastic deformation and fracture of binary TiAl-base alloys

The mechanical behavior of binary TiAl alloys containing 46 to 60 at. pct Al has been studied in bulk materials preparedvia rapid solidification processing. Bending and tensile tests were carried out at room temperature as a function of Al concentration. A few alloys were also tested from liquid nitrogen temperature to ∼ 1000°C. Deformation substructures were studied by analytical transmission electron microscopy and fracture modes by scanning electron microscopy (SEM). It was found that both microstructure and composition strongly affect the mechanical behavior of TiAl-base alloys. A duplex structure, which contains both primary y grains and transformedγ/α ₂ lamellar grains, is more deformable than a single-phase or a fully transformed structure. The highest plasticities are observed in duplex alloys containing 48–50 at. pct Al after heat treatment in the center of theγ + α phase field. The deformation of these duplex alloys is facilitated by 1/2[110] slip and {111} twinning, but very limited superdislocation slip occurs. The twin deformation is suggested to result from a lowered stacking fault energy due to oxygen depletion or an intrinsic change in chemical bonding. Other factors, such as grain size and grain boundary chemistry and structure, are important from a fracture point of view. The results on the deformation and fracture modes as a function of test temperature are also discussed.     

Development of ultrafine lamellar structures in two-phase γ-TiAl alloys

Processing of two-phase γ-TiAl alloys (Ti-47Al-2Cr-2Nb, or minor modifications thereof) above the α-transus temperature (T _α ) produced unique refined-colony/ultrafine lamellar structures in both powder-and ingot-metallurgy (PM and IM, respectively) alloys. These ultrafine lamellar structures consist of fine laths of the γ and α ₂ phases, with average interlamellar spacings (λ _L ) of 100 to 200 nm and α ₂-α ₂ spacings (λ _α ) of 200 to 500 nm, and are dominated by γ/α ₂ interfaces. This characteristic microstructure forms by extruding PM Ti-47Al-2Cr-2Nb alloys at 1400 °C and also forms with finer colony size but slightly coarser, fully lamellar structures by hot-extruding similar IM alloys. Alloying additions of B and W refine λ _L and λ _α in both IM Ti-47Al (cast and heat treated at 1400 °C) and IM Ti-47Al-2Cr-2Nb alloys (extruded at 1400 °C). The ultrafine lamellar structure in the PM alloy remains stable during heat treatment at 900 °C for 2 hours but becomes unstable after 4 hours at 982 °C; the ultrafine lamellar structure remains relatively stable after aging for >5000 hours at 800 °C. Additions of B+W dramatically improve the coarsening resistance of λ _L and λ _α in the IM Ti-47Al alloys aged for 168 hours at 1000 °C. In both the PM and IM Ti-47Al-2Cr-2Nb alloys, these refined-colony/ultrafine lamellar structures correlate with high strength and good ductility at room temperature, and very good strength at high temperatures. While refining the colony size improves the room-temperature ductility, alloys with finer λ _L are stronger at both room and high temperatures. Additions of B + W produce finer as-processed λ _L and λ _α in IM TiAl alloys and stabilize such structures during heat treatment or aging. This article is based on a presentation made in the symposium “Fundamentals of Gamma Titanium Aluminides,” presented at the TMS Annual Meeting, February 10–12, 1997, Orlando, Florida, under the auspices of the ASM/MSD Flow & Fracture and Phase Transformations Committees.     

Deformation structure in a Ti-24Al-11Nb alloy

A Ti-24Al-11Nb alloy has been heat-treated so as to obtain a microstructure of coarse α₂ particles (D0₁₉ structure based on Ti₃Al) in a matrix of the ordered β_o phase (B2 structure based on Ti₂AlNb). Dislocation structures generated by tensile strains of ∼2 pct at room temperature have been analyzed by transmission electron microscopy The β_o phase is shown to deform inhomogeneously on {110}, {112}, and {123} planes by α/〈211〉 slip. The slipband structure is complex, consisting of segments of heavily pinned edge dislocations with periodic cross slip of screw components on to secondary slip planes. Incompatibility stresses at α₂/β_o interfaces can generate fine α[100] slip as well. The α₂ phase deforms independently by α dislocation slip. Slipbands in the β_o phase can shear the α₂ phase by activatingc +a/2 slip on and slip planes, as well asa slip on higher order pyramidal planes, where the parallelism of the specific slip system is permitted by the Burgers relationship between the two phases.     

Surface cracking in α- β titanium alloys under unidirectional loading

Observations have been made of cracking which develops after small plastic strains in the Ti-6Al-2Sn-4Zr-6Mo and Ti-6A1-4V alloys at α-@#@ β interfaces, and a long slip band in α. Hydrogen and surface stresses and heat treat condition,i.e., solution treated or solution treated and aged have been ruled out. Cracking is attributed to intense slip commencing at the α-@#@ β interfaces, and progressing into the α, or at martensite-matrix interfaces.     

Primary creep behavior of Ti-48Al-2W as a function of stress and lamellar morphology

The fully lamellar microstructure of powder metallurgy Ti-48Al-2W after cooling from the α region to 1280 °C, followed by air cooling and aging at 950 °C for up to 96 hours, is presented. Aging times as short as 5 hours result in acicular-shaped precipitates of W-rich β ₀ along lamellar interfaces, with the β ₀ size increasing with aging time. The β ₀ precipitates nucleate and grow in the α ₂ lamellae. Concurrently, with the formation of β ₀, the α ₂ decomposes into discontinuous lamellae. Aging to precipitate β ₀ along lamellar interfaces increases the 760 °C tensile strength (with a slight reduction of ductility) and reduces the instantaneous creep strain, since β ₀ precipitates at lamellar interfaces hinder interface dislocation mobility. The deformed microstructures from interrupted creep tests at 140 to 276 MPa at 760 °C indicate that the precipitation of β ₀ along interfaces substantially reduces the primary creep strain, primarily due to the influence of β ₀ on interface dislocation emission and motion. These results are discussed in terms of the influence of lamellar morphology on the instantaneous creep strain and primary creep transient, and the possible creep mechanisms are highlighted. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee of Mechanical Behavior of Materials.     

Importance of slip mode for dispersion-hardened β-titanium alloys

The mechanical properties of Ti-7 Mo-7 Al and Ti-7 Mo-16 Al (in at. pct) were correlated to the microstructure. The mechanical properties of the alloy with low aluminum content, consisting of α+ β phases, were dependent on the size of the α particles. Although the α phase is softer than the β phase, the small α particles, upon plastic deformation of the alloy, functioned as typical hard agents in a dispersion-hardened system and the volume fraction of the particles controlled the macroscopic ductility. A rapid strain-hardening behavior of the small α particles seemed to be responsible for this effect. Large α particles behaved like soft, incoherent particles, the volume fraction having little effect on the inherent ductility of the alloy. The two phase (β+ Ti₃Al) microstructure of the alloy with high aluminum content resulting from high temperature aging to 900°C exhibited a yield stress of 130 ksi and an elongation to fracture of 5 pct. The ductility of this microstructure was controlled by the volume fraction of the Ti₃Al particles inducing homogeneous slip. The favorable ductility properties of the microstructures with low Ti₃Al volume fraction were lost if the slip mode was changed from homogeneous slip to planar slip. Formerly Staff Member, Materials Research Center, Allied Chemical Corp., Morristown, N. J.     

Ordering and the strength of an aligned Ag3Mg-AgMg eutectic

A fine lamellar structure with interlamellar spacings from 1 to 7μ has been produced by directional solidification of an Ag₃Mg-AgMg eutectic alloy. The tensile properties were measured as a function of test temperature, interlamellar spacing,λ, and degree of order in the Ag₃Mg phase. The dependence of flow stress onλ ^-1/2 increased sharply with ordering of Ag₃Mg and this strengthening persisted at elevated temperatures. Work hardening rate and ductility of the eutectic at low temperatures also were affected, leading to the conclusion that ordering changes the compatibility of slip across interphase boundaries.