Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials.

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental-computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS2 and MoSe2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).

Fracture Mechanism and Fracture Toughness at the Interface Between Cortical and Cancellous Bone.

The microstructure at the interface of cortical and cancellous bone is quite complicated. The fracture mechanisms at this location are necessary for understanding the comprehensive fracture of the whole bone. The goal of this study is to identify fracture toughness in terms of J integral and fracture mechanism at the interface between cortical and cancellous bone. For this purpose, single edge notch bend (SENB) specimens were prepared from bovine proximal femur according to ASTM-E399 standard. Bone samples were prepared such that half of the sample width consists of cortical bone and other half of the width was cancellous bone; this interfacial bone is referred as a corticellous bone. Elastic-plastic fracture mechanics was used to measure fracture toughness. The J integral (both elastic and plastic) was used to quantify the fracture toughness. The plastic part of J integral value (Jpl) of corticellous specimen was 9310 J m-2, and shown to be 27 times of the J integral of the elastic part (Jel), 341 J m-2. The total J integral of the corticellous bone was found to be 9651 J m-2, which is close to two times of the cortical bone, 4731 J m-2. This study observed that J integral of corticellous bone is higher than the cortical bone since more energy is required for plastic deformation of corticellous bone due to crack branches and slowdown at the interface between cortical and cancellous bone.

Effects of testing speed on the tensile and mode I fracture behavior of specimens printed through the Fused Deposition Modeling technique.

Additive Manufacturing (AM) processes are known as revolutionary manufacturing processes that fabricate a part using a 3D model layer upon layer. These techniques gained more attention from various industries due to their advantages like low waste material. Also, these processes can produce any part with high degrees of complexity in a short period of time. The Fused Deposition Modeling (FDM) process is a material extrusion-based technique which works by extruding a fine molten polymeric filament through a heated nozzle on the heated platform named printer bed. In this method, some important manufacturing parameters play a crucial role in controlling the mechanical properties and quality of the final fabricated part. However, all printed specimens through the FDM process should be tested based on the standards under some critical circumstances. Thus, in the current research paper, five and three test speeds are considered in tensile and fracture testing procedures, respectively to evaluate how these speeds can affect the mechanical and mode I fracture properties. Also, as the FDM specimens present elastic-plastic behavior, the critical value of J-integral is assumed as a fracture assessment and calculated from the finite element analysis. Among the mechanical properties, ultimate tensile strength is affected significantly by the test speed. For instance, the ultimate tensile strength of FDM specimens is 39.02, 38.58, 42.33, 48.09, and 52.11 for test speeds of 2, 4, 6, 8, and 10 mm/min, respectively. But vice-versa results are detected for the mode I fracture behavior and corresponding values of J for the FDM-PLA specimens. Finally, experimental and numerical results together with comprehensive discussions about the considered speeds and obtained results are reported.

Micromechanical modelling of transverse fracture behaviour of lamellar bone using a phase-field damage model: The role of non-collagenous proteins and mineralised collagen fibrils.

At the tissue-scale and above, there are now well-established structure-property relationships that provide good approximations of the biomechanical performance of bone through, for example, power-law relationships that relate tissue mineral density to elastic properties. However, below the tissue-level, the individual role of the constituents becomes prominent and these simple relationships tend to break down, with more detailed theoretical and computational models are required to describe the mechanical response. In this study, a two-dimensional micromechanics damage-based representative volume element (RVE) of lamellar bone was developed, which included a novel implementation of a phase-field damage model to describe the behaviour of non-collagenous proteins at mineral-mineral and mineral-fibril interface regions. It was found that, while the stiffness of the tissue was governed by the relative proportion of extra-fibrillar mineral and mineralised collagen fibrils, the strength and toughness of the tissue in transverse direction relied on the interactions occurring at mineral-mineral and mineral-fibril interfaces, highlighting the prominence of non-collagenous proteins in determine fracture-based processes at this scale. While fractures tended to initiate in mineral rich areas of the extra-fibrillar mineral matrix, it was found that the presence of mineralised collagen fibrils at low density did not provide a substantial contribution to crack propagation behaviour under transverse loading. However, at physiological volume fraction (VfMCF=50%), different scenarios could arise depending on the relative strength value of the interphase around the MCFs ( [Formula: see text] ) to the interphase between individual minerals ( [Formula: see text] ): (i) When [Formula: see text] , MCFs appear to facilitate crack propagation with MCF-mineral debonding being the dominant failure mode; (ii) once γ>1, the MCFs hinder the microcracks, leading to inhibition of crack propagation, which can be regarded as an energy dissipation mechanism. The effective fracture properties of the tissue also experience a sudden increase in fracture work density (J-integral) once the crack is arrested by MCFs or severely deflected. Collectively, the predicted behaviour of the model compared well to those reported through experimental and computational methods, highlighting its potential to provide further understanding into the mechanistic response of bone ultrastructure alterations related to the structural and compositional changes resulting from disease and aging.

Experimental Study on the Fracture Toughness of Bamboo Scrimber.

In the past decade, bamboo scrimber has developed rapidly in the field of building materials due to its excellent mechanical properties, such as high toughness and high tensile strength. However, when the applied stress exceeds the ultimate strength limit of bamboo scrimber, cracks occur, which affects the performance of bamboo scrimber in structural applications. Due to the propensity of cracks to propagate, it reduces the load-bearing capacity of the bamboo scrimber material. Therefore, research on the fracture toughness of bamboo scrimber contributes to determining the material's load-bearing capacity and failure mechanisms, enabling its widespread application in engineering failure analysis. The fracture toughness of bamboo scrimber was studied via the single-edge notched beam (SENB) experiment and compact compression (CC) method. Nine groups of longitudinal and transverse samples were selected for experimental investigation. The fracture toughness of longitudinal bamboo scrimber under tensile and compressive loadings was 3.59 MPa·m1/2 and 2.39 MPa·m1/2, respectively. In addition, the fracture toughness of transverse bamboo scrimber under tensile and compressive conditions was 0.38 MPa·m1/2 and 1.79 MPa·m1/2, respectively. The results show that, for this material, there was a significant distinction between longitudinal and transverse. Subsequently, three-point bending tests and simulations were studied. The results show that the failure mode and the force-displacement curve of the numerical simulation were highly consistent compared with the experimental results. It could verify the correctness of the test parameters. Finally, the flexural strength of bamboo scrimber was calculated to be as high as 143.16 MPa. This paper provides data accumulation for the numerical simulation of bamboo scrimber, which can further promote the development of bamboo scrimber parameters in all aspects of the application.

Fracture Toughness and Fatigue Crack Growth Analyses on a Biomedical Ti-27Nb Alloy under Constant Amplitude Loading Using Extended Finite Element Modelling.

The human body normally uses alternative materials such as implants to replace injured or damaged bone. Fatigue fracture is a common and serious type of damage in implant materials. Therefore, a deep understanding and estimation or prediction of such loading modes, which are influenced by many factors, is of great importance and attractiveness. In this study, the fracture toughness of Ti-27Nb, a well-known implant titanium alloy biomaterial, was simulated using an advanced finite element subroutine. Furthermore, a robust direct cyclic finite element fatigue model based on a fatigue failure criterion derived from Paris' law is used in conjunction with an advanced finite element model to estimate the initiation of fatigue crack growth in such materials under ambient conditions. The R-curve was fully predicted, yielding a minimum percent error of less than 2% for fracture toughness and less than 5% for fracture separation energy. This provides a valuable technique and data for fracture and fatigue performance of such bio-implant materials. Fatigue crack growth was predicted with a minimum percent difference of less than nine for compact tensile test standard specimens. The shape and mode of material behaviour have a significant effect on the Paris law constant. The fracture modes showed that the crack path is in two directions. The finite element direct cycle fatigue method was recommended to determine the fatigue crack growth of biomaterials.

Effects of Grain Boundary Misorientation Angle on the Mechanical Behavior of Al Bicrystals.

This research article explores the effect of grain boundary (GB) misorientation on the mechanical behavior of aluminum (Al) bicrystals by means of molecular dynamics (MD) simulations. The effect of GB misorientation on the mechanical properties, fracture resistance, and crack propagation are evaluated under monotonic and cyclic load conditions. The J-integral and the crack tip opening displacement (CTOD) are assessed to establish the effect of the GB misorientation angle on the fracture resistance. The simulations reveal that the misorientation angle plays a significant role in the mechanical response of Al bicrystals. The results also evidence a gradual change in the mechanical behavior from brittle to ductile as the misorientation angle is increased.

Application of the J-Integral and Digital Image Correlation (DIC) to Determination of Multiple Crack Propagation Law of UHPC under Flexural Cyclic Loading.

This study investigated the fatigue crack propagation behavior of ultra-high-performance concrete (UHPC) incorporated with different steel fiber lengths of 6, 13, and 20 mm under flexural cyclic loading, based on the Paris law and nonlinear fracture mechanics. In addition, multiple crack covering areas and fatigue J-integral amplitudes were employed to quantitatively evaluate the fatigue crack propagation rate and predicate the fatigue life of the UHPC during the steady development stage. The results indicated that the maximum crack opening displacement (COD) values were 0.312, 0.673, and 1.265 mm and the minimum crack growth rates were -3.05, -4.48 and -4.62 for SF6, SF13, and SF20, respectively. The critical crack length was approximately 65 mm for UHPC specimens containing different fiber length at a given fiber volume fraction (2.0%), indicating that the critical crack length was simply related to the fiber length. Interestingly, when the fatigue crack area of all the tested series reached approximately 35 mm2, fracture failure occurred. There were very small predictions between the actual tested and predicated fatigue lives, all less than 7.21%. Hence, it was reasonable to predict the fatigue life of the UHPC based on the J-integral according to the DIC technique.

Experimental evaluation of fracture properties of bovine hip cortical bone using elastic-plastic fracture mechanics.

BACKGROUND: Understanding the fracture mechanics of bone is very important in both the medical and bioengineering field. Bone is a hierarchical natural composite material of nanoscale collagen fibers and inorganic material. OBJECTIVE: This study investigates and presents the fracture toughness of bovine cortical bone by using elastic plastic fracture mechanics. METHODS: The J-integral was used as a parameter to calculate the energies utilized in both elastic deformation (Jel) and plastic deformation (Jpl) of the hipbone fracture. Twenty four different types of specimens, i.e. longitudinal compact tension (CT) specimens, transverse CT specimens, and also rectangular unnotched specimens for tension in longitudinal and transverse orientation, were cut from the bovine hip bone of the middle diaphysis. All CT specimens were prepared according to the American Society for Testing and Materials (ASTM) E1820 standard and were tested at room temperature. RESULTS: The results showed that the average total J-integral in transverse CT fracture specimens is 26% greater than that of longitudinal CT fracture specimens. For longitudinal-fractured and transverse-fractured cortical specimens, the energy used in the elastic deformation was found to be 2.8-3 times less than the energy used in the plastic deformation. CONCLUSION: The findings indicate that the overall fracture toughness measured using the J-integral is significantly higher than the toughness calculated by the stress intensity factor. Therefore, J-integral should be employ to compute the fracture toughness of cortical bone.

A critical evaluation of cortical bone fracture toughness testing methods.

Cortical bone fracture mechanics which quantifies the tissue's resistance to fracture is widely regarded as important to finding key determinants of bone fragility and fracture. Currently, the most widely used fracture mechanics approach is the J-integral resistance (J-R) curve as defined in ASTM E1820 standard. This standard employs an unloading compliance (UC) method to estimate crack extension, necessary for fracture toughness and resistance curve (R-curve) quantification. Further, this UC method requires a series of unload-reload cycles to be conducted during the fracture test. However, cortical bone violates some assumptions on which the UC method is based, which are: no energy loss during the unload-reload cycles and any change in unloading compliance is only due to crack extension. Consequently, the aim of this study was to examine the impact of the UC method on the accuracy of fracture toughness measurement for bovine cortical bone. Ten pairs of single edged notched bend specimens were prepared from the posterior diaphysis of bovine tibiae and underwent three-point bending fracture tests. The paired specimens were divided into two groups: a cyclic loaded group and a monotonic loaded group. Further, crack extension was determined by the UC method for the cyclic group and by an optical method for both the cyclic and monotonic groups. From these, three different approaches were used to generate J-R curves from which three fracture toughness parameters were computed and compared between the three approaches. This comparison allowed the impact of crack extension estimation by the UC method as well as the unload-reload cycles on the accuracy of the fracture toughness measures to be assessed. Results show that the UC method underestimates crack extension by an average error of 73%. In addition, the combined effects from crack extension estimation using the UC method and the unload-reload cycles lead to a significant overestimation of the specimen's fracture toughness measures. This highlights the need for more studies to establish a standardized approach to cortical bone fracture testing.

Fatigue Analysis and Defect Size Evaluation of Filled NBR including Temperature Influence.

The fatigue behavior of a filled non-crystallizing elastomer was investigated on axisymmetric dumbbell specimens. By plotting relevant Wöhler curves, a power law behavior was found. In addition, temperature increases due to heat build-up were monitored. In order to distinguish between initiation and crack growth regimes, hysteresis curves, secant and dynamic moduli, dissipated and stored energies, and normalized minimum and maximum forces were analyzed. Even though indications related to material damaging were observed, a clear trend to recognize the initiation was not evident. Further details were revealed by considering a fracture mechanics. The analysis of the fracture surfaces evidenced the presence of three regions, associated to initiation, fatigue striation, and catastrophic failure. Additional fatigue tests were performed with samples in which a radial notch was introduced. This resulted in a reduction in lifetime by four orders of magnitude; nevertheless, the fracture surfaces revealed similar failure mechanisms. A fracture mechanics approach, which considered the effect of temperature, was adopted to calculate the critical defect size for fatigue, which was found to be approximately 9 µm. This value was then compared with the particle size distribution obtained through X-ray microcomputed tomography (µ-CT) of undamaged samples and it was found that the majority of the initial defects were indeed smaller than the calculated one. Finally, the evaluation of J-integral for both unnotched and notched dumbbells enabled the assessment of a geometry-independent correlation with fatigue life.

Studies on the Mechanical Models and Behaviors for the Stamp/Film Interface in Microtransfer Printing.

The adhesion/delamination characteristics at the stamp/film interface are critical for the efficiency of film microtransfer printing technology. To predict and regulate the interface mechanical behaviors, finite element models based on the J-integral, Virtual Crack Closure Technology (VCCT), and the cohesive zone method (CZM) were established and compared. Then, the effects of pulling speed and interface parameters on the pull-off force, which is used to characterize the interface adhesion strength, were investigated. Comparisons between the simulation results and previous experimental results demonstrated that the model based on the CZM was more applicable than the models based on the J-integral and VCCT in analyzing the adhesion/delamination behaviors of the stamp/film interface. Furthermore, the increase in pulling speed could enlarge the pull-off force for the viscoelastic stamp/film interface, while it had no influence on the pull-off force for the elastic stamp/film interface. In addition, a larger normal strength and normal fracture energy resulted in a larger pull-off force, which was beneficial to the realization of the picking-up process in microtransfer printing.

Elasto-Plastic Fatigue Crack Growth Behavior of Extruded Mg Alloy with Deformation Anisotropy Due to Stress Ratio Fluctuation.

Fatigue crack growth (FCG) experiments were performed using a low-temperature extruded magnesium alloy AZ31 with texture. Under a constant maximum stress intensity factor (Kmax), the stress ratio R was changed from 0.1 to -1 during the fatigue crack growth process, and the FCG behavior before and after the R change was investigated. As a result, tensile twins were generated owing to the fatigue load on the compression side of R = -1, and the FCG velocity was accelerated. In addition, when the maximum compressive stress at R = -1 (|(σmin)R = -1|) exceeded the compressive yield strength of the material (σcy), the FCG velocity after R fluctuation greatly accelerated. On the other hand, under the condition |(σmin)R = -1| < σcy, the degree of acceleration of the FCG velocity due to R fluctuation was small. In either case, the degree of acceleration in the FCG increased as the Kmax value increased. The above FCG acceleration mechanism due to the R fluctuation was considered based on the observation of the deformation and twinning states of the fatigue crack tip, the fatigue crack closure behavior, and the cyclic stress-strain curve of the fatigue process. The FCG acceleration mechanism was as follows: First, the driving force of the FCG increased owing to the increase in crack opening displacement due to the generation of tensile twins. Second, the coalescence of the main crack and a plurality of microcracks were generated at the twin interface. The elasto-plastic FCG behavior after the stress ratio fluctuations is defined by the effective J-integral range ΔJeff.

Numerical Evaluation of the Fracture Process of 41Cr4 Steel: Analysis of Cracks Grown in a Plane Strain State Domination Based on Experimental Results.

The paper presents the evaluation of the fracture process of 41Cr4 steel, based on experimental tests and numerical analysis carried out for growing cracks. Selected results of experimental studies presented in previous publications in 2015-2016 which were used in the construction of FEM models of SEN(B) specimens dominated by a plane strain state, are quoted. Using FEM simulations, the tensile curves and crack growth curves recorded during laboratory tests, several calculations were performed, among which can be distinguished the evaluation of plastic zones in the considered specimens, stress distributions, selected measures of geometric constraints, accumulated plastic strains and selected parameters of fracture mechanics. The numerical calculations presented in this paper allow to estimate the changes of the J-integral for the tested steel, the crack tip opening displacement, the size of the plastic zone and the stress distribution in front of the crack tip. Comprehensive numerical analysis with the use of the actual tensile curve clearly characterizes the behavior of the material under the influence of increasing external loads.

Notch Effects on the Stress Intensity Factor and on the Fatigue Crack Path for Eccentric Circular Internal Cracks in Elliptically Notched Round Bars under Tensile Loading.

In this paper, stress intensity factor (SIF) solutions are numerically obtained for notched bars subjected to tensile loading containing an eccentric circular inner crack located in the cross-section corresponding to the notch root. The finite element method and the J-integral have been used to obtain the SIF and to analyze the effect on it of three elliptical notch geometries (of equal radial depth). The results show how the SIF is greater in the notched bars than in the smooth bar and within the former when the axial semi-axis of the notch rises, its effect being greater as the diameter and eccentricity of the inner crack increase. In addition, the fatigue growth of an eccentric crack induces an increase in such eccentricity, greater as the notch axial semi-axis increases. The cause of these phenomena can be attributed to the constraint loss caused by the notch, which also facilitates bending of the specimen due to the asymmetry generated by the crack eccentricity.

Fatigue Crack Growth Behavior and Fracture Toughness of EH36 TMCP Steel.

The fatigue crack growth behavior and fracture toughness of EH36 thermo-mechanical control process (TMCP) steel were investigated by fatigue crack growth rate testing and fracture toughness testing at room temperature. Scanning electron microscopy was used to observe the fracture characteristics of fatigue crack propagation and fracture toughness. The results indicated that the microstructure of EH36 steel is composed of ferrite and pearlite with a small amount of texture. The Paris formula was obtained based on the experimental data, and the value of fracture toughness for EH36 steel was also calculated using the J-integral method. The observations conducted on fatigue fracture surfaces showed that there were a lot of striations, secondary cracks and tearing ridges in the fatigue crack propagation region. Additionally, there existed many dimples on the fracture surfaces of the fracture toughness specimens, which indicated that the crack was propagated through the mechanism of micro-void growth/coalescence. Based on the micromechanical model, the relationship between the micro-fracture surface morphology and the fracture toughness of EH36 steel was established.

Elasto-Plastic Fracture Mechanics Analysis of the Effect of Shot Peening on 300M Steel.

A modified J-integral calculation method is adopted to fix the problem of the quantitative evaluation of the crack propagation of shot-peened structures. Considering the residual stress, residual strain, and residual strain energy, the effect of shot peening on the J-integral parameters of semi-elliptic surface crack fronts is quantitatively calculated and a method is provided for the performance evaluation of the shot peening layer. First, the shot peening process is simulated, then the fatigue crack is generated by changing the constraint condition and a far-field load is applied to calculate the J-integral parameters, crack propagation rate, and crack kinking angle. The effects of different crack depths and shot velocities on the fracture parameters are analyzed. The results show that the reduction in the J-integral value after shot peening decreases with the increase in the crack depth when the shot velocity is a certain value, which indicates that shot peening is more beneficial for suppressing the fatigue crack propagation. When the crack depth is greater than the depth of the compressive stress layer, shot peening accelerates the crack propagation. The reduction in the J-integral value decreases with the increase in shot velocity when the crack depth is a certain value; therefore, increasing shot velocity is more beneficial for retarding fatigue crack propagation.

Investigation by Digital Image Correlation of Mixed-Mode I and II Fracture Behavior of Polymeric IASCB Specimens with Additive Manufactured Crack-Like Notch.

In this work, the fracture mechanics properties of polyamide (PA) specimens manufactured by the selective laser sintering (SLS) technology are investigated, in which an embedded crack-like notch was inserted in the design and produced during the additive manufacturing (AM) phase. To cover a wide variety of mode I/II mixity levels, the inclined asymmetrical semicircular specimen subjected to three points loading (IASCB) was employed. The investigation was carried out by analyzing the full displacement field in the proximity of the crack tip by means of the digital image correlation (DIC) technique. To characterize the material, which exhibits a marked elastic-plastic behavior, the quantity J-integral was evaluated by two different methods: the first one exploits the full fields measured by the DIC, whereas the second one exploits the experimental load-displacement curves along with FEM analysis. The DIC methodology was experimentally validated and proposed as an alternative method to evaluate the J-integral. It is especially suited for conditions in which it is not possible to use the conventional LDC method due to complex and possibly unknown loading conditions. Furthermore, results showed that the AM technique could be used effectively to induce cracks in this type of material. These two aspects together can lead to both a simplification of the fracture characterization process and to the possibility of dealing with a wider number of practical, real-world scenarios. Indeed, because of the nature of the additive manufacturing process, AM crack-like notches can be sintered even having complex geometry, being three-dimensional and/or inside the tested structure.

Stress Intensity Factors for Embedded, Surface, and Corner Cracks in Finite-Thickness Plates Subjected to Tensile Loading.

The aim of this study is to obtain the stress intensity factor (SIF) along the crack front of elliptical cracks located in finite-thickness plates subjected to imposed displacement or applied tensile load, for different crack geometries (relative depths and aspect ratios) and crack configurations (embedded, surface, and corner). The SIF was calculated from the J-integral, obtained by the finite element method. The results show how the SIF grows with the increase in the relative crack depth and with the decrease in the aspect ratio, with the corner crack being the most dangerous configuration and the embedded crack the most favorable configuration. By increasing the plate length, the SIF rises when the plate is under imposed displacement and decreases when the plate is subjected to applied tensile load, both cases tending towards the same SIF curve.

Comparison of J Integral Assessments for Cracked Plates and Pipes.

The purpose of this article is to compare two predictive methods of J integral assessments for center-cracked plates, single-edge cracked plates and double-edge cracked plates produced from X52 and X70 steels, and a longitudinally cracked pipe produced from X70 steel. The two methods examined are: the GSM method and the Js procedure of the French RCC-MR construction code, designated here as the FC method. The accuracy of J integral predictions by these methods is visualized by comparing the results obtained with the "reference" values calculated by the EPRI method. The main results showed that both methods yielded similar J integral values, although in most cases, the GSM predictions were slightly more conservative than the FC predictions. In comparison with the "reference" values of the J integral, both methods provided conservative results for most crack configurations, although the estimates for cracks of a relative length smaller than 1/8 were not found to be so conservative. The prediction of burst pressures for external longitudinal semielliptical part-through cracks in X70 steel pipe showed that the magnitudes of predicted burst pressures came very close to each other, and were conservative compared to FEM (finite element method) calculations and experimentally determined burst pressures.