Fracture Toughness Measurements Research Articles

Understanding the Fatigue Notch Sensitivity of High-Strength Steels through Fracture Toughness

This study presents an innovative approach for selecting high-strength materials for fatigue dimensioning parts, considering both fracture toughness and fatigue performance. Warm and hot forming processes enable the construction of high-strength parts above 1000 MPa with complex geometries, making them suitable for lightweight chassis in automotive and freight applications. This research reveals that high-strength steels can experience up to a 40% reduction in fatigue performance due to manufacturing defects introduced during punching and trimming. Fracture toughness has been proposed as a good indicator of notch sensitivity, with a strong correlation of 0.83 between fracture toughness and fatigue notch sensitivity. Therefore, by combining fracture toughness measurements and fatigue resistance obtained through the rapid fatigue test, it becomes possible to quickly identify the most fatigue-resistant materials to deal with defects. Among the nine materials analysed, warm-formed steels show promising characteristics for lightweight chassis construction, with high fatigue resistance and fracture toughness exceeding the proposed fracture threshold of 250 kJ/m2.

Effect of pre-crack non-uniformity for mini-CT geometry in ductile tearing regime

The mini-CT specimen attracts the attention from all over the world for application in fracture toughness measurement. However, one of the shortcomings of this geometry is related to the required tight accuracy of the specimen dimensions, in particular the fatigue pre-crack curvature which often violates the requirements of the ASTM standards. Given the limited thickness of mini-CT geometry, non-uniform pre-crack tends to develop during fatigue pre-cracking, resulting in a large proportion of mini-CT specimens being considered invalid.Previous investigations have demonstrated that mini-CT specimens with excessive crack front curvature can still provide meaningful fracture toughness results. In this paper, the effect of pre-crack front non-uniformity on ductile fracture is studied: first, the difference of macro parameters such as the applied load, J-integral and crack tip stress–strain field are investigated to illustrate the varying fracture behavior related to non-uniform pre-crack. Next, two micro-mechanics-based approaches, the Rice-Tracey void growth model and Thomason void coalescence model, are integrated to compare the ductile fracture initiation conditions associated with uniform and non-uniform fatigue pre-crack. Finally, the experimental verification of the ductile fracture simulations is performed for mini-CT specimens with uniform and 30° tilted initial cracks. The results indicate that the pre-crack non-uniformity plays a major role in the redistribution of local J-integral and stress–strain state, further affects the position of crack initiation and the early stages of crack propagation. Nevertheless, the pre-crack non-uniformity has limited effect on the global properties that are usually expected from fracture toughness tests, such as applied load, J-R curve and critical fracture toughness. The requirements in the ASTM E1820 regarding pre-crack front curvature need thus to be relaxed.

Mechanical Behavior of Transparent Spinel Fabricated by Spark Plasma Sintering

In this work, a transparent nanostructured ceramic magnesium aluminate spinel (MgAl2O4) was fabricated by Spark Plasma Sintering (SPS) from commercial spinel nano-powders at different temperatures (1300, 1350 and 1400 °C). The sintered samples were thoroughly examined to assess their microstructural, optical, and mechanical properties. Various techniques such as SEM, AFM, spectrophotometer with an integrating sphere, instrumented Vickers indenter, Pin-on-Disk tribometer, scratch tester, and sandblasting device were employed to characterize the sintered samples. The results indicated the significant impact of the sintering temperature on the properties of the spinel samples. Particularly, the samples sintered at T = 1350 °C exhibited the highest Real In-line Transmission (RIT = 72% at 550 nm and 80% at 1000 nm). These samples demonstrated the highest hardness value (HV = 16.7 GPa) compared to those sintered at 1300 °C (HV = 15.6 GPa) and 1400 °C (HV = 15.1 GPa). The measured fracture toughness of the sintered samples increased substantially with increasing sintering temperature. Similarly, the tribological study revealed that the friction coefficient of the sintered spinel samples increased with the sintering temperature, and the spinel sintered at 1350 °C exhibited the lowest wear rate. Additionally, sandblasting and scratch tests confirmed the significant influence of the sintering temperature on the mechanical properties of the fabricated spinels. Overall, the spinel sintered at 1350 °C presented the best compromise in terms of all the evaluated properties.

The influence of aspect ratio on the determination of tearing energy in mode I fracture tests

The energy for tearing is a classical measure of fracture toughness for elastic materials at finite strains. The prominent approach to quantify the tearing energy utilizes a tensile test on edge-cut thin rectangular specimens with low height-to-width ratio to determine the critical stretch at which a crack propagates from the tip of the cut. The analysis of the experiment, proposed by Rivlin and Thomas (1953), relies on the assumption that a large portion of the test piece is in a state of plane strain, and that the change of the total elastic energy is equal to the energy release due to the formation of new crack surfaces. While these assumptions are well justified for test pieces with sufficiently low height-to-width ratio, limitations in the availability and homogeneity of various sample materials have enforced the use of specimens with higher height-to-width ratios. In order to analyse the applicability of the classical theory and the corresponding errors, we investigate in the present work the influence of the sample’s height-to-width ratio on the estimation of the tearing energy in mode I fracture tests. Exemplified with experiments and simulations for the elastomer Ecoflex 1:1, we show that reliable measurements can be obtained even for a quadratic sample geometry. For tough materials, however, significant overestimation of the tearing energy is expected already for a height-to-width ratio larger than 1/2. Surprisingly, in very brittle materials the tearing energy is vice-versa prone to be underestimated by up to 10% for ratios up to 1. The error also depends on the non-linear stress–strain characteristics, as illustrated by the use of different constitutive models. While a generally valid geometrical criterion cannot be defined based on the present results, our results suggest that the error hardly exceeds 10% for height-to-width ratios of up to 1/2.

Cr-containing diamond-like carbon coatings deposited on 316 stainless steel substrates: Characterization and interfacial fracture toughness measurements

A series of Cr-containing hydrogenated amorphous carbon (a-C:H:Cr) coatings were deposited onto 316 stainless steel (316SS) substrates using inductively coupled plasma assisted reactive sputter deposition. Elemental Cr interlayers with different thicknesses of 100, 200, and 300 nm were deposited between a-C:H:Cr and 316SS. Detailed composition, structure, and mechanical behavior characterization of deposited a-C:H:Cr/Cr/316SS specimens were performed. Fracture toughness values of the a-C:H:Cr layer, the Cr layer, and the a-C:H:Cr/Cr/316SS interfacial regions were measured by bending of microcantilever beams with focused ion beam milled pre-notches in-situ a scanning electron microscope. Measured fracture toughness of a-C:H:Cr/Cr/316SS interfacial regions exhibits an approximately linear correlation with the area fraction of the fracture surface occurring in the Cr interlayer, indicating that the interfacial fracture toughness depends on the detailed path of crack propagation and suggesting that interfacial toughness can be engineered through materials design of the interfacial region.

Fracture toughness of organic rich shale via nanoindentation: A comparison of energy-based methods

Fracture toughness is an important mechanical parameter for proper modeling of reservoir stimulation which is necessary for production from tight formations. To measure fracture toughness, several models have been proposed based on nanoindentation data, however, the comparison of these models in organic rich shale is still limited in the literature. To obtain a better understanding of the suitability of these models, we applied two distinct energy based methods, one which takes advantage of the whole force-displacement curve (KIC_whole) and the other one that considers the fracturing-induced pop-in events (KIC_pop). To estimate and compare the fracture toughness from either of these methods, nanoindentation data is acquired from a sample that was collected from the Wolfcamp Formation, USA. The results showed that for the soft mechanical phase (clay minerals), the KIC_whole varied from 0.020 to 0.313 MPa m0.5 while the KIC_pop from 0.02 to 0.330 MPa m0.5. In the hard mechanical phase (carbonate and quartz), the KIC_whole was found between 0.380 and 0.84 MPa M0.5, and the KIC_pop was estimated from 0.38 to 0.780 MPa m0.5. These values for the intermediate phase was, 0.220–0.588 MPa m0.5 and 0.215–0.500 MPa m0.5, respectively for each method. Statistical analysis of the results based on the t-tests verified that the fracture toughness of different mechanical phases that is derived from these two different models is quite comparable. Overall, considering the simplicity of the calculations and the limitations in the approach that is based on pop-in events, our recommendation would be to use the whole force-displacement curve to obtain the fracture toughness of geomaterials.

Effect of using unpyrolyzed powder on mechanical properties of vertically cracked thermal barrier coatings

In this study, thermal barrier coatings with segmentation cracks produced using synthesized unpyrolyzed powder (UP TBC) and dense vertically cracked (DVC) thermal barrier coatings with varying vertical crack density and porosity were produced by air plasma spray technique. The mechanical properties of the coatings including microhardness, Young's modulus and fracture toughness were evaluated by indentation technique and the correlation of the results with porosity is discussed. The results of elastic modulus indicated that higher percentage of porosity results in a lower elastic modulus and consequently lower fracture toughness for DVC TBCs. In the case of the UP TBC samples, the porosity percentage, compared to the conventional one, is higher but in contrary a higher elastic modulus was measured; probably due to the existence of submicron size unmelted zones. The results of fracture toughness measurement showed that the UP TBC has a lower elastic modulus compared to that of DVC TBCs. However, due to non-melted zones which are consisted of unpyrolyzed particles, UP TBC demonstrates a higher fracture toughness than the DVC TBCs.

Discrete crack mechanics of disk compression for measurement of low fracture toughness

Discrete crack mechanics of disk compression for measurement of low fracture toughness

Influence of fatigue precracking and specimen size on Master Curve fracture toughness measurements of EUROFER97 and F82H steels

EUROFER97 and F82H steels are two leading reduced-activation ferritic-martensitic (RAFM) steels for fusion first wall and blanket applications. Exposure to the harsh environment of fusion reactors can result in severe degradation of fracture toughness. Thus, the post-irradiation evaluation of fracture toughness is critical for understanding the material behavior. Due to the space constraints of irradiation facilities and challenges in controlling a uniform irradiation condition for large size specimens, the development of small specimen test techniques (SSTT) is indispensable to evaluate the performance of irradiated materials. In this study, we evaluated specimen size effects on the Master Curve fracture toughness of EUROFER97 and F82H steels. A wide variety of specimens, including 0.5 T compact tension (C(T)) specimens, 0.16 T mini-compact tension (miniC(T)) specimens, and 1.65 mm miniature bend bar specimens, were tested. The testing methodology was based on the Master Curve method in the ASTM E1921 standard. No specimen size effect was observed in 0.5 T C(T) and 0.16 T miniC(T) specimens on the Master Curve reference temperature T0, while 1.65 mm miniature bend bar specimens yielded a higher T0Q. A strong effect of fatigue precracking on T0 for 0.5 T C(T) and 0.16 T miniC(T) specimens was observed, such that testing on specimens with skewed fatigue precrack fronts resulted in lower T0 than for specimens with ASTM standard qualified straight fatigue precrack fronts. The results highlight the importance of experimental quality control in developing SSTT for Master Curve fracture toughness testing. Lastly, we also evaluated and provided recommendations on the minimum number of specimens needed for each specimen type for yielding reliable T0Q values.

Determination of fracture toughness and traction–separation relation in Mode I/II of a natural quasi-brittle orthotropic composite using multi-specimen approach

The fracture behavior of quasi-brittle naturally occurring composites is characterized by the presence of fracture process zone (FPZ), which is attributed by crack bridging and micro-cracking in wood. The FPZ limits the use of existing standards for fracture toughness. Also, the repeated loading–unloading approach using single specimen is difficult due to crack face interference. Further, the crack growth monitoring is difficult since the crack tip may be buried inside FPZ. So far, the compliance based beam method (CBBM) has offered a reasonable solution to these challenges. However, the CBBM is not an absolutely independent approach as it uses elastic constant and compliance determined from other experiments. Naturally occurring materials, like wood, exhibits large variations in its properties. Therefore, the use of parameters from multiple other experiments decreases the confidence in measured fracture toughness. Considering this, the present work evaluates the fracture toughness attributed by critical energy release rate of New Zealand Pine wood. Firstly, the research method follows a stand-alone multi-specimen approach to evaluate fracture toughness without any requirement for crack growth monitoring. Secondly, it experimentally establishes the traction–separation relation for both Mode I and II. This work has a general applicability to other natural quasi-brittle orthotropic solids like bone.

XFEM Analysis of Strain Rate Dependent Mechanical Properties of Additively Manufactured 17-4 Precipitation Hardening Stainless Steel

AbstractAdditively manufactured (AM) specimens of 17-4 precipitation hardening (PH) stainless steel (SS) corresponding to the three-point bend test, compact tension test, and single edge cracks were analyzed using the extended finite element method (XFEM) approach. A two-dimensional and three-dimensional elastic-plastic simulation were conducted using “abaqus 6.14” software based on the experimental results and validated with the simulation results. In XFEM, the partition of unity was used to model a crack in the standard finite element mesh. Based on simulation results, the present study compares the mechanical properties of AM 17-4 PH stainless steel samples with those of wrought 17-4 PH samples. Stress intensity factor and J integral were used to measure fracture toughness of the specimens. The change in fracture toughness with strain rate was evaluated by simulating two-dimensional compact tension specimens. The presence of defects such as pores resulting from entrapped gas, un-melted regions, and powder particles resulting from lack of fusion were the main reasons for lower elongation to failure of laser powder bed fusion (L-PBF) produced 17-4 PH SS reported in the literature.

A fracture model for assessing tensile mode crack growth resistance of rocks

Evaluating the fracture resistance of rocks is essential for predicting and preventing catastrophic failure of cracked structures in rock engineering. This investigation developed a brittle fracture model to predict tensile mode (mode I) failure loads of cracked rocks. The basic principle of the model is to estimate the reference crack corresponding to the fracture process zone (FPZ) based on the maximum normal strain (MNSN) ahead of the crack tip, and then use the effective crack to calculate the fracture toughness. We emphasize that the non-singular stress/strain terms should be considered in the description of the MNSN. In this way, the FPZ, non-singular terms and the biaxial stress state at the crack tip are simultaneously considered. The principle of the model is explicit and easy to apply. To verify the proposed model, laboratory experiments were performed on a rock material using six groups of specimens. The model predicted the specimen geometry dependence of the measured fracture toughness well. Moreover, the potential of the model in analyzing the size effect of apparent fracture toughness was discussed and validated through experimental data reported in the literature. The model was demonstrated superior to some commonly used fracture models and is an excellent tool for the safety assessment of cracked rock structures.

Influences of notch width and notch-tip angle on the fracture toughness measurement using the semi-circular bend (SCB) specimen

Semi-circular bend (SCB) method has been proposed by the International Society for Rock Mechanics and Rock Engineering (ISRM) as one of the four suggested methods for measuring the mode I fracture toughness of rocks. Due to limitations in the machining precision and the quasi-brittle nature of rocks, there exists inevitable measurement error in the measurement results using this method. Our previous study concluded that the SCB specimen with a sharp notch-tip (sharp-SCB) is the optimal configuration for minimizing the measurement error. This study further investigates the effects of notch width and notch-tip angle on the fracture toughness measurement using the sharp-SCB specimens. Five tip angles (i.e., 30°, 60°, 90°, 120°, and 150°) and three notch widths (i.e., 1 mm, 2 mm, and 3 mm) are considered. Within the theoretical framework of K-resistance (KR) curve, the results indicate that the initial load, peak load, critical crack length, and initial fracture toughness are all significantly dependent on the notch width and the notch-tip angle. As the intrinsic property of the rock material, the unstable fracture toughness is however relatively insensitive to these geometrical parameters. The error analysis of the experimental results shows that the ISRM suggested SCB method is reliable within certain ranges of these geometrical parameters. This study provides useful guidance on applying the ISRM suggested SCB method for quantifying rock fracture toughness.

Mechanical Stability of Self-Adhesive/Ion-Releasing Resin Composites

The purpose of this study was to assess the effects of water storage on the surface microhardness (VHN) and fracture toughness (K1C) of two self-adhesive restorative materials compared to traditional resin composite and resin-modified glass ionomer cement (RMGIC) restorative materials. Methods: Two self-adhesive materials (Activa and Vertise Flow), a nonflowable composite (Filtek Z250), and an RMGIC (Fuji II) were evaluated. Hardness measurements (n = 12) were recorded at three time intervals: (i) one-hour post-irradiation; (ii) after one day of storage in water at 37 °C; and (iii) after 90 days of storage in water at 37 °C. Fracture toughness (K1C) measurements (n = 12) were conducted after one day of storage in water at 37 °C and 90 days of storage in water at 37 °C. ANOVA and Tukey post hoc tests were used for statistical analysis. Results: Baseline VHN data were 38.2–58.3, decreasing significantly to 28.8–55.6 following 90 days of water storage. The Filtek Z250 had the highest VHN before and after storage, while the Activa had the lowest. KIC values varied between 0.98–1.32 MPa·m0.5. The highest value was for the Filtek Z250 while the Fuji II showed the lowest value (after both 1 and 90 days of storage in water). However, KIC values decreased significantly after storage, except for the Fuji II. Conclusion: Self-adhesive/ion-releasing resin composites were negatively affected by water storage. Material reinforcements are possible future areas to explore.

Using Mini-CT Specimens for the Fracture Characterization of Ferritic Steels within the Ductile to Brittle Transition Range: A Review

The use of mini-CT specimens for the fracture characterization of structural steels is currently a topic of great interest from both scientific and technical points of view, mainly driven by the needs and requirements of the nuclear industry. In fact, the long-term operation of nuclear plants requires accurate characterization of the reactor pressure vessel materials and evaluation of the embrittlement caused by neutron irradiation without applying excessive conservatism. However, the amount of material placed inside the surveillance capsules used to characterize the resulting degradation is generally small. Consequently, in order to increase the reliability of fracture toughness measurements and reduce the volume of material needed for the tests, it is necessary to develop innovative characterization techniques, among which the use of mini-CT specimens stands out. In this context, this paper provides a review of the use of mini-CT specimens for the fracture characterization of ferritic steels, with particular emphasis on those used by the nuclear industry. The main results obtained so far, revealing the potential of this technique, together with the main scientific and technical issues will be thoroughly discussed. Recommendations for several key topics for future research are also provided.

The effect of groove and notch tip angles on testing fracture toughness by SEVNB method: models and experimental validation

ABSTRACT The single-edged V-notch beam (SEVNB) method is considered as an effective method for evaluating the fracture toughness values of brittle materials. In this method, it is assumed that the V-notch is a natural crack. However, this assumption may cause an overestimation of the fracture toughness due to the “notch passivation effect”. To investigate the effects of the V-notch and groove tip angles on the fracture toughness testing of ceramic materials, three typical models were established in this work. The stress intensity factors of these models were calculated using a J-integral based on the linear finite element method (LFEM). The results indicated that the measured fracture toughness values could be overestimated by 0.5%- 13.7% when the angle of the V-notch tip increased from 10° to 60°. Increasing the angle formed by the V-notch and groove from 10° to 60°, fracture toughness was overevaluated by about 0% – 2.0%. When the angle formed by the V-notch and groove increased to 120°, the fracture toughness was overevaluated by about 31%. Finally, two equations were fitted to assess the angles effects on fracture toughness, and the results have been validated by experiments. An important reference for the SEVNB method can be found in this work.

A versatile device for measuring the mode I fracture toughness with application to estimate the impact of water weakening in chalks

A newly built versatile device for mode I fracture toughness measurement is presented. To test this apparatus, measurements have been conducted on two crystalline rocks, the Aue Granite and the Äspö Diorite, and two chalks from the Paris basin, Obourg and Ciply chalks. The fracture toughness KIC can be measured with two different testing procedures, the Semi-Circular Bend (SCB) and the Straight Edge Cracked Round Bar Bend (SECRBB) methods, both known for the easiness of the notched sample preparation. For the SCB tests, ultrasonic sensors were mounted at the sample surface to monitor changes in P-wave velocity and record acoustic emission activity. Our results are in reasonably good agreement with published data on the same rocks. The SECRBB test provides values of the fracture toughness 37% higher compared to the SCB test for the Obourg chalk. This discrepancy may be explained by a sample size effect. The fracture toughness of water saturated chalks is strongly reduced compared to that of the dry chalks by almost 50%. This shows that fracture toughness is a valuable parameter to assess the importance of water weakening in porous rocks.

On the use of mini-CT specimens to define the Master Curve of unirradiated reactor pressure vessel steels with relatively high reference temperatures

The safe operation of nuclear plants requires an accurate characterization of the fracture toughness of reactor pressure vessel materials, which can be reduced over time due to irradiation or thermal aging processes. This necessity is a challenge itself since the availability of specimens inside the surveillance capsules of the vessels is generally scarce. Therefore, innovative techniques have to be applied, in order to increase the reliability of fracture toughness measurements and at the same time to reduce the volume of material needed for the tests. In this paper, the Master Curve (MC) approach has been employed, combined with the use of mini-CT specimens made from two different reactor pressure vessel (RPV) steels (ANP-5 and A533B LUS). The MC methodology allows the fracture toughness of the material to be evaluated by using a single parameter: the reference temperature, T0. This parameter has been previously estimated using mini-CT specimens in a number of unirradiated steels, most of them with relatively low T0 values (-120 °C to −60 °C), providing satisfactory results. This paper adds further validation of the use of mini-CT specimens to define the T0 of unirradiated RPV steels with relatively high values of this parameter. Additionally, the analysis of the fracture surfaces confirms the existence of cleavage fracture following the weakest link theory (i.e., one single initiation point), as required by the Master Curve approach.

A unified method to estimate J-resistance curve of thin-walled metallic tube containing axial cracks

Fracture toughness of thin-walled metallic tubes is an important mechanical property index to ensure their safety in service. Because of the particularity of geometric structure, the fracture toughness test of thin-walled metallic tubes cannot be carried out using traditional standard specimens. In this work, the expressions of load–displacement relationship and J-integral of thin-walled tube specimens containing bilateral axial cracks are proposed based on the energy density equivalence principle, in which the effect of material and specimen geometry has been considered. Through three-dimensional finite element simulation analysis, the relevant parameters of the expression are obtained and validated, and then a fracture toughness test method for thin-walled metallic tubes is established. The method is applicable to the fracture toughness measurement of thin-walled metallic tubes with different sizes and materials. Finally, the fracture toughness tests of two thin-walled alloy tubes were completed by the new method, and the J-resistance curves were obtained.

Comparison of shale fracture toughness obtained from scratch test and nanoindentation test

Fracture toughness is an important parameter in the hydraulic fracturing design, which is the major tool in the development of unconventional resources. Laboratory techniques for fracture toughness measurements usually require intact core samples and time-consuming sample preparation. The objective of this study is to compare fracture toughness values obtained by two less conventional methods: nanoindentation test and scratch test, which could facilitate the evaluation of this important parameter on smaller samples and at different scales. A set of 5 Antrim shale samples characterized by different mineral compositions is used to test this approach. For the scratch test, the fracture toughness and hardness are linearly correlated and show the same changing trend along the scratch length on all tested samples. For the nanoindentation test, the fracture toughness also increases with the increasing hardness. Most importantly, the results show that the fracture toughness values derived from these two methods are very similar, despite the difference in the scale of the measurements. This study is the first to compare fracture toughness between scratch and nanoindentation tests. Our results suggest that these two methods can be used to quickly evaluate fracture toughness from the shale core intervals containing both intact and nonintact parts.