Quasi-static Fracture Toughness Research Articles

Spatiotemporal Characterization of Microstructure Morphology, Mechanical Properties and Bone Remodeling of Rat Tibia Under Uniaxial Compressive Overload Loading.

Bone tissue is subjected to increased mechanical stress during high-intensity work. Inadequate bone remodeling reparability can result in the continuous accumulation of microdamage, leading to stress fractures. The aim of this work was to investigate the characteristics and repair mechanisms of tibial microdamage under several degrees of overload. Also, we aimed at better understanding the effects of overload on the multi-scale structure and mechanical properties of bone. Sixty 5-month female rats were divided into three groups with different time points. Micro-CT was used to evaluate the three-dimensional microstructure, and three-point bending, quasi-static fracture toughness and creep mechanical test were carried out to evaluate the mechanical properties. SEM was used to observe the morphological characteristics of fracture surfaces. Section staining was used to count the microdamage parameters and numbers of osteoblasts and osteoclasts. The microarchitectures of cancellous and cortical bones in the three overload groups showed different degrees of damage. Overload led to a messy crystal structure of cortical bone, with slender microcracks mixed in, and a large number of broken fibers of cancellous bone. The properties associated with the elastic plasticity, fracture toughness, and viscoelasticity of cortical bone reduced in three groups, with that corresponding to day 30 presenting the highest damage. The accumulation of microdamage mainly occurred in the first 14days, that is, the crack density peaked on day 14. Peak-targeted bone remodeling of cortical and cancellous bones occurred mainly between days 14 and 30. The influence of overload mechanical environment on bone quality at different time points was deeply investigated, which is of great significance for the etiology and treatment of stress fractures.

Quasi-Static Fracture Toughness and Damage Monitoring in Liquid Metal Reinforced Hybrid Composites

An experimental study is performed to investigate the quasi-static fracture toughness and damage monitoring capabilities of liquid metal (75.5% Gallium/24.5% Indium) reinforced intraply glass/carbon hybrid composites. Two different layups (G-0, where glass fibers are along the crack propagation direction; C-0, where carbon fibers are along the crack propagation direction) and two different weight percentages of liquid metal (1% and 2%) are considered in the fabrication of the composites. A novel four-probe technique is employed to determine the piezo-resistive damage response under mode-I fracture loading conditions. The effect of layups and liquid metal concentrations on fracture toughness and changes in piezo-resistance response is discussed. The C-composite without liquid metal demonstrated higher fracture toughness compared to that of the G-composite due to carbon fiber breakage. The addition of liquid metal decreases the fracture initiation toughness of both G- and C-composites. Scanning electron microscopy images show that liquid metal takes the form of large liquid metal pockets and small spherical droplets on the fracture surfaces. In both C- and G-composites, the peak resistance change of composites with 2% liquid metal is substantially lower than that of both no-liquid metal and 1% liquid metal composites.

INFLUENCE OF PLY ORIENTATION ON INTERLAMINAR FRACTURE TOUGHNESS OF CARBON/EPOXY COMPOSITES

Delamination is a concern for the structural integrity of fiber-reinforced polymer composite structures. The decisive material parameter for delamination is fracture toughness (G<sub>Ic</sub>). The main objective of this study was to investigate the in-plane, quasi-static fracture toughness (both initiation and propagation) of two laminate composites. Both composites contain carbon fibers in an epoxy matrix. The tests were performed using double cantilever beam specimens with different ply orientations according to ASTM standards. The effect of ply orientation was evaluated using data reduction methods to obtain fracture toughness. The experiments revealed that the ply sequence changed the crack propagation mechanism, increasing the initiation and propagation fracture toughness values for 90/90 layup during mode I interlaminar tests, by 80% and 69%, respectively. In addition, the mode I fracture toughness increased by 40% after 50 mm crack extension.

A novel fractal-statistical scaling model of rocks considering strain rate

The scaling-dependent behaviors of rocks are significant to the stability and safe operation of the structures built in or on rock masses for practical engineering. Currently, many size effect models are employed to connect laboratory measurements at small scales and engineering applications at large scales. However, limited works consider the strain rate effect. In this study, an fractal-statistical scaling model incorporating strain rate is proposed based on a weakest-link approach, fractal theory and dynamic fracture mechanics. The proposed scaling model consists of 8 model parameters with physical meaning, i.e. rate-dependent parameter, intrinsic material parameter, dynamic strain rate, quasi-static strain rate, quasi-static fracture toughness, micro-crack size, micro-crack intensity and fractal dimension, enabling the proposed scaling model to model the scaling behaviors under different external conditions. Theoretical predictions are consistent with experimental data on red sandstone, proving the reliability and effectiveness of the proposed scaling model. Thus, the scaling behaviors of rocks under dynamic loading conditions can be captured by the proposed fractal-statistical scaling model. The sensitivity analysis indicates that the size effect becomes more obvious with a higher strain rate, larger fractal dimension, smaller micro-crack size or lower micro-crack intensity. Therefore, the proposed scaling model has the potential to capture the scaling behaviors considering the thermal effect, weathering effect, anisotropic characteristic etc., as the proposed scaling model incorporated model parameters with physical meaning. The findings of this study are of fundamental importance to understand the scaling behaviors of rock under dynamic loading condition, and thus would facilitate the appropriate design of rock engineering.

Experimental study of the quasi-static and dynamic fracture toughness of notched and repaired concrete using semi-circular bend method

Concrete constructions commonly contain cracks or defects during forming and service, repair operations are necessary in many situations. However, limited investigations conducted on the dynamic fracture toughness (DFT) of repaired concrete structures. This paper investigates the cracking behavior of concrete structures through notched dynamic semi-circular bend (NSCB) tests performed using a split Hopkinson pressure bar (SHPB) apparatus with two measurement techniques, namely digital image correlation (DIC) and crack propagation gauge (CPG), to capture the flying half angular velocity and crack propagation speed of NSCB concrete specimens under various loads. The results demonstrate a linear increase in both DFT and crack propagation speed of concrete with the loading rate. Additionally, a threshold value exists beyond which the crack speed stabilizes, and the DFT is not evidently influenced by the notch depths. The cracks propagate along the aggregates and remain mostly intact under a relatively low loading rate. With an increased loading rate, the damage pattern of some otherwise deflected aggregates changes resulting in crack penetration and significantly reducing the fracture surface roughness. Repaired specimens exhibit greater energy dissipation at the same loading rate, thereby producing flying fragments with lower kinetic energy, which can prevent secondary damage to internal personnel and structures.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were first investigated through finite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is different from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the difference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modified. The quasi-static fracture toughness determined from the modified CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The effectiveness of the newly proposed method was verified through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

Fracture toughness and wear resistance of heat-treated H13 tool steel processed by laser powder bed fusion

In today's industry, complex parts made of steel are a reality thanks to the introduction of additive manufacturing, which offers technological improvements in conventional and large manufacturing industries that rely on molds and dies for mass production. However, the rapid solidification, remelting and reheating during the process and the uneven properties of the parts might present some difficulties in expanding its application in some sectors. For example, H13 tool steel offers exceptional properties, but finding the correct post-heating treatment for additively manufactured parts with reliable and repeatable properties is still a challenge. In this study, we focused on investigating different heat treatments to better understand the microstructure evolution and consequently the mechanical behavior under quasi-static loads, fracture toughness and wear resistance. Conclusions could be drawn on the structure-property relationships involving the strengthening and toughening mechanisms, as well as the evolution of the martensitic microstructure, retained austenite and carbides in parts processed by laser-based powder bed fusion. We found that low temperature tempering (550 °C) provides the lowest fracture toughness (KQ = 36 MPa.m0.5, J = 6.5 kJ.m−2, δ = 2.0 µm), the highest mechanical strength (YS up to 2270 MPa) and the lowest wear rate (circa 2.0 ×10−5 mm3/N.m). On the other hand, high temperature tempering (650 °C) with prior austenitizing and quenching provides the best fracture toughness (KQ = 87 MPa.m0.5, J = 70 kJ.m−2, δ = 40 µm), average mechanical properties (YS = 1104 MPa) and wear rate (3.4 ×10−5 mm3/N.m). Thus, different heat treatment processes can be applied depending on the requirements of the project.

Quasi-static modes I, II and mixed modes I/II fracture toughness of two laminate composites: Part II — micro-computerized tomography and numerical simulations

In Part I of this paper, quasi-static fracture toughness tests were reported which were carried out on two carbon fiber reinforced polymer materials. One laminate was unidirectional and the second was composed of plies fabricated from a twill fabric. In Part II, which is presented here, micro-computerized tomography was performed providing a relationship between the observed experimental behavior and the micromechanical structure of the materials. This was carried out for the double cantilever beam (DCB), mixed mode bending (MMB) and end-notched flexure (ENF) specimens. Load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to obtain better insight into the failure mechanisms observed for DCB and ENF specimens.

Quasi-static modes I, II and mixed modes I/II fracture toughness of two laminate composites: Part I — Testing

In Part I of this study, fracture toughness tests were carried out in modes I, II and mixed modes I/II on two laminate composites. Both composites contain carbon fibers in an epoxy matrix. One laminate is unidirectional and the second is composed of plies fabricated from a twill fabric. The tests were carried out using double cantilever beam, end-notched flexure and mixed mode bending specimens according to ASTM and ISO standards. This is an extensive and complete study of the in-plane, quasi-static fracture toughness (both initiation and resistance) of two material systems. In Part II of this study, micro-computerized tomography carried out on some of the specimens is reported. On the basis of these images, the experimental behavior was related to the micromechanical structure of the materials. In addition, load–displacement curves were simulated numerically by means of a cohesive zone model and the finite element method to gain better insight into the failure behavior observed.

Estimation of fatigue crack growth rate in different zones of friction stir welded AA7039

The present research aims to study the fatigue crack propagation and fracture toughness behavior of different zones of friction stir welds of AA7039 alloy, as different zones had varying microstructural and mechanical properties. Compact tension specimens with an initial notch in distinct weld zones parallel to the welding direction were machined using welded plates. Friction stir welding altered the base metal grain structure momentously, refined the grain structure in the weld nugget zone, and coarsen the same in the heat-affected zone. No correlation was observed between grain size and weld zone(s) hardness. Weld tensile properties were slightly inferior to base metal despite significantly higher hardness and alternation of grain structure. The fatigue life was dominated by the cycles consumed in crack propagation than crack initiation. The heat-affected zone had higher quasi-static fracture toughness, energy release rate, and resistance toward fatigue crack growth than other zones, because coarse grains and precipitates acted as effective impediments and slowed crack propagation. The heat-affected zone had a mixed-mode fracture, but the weld nugget zone and thermo-mechanically affected zone had an I mode fracture. On fracture surfaces, fracture characteristics such as microvoid coalescence were apparent.

High-rate mode II fracture toughness testing of polymer matrix composites using the Transverse Crack Tension (TCT) test

This paper describes the novel high-rate transverse crack tension (TCT) test to determine mode II fracture toughness for high strain rates and compares this to quasi-static fracture toughness obtained with the standardized End Notch Flexure (ENF) test and the modified Transverse Crack Tension (mTCT) test suggested in the literature. The novel, miniaturized mTCT specimen is used to determine the fracture toughness under quasi-static and high-rate loading conditions with an electro-mechanical test machine and a Split Hopkinson Tension bar, respectively. For the high-rate tests, almost no interfering oscillations were observed in the load signal. A novel data reduction scheme allows achieving repeatable results with a very small standard deviation. The fracture toughness for the tested composite at a loading rate of about 5 m/s was found to be at least 50% higher than the one obtained under quasi-static loading.

Resistance-curve envelopes for dental lithium disilicate glass-ceramics

Recent investigations on the mechanics of dental lithium disilicates have gathered mounting evidences of a probable R-curve behavior. Here we use an indirect approach to obtain the contours of the R-curve using the relationship between strength and initial crack size obtained from quasi-static fracture toughness tests. The tangent condition formed by the multiple KI,appl (ai,j) curves give a smoothened polygonal envelope for the R-curves. The R-curves obtained this way were extended toward an initial value at the onset of stable crack extension, obtained hereusing a microcantilever specimen featuring a sharp notch produced by focused-ion-beam milling. The presence of an R-curve effect was confirmed for the three evaluated lithium disilicates, being more pronounced for the injection-molded material having an oriented elongated Li2Si2O5 microstructural architecture, with crystal fraction playing an important role for low-aspect ratio randomly-oriented microstructures.

Geometrical effect of a notch tip on fracture toughness test

It is well-known that the geometrical shapes of a notch tip affect the experimental values of the K-based Mode-I fracture toughness, the physical mechanism of which yet remains unknown. Based on the geometrical modelling for multiple-cracks initiation, the distribution of the energy-based driving forces acting around the Mode-I crack and notch tip and underlying fracture configurations in form of crack extension can be found. The geometrical shapes of a narrow notch tip, unlike the well-defined crack tip, cause a perturbation on the fracture configurations and the functional points of the energy-based driving forces, resulting in overvalued the K-based Mode-I fracture toughness values. This process has been formulized by the geometrical modelling. The present investigation theoretically reveals a certain inevitability to the scattered experimental data in the static or quasi-static K-based Mode-I fracture toughness tests, which is beneficial to refresh the understanding of fracture behaviors and data processing.

Simplified Prediction Method of Stress Intensity Factor in Mid-thick Plane in 3D Cracked Body and Its Difference from 2D Handbook Formula

Abstract The authors have been working to improve the crack tip opening displacement (CTOD) evaluation standard as a fracture parameter for the cleavage-type brittle fracture critical condition of carbon steel. In 2016, WES1108, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement, which is the CTOD test standard in Japan, was revised, and subsequently, the CTOD calculation formula of ISO 15653:2010, Metallic Materials – Method of Test for the Determination of Quasistatic Fracture Toughness of Welds, was revised in 2018, focusing on the study of the formula that constitutes the basis of the standard. Similar to the original British Standards equation, the proposed CTOD calculation formula consists of a small-scale yield (SSY) term and a plastic term, but in the SSY term, the two-dimensional (2D) stress intensity factor (SIF) is used. The authors focused on the incorrectness of this treatment derived from the difference between 2D and three-dimensional (3D). Here, two accurate relationships have been explored through systematic finite element method analyses; one is the correlation of the 3D SIF values in the mid-thickness plane and 2D SIF, and the second is the relationship between the actual 3D SIF in mid-thickness and the CTOD in mid-thickness. The KI ratio (K3D/K2D) sharply coincides with the value 1.11, as inferred in several previous pieces of research in the idealistic infinite plate with a crack. However, if the ligament size is finite as in the actual fracture toughness test, the KI ratio drops significantly from 1.11, and in some cases, the KI ratio is less than 1. By unifying these findings, a new precise CTOD formula has been established. Lastly, the study inferred that the error of the calculation formula is improved, especially in small thickness regions, as compared with the current standard proposed in 2016 and 2018 by the authors.

An Industrial Approach to High Strain Rate Testing

Some industrial applications require properties of materials to be determined to evaluate components’ safety in the event of loading and impact. Understanding the behaviour of materials subjected to extreme dynamic loading will aid in enhancing their design. This work is based on developing methods to appraise high loading rate measurements. Different approaches to quantify material properties such as finite element method (FEM), instrumented Charpy testing, and impact testing using servo-hydraulic testing machines are included. Testing is performed at various loading rates, extending existing quasi-static fracture toughness determination to higher loading rates, and accounting for strain-rate dependent properties. The high loading rate servo-hydraulic test machine located at TWI, Cambridge has the capacity to test up to a displacement rate of 20 m/s. The force, displacement, and time parameters are captured by Digital Image Correlation (DIC), which improves the accuracy of the results obtained from experiments. Moreover, the underlying plasticity theory to capture the influence of the strain rate is presented, along with damage constants for FEM calculations adopting the Johnson-Cook model. In addition to the Johnson-Cook approach, analytical solutions using dislocation evolution theory were applied which features the effects of phonon drag and dynamic recovery coefficient in body-centered cubic materials of which X65 grade steel was applied. Also, a deep learning framework was built to predict the tensile curves when given specific test conditions and sample specifications. It was found that high strain rate tests lead to local change at the crack tip which increases plasticity and reduces fracture toughness with single-edged notched three-point bend specimen. The yield strength of the material increased with loading rates during tensile testing leading to a ductile to brittle transition of metals. These strategies were used to establish a revised approach for high strain rate testing and predicting stress-strain curves with a machine learning algorithm.

Search for Good Local Compression Condition with Bayesian Optimization

ISO 12135 provide a unified method of test for the determination of quasistatic fracture toughness. This test is conducted by using three-point bending specimen with a notch and fatigue pre-crack, and with regards to the fatigue pre-crack, ISO 12135 and ISO 15653 require some requirements such as minimum length and straightness. A base material specimen often meets the requirements without any special techniques, however, welds specimen cannot meet them due to welding residual stress. In order to meet the requirements, the local compression technique is used in general and ISO 15653 provides the recommended conditions. However, some interested parties have reported that the recommended conditions decrease the fracture toughness values. Based on the above, the authors developed prediction method for fatigue pre-crack straightness and fracture toughness evaluation value with numerical analysis and searched the good local compression condition, such as shape, size and location, with Bayesian optimization. As a result, we found that the area and location significantly effect on the fatigue pre-crack straightness and fracture toughness evaluation value and proposed new recommended local compression condition, which securing a straight fatigue pre-crack while maintaining the fracture toughness evaluation value. This proposed condition is validated through fracture toughness test and the fracture toughness evaluation values were compared with ISO recommended condition and so on. These experimental results also showed the effectiveness of proposed condition.

Experimental Proof of Reverse Bending Technique for Modifying Weld Residual Stress in Weld CTOD Specimen and Comparison of Effect with Other Techniques

Abstract In fracture toughness testing of welds, weld residual stress often makes it difficult to obtain a straight precrack front. Therefore, BS 7448-2, Fracture Mechanics Toughness Tests. Method for Determination of KIc, Critical CTOD and Critical J Values of Welds in Metallic Materials, and ISO 15653, Metallic Materials – Method of Test for the Determination of Quasistatic Fracture Toughness of Welds, recommend techniques for modifying weld residual stress to achieve a straight precrack front. BS 7448-2 prescribes three techniques: local compression, reverse bending, and a stepwise high stress ratio (R-ratio) technique. However, in ISO 15653, which was newly published in 2010, the reverse bending technique was rejected because detailed conditions for obtaining a reliable effect were not provided. In the revision of ISO 15653 in 2018, the reverse bending technique was revived with a proposal of appropriate conditions. The present paper reviews the conditions of reverse bending proposed in the revision of ISO 15653, together with the technical background. The effectiveness of the proposed reverse bending conditions is demonstrated experimentally by precracking in weld specimens with a thickness of 127 mm (5 inches). The effects of the two other techniques, i.e., the local compression and stepwise high R-ratio techniques, are also examined, and the effects of each technique on crack front straightness and the required fatigue cycles to finalize precracking are discussed.

Quasi-static and dynamic fracture toughness of a γ-TiAl alloy: Measurement techniques, fractography and interpretation

Intermetallic titanium aluminides (TiAl) offer an enormous potential for high temperature applications due to their high specific strength, creep and oxidation resistance. However, their use for structural components is limited by their low ductility and fracture toughness. During service, along with a high number of load cycles, the material may also be subjected to unexpected impact loads, which requires therefore knowledge about dynamic material parameters for a damage-tolerant component design. Here we present a feasibility study to determine the fracture toughness of a third generation TiAl-alloy over a wide range of loading rates. Quasi-static crack resistance curves (R-curves) were determined using the direct current potential drop (DCPD) technique. The dynamic experiments were performed with a drop tower with impact velocities ranging from 1 to 10 m/s on pre-cracked SENB specimens. To exclude the influence of inertial forces, the measurements were carried out with strain gauges applied in the elastic near-field of the crack tip. Despite a critical consideration of possible systematic errors of this measurement method, it was found that the dynamic fracture initiation toughness slightly increases up to loading rates of K̇I = 106 MPa√m/s. The fracture behaviour of the material and possible reasons for the toughness increase are discussed based on comprehensive fractographic investigations as well as crack path analyses within the microstructure.

Development of a method for extracting fracture toughness from instrumented Charpy impact tests in the ductile and transition regimes

The Charpy impact test is often used to qualify the structural materials used for the fabrication of industrial components, in particular steel-based components. This relatively simple test used for more than a century was originally designed to contribute to ensure steel quality. Later, it was used to determine the so-called ductile-to-brittle transition temperature (DBTT) to characterize the fracture resistance of body-centered cubic (bcc) structural materials. In the nuclear field, it was also used in surveillance programs monitoring the property degradation of the reactor pressure vessels avoiding prohibitive fracture toughness tests that would require large specimens. With the advances in fracture mechanics achieved over the last decades, it is possible nowadays to reliably measure fracture toughness from significantly smaller specimens. In particular, the master curve offers a simple method to derive the fracture toughness – temperature dependence curve that can be further used for integrity assessment. A number of empirical correlations were established by relating the DBTT measured with Charpy impact tests to the master curve reference temperature, T0. However, all those correlations are essentially empirical and rely heavily on experimental databases on which they were derived.The main objective of this work is a more direct derivation of quasi-static fracture toughness from the Charpy impact test that can be directly compared to measured quasi-static fracture toughness data. This way, the consistency between the multiple properties delivered by the various tests guarantees the overall quality of the experimental data used to characterize the mechanical properties of structural materials. The proposed procedure relies on the J-integral derived from the instrumented Charpy impact test and on the normalization of the crack resistance curve by accounting for dynamic effects, notch/crack configuration effects, loading rate effects, side grooving effects and eventually specimen size effects. The results obtained on several materials in the unirradiated and irradiated conditions are very promising and provide an interesting property-to-property correlation tool, not only as a quality control but they also offer a cheap and fast estimate of fracture toughness for material design purposes.

Dynamic fracture mechanics and energy distribution rate response characteristics of coal containing bedding structure.

To investigate the influence of bedding structure and different loading rates on the dynamic fracture characteristics and energy dissipation of Datong coal, a split Hopkinson bar was used to obtain the fracture characteristics of coal samples with different bedding angles. The process of crack initiation and propagation in Datong coal was recorded by the high-speed camera. The formula for the model I fracture toughness of the transversely isotropic material is obtained on the basis of the finite element method (FEM) together with the J-integral. By comparing the incident energy, absorbed energy, fracture energy and residual kinetic energy of Datong coal samples under various impact speeds, the energy dissipation characteristics during the dynamic fracture process of coal considering the bedding structure is acquired. The experimental results indicate that the fracture pattern of notched semi-circular bending (NSCB) Datong coal is tensile failure. After splitting into two parts, the coal sample rotates approximately uniformly around the contact point between the sample and the incident rod. The dynamic fracture toughness is 3.52~8.64 times of the quasi-static fracture toughness for Datong coal. Dynamic fracture toughness increases with increasing impact velocity, and the effect of bedding angle on fracture toughness then decreases. In addition, the residual kinetic energy of coal samples with the same bedding angle increases with the increase of impact speed. The energy utilization rate decreases continuously, and the overall dispersion of statistical data decreases gradually. In rock fragmentation engineering, the optimum loading condition is low-speed loading regardless of energy utilization efficiency or fracture toughness. These conclusions may have significant implications for the optimization of hydraulic fracturing process in coal mass and the further understanding of crack propagation mechanisms in coalbed methane extraction (CME). The anisotropic effect of coal should be fully considered in both these cases.