Stress-strain Measurements Research Articles

A Comparative Study of Compressible and Conductive Vertically Aligned Carbon Nanotube Forest in Different Polymer Matrixes for High-Performance Piezoresistive Force Sensors.

In the present scenario, conducting and lightweight flexible polymer nanocomposites rival metallic and inorganic semiconducting materials as highly sensitive piezoresistive force sensors. Herein, we explore the feasibility of vertically aligned carbon nanotube (VACNT) nanocomposites impregnated in different polymer matrixes, envisioned as highly efficient piezoresistors in sensor applications. Polymer nanocomposites are selectively designed and fabricated using three different polymer matrixes, i.e., polydimethylsiloxane (PDMS), polyurethane (PU), and epoxy resins with ideal reinforcement of VACNTs to enhance the thermal stability, conductivity, compressibility, piezoresistivity, and sensitivity of these nanocomposites. To predict the best piezoresistive force sensor, we evaluated the structural, optical, thermal, electrical, mechanical, and piezoresistive properties of the nanocomposites using field-emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), Raman spectroscopy, thermogravimetric analysis (TGA), I-V measurements, compressive stress-strain measurements, hysteresis, sensitivity, and force studies. The results demonstrate that the PDMS/VACNT nanocomposite is capable of sustaining large force with almost complete recovery and enhanced sensitivity, thereby fulfilling the desirable need for a highly efficient conductive and flexible force sensor as compared to PU/VACNT and epoxy/VACNT nanocomposites.

Silicone elastomers filled with rare earth oxides

Silicones which possess, amongst others, remarkable mechanical properties, thermal stability over a wide range of temperatures and processability, and rare earth oxides (REO), known for their unique optic, magnetic and catalytic properties can be coupled into multifunctional composite materials (S-REOs). In addition, the intrinsic hydrophobicity of REO and polysiloxanes makes them easily compatible without the need for surface treatments of the former. Thus, europium oxide (Eu2O3), gadolinium oxide (Gd2O3) and dysprosium oxide (Dy2O3) in amounts of 20 pph are incorporated as fillers into silicone matrices, followed by processing mixture as thin films and crosslinking at room temperature. The analysis of the obtained films reveals the changes induced by these fillers in the thermal, mechanical, dielectric and optical properties, as well as the hydrophobicity of the silicones. The luminescence properties of S-REO composites were investigated by fluorescence spectra and lifetime - resolved measurements with a multiemission peaks from blue to greenish register. The thermogravimetrical analysis indicates an increasing of thermal stability of the composites that contain REO, compared to pure silicone. As expected, the dielectric permittivity significantly increased due to nature of the fillers, while the dielectric loss values are relatively low for all samples, indicating a minimal conversion of electrical energy in the form of heat within bulk composites. The presence of rare earth oxides into the silicone matrix facilitates the motions of long-range charge carriers through the network resulting in higher values of conductivity of the composite films. The stress-strain measurements revealed the reinforcing effect of the rare earth metal oxides on a silicone matrix, leading to a significant increase of Young modulus. The known hydrophobicity of silicones is further enhanced by the presence of REO.

Crystal Strengths at Micro- and Nano-Scale Dimensions

Higher strength levels, achieved for dimensionally-smaller micro- and nano-scale materials or material components, such as MEMS devices, are an important enabler of a broad range of present-day engineering devices and structures. Beyond such applications, there is an important effort to understand the dislocation mechanics basis for obtaining such improved strength properties. Four particular examples related to these issues are described in the present report: (1) a compilation of nano-indentation hardness measurements made on silicon crystals spanning nano- to micro-scale testing; (2) stress–strain measurements made on iron and steel materials at micro- to nano-crystal (grain size) dimensions; (3) assessment of small dislocation pile-ups relating to Griffith-type fracture stress vs. crack-size calculations for cleavage fracturing of α-iron; and (4) description of thermally-dependent strain rate sensitivities for grain size strengthening and weakening for macro- to micro- to nano-polycrystalline copper and nickel materials.

Icephobic, Pt-Cured, Polydimethylsiloxane Nanocomposite Coatings.

To explore novel coatings with potential for easy release of ice (icephobicity), a series of platinum-cured silicone coatings was prepared incorporating SYL-OFF 7210, designated MQ-R, as a nanoscale reinforcing component. These optically transparent coatings are designated according to cure temperature and MQ-R wt %, for example, Pt-PDMS(25)-20 for 25 °C cure and 20 wt % MQ-R. Surface characterization included dynamic contact angles and morphology by atomic force microscopy. Bulk characterization was accomplished with stress-strain measurements at 25 °C and dynamic mechanical analysis from -110 to 150 °C. Ice adhesion tests at -10 °C showed modulus had a dominant effect in increasing τice, the peak removal force. At -30 °C, storage modulus was greater for coatings cured at 100 °C compared to 25 °C, but ice removal tests at -30 °C (-22 °F) consistently showed τice for Pt-PDMS(100) MQ-R compositions was less than τice for corresponding Pt-PDMS(25) coatings. This unexpected result was explained by proposing that supercooled water at hydrophilic interfacial sites (-10 °C) does not impede ice removal but frozen water pins ice at -30 °C. Interestingly, MQ-R was found to be a reactive filler that increased modulus after 100 °C cure especially for Pt-PDMS(100)-30 (3 MPa) and Pt-PDMS(100)-40 (5 MPa). In summary, by virtue of resistance to ice adhesion Pt(PDMS) coatings with low MQ-R content have potential for conferring energy savings and safety while high MQ-R content results in noteworthy mechanical properties.

Stress-strain curve measurements of wood plastic composites at intermediate strain rates

Stress-strain curve measurements of wood plastic composites at intermediate strain rates

Improvement in the properties of silica-reinforced natural rubber with the sustainable interfacial modifier: Effect of molecular weight and content of interfacial modifier

Silica is the most reinforcing filler for enhancing the rubber properties. However, the incompatibility of silica with non-polar rubber is the main problem for application. Therefore, the researchers attempted to use the several methods in order to solve the problem. In this work, the appropriated hydroxyl telechelic natural rubber (HTNR) was determined by varying molecular weights in the range of 2,000-3,000 g·mol-1 and contents in the range of 4-16%w/w of silica content in order to enhance the rubber properties. It was found that the decrease in Payne effect and the improvement in cure characteristics of silica-reinforced NR were achieved by using HTNR. However, the incorporation of various molecular weights and contents of HTNR in rubber influenced C1 (crosslink density determined by stress-strain measurement) in rubber, which related to rubber properties. The increasing in C1 caused the increases in tensile strength and abrasion index and the decrease in heat build-up. The optimum properties of rubber with silica loading at 30 phr was achieved by adding 2,000 g·mol-1 HTNR at a loading of 8%w/w of silica content. However, for silica-reinforced NR, TESPT provided better properties than HTNRs.

A Methodology Towards Mechanical Properties Optimization of Three-Component Polymers by the Gradual Variation of Feed Composition in Semi-Continuous Emulsion-Free Radical Polymerization.

In this work, a new methodology for the synthesis of three-component polymers (TCPs) was developed using a seeded, semi-continuous free-radical emulsion polymerization towards the optimization of the moduli–ultimate deformation performance and energy dissipation capacity for a styrene (S), n-butyl acrylate (BA), and 4-vinylbenzyl chloride (VBC) system. The three components were sequentially fed in pairs, varying feed composition along the conversion using S as the common monomer. To prepare a reference material, an industrial method was utilized with those monomers, using an equivalent global composition in a two-stage batch process (TS). Nanophase formation in the particles was observed by transmission electron microscopy (TEM), while the separation of the phases in the solid samples was observed by atomic force microscopy (AFM). The changes in glass transition temperature were determined by differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). The latter was primarily used to compare mechanodynamic properties as a function of temperature for the two synthesis methods used. Thus, the higher toughness of the forced composition three-component polymeric materials was evaluated by means of their energy dissipation capacity, toughness, and stress–strain measurements at several temperatures.

Thermomechanical Properties of Polymers for Use in Superconducting Magnets

The coefficient of thermal expansion (CTE) and the thermomechanical properties of the polymers used in superconducting magnets need to be known in order to predict their stress state under the different magnet assembly and operating conditions. We have measured Young's moduli of typically used polymers during in situ heat cycles with the dynamic resonance method. The dynamic test results are compared with Young's moduli determined from quasi-static stress-strain measurements at room temperature, 77 K and 4.2 K. A moderate elastic anisotropy is found for the fiber reinforced polymers. CTEs are compared based on dilation experiments. The CTEs of the fiber reinforced polymers studied are similar to those of copper or steel. In contrast, the pure resins exhibit relatively larger CTEs.

A Bayesian Framework for the Estimation of the Single Crystal Elastic Parameters From Spherical Indentation Stress-Strain Measurements

This paper presents a two-step Bayesian framework for the estimation of the intrinsic single crystal elastic stiffness parameters from the measurements of spherical indentation stress-strain responses in multiple individual grains of a polycrystalline sample, whose crystal lattice orientations have been measured using electron back-scattered diffraction technique. The first step requires the establishment of the functional dependence of the indentation elastic modulus given the lattice orientation and the intrinsic single crystal elastic stiffness parameters. Previous efforts for this step required a large database of computationally expensive finite element (FE) simulations in order to establish this function with adequate accuracy. In this paper, it is shown that the introduction of a Bayesian framework can greatly reduce the number of simulations necessary to establish this function, while introducing practically useful measures of uncertainty which can guide the selection of specific additional simulations that are expected to best improve the predictive accuracy of the function. The second step involves a Markov Chain Monte-Carlo (MCMC) sampling of the distribution of possible values for the single crystal elastic stiffness parameters based on a given set of experimentally measured elastic indentation moduli in individual grains of different lattice orientations. This second step is accomplished by calibrating the available experimental data to the function established in the first step. This novel framework is presented and demonstrated in this paper for an as-cast cubic polycrystalline Fe-3% Si sample and a hexagonal polycrystalline commercially pure (CP-Ti) titanium sample.

Noncovalent Hydrogen Bonds Tune the Mechanical Properties of Phosphoester Polyethylene Mimics.

Polyethylene mimics of semicrystalline polyphosphoesters (PPEs) with an adjustable amount of noncovalent cross-links were synthesized. Acyclic diene metathesis copolymerization of a phosphoric acid triester (M1) with a novel phosphoric acid diester monomer (M2) was achieved. PPEs with different co-monomer ratios and 0, 20, 40, and 100% of phosphodiester content were synthesized. The phosphodiester groups result in supramolecular interactions between the polymer chains, with the P–OH functionality as an H-bond donor and the P=O group as an H-bond acceptor. A library of unsaturated and saturated PPEs was prepared and analyzed in detail by NMR spectroscopy, size exclusion chromatography, differential scanning calorimetry, thermogravimetry, rheology, and stress–strain measurements. The introduction of the supramolecular cross-links into the aliphatic and hydrophobic PPEs showed a significant impact on the material properties: increased glass-transition and melting temperatures were observed and an increase in the storage modulus of the polymers was achieved. This specific combination of a flexible aliphatic backbone and a supramolecular H-bonding interaction between the chains was maximized in the homopolymer of the phosphodiester monomer, which featured additional properties, such as shape-memory properties, and polymer samples could be healed after cutting. The P–OH groups also showed a strong adhesion toward metal surfaces, which was used together with the shape-memory function in a model device that responds to a temperature stimulus with shape change. This systematic variation of phosphodiesters/phosphotriesters in polyethylene mimics further underlines the versatility of the phosphorus chemistry to build up complex macromolecular architectures.

Symbiotic Aerogel Fibers Made via In-Situ Gelation of Aramid Nanofibers with Polyamidoxime for Uranium Extraction.

The uranium reserve in seawater is enormous, but its concentration is extremely low and plenty of interfering ions exist; therefore, it is a great challenge to extract uranium from seawater with high efficiency and high selectivity. In this work, a symbiotic aerogel fiber (i.e., PAO@ANF) based on polyamidoxime (PAO) and aramid nanofiber (ANF) is designed and fabricated via in-situ gelation of ANF with PAO in dimethyl sulfoxide and subsequent freeze-drying of the corresponding fibrous gel precursor. The resulting flexible porous aerogel fiber possesses high specific surface area (up to 165 m2·g−1), excellent hydrophilicity and high tensile strength (up to 4.56 MPa) as determined by BET, contact angle, and stress-strain measurements. The batch adsorption experiments indicate that the PAO@ANF aerogel fibers possess a maximal adsorption capacity of uranium up to 262.5 mg·g−1, and the absorption process is better fitted by the pseudo-second-order kinetics model and Langmuir isotherm model, indicating an adsorption mechanism of the monolayer chemical adsorption. Moreover, the PAO@ANF aerogel fibers exhibit selective adsorption to uranium in the presence of coexisting ions, and they could well maintain good adsorption ability and integrated porous architecture after five cycles of adsorption–desorption process. It would be expected that the symbiotic aerogel fiber could be produced on a large scale and would find promising application in uranium ion extraction from seawater.

Methylene Blue/PVA composite film for flexible, wide-scale UV–VIS laser cut-off filter

Optical filter, especially the laser cut-off filter is an essential component of optoelectronics technology. In this work, we report preparation of self-standing, low cost, flexible methylene blue /poly (vinyl alcohol) composite film by simple solution casting technique for application in optical filter. Poly (vinyl alcohol) (PVA) is doped with different concentrations of the methylene blue (MB) dye (0.5 wt%, 1 wt%, 2 wt%, 3 wt%, 5 wt%) to modify its optical properties. The structural, morphological and mechanical properties of MB/PVA composite films were investigated by x-ray diffraction, FESEM and stress-strain measurement techniques. The XRD histogram shows decrease in crystallinity in the structure of the composite films with MB doping. The optical properties of the films were studied by UV–vis spectroscopy technique which shows that transmittance of the films in the UV–vis region is decreased with increasing loading concentration of the dye in the PVA matrix. A significant decrease in the band gap of the composite is observed with MB doping. The modifications in optical properties of PVA are attributed to the interaction between the dye molecule and the PVA matrix. As prepared 3 wt% MB/PVA film having thickness ∼280 ± 20 μm can effectively block incident light of entire UV–vis region (200–695 nm) with zero transmittance(T ∼ 10−4), but remain fairly transparent in IR zone(above 705 nm), which confirms the strong potential of the composite as efficient optical filter. This work also substantiates that the 3 wt% MB/PVA composite film is able to completely block high power laser radiation (3.6 mW) of wavelength 544 nm without showing any degradation in structure with time, which makes MB/PVA a prospective candidate for high power laser cut-off filter in UV–vis region.

A physical interpretation of fractional viscoelasticity based on the fractal structure of media: Theory and experimental validation

In this work, a physical connection between the fractional time derivative and fractal geometry of fractal media is developed and applied to viscoelasticity and thermal diffusion in elastomers. Integral to this formulation is the application of both the fractal dimension and the spectral dimension which characterizes diffusion in fractal media. The methodology extends the generalized molecular theory of Rouse and Zimm where generalized Gaussian structures (GGSs) replace the Rouse matrix with the generalized Gaussian Rouse matrix (GRM). Importantly, the Zimm model is extended to fractal media where the new relaxation formulation contains internal state variables that naturally depend on the fractional time derivative of deformation. Through the use of thermodynamic laws in fractal media, we derive the linear fractional model of viscoelasticity based on both spectral and fractal dimensions. This derivation shows how the order of the fractional derivative in the linear fractional model of viscoelasticity is a rate dependent material property that is strongly correlated with fractal and spectral dimensions in fractal media. To validate the correlation between fractional rates and fractal material structure, we measure the viscoelasticity and thermal diffusion of two different dielectric elastomers: Very High Bond (VHB) 4910 and VHB 4949. Using Bayesian uncertainty quantification (UQ) based on uniaxial stress–strain measurements, the fractional order of the derivative in the linear fractional model of viscoelasticity is quantified. Two dimensional fractal dimensions are also independently quantified using the box counting method. Lastly, the diffusion equation in fractal media is inferred from experiments using Bayesian UQ to quantify the spectral dimension by heating the polymer locally with a laser beam and quantifying thermal diffusion. Comparing theory to experiments, a strong correlation is found between the viscoelastic fractional order obtained from stress–strain measurements in comparisons with independent predictions of fractional viscoelasticity based on the fractal structure and fractional thermal diffusion rates.

Aromatic polyesters containing pendant azido groups: Synthesis, characterization, chemical modification and thermal cross-linking

A partially bio-based bisphenol containing pendant azido group viz., 4,4′-(5-azidopentane-2,2-diyl) diphenol (AZBPA) was synthesized starting from 4,4′-bis (4-hydroxyphenyl) pentanoic acid. AZBPA was reacted with isophthaloyl chloride (IPC), terephthaloyl chloride (TPC) and a mixture of IPC/TPC (50:50 mol%) by phase transfer-catalyzed interfacial polycondensation route to obtain aromatic polyesters containing pendant azido groups. Copolyesters containing pendant azido groups were also synthesized by polycondensation of different molar proportions of AZBPA and commercially available 4,4′-(1-phenylethane-1,1-diyl) diphenol (BPA-AP) with IPC. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.85–1.64 dL/g and 58,900–190,400, respectively, indicating the formation of reasonably high molecular weight polymers. Tough, transparent, and flexible films could be cast from chloroform solutions of these polyesters. X-Ray diffraction analysis showed that (co)polyesters were amorphous in nature. (Co)polyesters were characterized using FT-IR, 1H NMR spectroscopy, XRD, TGA and DSC analysis. The chemical modification of a representative copolyester containing pendant azido groups was carried out quantitatively using copper-catalyzed azide-alkyne cycloaddition (CuAAC) with two alkynes viz., phenyl acetylene (PA) and ethynyl-4-nitrobenzene (ENB). Additionally, (co)polyesters containing pendant azido groups were thermally cross-linked (170 °C/12 h) leading to the formation of network structures based on azide to nitrene decomposition and subsequent reactions on polyester backbone. The selected cross-linked polyesters were characterized by stress-strain measurements. The cross-linked polymers exhibited higher tensile strength and Young’s modulus and lower % elongation at break compared to corresponding pristine polyesters containing pendant azido groups.

Synthesis and characterization of poly(urethane-sulfone)s networks

ABSTRACTNew poly(urethane-sulfone)s networks were prepared by the [3 + 2] dipolar cycloaddition of azidomethyl polyethersulfone to urethane-bismaleimides based on various polyols different by their structure and molecular weight. The chemical structure of these polymers was confirmed by the Fourier transform infrared and nuclear magnetic resonance spectroscopy. The new polymers were characterized using thermogravimetric analysis, differential scanning calorimetry, dynamic mechanical analysis, as well as by stress-strain and water contact angle measurements.

PH-responsive cellulose\u2013chitosan nanocomposite films with slow release of chitosan

Cellulose–chitosan films were prepared using a physical method in which cellulose and chitosan were separately dissolved via freeze thawing in LiOH/urea and mixed in different proportions, the resulting films being cast and regenerated in water/ethanol. X-ray diffraction and Fourier transform infrared spectroscopy (FT-IR) spectroscopy verified the composition changes in the nanocomposites due to different mixing ratios between the polymers. Tensile stress–strain measurements indicated that the mechanical performance of the cellulose–chitosan nanocomposites slightly worsened with increasing chitosan content compared with that of films comprising cellulose alone. Field emission scanning electron microscopy revealed the spontaneous formation of nanofibers in the films; these nanofibers were subsequently ordered into lamellar structures. Water uptake and microscopy analysis of film thickness changes indicated that the swelling dramatically increased at lower pH and with increasing chitosan content, this being ascribed to the Gibbs–Donnan effect. Slow material loss appeared at acidic pH, as indicated by a loss of weight, and quantitative FT-IR analysis confirmed that chitosan was the main component released. A sample containing 75% chitosan reached a maximum swelling ratio and weight loss of 1500% and 55 wt%, respectively, after 12 h at pH 3. The study presents a novel way of preparing pH-responsive cellulose–chitosan nanocomposites with slow-release characteristics using an environmentally friendly procedure and without any chemical reactions.Graphical abstract

Anisotropic coal permeability estimation by determining cleat compressibility using mercury intrusion porosimetry and stress–strain measurements

This paper presents a novel method to calculate the anisotropic and stress-dependent coal permeability by determining cleat compressibility using the Mercury Intrusion Porosimetry (MIP) and stress–strain measurements. Cleat compressibility is often assumed isotropic and constant in the literature and is usually obtained by numerical fitting to a matchstick permeability model e.g. the model by Seidle et al. (1992) despite the gross simplification of this representation of the coal pore network. This paper provides a method to calculate anisotropic cleat compressibility using only MIP and stress–strain measurements which are easy to conduct, and without permeability information, which is harder to come by, requiring laboratory experiments on the core or through fitting field data. We report the measured stress–strain behaviour of a coal sample, with hydrodynamic loading/unloading over the range 0.5–4.0 MPa, and the permeability in face cleat (kF) and butt cleat (kB) directions using the Triaxial Stress Permeameter (TSR). The stress–strain measurement is used to calculate the anisotropic modulus of elasticity (EF, EB, and EV) in face cleat, butt cleat and bedding plane directions, and cleat compressibility in the face cleat (CfF) and butt cleat (CfB) directions using the fractal dimension analysis with MIP measurement. Finally, the cleat compressibilities are used to calculate the anisotropic coal permeability by Seidle et al. (1992) permeability model and compared with the measured permeability of the coal sample.

Ecofriendly Autoxidation of Castor Oil/Ricinoleic Acid. Multifunctional Macroperoxide Initiators for Multi Block/Graft Copolymers

AbstractEcofriendly autoxidation is a reaction of air oxygen with unsaturated organic molecules at room temperature. Castor oil and ricinoleic acid were ecofriendly autoxidized for 5 months to obtain castor oil macroperoxide with a Mn of 1935 g mol−1 (Pcast5m) and the ricinoleic acid macroperoxide initiator (Prici5m) with a Mn of 1169 g mol−1. Peroxide groups thermally initiated the free radical polymerization of methyl methacrylate (MMA), n‐butyl methacrylate (nBMA), and styrene (S). Peroxide formation in the oxidized castor oil and ricinoleic acid was confirmed using iodometric analysis, elemental analysis, and differential scanning calorimetry technique. Peroxide decomposition in both macroperoxide initiators was observed at 166 °C for Prici5m and 170 °C for Pcast5m. Hydroxyl groups of Pcast5m were reacted with methacryloyl chloride to obtain methacrylated castor oil macroperoxide (PcastMA). The polymerization rates of the obtained macroinitiators were compared. The polymerization rate order is Pcast5m > Prici5m > PcastMA. Polymerization of styrene by PcastMA resulted in an increase in molar masses and an increase in the polymerization time while those of the styrene polymerization by Pcast5m and Prici5m remained constant. Carboxylic acid groups were reacted with amine‐terminated polyethylene glycol (PEG), polydimethyl siloxane (PDMS), and polytetrahydrofuran (PTHF) while the hydroxyl functionality initiated the ring‐opening polymerization of ε‐caprolactone (CL). Prici‐PEG‐PMMA, Prici‐PS‐PDMS, Prici‐PS‐PTHF, Pcast‐PS‐PCL, Pcast‐PCL‐PMMA, and Pcast‐PS‐PnBMA multiblock copolymers were prepared and characterized using spectrometric, thermal, and stress–strain measurement techniques.

The weldability of Shape Memory Alloy

In this work a Nd:YAG laser was used for welding 2mm thick tapes of Ti–50.9at.%Ni shape memory alloy (SMA). Both reference and laser welded samples were chosen to investigate mechanical and shape memory behaviour. Their mechanical properties were tested by stress-strain measurements respectively. Comparative microstructures of the reference and the welded materials were studied with SEM and XRD analysis. Moreover, hardness measurements allowed further clarification that the modification was induced by the welding procedure. The results obtained on the weld joint material indicate that the stress-induced martensite and the recovery mechanisms are weakly modified by the presence of the welding zone, while the microstructure of the weld joint is strongly affected.

Dislocation Mechanics Pile-Up and Thermal Activation Roles in Metal Plasticity and Fracturing

Dislocation pile-up and thermal activation influences on the deformation and fracturing behaviors of polycrystalline metals are briefly reviewed, as examples of dislocation mechanics applications to understanding mechanical properties. To start, a reciprocal square root of grain size dependence was demonstrated for historical hardness measurements reported for cartridge brass, in line with a similar Hall-Petch grain size characterization of stress-strain measurements made on conventional grain size and nano-polycrystalline copper, nickel, and aluminum materials. Additional influences of loading rate (and temperature) were shown to be included in a dislocation model thermal activation basis, for calculated deformation shapes of impacted solid cylinders of copper and Armco iron materials. Connection was established for such grain size, temperature, and strain rate influences on the brittle fracturing transition exhibited by steel and other related metals. Lastly, for AISI 1040 steel material, a fracture mechanics based failure stress dependence on the inverse square root of crack size was shown to approach the yield stress at a very small crack size, also in line with a Hall-Petch dependence of the stress intensity on polycrystal grain size.