Orientation Angle Research Articles

Velocity prediction program for windsurfing: A hierarchical approach integrating biomechanical insights

Windsurfing sails have three degrees of controllable angular freedoms and rely heavily on the sailor’s gravity to balance the heeling moments. The position of the sailor’s centre of gravity that affect the moment generation is greatly influenced by the posture. These factors result in the complexity of predicting windsurfing velocity during steady sailing, which is shown to be an under-defined problem. To address the challenges, this study proposes a hierarchical approach. At the lower levels of the hierarchy, a mechanical model of windsurfing is constructed by incorporating a tailor-made biomechanical model of the sailor, as well as the aero- and hydrodynamic properties of the sail, board, and sailor. The mechanical model allows the investigation of control variables that lead to different steady states, including sail roll, yaw and hydrofoil roll. At a higher level, these variables are optimized to maximize sailing speed. The proposed approach provides intermediate results that explore factors affecting sailing velocity, such as sail and board orientation angles, the sailor’s center of gravity, and wind conditions. Furthermore, the approach generates a velocity polar chart that illustrates the maximum sailing speed for different travel directions. The chart indicates the maximum VMG and optimal sailing angle for achieving an upwind or downwind mark. This study contributes to a deeper understanding of the critical variables influencing windsurfing velocity and provide insights for improving sailing performance.

In-situ EBSD study of the active slip systems and substructure evolution in a medium-entropy alloy during tensile deformation

Electron backscatter diffraction (EBSD) coupled with in-situ tensile loading is powerful for investigating the microstructural evolution of alloys. Thermo-mechanically treated f.c.c. medium-entropy alloys (MEAs) typically have high densities of annealing twin boundaries (ATBs), which can not only strengthen but also toughen the MEA via interacting with dislocations. However, the evolution of ATBs and other substructures in plastically-deformed MEA has not yet been revealed. Plastic deformation involving dislocation evolution, active slip systems, lattice rotation, boundary transformation, and grain subdivision in a polycrystalline MEA Ni41.4Co23.3Cr23.3Al3Ti3V6 was studied using in-situ EBSD. The slip was accompanied by heterogeneous lattice rotation among grains and within grains, where inhomogeneous plasticity was accommodated by geometrically-necessary dislocations (GNDs). Both GND and low-angled boundaries (LABs) densities substantially increased with progressive strain, which was mainly concentrated in sites approaching ATBs or grain boundaries (GBs). Located stress, lattice rotation, or curvature caused a loss in the coherence of ATBs, which resulted in integrity loss with increasing strain and promoted a decrease in density by 60 %. Further, lattice rotation incompatibility due to constraints from neighboring grains leads to grain fragmentation into various misorientated volumes, which were separated by LABs or high-angle boundaries (HABs). The grain orientation angle increased with progressive strain and crystallographic 〈111〉 orientation gradually spread toward a tensile direction. Slip systems with maximum Schmid factor were activated first at ε ≥ 3.9 %, which is almost the same with experimental slip traces. Both single slip and double slip occurred during plasticity, where straight slip traces tend to curve due to lattice curvature. Slip transfers are not only controlled by geometric compatibility factor, which can occur between some neighboring grains with low geometric compatibility factor but high Schmid factor.

Elliptic Hermite-Gaussian soliton and transformations in nonlocal media induced by linear anisotropy.

Elliptic Hermite-Gaussian (HG) soliton clusters in nonlocal media with anisotropic diffractions are studied comprehensively. The relations among solitons parameters, diffraction indices, and the degree of nonlocality are derived analytically with the Lagrangian method. Stable elliptic HG soliton clusters can be obtained when linear diffraction is anisotropic. When the solitons are launched with an initial orientation angle, we also demonstrate numerically mode transformations between HG and Laguerre-Gaussian (LG) solitons induced by linear anisotropy. Our results will enrich the soliton phenomenon with linear anisotropic diffraction and may lead to novel applications in all-optical switching, interconnection, etc.

Effect of chemical modification on hydraulic conductivity of stratified porous media

ABSTRACT Understanding hydraulic conductivity is essential in porous media as it dictates the capacity of fluids to permeate through these substances. This research investigated the impact of chemical modification using fly ash on hydraulic conductivity. The coefficient of hydraulic conductivity along the bedding plane at different angles of orientations was predicted by employing machine learning techniques such as gene expression programming (GEP), artificial neural networks (ANNs), and regression tree (RT), considering various influencing parameters. As the amount of fly ash in the porous medium rises, the hydraulic conductivity decreases. The statistical results demonstrate that the proposed ANN model effectively forecasted the horizontal hydraulic conductivity. It achieved the highest R2 value (0.989), the lowest mean absolute percentage error value (5.772), the lowest scatter index value (0.040), and the lowest Akaike Information Criterion value (−2,359.914) compared to the GEP, RT, and previously established approaches. Moreover, a novel equation has been proposed for determining horizontal hydraulic conductivity, which can be used for any stratified medium, distinguishing this work from previous ones. These findings can inform global practices in mitigating groundwater contamination, enhancing irrigation efficiency, and improving the design of subsurface fluid flow systems, making it a valuable contribution to both academic and practical applications worldwide.

Piezoelectricity and flexoelectricity in biological cells: the role of cell structure and organelles.

Living tissues experience various external forces on cells, influencing their behaviour, physiology, shape, gene expression, and destiny through interactions with their environment. Despite much research done in this area, challenges remain in our better understanding of the behaviour of the cell in response to external stimuli, including the arrangement, quantity, and shape of organelles within the cell. This study explores the electromechanical behaviour of biological cells, including organelles like microtubules, mitochondria, nuclei, and cell membranes. A two-dimensional bio-electromechanical model for two distinct cell structures has been developed to analyze the behavior of the biological cell to the external electrical and mechanical responses. The piezoelectric and flexoelectric effects have been included via multiphysics coupling for the biological cell. All the governing equations have been discretized and solved by the finite element method. It is found that the longitudinal stress is absent and only the transverse stress plays a crucial role when the mechanical load is imposed on the top side of the cell through compressive displacement. The impact of flexoelectricity is elucidated by introducing a new parameter called the maximum electric potential ratio ( ). It has been found that depends upon the orientation angle and shape of the microtubules. The magnitude of exhibit huge change when we change the shape and orientation of the organelles, which in some cases (boundary condition (BC)-3) can reach to three times of regular shape organelles. Further, the study reveals that the number of microtubules significantly impacts effective elastic and piezoelectric coefficients, affecting cell behavior based on structure, microtubule orientation, and mechanical stress direction. The insight obtained from the current study can assist in advancements in medical therapies such as tissue engineering and regenerative medicine.

Effect of Printing Orientation Angle and Heat Treatment on the Mechanical Properties and Microstructure of Binder-Jetting-Printed Parts in 17-4 PH Stainless Steel

The present work aims to study the effect of printing orientation angle and heat treatment on the mechanical properties and microstructure of 17-4 PH stainless steel 3D-printed parts obtained by the binder jetting process to assess the suitability of the process and material for rapid tooling applications. To this purpose, tensile specimens were printed at different printing orientation angles (0°, 45°, and 90°). Half of the specimens were left in the as-sintered condition after the 3D-printing operation, while the other half of the specimens was subjected to H900 heat treatment. Then, tensile and hardness tests were performed to investigate the macro-mechanical properties as a function of the printing orientation angles and postprocessing thermal treatment. Scanning electron microscopy with energy dispersive X-ray spectroscopy was used to observe the fracture surfaces and microscopical defects on the binder jetting printed parts to evaluate the fracture mechanisms. It was demonstrated that printing orientation angles do not affect the mechanical properties of 3D-printed parts, while a significant improvement in the microstructure and mechanical properties is observed after the H900 heat treatment.

Optimizing energy absorption and peak force in metal/glass fiber sandwich panels with trapezoidal cores

Sandwich panels with trapezoidal metal/glass fiber cores are increasingly popular due to their lightweight and energy-absorption properties. This study employs response surface methodology (RSM) and Box-Behnken design to investigate the effects of core angle, fiber orientation, and MCM-48 nanoparticles on the panels’ energy absorption and peak force, developing regression models with high R2 values of 0.9027 and 0.9228, respectively. Experimental tests were conducted to validate these models, showing minimal deviation from predicted values. Results indicate that increasing the fiber orientation angle from 30° to 90° enhances energy absorption and peak force by 72.18 and 46.9%, respectively, and adding MCM-48 nanoparticles up to 0.25% weight improves energy absorption by 60.8%. A core angle of 52° balances energy absorption and peak force, while integrating a metal wire mesh within the panels significantly enhances energy absorption and reduces core brittleness. The optimal parameters for maximum energy absorption and minimum peak force include a core angle of 58°, fiber orientation of 73.5°, and no nanoparticles. These findings provide valuable insights into the design and optimization of sandwich panels for various applications.

Investigation of Effect of Part-Build Directions and Build Orientations on Tension-Tension Mode Fatigue Behavior of Acrylonitrile Butadiene Styrene Material Printed Using Fused Filament Fabrication Technology.

This article explores the fatigue characteristics of acrylonitrile butadiene styrene (ABS) components fabricated using fused filament fabrication (FFF) additive manufacturing technology. ABS is frequently used as a polymeric thermoplastic material in open-source FFF machines for a variety of engineering applications. However, a comprehensive understanding of the mechanical properties and execution of FFF-processed ABS components is necessary. Currently, there is limited knowledge regarding the fatigue behavior of ABS components manufactured using FFF AM technology. The primary target of this study is to evaluate the results of part-build directions and build orientation angles on the tensile fatigue behavior exhibited by ABS material. To obtain this target, an empirical investigation was carried out to assess the influence of building angles and orientation on the fatigue characteristics of ABS components produced using FFF. The test samples were printed in three distinct directions, including Upright, On Edge, and Flat, and with varying orientation angles ([0°, 90°], [15°, 75°], [30°, 60°], [45°]), using a 50% filling density. The empirical data suggest that, at each printing angle, the On-Edge building orientation sample exhibited the most prolonged vibrational duration before fracturing. In this investigation, we found that the On-Edge printing direction significantly outperformed the other orientations in fatigue life under cyclic loading with 1592 loading cycles when printed with an orientation angle of 15°-75°. The number of loading cycles was 290 and 39 when printed with the same orientation angle for the Flat and Upright printing directions, respectively. This result underscores the importance of orientation in the mechanical performance of FFF-manufactured ABS materials. These findings enhance our comprehension of the influence exerted by building orientation and building angles on the fatigue properties of FFF-produced test samples. Moreover, the research outcomes supply informative perspectives on the selection of building direction and building orientation angles for the design of 3D-printed thermoplastic components intended for fatigue cyclic-loading applications.

Quantification of muscle fiber malformations using edge detection to investigate chronic muscle pressure ulcers

BackgroundMicroscopy of regenerated tissue shows different morphologies between the healing of acute wounds and chronic wounds. This difference can be seen manually by biologists, but computational methods are needed to automate the characterization of morphology and regenerative quality in regenerated muscle tissue.ResultsFrom the detected edge segments, we computed several imaging biomarkers of interest, such as median tortuosity, number of edge segments normalized by area, median edge segment distance and interquartile range of orientation angles of edge segments of the microscope images of successful and unsuccessful muscle regeneration. We observed that muscle fibers in saline-treated pressure ulcers had a larger interquartile range of orientation angles of the edge segments (p = 0.05) and shorter edge segment distances (p = 0.003) compared to those of acute cardiotoxin injuries.ConclusionOur edge detection method was able to identify statistically significant differences in some of the imaging biomarkers between saline-treated pressure ulcers and cardiotoxin injuries, suggesting that chronic pressure ulcers have increased muscle fiber malformations compared to cardiotoxin injuries.

Retention and interfacial failure mechanism of single diamond grains in resin-bonded grinding tools

Abrasive grains and the associated bonding agent are the two significant components in the manufacturing of fixed abrasive machining tools. The material properties and interfacial bonding behavior between the grains and the bonding matrix determine machining performance. In precision machining processes with diamond abrasives, the primary failure modes of fixed abrasive tools are grain dislodgement and premature loss, leading to abrupt change in machining load and ultimately causing inaccurate and inefficient machining performance. This study develops a comprehensive model for understanding abrasive grain retention and interfacial failure mechanisms in resin-bonded diamond tools. Finite element analysis of a single diamond grain embedded in a resin matrix was conducted to examine the influence of the grain shape, protruding height, and orientation angle on critical interfacial failure force. A series of single diamond scratching experiments validated the model, revealing that the maximum retention force reached 43.56 N for grains with a 0.9 mm protruding height and a 60° orientation angle. The results also show that, within a specific grain size range, grain shape—quantified by the sphere deviation coefficient proposed in this paper, has the greatest impact on retention and failure behavior. Protruding height plays a secondary role, while the contribution of orientation angle is minimal. These findings provide valuable insights for the design, manufacture, and optimization of precision abrasive machining tools, particularly for applications requiring high precision and reliability.

Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects

Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are uniformly distributed cracks that do not interact with each other, the plane of which is normal to the surface, and the depth is much less than its length on the surface. The cracks’ depth and angle of orientation are random values, and their joint distribution density is specified. Plates made of this material are under the influence of biaxial loading. The probability of failure, along with the mean value, the dispersion, and the variation coefficient of the plate’s strength, taking into account the surface defects under different types of stress, were determined. Their dependence on the type of loading, the size of the plate, and the surface structural heterogeneity of the material were studied graphically. Joint consideration of the influence of the interrelated properties of real materials, such as defectiveness and stochasticity, on strength and fracture, opens up new opportunities in creating a theory of strength and fracture of deformable solids.

Effect of Printing Orientation on the Mechanical Properties of Low-Force Stereolithography-Manufactured Durable Resin

This study presents the results of fracture toughness tests conducted on specimens obtained by additive manufacturing techniques, specifically using low-force stereolithography. The samples were manufactured from a transparent 3D printing material for biocompatible applications, the so-called BioMed Durable Resin, which is a Formlabs-patented polymer material that simulates the strength and rigidity of polyethylene. The selected toughness tests in this context were performed following the ASTM D5045-99 guidelines. All tests were conducted under controlled laboratory conditions at 23 °C and 50% relative humidity, ensuring adherence to the standard and the replicability of the experimental results. To investigate the influence of printing plane orientation, specimens were produced at three printing orientation angles (0, 45, and 90 degrees). These angles were selected to provide a comprehensive evaluation of the anisotropy effects in the material. They cover both extreme orientations (0° and 90°) and include an intermediate value (45°), allowing us to assess variations in mechanical behavior across a representative range of printing orientations, consistent with prior research in the field. The experimental tests yielded data on the crack resistance and energy release rate for each angle of orientation. There are various implications of the findings, beyond materials engineering, for applications in biomedicine. Indeed, this same approach opens the door to new research methods for manufacturing certified biocompatible materials from such durable resins. Finally, complementary issues such as related medical applications have been slightly addressed for future work, since biomedicine innovation clusters can contribute to accelerating growth in this crucial field for productive sector activity and the local business environment.

Influence of the rigidity of the backbone and arms on the dynamical and conformational properties of the comb polymer in shear flow.

The dynamical and conformational properties of the comb polymer with various rigidities of the backbone and arms in steady shear flow are studied by using a hybrid mesoscale simulation approach that combines multiparticle collision dynamics with standard molecular dynamics. First, during the process of the comb polymer undergoing periodic tumbling motion, we find that the rigidity of the arms always promotes the tumbling motion of the comb polymer, but the rigidity of the backbone shifts from hindering to promoting it with increasing the rigidity of the arms. In addition, the comb polymer transitions from vorticity tumbling to gradient tumbling with the increase in shear rate. Second, the range of variation of the end-to-end distance of the backbone and the average end-to-end distance of the arms increases with the increase in the rigidity of the arms and backbone, respectively, and the range of both changes grows with the increase in shear rate. Furthermore, as the rigidity increases, the moldability of the comb polymer decreases and the orientation angle of the comb polymer increases.

Self-Repairable Carbon Fiber-Reinforced Epoxy Vitrimer Actuator with Multistimulus Responses and Programmable Morphing.

Smart shape-changing structures in aerospace applications are vulnerable to damage in harsh environments. Balancing high mechanical performance with self-repair capabilities poses a challenge due to inherent trade-offs between strength and flexibility. To address this challenge, an asymmetric bilayer-structured actuator was fabricated using commercially available continuous carbon fiber tows (CFs) as the passive layer and a dynamic cross-linked epoxy vitrimer as the active layer. The construction of the vitrimer-CF actuator involves a simple and scalable hot-pressing process, resulting in a tensile strength of 234 MPa and an interfacial bonding strength of 405 N·m-1. This actuator exhibits remarkable deformation capability (210°/7 s) and an efficient self-repair ability under various stimuli, including thermal (60-160 °C), light (0.4-1.0 W·cm-2), electric (2-4 V), and solvent (acetone). By adjustment of the orientation angle of CFs, complex left-handed and right-handed curling structures can be achieved. Leveraging the insights from photothermal/electrothermal actuation mechanisms, a quadruped crawling robot is developed capable of crawling 4 cm with a single light illumination. The actuator can lift objects 45 times its weight when subjected to light stimuli. Additionally, a flap actuator is constructed to achieve an angle change of 63° within 10 s under an electric stimulus, enabling remote control over the aircraft flight angle. These results demonstrate the potential of the vitrimer-CF actuator for advanced applications in intelligent aerospace structures.

Structure Design on Thermoplastic Composites Considering Forming Effects.

Carbon fiber reinforced polypropylene (CF/PP) thermoplastics integrate the superior formability of fabrics with the recoverable characteristics of polypropylene, making them a pivotal solution for achieving lightweight designs in new energy vehicles. However, the prevailing methodologies for designing the structural performance of CF/PP vehicular components often omit the constraints imposed by the manufacturing process, thereby compromising product quality and reliability. This research presents a novel approach for developing a stamping-bending coupled finite element model (FEM) utilizing ABAQUS/Explicit. Initially, the hot stamping simulation is implemented, followed by the transmission of stamping information, including fiber yarn orientation and fiber yarn angle, to the follow-up step for updating the material properties of the cured specimen. Then, the structural performance analysis is conducted, accounting for the stamping effects. Furthermore, the parametric study reveals that the shape and length of the blank holding ring exerted minimal influence on the maximum fiber angle characteristic. However, it is noted that the energy absorption and crushing force efficiency metrics of the CF/PP specimens can be enhanced by increasing the length of the blank holding ring. Finally, a discrete optimization design is implemented to enhance the bending performance of the CF/PP specimen, accounting for the constraint of the maximum shear angle resulting from the stamping process. The optimized design resulted in a mass reduction of 14.3% and an improvement in specific energy absorption (SEA) by 17.5% compared to the baseline sample.

A Deep Learning Biomimetic Milky Way Compass.

Moving in straight lines is a behaviour that enables organisms to search for food, move away from threats, and ultimately seek suitable environments in which to survive and reproduce. This study explores a vision-based technique for detecting a change in heading direction using the Milky Way (MW), one of the navigational cues that are known to be used by night-active insects. An algorithm is proposed that combines the YOLOv8m-seg model and normalised second central moments to calculate the MW orientation angle. This method addresses many likely scenarios where segmentation of the MW from the background by image thresholding or edge detection is not applicable, such as when the moon is substantial or when anthropogenic light is present. The proposed YOLOv8m-seg model achieves a segment mAP@0.5 of 84.7% on the validation dataset using our own training dataset of MW images. To explore its potential role in autonomous system applications, we compare night sky imagery and GPS heading data from a field trial in rural South Australia. The comparison results show that for short-term navigation, the segmented MW image can be used as a reliable orientation cue. There is a difference of roughly 5-10° between the proposed method and GT as the path involves left or right 90° turns at certain locations.

Analytical investigation of green composite lamina utilizing natural fiber to strengthen PLA

This work’s main goal is to investigate the effects of the natural fiber orientation angle on the lamina’s engineering constants, such as the shear modulus, major Poisson’s ratio, longitudinal and transverse Young’s moduli, and lamina level shear coupling coefficients. The PLA matrix of the three green composite laminas under study is reinforced with natural fiber. The three natural fibers under study are flax, jute, and bamboo fibers. The study assesses the performance of three PLA laminas reinforced with natural fibers for each of the previously listed engineering constants. The behavior of the green composite lamina for various fiber volume fractions is also presented in this study. This analytical investigation employs the macromechanics of lamina to do the examination. The investigation’s findings demonstrated that the volume % and fiber orientation have a considerable impact on the lamina’s engineering constants. The study offers a comprehensive variation of the lamina’s engineering constants for each fiber orientation angle between 0 and 90° and for each fiber volume fraction between 0 % (entirely matrix) and 100 % (completely fibers) in steps of 5 %. The outcomes of the presented study will help in the design of the facesheets for the composite sandwich structures. The results presented can be used to check the viability of using natural fibers to strengthen different polymer matrices. Bamboo-PLA lamina outperforms flax-PLA and jut-PLA laminae.

Evolution of Rotating Internal Channel for Heat Transfer Enhancement in a Gas Turbine Blade

To achieve higher thermal efficiency in a gas turbine, increasing the turbine inlet temperature is necessary. The rotor blade at the first stage tolerates the highest temperature, and the serpentine internal channel located in the middle chord of the rotor blade is vital in guaranteeing the blade’s service life. Therefore, it is essential to illustrate the evolution of the rotating internal channel in a gas turbine blade. In the paper, the influence of the Coriolis force, including its mechanisms, on the conventional rotating channel are reviewed and analyzed. A way to utilize the positive heat transfer effect of the Coriolis force is proposed. Recent investigations on corresponding novel rotating channels with a channel orientation angle of 90° (called bilaterally enhanced U-channels) are illustrated. Moreover, numerical investigations about the Re effects on bilaterally enhanced smooth U-channels were carried out in the study. The results indicated that bilaterally enhanced U-channels can utilize the Coriolis force positive heat transfer effect on the leading and the trailing walls at the same time. Re and Ro are vital non-dimensional numbers that influence the performance of bilaterally enhanced U-channels. Re and Ro have an independent influence on the heat transfer performance of the bilaterally enhanced U-channel. Ro is good for the heat transfer of the bilaterally enhanced U-channel on both the leading and the trailing walls. Therefore, the bilaterally enhanced U-channel is suitable for application in the middle chord region of a turbine blade, since it can utilize the rotation effect of the rotating blade to improve the heat transfer ability of the blade and thus reduced the blade temperature. At the same Ro, Re positively affects the Nu on the leading and the trailing walls of the Coriolis-utilization rotating smooth U-channel, but plays a negligible role on Nu/Nu0.

Uniaxial Molecular Alignment in Thin Films Composed of Discrete NDI‐T2 Oligomers Investigated by Variable‐Angle Spectroscopic and Imaging Ellipsometry

The understanding of the optical characteristics and the influence of thermally induced crystallization is vital to evaluate newly synthesized organic semiconductors for their potential applications. Variable‐angle spectroscopic ellipsometry (VASE) is employed to determine the complex dielectric function of two recently developed discrete oligomers based on naphthalene diimide (NDI) and bithiophene (T2), applying an anisotropic optical model. It is shown that the as‐cast films are optically near‐isotropic, while the annealed films exhibit pronounced anisotropies with respect to the orientation of the π−π* transition. Differences between the two distinct molecules are observed and discussed. The degree of optical anisotropy is quantified using the average molecular orientation angle φ, associated with the orientation of the π−π* transition dipole, and the related orientation order parameter S. The molecules are shown to form crystallites of several microns in size upon annealing. Imaging ellipsometry is thus additionally employed to study their optical anisotropy on a microscopic scale, and the agreement with results from macroscopic measurements is evaluated.

Method of understanding for investigation of crack propagation trajectory and fracture aspects in dental cracks on view of fracture mechanics theories.

Current research introduces understanding of dental-cracks mechanistic with fundamental fracture behavior in natural-teeth and orthodontics including mode I crack under both tension and compression, mode II crack under both clockwise-shear and anticlockwise-shear and mixed-mode cracks under both compression-shear and tension-shear. It depends on experimental models of transparent-Plexiglas including pre-cracks of different orientations angle (b) based on fundamental theoretical fracture analysis with comparison. Problem-concept, cracking aspects of fracture-initiation, propagation-direction, fracture-increment length, critical external-load and fracture path are predicted experimentally and theoretically using directional fracture approach and directional strain-energy density theory. Tests are carried out for (36) samples for compression and tension in LEFM. Friction-resistance between crack-surfaces is considered with derivation of equations and charts. Negative stress-intensity factor (-KI) is developed for solving complicated problems of cracks under occlusal compression loads. The occlusal loads are compression and shear producing lateral tensile mixed mode cracks. The critical propagation angle (qc), critical propagation load (sc) and critical propagation envelope of stress intensity factors (KI-KII) are developed with respect to crack orientation angle (b) with comparisons. They are necessary to predict the fracture propagation early before teeth-failure. It helps for prevention and control of dental-cracks, correct-restoration, prosthodontics, orthodontics, and development of new dental-materials and technologies.