A review on experimental and numerical investigations of cortical bone fracture

This paper comprehensively reviews the various experimental and numerical techniques, which were considered to determine the fracture characteristics of the cortical bone. This study also provides some recommendations along with the critical review, which would be beneficial for future research of fracture analysis of cortical bone. Cortical bone fractures due to sports activities, climbing, running, and engagement in transport or industrial accidents. Individuals having different diseases are also at high risk of cortical bone fracture. It has been observed that osteon orientation influences cortical bone fracture toughness and fracture mechanisms. Apart from this, recent studies indicate that fracture parameters of cortical bone also depend on many factors such as age, sex, temperature, osteoporosis, orientation, location, loading condition, strain rate, and storage facility, etc. The cortical bone regains its fracture toughness due to various toughening mechanisms. Owing to these factors, several experimental, clinical, and numerical investigations have been carried out to determine the fracture parameters of the cortical bone. Cortical bone is the dense outer surface of the bone and contributes to 80%–82% of the skeleton mass. Cortical bone experiences load far exceeding body weight due to muscle contraction and the dynamics of motion. It is very important to know the fracture pattern, direction of fracture, location of the fracture, and toughening mechanism of cortical bone. A basic understanding of the different factors that affect the fracture parameters and fracture mechanisms of the cortical bone is necessary to prevent the failure and fracture of cortical bone. This review has summarized the advancement considered in the various experimental techniques and numerical methods to get complete information about the fracture mechanisms of cortical bone.

Simplified equations for determining double-k fracture parameters of concrete for compact tension test

Polynomial equations in non-dimensional form for various fracture parameters of double-K fracture model for compact tension specimen have been derived and presented in this paper. These equations can be used for computing different double-K fracture parameters of concrete for known material properties and specimen size having relative size of initial crack length of 0.3 without involving much complexity in numerical computations. Values of peak load and corresponding crack opening displacement as necessary to compute the double-K fracture parameters of concrete have been derived from the established fictitious crack model in the present study. A simplified equation in non-dimensional form between peak load and critical crack opening displacement as obtained from a fictitious crack model has also been presented.

Fatigue life assessment of polyamide 12 processed by selective laser sintering. Damage modelling according to fracture mechanics

Purpose Polyamide 12 (PA12) processed by the additive manufacturing technique of selective laser sintering (SLS) is acquiring a leading role in cutting-edge technological sectors pertaining to transport and biomedical among others. In many of these applications, design requirements must ensure fatigue structural integrity. One of the characteristic features of these SLS PA12 is the layer-wise structure that may influence the mechanical response. Therefore, this paper aims to assess the fatigue life behavior of PA12, focusing on the effect of the load direction with respect to the load orientation. Design/methodology/approach With the aim of analyzing the effect of the load direction with respect to the layer wise structure, fatigue tests on plain samples of SLS PA12 were carried out with the load applied parallel and perpendicular to the layer planes. The S-N stress life curves and the fatigue limit at 106 cycles were determined at room temperature and at a stress ratio of 0.1. The fracture surfaces were inspected to evaluate the damage evolution, modeled via the fracture mechanics methodology to obtain the fracture parameters. Findings The fatigue resistance was better when the load was applied parallel than when was applied perpendicularly to the layered structure. The analysis of the postmortem specimens evidenced three regions. The inspection of the fatigue macro crack growth region revealed that crazing was the mechanism responsible of nucleation and growth of damage till a macroscopic crack was generated, as well as of the consequent crack advancement. The calculated fracture parameters computed from the application of the fracture mechanics approach were similar to those obtained from standardized fracture tests, except when the stress levels were close to the yield strength. Originality/value The fatigue knowledge of polymers, and especially of polymers processed via additive manufacturing techniques, is still scarce. Therefore, the value of this investigation is not only to obtain fatigue data that could be used for structural design with SLS PA12 materials but also to advance in the knowledge of damage evolution during the fatigue process.

Research on the Fracture Behavior of Steel-Fiber-Reinforced High-Strength Concrete

The behavior of steel fiber concrete, which is the most widely used building material, has been widely examined. However, methods for calculating Fracture parameters differ by fracture behavior of SFHSC with different strengths. In this study, the fracture behavior of steel-fiber-reinforced high-strength concrete (SFHSC) was -investigated using three-point bending tests. A total of 144 notched concrete beams with a size of 100 mm × 100 mm × 515 mm were tested for three-point bending in 26 groups. The effects of the steel fiber volume ratio, steel fiber type, and relative notch depth on the fracture toughness (KIC) and fracture energy (GF) of SFHSC specimens were studied. The results show that an increase in the volume fraction of steel fiber (ρf) added to high-strength concrete (HSC) significantly improves the fracture behavior of HSC. As compared to milled and sheared corrugated steel fibers, cut bow steel fibers significantly improve the fracture behavior of SFHSC. The effect of incision depth changes on the KIC and GF of SFHSC and HSC for the comparison group has no common characteristics. With an increase in incision depth, the values of KIC of the SFHSC specimens decrease slightly. The GF0.5/GF0.4 of the SFHSC specimens show a decreasing trend with an increase in ρf. According to the test results, we propose calculation models for the fracture behavior of SFHSC with different strengths. Thus, we present a convenient and accurate method to calculate fracture parameters, which lays a foundation for subsequent research.

A Novel Mathematical Model for Fracturing Effect Evaluation Based on Early Flowback Data in Shale Oil Reservoirs

For shale oil reservoirs, the horizontal well multistage fracturing technique is mostly used to reform the reservoir in order to achieve economic and effective development. The size of the reservoir reconstruction volume and the quantitative characterization of the fracture system are of great significance to accurately predict the productivity of shale oil wells. There are few flowback models for shale oil reservoirs. To solve this problem, first, a physical model of the simultaneous production of oil, gas, and water in the early flowback stage of shale oil development is established using the material balance equation for a fracture system. Second, the physical model of the underground fracture system is simplified, which is approximately regarded as a thin cylindrical body with a circular section. The flow of the fluid in the fracture system is approximately regarded as radial flow. In this model, the expansion of the fluid and the closure of the fracture are defined as integrated storage coefficients to characterize the storage capacity of the fracture system. Then, the curves illustrating the relationships between the oil-water ratio and the cumulative oil production and between the gas-water ratio and the cumulative gas production are drawn, and the curves are used to divide the flowback stage into an early stage and a late stage because the flowback process of shale oil wells exhibits obvious stage characteristics. Finally, the reservoir reconstruction volume and the related hydraulic fracture parameters are estimated based on the material balance method, and the rationality of the model is verified via numerical simulation. The interpretation results of this novel model are more accurate, making it an effective way to evaluate the hydraulic fracture parameters and transformation effect, and it has guiding significance for the evaluation of the hydraulic fracturing effect in the field.

Mechanical fracture parameters of concrete drill-core specimens supported by a slenderness ratio study

The detailed analytical and experimental investigation of the fracture behaviour of quasi-brittle materials is an endeavour which has been ongoing worldwide for many years. Such materials are usually characterized in terms of their mechanical fracture parameters, which are determined based on the evaluation of quasi-static fracture experiments. One of the most commonly used building materials with a quasi-brittle response is concrete, which is most often based on a cement matrix. It is sometimes also necessary to characterize concrete included in existing structures. In this case, test specimens are obtained by core drilling, and the investigation is conducted with the requirement to maximize the number of parameters obtained while minimizing the number of test specimens drilled from the structure. This paper focuses on the mechanical fracture parameters of core-drilled specimens taken from a selected concrete structure. Tests were performed on cylindrical specimens with a chevron-notched stress concentrator in the three-point bending configuration in order to determine modulus of elasticity, fracture toughness and fracture energy. Subsequently, theoretical compressive strength was estimated and tests for the determination of compressive strength values were performed focusing on dependence on the slenderness ratio, i.e. the relationship between the compressive strength and the length to diameter ratio of the cylindrical specimens. In relation to the obtained mechanical fracture parameters, selected specimens were analysed and three-dimensionally characterized via high-resolution X-ray computed tomography.

RILEM Standard: testing methods for determination of the double-K criterion for crack propagation in concrete using wedge-splitting tests and three-point bending beam tests, recommendation of RILEM TC265-TDK

In this recommendation, standard testing methods for determination of the double-K criterion for Mode I crack propagation in concrete using wedge-splitting tests and three-point bending beam tests are specified for the fracture parameters of the initial cracking toughness $$K_{Ic}^{ini}$$ K Ic ini and the unstable fracture toughness $$K_{Ic}^{un}$$ K Ic un . Along with the recommendation of the standard testing methods, the theoretical background of the double-K criterion, the calculation methods and the results of round-robin testing for determining the double-K fracture parameters are presented in technical reports [1, 2]. The recommendation of the standard testing methods includes geometry for specimens, fabrication of specimens, testing machine, load transmission system and supports, measuring instruments, determination of initial cracking load Pini, determination of measured maximum load Pmax and initial compliance ci, calculation methods for wedge-splitting test and three-point bending beam test, as well as the testing results and testing report forms. According to these methods, the measured fracture parameters of double-K criterion can be used to describe the onset of cracking, and the onset of unstable cracking or failure for predicting crack initiation, structure failure and crack stability in concrete structures.