Anisotropic threshold stress intensity factor,K IH and crack growth rate in delayed hydride cracking of Zr-2.5Nb pressure tubes

The objectives of this study are to systematically investigate the delayed hybride cracking (DHC) velocity and the threshold-stress intensity factor, K _IH, of a Zr-2.5Nb pressure tube as a function of orientation and elucidate the cause of this anistropic DHC behavior. The DHC velocity as a function of orientation was determined using flattened cantilever beam specimens with 60 ppm H while the threshold-stress intensity factor K _IH, was evaluated as a function of orientation on the curved compactension (CT) and cantilever-beam (CB) specimens charged with hydrogen to 200 ppm H. To infer a difference in a stress gradient ahead of the crack tip as a function of orientation, tensile tests were conducted at temperatures ranging from room temperature (RT) to 560°C using small tensile specimens of 2-mm-gage length taken from three directions of the tube. A textural change was investigated by comparing the inverse pole figures before and after DHC while the pole figures were constructed to find out the growth pattern of the DHC crack as a function of orientation. Faster DHC velocity and lower K _IH were obtained over temperatures of 170 °C to 270 °C, when the DHC crack grew in the longitudinal direction of the Zr-2.5Nb pressure tube. The strain hardening after yielding and the extent of the textural change accompanied by DHC were higher in the longitudinal direction of the tube, suggesting a higher stress gradient ahead of the crack tip. Thus, the anisotropic DHC behavior of a Zr-2.5Nb pressure tube is discussed based on the stress gradient ahead of the crack tip governed by strain-hardening rate after yielding and a change in texture accompanied by DHC, and the distribution of the hydride habit planes. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Deformation twinning and texture variation in Zr-2.5 pct Nb alloy during rolling

Recently, it was proven that delayed hydride cracking (DHC) is accompanied by deformation twinning through the texture analysis of a fractured surface. Thus, in order to understand the operation of deformation twinning, the texture variations by rolling were investigated using Zr-2.5 pct Nb alloy with {11 0} 〈10 0〉 texture. It was observed that deformation twinning was operated predominantly in the range of a 5 to 15 pct strain. The basal poles were rotated in the normal direction of a rolling plane with the strain, and the (0002) texture was fully reversed after 15 pct strain. This finding was established to be due to the operation of the {10 2} and {11 1} twinning systems through the analysis of the inverse pole figure. It appeared that the degree and easiness of the twinning operation was affected by changing the direction of compression during rolling with respect to the initial {11 0} 〈10 0〉 texture. The contribution of deformation twinning to strain was quantitatively calculated using the change in the basal pole components. This article is based on a presentation made in the symposium entitled “Processing and Properties of Structural Materials,” which occurred during the Fall TMS meeting in Chicago, Illinois, November 9–12, 2003, under the auspices of the Structural Materials Committee.     

Fracture and fatigue-crack growth behavior in ductile-phase toughened molybdenum disilicide: Effects of niobium wirevs particulate reinforcements

A study has been made of the fracture toughness/resistance-curve (R-curve) and cyclic fatigue-crack propagation behavior in a molybdenum disilicide composite, ductile-phase toughened with nominally 20 vol pct Nb-wire mesh reinforcements (Nb _m /MoSi₂); results are compared with monolithic MoSi₂ and MoSi₂ reinforced with 20 vol pct spherical Nb particles (Nb _p /MoSi₂). It is found that the high aspect ratio wire reinforcements induce significant toughening in MoSi₂, both under monotonic and cyclic fatigue loading conditions. Specifically, the Nb _m /MoSi₂ composite exhibits R-curve behavior with a steady-state fracture toughness of ∼13 MPa , compared to unstable fracture atK _c values below 5 MPa in unreinforced MoSi₂ or Nb _p /MoSi₂. Such behavior is seen to be associated with extensive crack deflection within the reaction layer between Nb and the matrix, which leads to crack bridging by the unbroken ductile phase. Similarly, resistance to fatigue-crack growth is found to be far superior in the wire-reinforced composite over pure MoSi₂ and Nb _p /MoSi₂. Although crack paths are again characterized by extensive deflection along the Nb/matrix reaction layer, the role of crack bridging is diminished under cyclic loading due to fatigue failure of the Nb. Instead, the superior fatigue properties of the Nb _m /MoSi₂ composite are found to be associated with high levels of crack closure that result from highly deflected crack paths along the (Nb,Mo)₅Si₃ reaction layer interface.     

Quasi-steady-state creep crack growth in a 3.5NiCrMoV steel

Creep crack growth rate ( ) is usually characterized in terms of macroscopic load parameters, such as C*, C _t and C(t), through the constant load test. However, load parameters are continuously changing during the test, and so is . Here, by conducting constant C _t and constant tests, quasi-steady-state crack growth was obtained where remained almost constant. Results indicate the ∼[C _t ]^0.76 correlation, which differ from the ∼[C _t ]^0.96 correlation of the constant load test. Discrepancies can be ascribed to the inclusion of the stage II data, which showed no correlation between and C _p in the constant load analysis. Finally, the crack growth rate was well predicted using the Monkmam-Grant analysis in creep crack growth.     

Crystallographic details of precipitates in Fe-22Cr-21Ni-6Mo-(N) superaustenitic stainless steels aged at 900 °C

Crystallographic features of second phases and the effect of nitrogen addition on the microstructural evolution in superaustenitic Fe-22Cr-21Ni-6Mo-(N) (all in wt pct) stainless steels during isothermal aging at 900 °C were investigated using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Both alloys with and without nitrogen contained sigma phase and M₂₃C₆ carbides in the solution treated condition. While four phases (sigma, M₂₃C₆, M₆C, and chi) of intermetallics and carbides appeared sequentially as a function of aging time in the nitrogen-free alloy, two nitrides (Cr₂N and AlN) were additionally observed after long time aging of the nitrogen-containing alloy. The addition of nitrogen into Fe-22Cr-21Ni-6Mo steel promoted a finer and more uniform distribution of precipitates during isothermal aging. The exact identification and crystallography of various second phases were confirmed from the analyses of selected area diffraction patterns from various orientations, stereographic projection, and energy dispersive spectroscopy. The orientation relationships between the precipitates and austenite matrix can be summarized as follows: (1) two carbides (M₂₃C₆ and M₆C): cube-on-cube orientation relationship; (2) chi phase: Kurdjumov-Sachs (K-S) orientation relationship; (3) two nitrides (Cr₂N and (AlN): (11 0)_nitrides //(211) _γ and [0001]_nitrides //[ 11] _γ ; and (4) sigma phase: (1) ( 11) _γ //(00 ) _σ and [ 0] _γ //[ 0] _σ or (2) ( 10) _γ //( 10) _σ and [ 2] _γ //[113] _σ . For the sigma phase, the former orientation relationship was predominant throughout aging, and the latter orientation relationship was occasionally observed under limited aging conditions.     

Microstructure evolution in Zr under equal channel angular pressing

Pure polycrystalline Zr was deformed by equal channel angular pressing (ECAP), and the microstructural characteristics were analyzed. By repeated alternating ECAP, it was possible to refine the grain size from 200 to 0.2 μm. Subsequent annealing heat treatment at 550 °C resulted in a grain growth of up to 6 μm. Mechanical twinning was an important deformation mechanism, particularly during the early stage of deformation. The most active twinning system was identified as 85.2 deg {10 2}〈 011〉 tensile twinning, followed by 57.1 deg {10 1}〈 012〉 compressive twinning. Crystal texture as well as grain-boundary misorientation distribution of deformed Zr were analyzed by X-ray diffraction (XRD) and electron backscattered diffraction (EBSD). The ECAP-deformed Zr showed a considerable difference in the crystallographic attributes from those of cold-rolled Zr or Ti, in that texture and boundary misorientation-angle distribution tend toward more even distribution with a slightly preferential distribution of boundaries of a 20 to 30 deg misorientation angle. Furthermore, unlike the case of cold rolling, the crystal texture was not greatly altered by subsequent annealing heat treatment. Overall, the present work suggests ECAP as a viable method to obtain significant grain refining in hexagonal close-packed (hcp) metals. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Microstructural aspects of sulfide stress cracking in an API X-80 pipeline steel

Crack growth in an API X-80 exposed to sour gas environments was investigated using modified wedge-opening-loaded (MWOL) specimens. The MWOL specimens were tested in the as-received condition and after annealing followed by water spraying to simulate improperly welded regions. It was found that water-sprayed MWOL specimens were susceptible to stress sulfide cracking in a NaCl-free NACE solution. Crack growth was relatively slow when subjected to an initially appliedK _I of 30 MPa . Under these conditions, crack growth rates continually decreased until crack arrest was exhibited at a thresholdK _I (K _ISSC) of 26 MPa . The exhibited crack growth rates were related to the facility with which nucleated microcracks joined the main crack front. Apparently, preferential nucleation and growth of microcracks within the main crack tip plastic zone accounted for the exhibited embrittlement. In particular, favorable microcrack growth followed a path consisting of fractured (cut) carbide regions, as well as various interfaces, including globular inclusions and grain boundary precipitates.     

Evolution of textures in zirconium alloys deformed uniaxially at elevated temperatures

Texture evolution inα-Zr due to uniaxial deformation at 923 to 1123 K was investigated in crystal-bar Zr and Zr-2.5Nb. The temperature range selected corresponds to the two-phase (α +β) field in the Zr-2.5Nb alloy. It was found that uniaxial compression causes a progressive rotation of the (0002) plane normals away from the compression direction and away from the compression plane. In the crystal-bar Zr, the compression texture consists of a [0001] fiber tilted 30 deg from the compression axis. By contrast, in Zr-2.5Nb, a [0001] fiber with an angular spread of 30 deg is obtained. The effect of theβ phase present in Zr-2.5Nb at the temperatures investigated was evaluated by testing a Zr-20Nb alloy in compression. The β-phase texture consisted of a weak 〈111〉-〈00l〉 double fiber. Comparison of this texture and the textures observed in Zr-2.5Nb indicates that theβ →α transformation takes place by the growth of pre-existing a grains and not according to the Burgers mechanism. This transformation has, therefore, no direct effect on the α-phase texture after cooling to room temperature from the (α +β) field. Uniaxial elongation by swaging of Zr-2.5Nb produces a dual fiber. Similar results are obtained in hot extruded rods. Modeling of the development of textures in the α phase was performed using linear programming and employing relaxed constraint (RC) models (“curling” for tension and ”pancake” for compression) implemented for hexagonal close-packed (hcp) grains. It is assumed that prismatic, basal, and 〈c +a〉 pyramidal slip were the active deformation modes at high temperatures. It is shown that these models reduce the activity of the pyramidal slip systems to realistic values, in contrast to the full constraint (FC) approach, where most of the deformation is accommodated by 〈c +a〉 slip. Microstructural evidence is presented regarding the occurrence of ”curling” during uniaxial elongation. Formerly Graduate Student with the Department of Metallurgical Engineering, McGill University     

Uniaxial tensile deformation of uranium 6 wt pct niobium: A neutron diffraction study of deformation twinning

The deformation of polycrystalline uranium 6 wt pct niobium (U6Nb) was studied in situ during uniaxial tensile loading by time-of-flight neutron diffraction. Diffraction patterns were recorded at incremental stresses to a maximum of 450 MPa (∼4 pct macroscopic strain). Consistent with reorientation of the martensite variants by twinning, significant changes in the diffraction peak intensities, which were proportional to the plastic contribution of the macroscopic strain, were observed. Both the lattice parameters (a, b, c, and γ) and interplanar spacings (d _hkl ) were determined as a function of applied stress. Phenomenologically, the highly anisotropic stress response of the lattice parameters as well as the individual lattice spacings can be related to deformation twinning. Preliminary transmission electron microscopy (TEM) studies identified the ( 30) and ( 72) as active deformation twinning systems of U6Nb in tension.     

Deformation of a Burgers oriented bimetallic bicrystal of alpha-beta (Ti-13Mn)

The deformation behavior of a Burgers oriented α-β-Ti-13Mn bimetallic bicrystal was studied at two plastic strains, 0.52 and 2.08 pct. Two single crystals, α and β, each corresponding to the orientation of its respective bicrystal component were also investigated. The stress axes were and [1218]_β. The interface planes were and and lay in the x’-z’ plane. The deformation behavior of the a component differed from that of the a single crystal because of plastically induced stresses,T _y’z’ ,T _x’z’ ,T _x’y’ , and σ _x’x’ . Prismatic slip and twinning were found in the single crystal α whereas the bicrystal revealed additionally pyramidal andc + a slip, the latter at the interface. Slip on the front and back surfaces was different and both thec + a and twinning systems acted to maintain compatibility. Slip in the β single crystal and the β bicrystal component were quite similar. However, there were differences in the intensity and amount of primary slip, (231) , on the front and back surfaces. The diminished amount of (231) slip on the back surface was due to plastically induced stresses, and on the front surface the primary slip cross slipped to slip which triggeredc + a slip in α. On the back surface the dominant slip system was which acted in response to the plastically induced stresses. An approximate calculation revealed that the interface deformation zone had about twice the flow stress of the average bicrystal stress. Formerly a Graduate Student in the Department of Physical and Engineering Metallurgy at Polytechnic Institute of New York, Brooklyn, NY     

Effect of solidification cooling rate on the morphology and number per unit volume of primary Mg<Subscript>2</Subscript>Si particles in a hypereutectic Al-Mg-Si alloy

Growth morphology and number per unit volume have been determined vs withdrawal velocity V over the range 0.1 to 4 mm/s for primary Mg₂Si in a Bridgman-solidified hypereutectic Al-Mg-Si alloy. Primary Mg₂Si shows a transition from irregular or regular polyhedral to dendritic with increasing V, and increases with solidification cooling rate according to the relationship . These results are compared with corresponding ones for Al-Mg-Si alloy wedge castings and for primary silicon in hypereutectic Al-Si alloys.     

Elastic interaction stresses: Part II. The influence of orientation on stresses generated in iso-axial bicrystals

The effects of four types of incompability on stresses generated in seven iso-axial bicrystals of 70-30 alpha brass subjected to tension were examined by finite element methods. The distribution of applied stress and resolved shear stresses was determined. The applied stress, { }, was higher at the interior than at the surface, while the resolved shear stresses were generally higher at the surface. For both applied { } and resolved shear stresses, the largest stresses occurred at the bicrystal boundaries. The effect of end constraints on a [213] oriented single crystal was found to create nonuniform stresses and strains, and an explanation for this behavior was proposed. The effect of orientation on the magnitude of grain boundary resolved shear stress, { }, and the relative extent (volume fraction) of enhanced grain boundary resolved shear stress,V _gb, were determined. The highest values of { } andV _gb were reached in different portions of the stereographic triangle. The elastic interactions producing this behavior were too complex to permit a simple interpretation. TZI-KANG CHEN formerly Graduate Student at Polytechnic University     

New stereology for the recovery of grain-boundary plane distributions in the crystal frame

A new experimental method is given for recovering the probability-distribution function S _v ( |Δg). The function S _v ( |Δg) is the grain-boundary area per unit volume as a function of grain-boundary plane orientation ( ), given a lattice misorientation (Δg) between the adjoining grains. The grain-boundary normal ( ) is expressed in the crystal frame in which the misorientation Δg originates. The proposed method recovers the three-dimensional S _v ( |Δg) function using data taken from two-dimensional section planes. The method requires the measurement of many grain-boundary trace (in-plane) angles and lengths associated with grain boundaries of lattice misorientation. All such boundary traces may be observed from a single section plane if the crystallographic texture is sufficiently random. In heavily textured microstructures, the method requires the researcher to observe traces from multiple oblique section planes cut through the material. A method of quantitatively estimating whether the texture is sufficiently random is given. Simulations on both textured and nontextured microstructures demonstrate the validity of the method. Experimentally, the new method is used to analyze boundaries of misorientation (Σ3) observed in 304 stainless steel. Calculated grain-boundary plane-probability functions are shown to be consistent with what is already known. This article is based on a presentation made at the symposium “Characterization and Representation of Material Microstructures in 3-D” held October 8–10, 2002, in Columbus, OH, under the auspices of ASM International’s Phase Transformations committee.     

The effect of hydrogen on the fracture toughness of alloy X-750

The effect of hydrogen on the fracture toughness behavior of a nickel-base superalloy, Alloy X-750, in the solutionized and aged condition was investigated. Notched bend specimens were tested to determine if the fracture process was stress or strain controlled. The fracture was observed to initiate at a distance between the location of maximum stress and maximum strain, suggesting that fracture required both a critical stress and strain. The effect of hydrogen was further investigated and modeled using fracture toughness testing and fractographic examination. The fracture toughness of the non-charged specimen was 147 . Charging with hydrogen decreased the fracture toughness, K _lc, to 52 at a rapid loading rate and further decreased the toughness to 42 for a slow loading rate. This is consistent with the rate-limiting step forthe embrittlement process being hydrogen diffusion. The fracture morphology for the hydrogen-charged specimens was intergranular ductile dimple, while the fracture morphology of noncharged specimens was a mixture of large transgranular dimples and fine intergranular dimples. The intergranular failure mechanism in Alloy X-750 was a microvoid initiation process at grain boundary carbides followed by void growth and coalescence. One role of hydrogen was to reduce the void initiation strain for the fine intergranular carbides. Hydrogen may have also increased the rate of void growth. The conditions ahead of a crack satisfy the critical stress criterion at a much lower applied stress intensity factor than for the critical fracture strain criterion. A model based on a critical fracture strain criterion is shown to predict the fracture behavior.     

Determination of fracture initiation in hydride blisters using acoustic emission

An experimental study based on acoustic emission techniques was carried out to determine the conditions that lead to the initiation and growth of cracks in and from zirconium hydride blisters. The stress to initiate, at room temperature, a crack in a blister previously grown on a tensile speci-men could be accurately determined using an acoustic emission (AE) method based on linear event-location techniques. It was found that the applied stress to first form a crack in an unbroken blister decreases with blister depth but also that this value is statistically distributed. This is likely due to a size distribution of microcracks or incipient flaws in the blister. The propagation, by the delayed hy-dride cracking (DHC) mechanism, of a crack from a pregrown blister at 516 K seems to require both a critical applied stress, which decreases with blister depth, and approach of the testing temperature from above. However, DHC initiation was possible at 563 K (approached from below) for blisters grown under stress, provided the applied stress was sufficiently high. The stress intensity factor,K _IB , to initiate DHC ranged from 10.7 to 15.4 MPa √m. This is above the range forK _IH the thresholdK ₁ for DHC obtained in other experiments. The characteristics of AE generated by crack propagation from a blister due to DHC always follows the same pattern. It has a low event rate both at the beginning and at the end of DHC and a maximum value in between. The DHC initiation stage has a high proportion of high amplitude events. The peak in the distribution of events with peak am-plitude shifts to lower peak amplitudes as DHC progresses. An explanation for this trend is sought in terms of the maximum hydride size required near the crack tip to propagate the crack as a func-tion ofK ₁ .     

Atomistic simulation of fracture in TiAl

Atomistic simulations of fracture in L1₀ TiA1 were carried out using embedded atom method (EAM) interatomic potentials and molecular statics. We studied the behavior of semi-infinite cracks under mode I loading in different orientations of the crack front and plane. For the (111) orientation, we observed dislocation emission involving the formation of superlattice intrinsic stacking fault (SISF). For the [001](110) orientation, we observed the emission of ordinary 1/2[110] edge dislocations that were highly mobile and had a compact core. We found that cracks with [001](100) orientation cleaved near the Griffith value of loading in a purely brittle manner. Similar behavior was observed for cracks with (100) orientation. 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.     

The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensites

The diffusivity of Ni in Fe-Ni and Fe-Ni-P martensite, , has been determined between 700 and 300 °C using electron microprobe (EMP) and scanning transmission electron microscope (STEM) techniques. Alloys of various bulk compositions (0 to 30 wt pct Ni, Fe) were homogenized in the single phase austenite (γ-fee) field and quenched to form martensite, α₂ (bcc). Appropriate alloys were tempered isothermally at 300 to 700 °C. The γ nucleated and grew in the parent α₂. The composition of the γ phase and the concentration gradients in the α₂ were measured with the EMP andJor STEM. In order to determine experimentally measured Ni concentration gradients were matched to Ni concentration gradients calculated by a simulation model. The calculated gradients were obtained by solving the appropriate form of Fick’s second law using the Crank-Nicholson numerical technique. The observed diffusivities varied with temperature. Above approximately 410 °C, while below 410°C, = (2.27 × 10⁻¹⁵) exp (− 10,600/RT) cm²/s. The effect of P is to increase the Fe-Ni diffusivities at any temperature by the factor (1 + 1.27C _p + 0.623C _p ² ) whereC _p is the amount of P (wt pct) in α₂. The discontinuous diffusion behavior of is attributable to the high dislocation density of the α₂. Above approximately 410 °C lattice diffusion is dominant while below 410 °C dislocation pipe diffusion is dominant. Formerly Research Assistant in the Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA     

Atomistic simulation of fracture in TiAl

Atomistic simulations of fracture in L1₀ TiAl were carried out using embedded atom method (EAM) interatomic potentials and molecular statics. We studied the behavior of semi-infinite cracks under mode I loading in different orientations of the crack front and plane. For the orientation, we observed dislocation emission involving the formation of superlattice intrinsic stacking fault (SISF). For the [001](110) orientation, we observed the emission of ordinary 1/2[110] edge dislocations that were highly mobile and had a compact core. We found that cracks with [001](100) orientation cleaved near the Griffith value of loading in a purely brittle manner. Similar behavior was observed for cracks with orientation. 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.     

Solidification paths and reinforcement morphologies in melt-processed (TiB + TiC)/Ti In Situ Composites

A novel in situ process was developed to produce titanium matrix composites reinforced with TiB and TiC of different mole ratios in which traditional ingot metallurgy plus self-propagation hightemperature synthesis (SHS) reactions between Ti and B₄C, graphite powder were used. Microstructures of (TiB+TiC)/Ti in situ composites were comprehensively characterized using scanning electron microscopy (SEM), transmission electron microscopy (TEM), and high-resolution transmission electron microscopy (HRTEM). Solidification paths were investigated using a differential scanning calorimeter (DSC). Results show that there is an apparent difference in morphologies of reinforcements. The reinforcements nucleate and grow from the melt in a way of dissolution precipitation. The different morphologies are related to their solidification paths and the particular crystal structure of the reinforcement. TiB grows along the [010] direction and forms short-fiber shape due to its B27 structure, whereas TiC with NaCl type structure grows in a dendritic, equiaxed, or near-equiaxed shape. The DSC results and analysis of the phase diagram yield three stages for the solidification paths of in situ synthesized titanium matrix composites: (1) primary phase, (2) monovariant binary eutectic, and (3) invariant ternary eutectic. The addition of graphite adjusts the solidification paths and forms more dendritic primary TiC. The addition of aluminum does not change the solidification paths. However, the reinforcements grow finer and lead to equiaxed or near-equiaxed TiC morphologies. The following consistent crystallographic relationships between TiB and titanium were observed by HRTEM, i.e., [010]_TiB//[ ]_Ti, (100)_TiB//( )_Ti, (001)_TiB//(0002)_Ti, ( )_TiB//( )_Ti and [001]_TiB//[ ]_Ti, ( )_TiB//( )_Ti, (200)_TiB//(0002)_Ti. The formation of the preceding crystallographic relationships is related to the growth mechanism of TiB. It also helps to minimize the lattice strain at the interfaces between TiB and the titanium matrix.