Numerical and Experimental Analysis of the Mode I Interlaminar Fracture Toughness in Multidirectional 3D-Printed Thermoplastic Composites Reinforced with Continuous Carbon Fiber.

It is well known that the use of continuous reinforcing fibers can largely improve the typical low in-plane mechanical properties of 3D-printed parts. However, there is very limited research on the characterization of the interlaminar fracture toughness of 3D-printed composites. In this study, we investigated the feasibility of determining the mode I interlaminar fracture toughness of 3D-printed cFRP composites with multidirectional interfaces. First, elastic calculations and different FE simulations of Double Cantilever Beam (DCB) specimens (using cohesive elements for the delamination, in addition to an intralaminar ply failure criterion) were carried out to choose the best interface orientations and laminate configurations. The objective was to ensure a smooth and stable propagation of the interlaminar crack, while preventing asymmetrical delamination growth and plane migration, also known as crack jumping. Then, the best three specimen configurations were manufactured and tested experimentally to validate the simulation methodology. The experimental results confirmed that, with the appropriate stacking sequence for the specimen arms, it is possible to characterize the interlaminar fracture toughness in multidirectional 3D-printed composites under mode I. The experimental results also show that both initiation and propagation values of the mode I fracture toughness depend on the interface angles, although a clear tendency could not be established.

Development of functional fillers as a self-healing system for dental resin composite.

OBJECTIVES: To evaluate the incorporation of repairing capsules containing different monomers and polymerization modulators on the self-healing efficiency of an experimental photopolymerizable resin-based composite. METHODS: Self-healing capsules containing different monomers and polymerization modulators were prepared by emulsion polymerization: TCDHEPT (TEGDMA and DHEPT), BTCDHEPT (Bis-GMA, TEGDMA, and DHEPT), and BTCBPO (Bis-GMA, TEGDMA, and BPO). The capsules were analyzed through Fourier transform infrared spectroscopy and scanning electron microscopy. The capsules were added into experimental photopolymerizable resin composites establishing the following groups: ER (Control without capsules), ER+BPO, ER+BPO+TCDHEPT, and ER+BTCBPO+BTCDHEPT. Filtek Z350 resin composite (3 M ESPE) was used as a commercial reference. The materials were tested for degree of conversion (DC), flexural strength (σf), elastic modulus (Ef), fracture toughness (virgin KIC), self-healing efficiency (healed KIC), and roughness. For statistical analysis, the significance value was established at an a = 0.05 level. RESULTS: When compared to the control material, the incorporation of repairing capsules did not affect DC, σf, and Ef. Fracture toughness was statistically similar between the experimental groups (p ≤ 0.05). Healed KIC was statistically different between the groups ER+TCDHEP and ER+BTCBPO+BTCDHEPT; the self-healing efficiency was higher for ER+TCDHEPT. Surface roughness was statistically similar among all groups. CONCLUSIONS: The use of self-healing capsules promoted repair of the material. Studies with material aging after the self-healing process are necessary to better demonstrate the effectiveness of this system. CLINICAL SIGNIFICANCE: The self-healing system seemed to be a promising technology to be used in self-repaired restorative materials, which may prevent restoration fractures.

Composite design bioinspired by the mesocarp of Brazil nut (Bertholletia excelsa).

The mesocarp ofBertholletia excelsais a rich source of inspiration for strong, stiff and damage-tolerant composites. The bioinspired composites developed here are composed of an epoxy matrix with a 3D printed polylactic acid reinforced with 30% of carbon fiber (PLA-30CF) inspired in fibers, and syntactic foam inspired by sclereids. Monotonic and cyclic four-point bending tests and compact tension fracture toughness tests were carried out assisted by digital image correlation (DIC) to evaluate flexural properties, damage tolerance, and theR-curve of the composite. Its microstructure and fracture surface were analyzed by scanning electron microscopy. The mechanical performance of the bioinspired composite is promising: density of 1.0 g cm-3, flexural apparent elastic modulus of 1.6 GPa, and flexural strength six times higher than the neat epoxy, i.e. 17 MPa. Although the PLA-30CF printed structure led to a risingR-curve, the syntactic foam needs optimization to have a synergistic effect.

Experimental Characterization and Analysis of the In-Plane Elastic Properties and Interlaminar Fracture Toughness of a 3D-Printed Continuous Carbon Fiber-Reinforced Composite.

The use of continuous fiber as reinforcement in polymer additive manufacturing technologies enhances the mechanical performance of the manufactured parts. This is the case of the Carbon-Fiber reinforced PolyAmide (CF/PA) used by the MarkForged MarkTwo® 3D printer. However, the information available on the mechanical properties of this material is limited and with large variability. In this work, the in-plane mechanical properties and the interlaminar fracture toughness in modes I and II of Markforged's CF/PA are experimentally investigated. Two different standard specimens and end-tabs are considered for the in-plane properties. Monolithic CF/PA specimens without any additional reinforcement are used for the interlaminar fracture toughness characterization. Two different mode I specimen configurations are compared, and two different test types are considered for mode II. The results show that prismatic specimens with paper end-tabs are more appropriate for the characterization of the in-plane material properties. The use of thick specimens for mode I fracture toughness tests complicates the characterization and can lead to erroneous results. Contrary to what has been reported in the literature for the same material, fracture toughness in mode I is lower than for mode II, which agrees with the normal tendency of traditional composite materials.

Effect of processing methods on the chipping resistance of veneered zirconia.

OBJECTIVES: To evaluate the edge chipping resistance (ReA) and the fracture toughness (KC) of 3Y-TZP bilayers produced with the following materials/processing combinations: fluorapatite glass-ceramic applied on zirconia using the traditional layering and hot-pressing (press-on) techniques; feldspathic porcelain using rapid layer technology (RLT); and lithium disilicate glass-ceramic using CAD-on method. The influence of the cooling rate (slow and fast) was analyzed for layering and hot-pressing. METHODS: Bilayer bars (25x4x2 mm) were made following manufacturers' instructions. The edge chipping test was performed in an universal testing machine, using a coupled Vickers indenter. ReA was calculated dividing the critical load at fracture by the edge distance. Fracture toughness was calculated by a regression fit with a fixed slope of 1.5 correlating the critical chipping load regarding edge distance and also with indentation fracture (IF) method. Data were statistically analyzed using ANOVA and Tukey's test (α = 5%). RESULTS: ReA and KC was significantly higher for the CAD-on bilayers. RLT showed intermediate ReA means, and layering and hot-pressing techniques showed the lowest ReA values. For both processing methods there was no effect of the cooling protocol on the ReA and fracture toughness. CONCLUSIONS: There is a significant effect of the material/processing association on the edge chipping resistance and fracture toughness of the bilayers. There was no effect of the cooling protocol on the edge chipping resistance and fracture toughness for the specimens processed by both the layering and hot-pressing techniques.

Crack Length Effect on the Fracture Behavior of Single-Crystals and Bi-Crystals of Aluminum.

Molecular dynamics simulations of cracked nanocrystals of aluminum were performed in order to investigate the crack length and grain boundary effects. Atomistic models of single-crystals and bi-crystals were built considering 11 different crack lengths. Novel approaches based on fracture mechanics concepts were proposed to predict the crack length effect on single-crystals and bi-crystals. The results showed that the effect of the grain boundary on the fracture resistance was beneficial increasing the fracture toughness almost four times for bi-crystals.

Fracture Toughness Estimation of Single-Crystal Aluminum at Nanoscale.

In this publication, molecular dynamics simulations are used to investigate the fracture behavior of single-crystal aluminum. The stress intensity factor is estimated by means of four different methods, the accuracy is assessed for each approach and the fracture toughness is estimated. The proposed methodology is also applied to estimate the fracture toughness for graphene and diamond using published data from other scientific articles. The obtained fracture toughness for the single-crystal aluminum is compared with other nanomaterials that have similar microstructures. Dislocation emission during the fracture simulation of the cracked nano-crystal of aluminum is analyzed to study the fracture behavior. Brittle fracture behavior is the predominant failure mode for the nanomaterials studied in this research.

Design Equations for Mixed-Mode Fracture of Dental Ceramic-Cement Interfaces Using the Brazil-Nut-Sandwich Test.

Dental interfaces are subject to mixed-mode loading. This study provides practical guidance for determining interfacial fracture toughness of dental ceramic systems. We address interfacial fracture of a composite resin cement sandwiched between two dental ceramic materials. Emphasis is placed on sandwich disc specimens with cracks originating from elliptical-shaped flaws near the center, for which analytical fracture mechanics methods fail to predict. The interaction integral method is used to provide accurate finite element solutions for cracks with elliptical-shaped flaws in a Brazil-nut-sandwich specimen. The developed model was first validated with existing experimental data and then used to evaluate the three most widely used dental ceramic systems: polycrystalline ceramics (zirconia), glass-ceramics (lithium disilicate), and feldspathic ceramics (porcelain). Contrary to disc specimens with ideal cracks, those with cracks emanating from elliptical-shaped flaws do not exhibit a monotonic increase in interfacial toughness. Also, interfacial fracture toughness is seen to have a direct relationship with the aspect ratio of elliptical-shaped flaws and an inverse relationship with the modulus ratio of the constituents. The presence of an elliptical-shaped flaw significantly changes the interfacial fracture behavior of sandwich structures. Semi-empirical design equations are provided for fracture toughness and stress intensity factors for interfacial cracks. The developed design equations provide practical guidance for determining interfacial fracture toughness of selected dental ceramic material systems. Those equations take into account four critical factors: size of the elliptical flaw, modulus ratio of constituent materials, loading angle, and applied load.

Effect of zirconia substructure thickness on the mechanical properties and adhesion of veneering porcelain

Aim: This study investigated the influence of yttrium-stabilized tetragonal zirconia polycrystals (Y-TZP) thickness on fracture load of porcelain-veneered crowns (FL), fracture toughness of porcelain (FT), and the shear bond strength zirconia/porcelain (SBS). Methods: Artificial first molar was prepared for full crown (N=45) with different occlusal reduction. Y-TZP cores were made with different thickness at the occlusal face (1mm, 2mm and 3mm) (n=15). The cores were veneered with VM9 ­ Vita porcelain with 1.0 mm layer. For FL testing, axial load was applied to the mesiolingual cusp of the crowns. For FT testing, flat Y-TZP plates (5X5 mm) with 1, 2 or 3 mm thickness were veneered with 1.0 mm porcelain layer (n=10). FT by indentation fracture technique was measured close to the interface and at the top surface. For SBS by knife-edge shearing rod, cylindrical porcelain with 5 mm in diameter and 3 mm was applied on flat Y-TZP plates (1, 2 and 3 mm thickness) (n = 10). Results: Data analyzed by 1-Way ANOVA for FL of crowns and SBS between Y-TZP and porcelain were not significant. Two-way ANOVA for FT was significant for zirconia thickness and measurement area. The post-hoc test showed higher values for the groups with 2 and 3mm, and higher values at the interface, irrespectively of Y-TZP thickness. Conclusion: The zirconia thickness did not affect the FL of veneered crowns and the SBS between the ceramics, but FT of porcelain was lower in thinner zirconia substructure and close to the interface Y-TZP/Porcelain

Leaf cellulose density as the key determinant of inter- and intra-specific variation in leaf fracture toughness in a species-rich tropical forest.

Leaves as the main photosynthetic organ of plants must be well protected against various hazards to achieve their optimal lifespans. Yet, within-species variation and the material basis of leaf strength have been explored for very few species. Here, we present a large dataset of leaf fracture toughness from a species-rich humid tropical forest on Barro Colorado Island, Panama, reporting both among- and within-species variation in relation to light environment (sun-lit canopy versus shaded understorey) and ontogeny (seedlings versus adults). In this dataset encompassing 281 free-standing woody species and 428 species-light combinations, lamina fracture toughness varied ca 10 times. A central objective of our study was to identify generalizable patterns in the structural and material basis for interspecific variation in leaf lamina fracture toughness. The leaf lamina is a heterogeneous structure in which strong materials in cell walls, such as cellulose and lignin, contribute disproportionately to fracture toughness. We found significant increases in leaf fracture toughness from shade to sun and from seedling leaves to adult leaves. Both within and across species, leaf fracture toughness increased with total bulk density (dry biomass per unit volume) and cellulose mass concentration, but decreased with mass concentrations of lignin and hemicelluose. These bivariate relationships shift between light environments, but leaf cellulose density (cellulose mass per unit leaf volume) exhibits a common relationship with lamina fracture toughness between light environments and through ontogeny. Hence, leaf cellulose density is probably a universal predictor of leaf fracture toughness.

Importance of tubule density to the fracture toughness of dentin.

OBJECTIVE: The fracture toughness of dentin is critical to the prevention of tooth fracture. Within the tooth crown, the mechanical properties of dentin are influenced by spatial variations in the density and diameter of the dentin tubules with distance from the pulp. There are also relevant changes to the microstructure of dentin with age. In this investigation the importance of tubule density to the fracture toughness of dentin was evaluated in "young" and "old" age groups. METHODS: The variations in microstructure (density and diameter of tubules) from young and old donor teeth were studied by means of optical microscopy. RESULTS: A reduction in the density and diameter of tubules was identified to occur with aging. An approach previously proposed to study the mechanical behavior of porous materials was used to model the fracture toughness of coronal dentin in terms of the tubule characteristics. Results were then compared with published results from previous studies. CONCLUSIONS: The model predictions were consistent with experimental results for the fracture toughness of dentin from young donor teeth, but overestimated the values that have been reported for "old" dentin.

Thio-urethanes improve properties of dual-cured composite cements.

This study aims at modifying dual-cure composite cements by adding thio-urethane oligomers to improve mechanical properties, especially fracture toughness, and reduce polymerization stress. Thiol-functionalized oligomers were synthesized by combining 1,3-bis(1-isocyanato-1-methylethyl)benzene with trimethylol-tris-3-mercaptopropionate, at 1:2 isocyanate:thiol. Oligomer was added at 0, 10 or 20 wt% to BisGMA-UDMA-TEGDMA (5:3:2, with 25 wt% silanated inorganic fillers) or to one commercial composite cement (Relyx Ultimate, 3M Espe). Near-IR was used to measure methacrylate conversion after photoactivation (700 mW/cm(2) × 60s) and after 72 h. Flexural strength and modulus, toughness, and fracture toughness were evaluated in three-point bending. Polymerization stress was measured with the Bioman. The microtensile bond strength of an indirect composite and a glass ceramic to dentin was also evaluated. Results were analyzed with analysis of variance and Tukey's test (α = 0.05). For BisGMA-UDMA-TEGDMA cements, conversion values were not affected by the addition of thio-urethanes. Flexural strength/modulus increased significantly for both oligomer concentrations, with a 3-fold increase in toughness at 20 wt%. Fracture toughness increased over 2-fold for the thio-urethane modified groups. Contraction stress was reduced by 40% to 50% with the addition of thio-urethanes. The addition of thio-urethane to the commercial cement led to similar flexural strength, toughness, and conversion at 72h compared to the control. Flexural modulus decreased for the 20 wt% group, due to the dilution of the overall filler volume, which also led to decreased stress. However, fracture toughness increased by up to 50%. The microtensile bond strength increased for the experimental composite cement with 20 wt% thio-urethane bonding for both an indirect composite and a glass ceramic. Novel dual-cured composite cements containing thio-urethanes showed increased toughness, fracture toughness and bond strength to dentin while demonstrating reduced contraction stress. All of these benefits are derived without compromising the methacrylate conversion of the resin component. The modification does not require changing the operatory technique.

Fracture behavior of a commercial starch/polycaprolactone blend reinforced with different layered silicates.

In the present work, composites based on a commercial starch/PCL blend (MaterBi-Z) reinforced with three different nanoclays: natural montmorillonite (Cloisite Na(+) (MMT)) and two modified montmorillonites (Cloisite 30B (C30B) and Cloisite 10A (C10A)) were prepared in an intensive mixer. The aim of this investigation was to determine the effect of the different nanoclays on the quasi-static fracture behavior of MaterBi-Z nanocomposites. An improvement in the fracture behavior for the composite with low contents of C30B was obtained, probably due to the easy debonding of clay achieved from a relatively weak filler-matrix interaction. On the other hand, a strong interaction had a detrimental effect on the material fracture toughness for the MaterBi-Z/C10A composites as a result of the higher compatibility of this organo-modified clay with the hydrophobic matrix. Intermediate values of fracture toughness, determined using the J-integral approach (Jc), were found for the composites with MMT due to its intermediate interaction with the matrix. The different filler-matrix interactions observed were also confirmed from the application of Pukánszky and Maurer model. In addition, multifractal analysis was applied to describe the topography of fracture surfaces. Thus, the complex fracture process could be successfully described by both experimental and theoretical tools. The obtained results suggest that it is possible to tailor the mechanical properties of the studied composites taking into account their further application.

Influência da composição da matriz orgânica, conteúdo inorgânico e tratamento térmico sobre diferentes propriedades de compósitos experimentais / Influence of composition of the organic matrix, filler content and thermic treatment on different properties of experimental composites

Objetivo: Analisar a influência da matriz orgânica, do conteúdo inorgânico e do tratamento térmico (TT) sobre diferentes propriedades de compósitos experimentais, tais como o grau de conversão (GC), tenacidade à fratura (KIC), resistência à flexão (RF) e módulo de elasticidade (ME). Métodos: Para o experimento foram analisadas seis formulações de compósitos experimentais com proporções molares de Bis-GMA:TEGDMA de 5:5 e 7:3, a carga utilizada foi o vidro de bário, nas concentrações de 30, 50 e 70% em peso, e os fotoiniciadores a amina e canforoquinona. O GC foi analisado através da espectroscopia no infra-vermelho (FTIR) (n=5). A KlC foi avaliada pelo método single-edge notched beam (SENB). As imagens das superfícies de fratura foram capturadas por um estereomicroscópio e a KlC calculada (n=10). A análise da RF e ME foi realizada através do teste dos três pontos (n=10). Para todos os fatores de variação estudados, metade dos espécimes imediatamente após à confecção receberam TT em estufa convencional, a 170º C por 10 minutos e a outra metade não. Após 24 horas, as amostras foram destinadas de acordo com os ensaios realizados...

Objective: To analyze the influence of organic matrix, the inorganic content and thermic treatment (TT) on different properties of experimental composites, such as the degree of conversion (DC), fracture toughness (KIC), flexural strength (FS) and elastic modulus (EM). Methods: This experiment analyzed six formulations of experimental composites with 5:5 and 7:3 molar proportions of Bis-GMA: TEGDMA. The load used was barium glass at concentrations of 30, 50 and 70% by weight and the photoinitiators, camphorquinone and amine. GC was analyzed by infrared spectroscopy (FTIR) (n=5). The KIC was evaluated by a "single-edge notched beam" (SENB). The images of the fracture surfaces were captured by a stereomicroscope and KIC calculated (n=10). The analysis FS and EM were performed by testing three points (n=10). For all the variation factors studied, half of the specimens immediately after the preparation received TT in conventional oven at 170º C for 10 minutes and the other half not. After 24 hours, the samples were designed according to the tests. Data were analyzed using ANOVA/Tukey the degree of conversion, fracture toughness and flexural strength, and Kruskal-Wallis test for the elastic modulus (=5%). Results: Analysis of GC (%) statistical significance was observed for the three variation factors analyzed individually (monomer, filler and TT), as well as for the interaction monomer x TT (p <0.001). For KIC and FS, significant changes were observed only in the three variation factors (monomer, filler and TT) analyzed individually (p<0.001). For EM, the individual factors (monomer, filler and TT) TT x filler interaction showed statistical significance (p <0.001), as well as the monomer x filler interaction (p = 0.001). Conclusions: The organic matrix and inorganic content of experimental composites influenced the GC, KIC, FS and EM, and the TT caused improvements in the properties studied.

FRAGILIDAD Y COMPORTAMIENTO MECÁNICO DEL ESMALTE DENTAL / BRITLENESS AND MECHANICAL BEHAVIOR OF DENTAL ENAMEL

El esmalte dental es el tejido duro más mineralizado del cuerpo humano. En este trabajo se estudiaron las propiedades mecánicas fundamentales de este tejido para terceros molares de pacientes jóvenes colombianos. Se establecieron la dureza, la tenacidad a la fractura aparente y la fragilidad del esmalte dental en función de la profundidad a partir de la superficie oclusal mediante técnicas de medición de microindentación. Se encontró que las mediciones de dureza son altamente dependientes de la carga utilizada, hallándose que para valores de carga pequeños las huellas alcanzan a representar la dureza de un solo prisma de hidroxiapatita, mientras que para valores altos de carga las huellas abarcan un número de prismas suficientes para estimar la dureza general del esmalte. En términos generales los valores de las propiedades medidas son semejantes a los encontrados en estudios realizados en pacientes jóvenes norteamericanos, evidenciando que estas propiedades del esmalte son independientes de las características raciales o étnicas para pacientes jóvenes, lo cual no es necesariamente extensible al comportamiento de estos tejidos en pacientes mayores.

Dental enamel is one of the hardest and most mineralized tissues of the human body. This work studied the main mechanical properties of this hard tissue for third molars obtained from young Colombian patients. The hardness, apparent fracture toughness and brittleness of enamel were measured as a function of distance from the occlusal surface to the Dental Enamel Junction (DEJ) by means of microndentation techniques. It was found that the hardness measurements are highly dependent on the indentation load, with high values of hardness found when low loads were used. This behavior is explained by the size of the indentations which approached the size of single hydroxyapatite prisms for low load values, while for high load values the size of the indents covered several prisms. Overall, the mechanical properties measured on the enamel from young Colombians are close to the properties reported in the literature for young North American patients. Whether these similarities among young patients persist for older patients deserves further investigation.

Efeito do tratamento térmico sobre a sorção e solubilidade, tenacidade à fratura e grau de conversão de compósitos restauradores diretos / Effect of post-curing heat cured treatment in sorption and solubility, fracture toughness and degree of conversion of direct composites

O tratamento térmico em compósitos restauradores diretos foi realizado a fim de verificar a influência sobre algumas propriedades, tais como a sorção, solubilidade, tenacidade à fratura e grau de conversão. Foram utilizados três compósitos: um nanoparticulado, um microhíbrido e um microparticulado. Duas fontes de luz (Halógena e LED) e dois períodos (48h e 28dias) de armazenagem, com exceção da solubilidade. O tratamento térmico foi realizado em estufa convencional (170o C por 5min), sendo metade dos corpos de prova (cps) tratados e a outra, apenas fotoativada.Para sorção e solubilidade, foram confeccionados 60 cps de acordo com os fatores analisados (n=5) em uma matriz metálica circular de dimensões 15 mm x1 mm. Para o cálculo da sorção e solubilidade, os cps foram pesados em uma Balança Analítica,inicialmente após a confecção do cp, 1hora, 24h, 48h, 7d, 14, 21 e 28d, a fim de estabelecer Massa Inicial (Mi) Massa absorvida (Ma) e Massa dessecada (Md). Para a tenacidade à fratura, foram confeccionados 240 cps de acordo com os fatores analisados (n=10) em uma matriz metálica de dimensões internas 25 mm x 5mm x 2,8 mm. O método utilizado foi o Single Edge Notch-Beam(SENB), com um entalhe de 2,3 mm posicionado no centro da matriz. Os cps eram levados à máquina universal para o ensaio de flexão e, após a ruptura, as superfícies de fratura eram analisadas no estereomicroscópio, para, em seguida, obter as imagens e calcular as dimensões do cps para inserir naequação da tenacidade à fratura.Já para o grau de conversão foram confeccionados 36 cps em uma matriz de acetato circular de 15 mm x 1 mm, posicionados entre duas lâminas microscópicas (n=3). O cálculo do grau de conversão foi determinado por espectroscopia no infravermelho (FTIR).Em geral, os estudos apresentaram uma influência significante do tratamento térmico...

The post-curing heat treatment in direct composite treatment was done to verify the influence on some properties like sorption, solubility, fracture toughness and the degree of conversion. During the referred study it was used three composites: nanoparticle, a microhybrid and a microfill. Two sources of light (Halogen and LED) and two periods (48 hours and 28 days) for each one, but not to solubility. The postcuringwas done in dry heat sterilizer of 170º C for five minutes for, half of the test samples (TS) were treated and the other half were only photoactivated. It was made 60 TS to sorption and solubility according to the analyzed factors (n=5) in a 15mm x 1mm round metal matrix. To calculate sorption and solubility the TS were weighted in a analytical balance, right after the beginning of the production in 1 hour, 24 hours, 7days, 14 days, 21 days and 28 days respectively in order to establish the initial absorbed mass (Mi), the absorbed mass (Ma) and the desiccated mass (Md ). It was produced 240 TS to the fracture toughness according to factors (n=10) in a 25mm x 5mm x 2,8mm in metallic matrix. The Single Edge Notch-Beam (SENB), was the used method during this study with a notch of 2,3mm placed in the center of the matrix. The TS were taken to a universal machine to flexural test so after the rupture referred surface fractures were analyzed in a stereomicroscope and then it was possible to get the images to calculate the size of the TS to insert the calculus of the fracture toughness...