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At least 343 records · Page 19

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NASA NTRS1972

Stress relaxation of high strength A-286 bolts in simulated storage at room temperature

It was concluded that thermally activated relaxation of the type customarily encountered at high temperatures was not expected to occur at the low temperatures where long time NERVA storage conditions will prevail. Instances where relaxation occurred by a different mechanism at such moderate temperatures were also reported. Twelve simulated bolted flange test specimens were prepared. Parameters that were varied among the twelve specimens were the flange material, the bolt shank diameter, and the bolt loading in terms of percent of yield strength.

Sampson, R. C.↗

DOE OSTI2024

Enhancing Mechanical Properties of Carbon–Silicon Steel through Two–Stage Quenching and Partitioning with Bainitic Transformation: Ultimate Tensile Strength of 1875 MPa and Total Elongation of 8.03%

To achieve the desired microstructural properties, the ongoing development and innovation in new structural steels require novel thermal processing. This study aims to improve the mechanical properties of a commercial spring carbon–silicon steel by tailoring its microstructure through a process involving quenching and partitioning (Q&P) followed by bainitic transformation. A two–stage Q&P process is proposed to generate a nanoscale dispersion of stable retained austenite and carbides within the tempered martensite and bainite microstructure. The resulting tensile properties demonstrate a yield strength of 1280 MPa, an ultimate tensile strength of 1875 MPa, and a total elongation of 8.03%. These values surpass those of conventional spring 9254 steel, highlighting the effectiveness of the thermal treatment design. Microstructure analysis reveals the presence of tempered martensite, bainite sheaves, nanoscale carbides, and aggregates of retained austenite. Moreover, the resulting body–centered cubic matrix exhibits minimal lattice tetragonality of ≈1.0051, coupled with stable retained austenite featuring a carbon concentration of ≈3.42 ± 0.5 wt%, resulting in outstanding strength–ductility properties. In conclusion, these findings indicate that the proposed two–stage Q&P process, followed by bainitic transformation, significantly enhances the mechanical properties of carbon–silicon steels, making it a promising candidate for high–performance spring applications.

36 MATERIALS SCIENCE↗

NASA NTRS1942

Tensile and pack compressive tests of some sheets of aluminum alloy, 1025 carbon steel, and chromium-nickel steel

Tensile and compressive stress-strain curves, stress-deviation curves, and secant modulus-stress curves are given for longitudinal and transverse specimens of 17S-T, 24S-T, and 24S-RT aluminum-alloy sheet in thicknesses from 0.032 to 0.081 inch, 1025 carbon steel sheet in thicknesses of 0.054 and 0.120 inch, and chromium-nickel steel sheet in thicknesses form 0.020 to 0.0275 inch. Significant differences were found between the tensile and the compressive stress-strain curves, and also the corresponding corollary curves; similarly, differences were found between the curves for the longitudinal and transverse directions. These differences are of particular importance in considering the compressive strength of aircraft structures made of thin sheet. They are explored further for the case of compression by giving tangent modulus-stress curves in longitudinal and transverse compression and dimensionless curves of the ratio of tangent modulus to Young's modulus and of the ratio of reduced modulus for a rectangular section to Young's modulus, both plotted against the ratio of stress to secant yield strength.

Atchison, C S↗

NASA NTRS2001

Structure-Property Correlations in Al-Li Alloy Integrally Stiffened Extrusions

The objective of this investigation was to establish the relationship between mechanical property anisotropy, microstructure and crystallographic texture in integrally 'T'-stiffened extruded panels fabricated from the Al-Li alloys 2195, 2098 and 2096. In-plane properties were measured as a function of orientation at two locations in the panels, namely mid-way between (Skin), and directly beneath (Base), the integral 'T' stiffeners. The 2195 extrusion exhibited the best combination of strength and toughness, but was the most anisotropic. The 2098 extrusion exhibited lower strength and comparable toughness, but was more isotropic than 2195. The 2096 extrusion exhibited the lowest strength and poor toughness, but was the most isotropic. All three alloys exhibited highly elongated grain structures and similar location-dependent variations in grain morphology. The textural characteristics comprised a beta + <100> fiber texture, similar to rolled product, in the Skin regions and alpha <111> + <100> fiber texture, comparable to axisymmetric extruded product, in the Base regions. In an attempt to quantitatively correlate texture with yield strength anisotropy, the original 'full constraint' Taylor model and a variant of the 'relaxed constraint' model, explored by Wert et al., were applied to the data. A comparison of the results revealed that the Wert model was consistently more accurate than the Taylor model.

Hales, Stephen J.↗

NASA NTRS1974

The resistance of selected high strength alloys to embrittlement by a hydrogen environment

Selected high strength iron base and cobalt base alloys were resistant to degradation of mechanical properties in a one atmosphere hydrogen environment at ambient temperature. These alloys were strengthened initially by cold working which produced strain induced martensite and fcc mechanical twins in an fcc matrix. Heat treatment of the cobalt base alloy after cold working produced carbide precipitates with retention of an hcp epsilon phase which increased the yield strength level. High strength alloys can be produced which have some resistance to degradation of mechanical properties by a hydrogen environment under certain conditions.

Benson, R. B., Jr.↗

NASA NTRS1985

Structure-property characterization of rheocast and VADER processed IN-100 superalloy

Two recent solidification processes have been applied in the production of IN-100 nickel-base superalloy: rheocasting and vacuum arc double electrode remelting (VADER). A detailed microstructural examination has been made of the products of these two processes; associated tensile strength and fatigue crack propagation (FCP) rate at an elevated temperature were evaluated. In rheocasting, processing variables that have been evaluated include stirring speed, isothermal stirring time and volume fraction solid during isothermal stirring. VADER processed IN-100 was purchased from Special Metals Corp., New Hartford, NY. As-cast ingots were subjected to hot isostatic pressing (HIP) and heat treatment. Both rheocasting and VADER processed materials yield fine and equiaxed spherical structures, with reduced macrosegregation in comparison to ingot materials. The rheocast structures are discussed on the basis of the Vogel-Doherty-Cantor model of dendrite arm fragmentation. The rheocast ingots evaluated were superior in yield strength to both VADER and commercially cast IN-100 alloy. Rheocast and VADER ingots may have higher crack propagation resistance than P/M processed material.

Cheng, J. J. A.↗

DOE OSTI2022

Additive manufacturing of ferritic/martensitic steel with improved high temperature strength

Techniques for using additive manufacturing (AM) to fabricate creep resistant ferritic/martensitic steel with improved high temperature strength are described. AM processing may be performed on Grade 91 steel powder. Beam powers from about 221 W to about 270 W may be used. Traverse rates from about 675 mm/s to about 825 mm/s may be used. Heat inputs ranging from about 55.7 J/mm3 to about 83.2 J/mm 3 may be produced. Creep resistant ferritic/martensitic steel, produced according to the present disclosure, has improved strain yield strength and ductility as compared to wrought steel.

Lienert, Thomas J.↗

DOE OSTI2022

Report on Evolution of Inconel 718 Following HFIR Irradiation

The report presents the microstructure and mechanical properties of 3D printed Inconel 718 after irradiation in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) to assess its potential use as a structural material. The structural components near the outlets of several proposed reactor cores will experience significant neutron fluxes and outlet coolant temperatures ranging from the hot standby temperature of 300 °C to nearly 550 °C at the center of the part. These components must support the core in appropriate loading conditions and require structural analysis at relevant temperatures. In FY21, three heat treatments were designed and conducted to simplify the microstructure and to determine how each precipitating phase contributed to the overall strength. In FY21, baseline mechanical properties were measured from uniaxial tensile tests on subsize SS-J2 specimens at room temperature and at elevated temperatures of 300, 450, and 600 °C to serve a comparison to the irradiated properties. Four capsules containing 3D printed Inconel 718 were inserted into HFIR in FY21 for a matrix of two temperatures and two doses. The lower of the two doses was available for characterization in FY22. Multiple heat treatments of Inconel 718 irradiated to nominal conditions of 2 displacements per atom (dpa) at either 300 or 600 °C were strained with uniaxial tensile tests at the Irradiated Material Examination and Testing (IMET) Facility to discern the mechanical properties. Transmission electron microscopy was performed to correlate the observed mechanical properties with nanoscale features. The initially homogenous AM718-HM increased in strength at both irradiation temperatures based on a high density of nanometer-scale radiation-induced cavities at lower temperature and nucleation and growth of γ" precipitates at higher temperatures. The precipitate-hardened AM718-HT2 showed very small differences in strength before and after irradiation: the contribution to strength from γ" precipitates was replaced with dislocation loops. Because the radioactivity of the nickel superalloys from neutron activation limited the scope of the analysis, a feasibility study examined the possibility of an ultra-miniature specimen geometry, colloquially SS-Tiny (SS-T), for mechanical property determination using the nonirradiated Inconel 718. This study found an overestimation of ductility from the SS-T geometry with yield strength and ultimate tensile strength slightly above the SS-J2 geometry: this could be contributed to a reduction in specimen thickness.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Small Punch Testing of Molybdenum-99 Targets

Northstar Medical Radioisotopes is developing an accelerator-based method to produce 99 Mo, which is a parent isotope of the commonly used 99m Tc medical isotope. The Mo targets being designed for the accelerator will be produced from enriched 100 Mo, also known as aMo . Pressed and sintered powder feedstock is used to fabricate aMo targets, producing 29 mm disk-shaped targets. The targets are subjected to 1–6 days in line of an electron beam with subsequent dissolution of the disk to retain the 99 Mo, which decays to 99m Tc at radio-pharmacies. The press and sinter method is advantageous because the inherent porosity produced by this method enables increased surface area and therefore increased flow of dissolution media, decreasing the dissolution time and reducing the need for a highly acidic media. Although porosity aids in dissolution, it reduces the mechanical strength and ductility. Targets require good mechanical integrity when subjected to the conditions in the accelerator. Therefore, Northstar is seeking methods to rapidly test disk samples after fabrication to assure mechanical performance metrics are achieved. This report details the design and testing of a small punch test (SPT) that accommodates the 29 mm disk. Initial data were used to relate the SPT data to tensile properties, such as the yield strength (YS), ultimate tensile strength (UTS), and total elongation to failure. Although the SPT has been established as a somewhat reliable method for testing metallic materials, few studies have applied the SPT to refractory materials such as Mo. Based on tensile testing performed at Oak Ridge National Laboratory on different Mo samples, correlation between the Mo tensile and SPT properties could be performed, establishing a standard calibration that could be applied to other Mo samples. To test the efficacy of the SPT with Mo, multiple different disk batches were fabricated under different conditions (e.g., pressure, lubricant) with commercially available pure Mo powder. Generally, only a UTS could be well defined because the press and sinter disks failed under brittle fracture, making it difficult to determine the YS and elongation. Compared with disks fabricated with aMo powder, the aMo samples underperformed their pure nat Mo counterparts. This report summarizes the current status of the SPT, but further evaluation is needed before it can be applied as a reliable quality assurance tool.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1972

Investigation of the plastic fracture of high strength steels

An investigation of the plastic fracture process to improve tensile strength in high strength steels is presented. Two generic types of steels are considered: a quenched and tempered grade and a maraging grade, in order to compare two different matrix microstructures. Each type of steel was studied in commercial grade purity and in special melted high purity form, low in residual and impurity elements. The specific alloys dealt with include AISI 4340 and 18 Ni, 200 grade maraging steel, both heat treated to the same yield strength level of approximately 200 ksi.

Cox, T. B.↗

NASA NTRS2001

Vapor Growth of Binary and Ternary Chalcogenides in Preparation for Microgravity Experiments

In the bulk crystal growth of some technologically important semiconducting chalcopyrites, such as ZnTe, CdS, ZnSe and ZnS, vapor growth techniques have significant advantages over melt growth techniques due to the high melting points of these materials. The realization of routine production of high-quality single crystals of these semiconductors requires a fundamental, systematic and in-depth study on the PVT growth process and crystal growth by vapor transport in low gravity offers a set of unique conditions for this study. Previously, two reasons have been put forward to account for this. The first is weight-related reductions in crystal strain and defects. These are thought to be caused by the weight of the crystals during processing at elevated temperatures and retained on cooling, particularly for materials with a low yield strength. The second, and more general, reason is related to the reduction in density-gradient driven convection. The PVT crystal growth process consists of essentially three processes: sublimation of the source material, transport of the vapor species and condensation of the vapor species to form the crystal. The latter two processes can be affected by the convection caused by gravitational accelerations on Earth. Reductions in such convection in low gravity is expected to yield a nearly diffusion-limited growth condition which results in more uniform growth rates (on the microscopic scale) and hence greater crystalline perfection and compositional homogeneity. The reduction of convective contamination by performing flight experiments in a reduced gravity environment will help to understand the relation between fluid phase processes (growth parameters) and defect and impurity incorporation in grown crystals.

Su, C.↗

NASA NTRS2001

Vapor Growth of Binary and Ternary Chalcogenides in Preparation for Microgravity Experiments

Su, Ching-Hua↗

DOE OSTI2024

Lightweight single-phase Al-based complex concentrated alloy with high specific strength

Developing light yet strong aluminum (Al)-based alloys has been attracting unremitting efforts due to the soaring demand for energy-efficient structural materials. However, this endeavor is impeded by the limited solubility of other lighter components in Al. Here, we propose to surmount this challenge by converting multiple brittle phases into a ductile solid solution in Al-based complex concentrated alloys (CCA) by applying high pressure and temperature. We successfully develop a face-centered cubic single-phase Al-based CCA, Al 55 Mg 35 Li 5 Zn 5 , with a low density of 2.40 g/cm 3 and a high specific yield strength of 344×10 3 N·m/kg (typically ~ 200×10 3 N·m/kg in conventional Al-based alloys). Our analysis reveals that formation of the single-phase CCA can be attributed to the decreased difference in atomic size and electronegativity between the solute elements and Al under high pressure, as well as the synergistic high entropy effect caused by high temperature and high pressure. The increase in strength originates mainly from high solid solution and nanoscale chemical fluctuations. Our findings could offer a viable route to explore lightweight single-phase CCAs in a vast composition-temperature-pressure space with enhanced mechanical properties.

42 ENGINEERING↗

DOE OSTI2026

TEM Approaches for Microstructure-Informed Prediction of Mechanical Properties in Structural Alloys

Predicting the mechanical performance of structural alloys from their evolving microstructure remains a major challenge in materials science, particularly for nuclear structural materials, where irradiation-induced defects span multiple types and length scales and interact through complex mechanisms. The dispersed barrier hardening (DBH) [1] and Friedel–Kroupa–Hirsch (FKH) [2,3] models have been widely used to evaluate the hardening contributions of individual obstacles and to estimate tensile strength from quantified microstructures; however, when multiple size-dependent obstacles coexist and evolve, predicting temperature-dependent tensile strength becomes significantly more complex, and a fully consistent hardening model is still lacking. Transmission electron microscopy (TEM) plays a central role in refining hardening models and enabling predictive assessments of tensile strength evolution by providing quantitative characterization of dislocations, irradiation-induced defects (e.g., dislocation loops and cavities), precipitates, and grain structure (Fig. 1.). These experimentally measured defect densities are incorporated into physically based hardening models with size- and shape- dependent obstacle strengths [4], using root-sum-square superposition for obstacles of comparable strength and linear superposition for dissimilar ones [5]. In addition, recent advances in TEM [6-8], including high-resolution imaging, 4D-STEM strain mapping, EDS/EELS elemental analysis, and flash-polishing-based TEM specimen preparation and extraction-replica methods (Fig. 2), further improve the accuracy of microstructural quantification. By comparison with prior studies as well as our own results, we show that when TEM-derived microstructural information is carefully integrated with physically grounded hardening models, yield strength (or irradiation-induced hardening) measured at room temperature can be predicted with good quantitative agreement across multiple alloy classes. In-situ TEM combined with high-temperature mechanical testing represents an important next step for refining hardening models by directly probing dislocation–obstacle interactions across varying irradiation doses and temperatures [9]. Because the barrier strength factor (α) depends on both temperature and obstacle size, it should not be treated as a constant fitting parameter; rather, it must be explicitly evaluated to achieve physically meaningful predictions of mechanical behaviour at operating temperatures. This presentation therefore discusses why all strengthening contributions (e.g., Peierls stress, solid-solution strengthening, voids, bubbles, dislocation loops, dislocation lines, and grain boundaries) must be considered collectively, why appropriate superposition methods are essential when obstacles possess different barrier strength factors, how hardness measurements can be meaningfully related to tensile properties, and how TEM-derived microstructural information can be systematically incorporated into hardening models. More broadly, it outlines a pathway toward microstructure-informed prediction of mechanical properties and supports the goal of establishing science-based tools for evaluating structural materials in extreme environments [10].

Lin, Yan-Ru [ORNL] (ORCID:0000000339991473)↗

NASA NTRS1979

Process for making a high toughness-high strength iron alloy

A steel alloy is produced by a process which includes using cold rolling at room temperature and subsequent heat treatment at temperatures ranging from 500 C to 650 C. The resulting alloys exhibits excellent strength and toughness characteristics at cryogenic temperatures. This alloy consists essentially of about 10 to 16 percent by weight nickel, to about 1.0 percent by weight aluminum, and 0 to about 3 percent by weight of at least one of the following additional elements: copper, lanthanum, niobium, tantalum, titanium, vanadium, yttrium, zirconium and the rare earth metals, with the balance being essentially iron. The improved alloy possesses a fracture toughness ranging from 200 to 230 ksi sq in. and yield strengths up to 230 ksi.

Stephens, J. R.↗

DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Homogenization of Dendritic Structures and the High-Temperature Strength of the Refractory High-Entropy Alloy MoNbTaVW

MoNbTaVW, a pioneering refractory high-entropy alloy (RHEA), is renowned for its exceptional strength at elevated temperatures. Like most RHEAs, it solidifies into a dendritic microstructure with steep concentration gradients, necessitating heat treatment for equilibration. Steep concentration gradients typically complicate mechanical property analysis and modeling, key challenges for high-throughput alloy discovery. This study examines the effects of high-temperature homogenization (1800 °C for 8 hours) on the microstructure and mechanical properties of MoNbTaVW across temperatures up to 1200 °C. Postmortem microstructural analysis, coupled with chemical, crystallographic, and mechanical assessments, revealed that yield strength was surprisingly insensitive to homogenization, with less than a 3 pct difference between as-cast and heat-treated materials. Nanoindentation confirmed minimal nanohardness changes across the dendritic structure at room temperature. However, homogenization significantly enhanced high-temperature work hardening, producing higher peak compressive strength. Both as-cast and homogenized MoNbTaVW exhibited room-temperature strengths of 1400 MPa, exceeding previously reported values. These findings demonstrate that high-temperature treatment enables microstructural homogenization without compromising strength, a unique behavior among RHEAs. In conclusion, while not universally applicable, this insight highlights the importance of understanding microstructural development in experimental alloys and offers a pathway to design alloys that achieve homogeneous-like properties without heat treatment.

Rietema, C. J. [Lawrence Livermore National Labora↗

NASA NTRS1992

Fracture resistance and fatigue crack growth characteristics of two Al-Cu-Mg-Zr alloys

The dependence of strength, fracture resistance, and fatigue crack growth rate on the aging conditions of two alloy compositions based on Al-3.7Cu-1.85Mg-0.2Mn is investigated. Mechanical properties were evaluated in two heat treatment conditions and in two orientations (longitudinal and transverse). Compact tension specimens were used to determine fatigue crack growth characteristics and fracture resistance. The aging response was monitored on coupons using hardness measurements determined with a standard Rockwell hardness tester. Fracture resistance is found to increase with increasing yield strength during artificial aging of age-hardenable 2124-Zr alloys processed by powder metallurgy techniques. Fatigue crack growth rate increases with increasing strength. It is argued that these changes are related to deformation modes of the alloys; a homogeneous deformation mode tends to increase fracture resistance and to decrease the resistance to the fatigue crack propagation rate.

Sarkar, Bhaskar↗