Notch Fracture Toughness Research Articles

Fracture assessment of polymethyl methacrylate using sharp notched disc bend specimens under mixed mode I + III loading

Mixed mode I/III behavior of Perspex (polymethyl methacrylate (PMMA)) is studied experimentally and theoretically in this research using a new and simple laboratory test configuration. The specimen is a circular disc containing a sharp V-notch along the diameter that is loaded by the conventional three-point bend fixture. The critical values of notch stress intensity factors (KIV and KIIIV) were obtained for the whole combinations of modes I and III simply by changing the notch inclination angle relative to the loading rollers. The value of notch fracture toughness under pure or dominantly tension loads was greater than its corresponding value under mode III or dominantly torsion loads. The experimental results were also predicted very well by employing the local strain energy density (SED) criterion.

Bulk Mechanical Properties Testing of Metallic Marginal Glass Formers

We developed a unique three-point bend testing apparatus to measure bulk mechanical properties of a model metallic glass alloy (SAM2X5 with nominal composition Fe49.7Cr17.1Mn1.9Mo7.4W1.6B15.2C3.8Si2.4) prepared by spark plasma sintering. The relatively large sample sizes in the present work allowed for the preparation of test specimens with a macroscale cross section (in the millimeter range) with well-controlled sample dimensions closer to standardized tests. Wire saw cutting allowed for a relatively sharp notch radius (3x smaller than previous studies) and minimal sample damage. We determined that Young’s modulus and notch fracture toughness measured by our three-point bending apparatus are 230 GPa and 4.9 MPa·m1/2. Also, Vickers indentation and flexure testing provided consistent results for Young’s modulus. Indentation fracture toughness measured by Vickers indentation produced values at least 50% lower than by flexure. The microscale mechanical properties testing technique presented in this work and subsequent analyses are applicable to specimens of other compositions or ones prepared by other methods.

Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass and the notch radius $\rho$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale $\tau^{pl}_0$ and an effective loading timescale $\tau^{ext}(\dot{K}_I,\rho)$, where $\dot{K}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to scale with $\sqrt{\rho}$ independently of $\xi\!\equiv\!\tau^{ext}\!/\tau^{pl}_0$ for $\xi\!\ll\! 1$, to scale as $T\sqrt{\rho}\,\log(\xi)$ for $\xi\!\gg\!1$ (related to thermal activation, where $T$ is the temperature) and to feature a non-monotonic behavior in the crossover region $\xi\!\sim\!{\cal O}(1)$ (related to plastic yielding dynamics). These predictions are verified using novel 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of timescales competition and far from steady-state elasto-viscoplastic dynamics for understanding the toughness, and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented.

Blunt defect assessment in the framework of the failure assessment diagram

In order to reduce over-conservatism in fitness-for-service assessment procedures, experimental evidence and recent analytical developments recognise the importance of considering the actual shape of non-sharp flaws and/or the real geometric constraint conditions at the crack tip. This paper addresses the effect of blunt defects on the structural integrity assessment of reactor pressure vessel (RPV) and pipeline steels. Parametric studies for compact tension specimens with various notch root radii are performed using finite element analysis. The notch fracture toughness, the resistance to the onset of ductile cracking and the J-integral, quantifying the notch driving force, are evaluated. A stress-modified fracture strain model is used as a virtual testing method. The results are analyzed in the framework of the failure assessment diagram (FAD), showing that the existing shape of the FAD is also suitable for assessments of blunt defects and how the concepts introduced can be used to reduce the conservatism in defect assessment, define margins on failure and indicate when plastic collapse is the dominant failure mechanism.

A two-parameter approach to assessing notch fracture behaviour in clay/epoxy nanocomposites

Fracture toughness and other mechanical properties of epoxy are known to be affected by the addition of nanoclays. Fracture toughness has been shown by many researchers to depend on the nanocomposite structure with well-dispersed and distributed nanoparticles resulting in improvements in this property by up to 50%. Notch fracture toughness depends on the acuity of the notch as well as on the structure of the nanocomposite. In the present work, a two-parameter fracture criterion based on a critical notch stress intensity factor, Kρ,c, and effective T-stress, Tef, was used to study the effect of notch severity and nanoclay addition on the fracture toughness of the epoxy matrix. The results show that the average value of Kρ,c for neat epoxy increased with increasing notch radius while the absolute value of Tef decreased with notch radius. The addition of nanoclay to pristine epoxy reduced the average value of Kρ,c and increased the absolute value of Tef. The critical notch radius was found to be around 1.0 mm and the notch sensitivity was higher for neat epoxy. SEM analysis of the fractured surfaces revealed that the lower Kρ,c for nanocomposites in both mode I and mixed mode fractures was due to early crack initiation at clay clusters or voids at the notch root.

Fracture behavior of magnesium alloys – Role of tensile twinning

In this work, Mode-I fracture experiments are conducted using notched compact tension specimens machined from a rolled AZ31 Mg alloy plate having near-basal texture with load applied along rolling direction (RD) and transverse direction (TD). Moderately high notched fracture toughness of JC∼46N/mm is obtained in both RD and TD specimens. Fracture surface shows crack tunneling at specimen mid-thickness and extensive shear lips near the free surface. Dimples are observed from SEM fractographs suggesting ductile fracture. EBSD analysis shows profuse tensile twinning in the ligament ahead of the notch. It is shown that tensile twinning plays a dual role in enhancing the toughness in the notched fracture specimens with reduced triaxiality. It provides significant dissipation in the background plastic zone and imparts hardening to the material surrounding the fracture process zone via operation of several mechanisms which retards micro-void growth and coalescence.

Brittle fracture analysis of blunt V-notches under compression

Brittle fracture was investigated both experimentally and theoretically in blunt V-notches under compression. A new test specimen, called flattened V-notched semi-disk (FVSD) specimen, was suggested for conducting fracture tests on PMMA under compression for different notch angles and various notch radii with the aim to measure experimentally the compressive notch fracture toughness. The experimental results were theoretically estimated by means of two stress-based brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria. With total accuracies of 91% and 90% for the PS and the MS criteria, respectively; it was found that both the criteria provide very good predictions to the experimental results.

Mode II notch fracture toughness measurement for key-hole notches by the disk test

A new version of the well-known Brazilian disk specimen weakened by a dumbbell-shaped slit with two key-shaped ends, called key-hole notched Brazilian disk specimen, made of polymethylmethacrylate, was utilized to measure experimentally the notch fracture toughness for key-hole notches of various radii and different lengths under pure mode I and pure mode II loading conditions. The experimental values of the mode II notch fracture toughness/mode I notch fracture toughness ratio were theoretically estimated by means of two brittle fracture criteria, namely, the maximum tangential stress and the mean stress criteria. Two groups of critical distances were used in the criteria. The first one was equal to that for sharp crack and the second one was directly determined from the mode I fracture tests. It was found that while both the criteria could estimate the experimental results satisfactorily, the agreement between the theoretical and the experimental results is excellent when one deals with larger notch lengths. Also found in the research was that choosing any of the critical distance groups did not affect the theoretical predictions significantly, meaning that the critical distances of sharp crack could be used in fracture prediction of key-hole notches.

Theoretical and experimental investigation of brittle fracture in V-notched PMMA specimens under compressive loading

The aim of the present investigation was twofold. First, to prepare a new set of experimental data on brittle fracture of blunt V-notches under compression and second to develop stress-based criteria for predicting the compressive notch fracture toughness of blunt V-notches. A new test specimen, called V-notch stepped cottage (VSC) specimen, made of PMMA was proposed to perform fracture experiments under compression. Two brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria, were also developed to estimate the experimental results. It was demonstrated that the experimental results could be satisfactorily predicted by using the two criteria.

Brittle fracture in key-hole notches under mixed mode loading: Experimental study and theoretical predictions

Brittle fracture was studied experimentally and theoretically for key-hole notches under mixed mode loading. Brazilian disk specimen containing a dumbbell-shaped slit and made of polymethyl-methacrylate was proposed to measure the notch fracture toughness and the fracture initiation angle at room temperature. The experimental results were predicted by the maximum tangential stress and the mean stress criteria. Two groups of critical distances were utilized in the criteria. The first one was equal to that for sharp cracks and the second one was directly obtained from the fracture tests. It was found that both the criteria could predict the experimental results successfully.

Fracture assessment of VO-notches under mode II loading: Experiments and theories

In the present investigation, two brittle fracture criteria were suggested to predict the onset of brittle fracture in engineering components weakened by V-notches with end holes (VO-notches) under pure mode II loading. These criteria, called VO-MTS and VO-MS were developed based on the two well-known failure concepts of the maximum tangential stress (MTS) and the mean stress (MS), respectively. In order to evaluate the accuracy of the criteria, 72 new brittle fracture tests were conducted at room temperature on the new disk type specimen containing a central slit, called the VO-notched Brazilian disk (VO-BD) specimen, made of PMMA. First, the experimental fracture loads were converted to the corresponding mode I and mode II notch fracture toughness (NFT) values and the important ratio mode II NFT/mode I NFT was experimentally achieved. Then, the theoretical values of the ratio were predicted by means of the VO-MTS and the VO-MS criteria. It was found that both the criteria could provide very good predictions to the experimental results of the ratio mode II NFT/mode I NFT, as well as those of the fracture initiation angle. Also, found in this research was that one can utilize the critical distances of sharp crack in the fracture predictions of VO-notches.

Fracture Study on Key-Hole Notches Under Tension: Two Brittle Fracture Criteria and Notch Fracture Toughness Measurement by the Disk Test

Notch fracture toughness expressions were developed for predicting tensile fracture in members containing key-hole notches based on the point stress and the mean stress criteria. The criteria were verified by using the experimental results obtained from new fracture tests on the key-hole notched Brazilian disk specimens, made of PMMA. It was found that the mean stress criterion predicts the experimental results very well. Also, found in this research was that while the point stress model provides generally satisfactory estimations, except for a special case, the accuracy of this criterion enhances as the notch radius increases.

Notch Fracture Toughness Evaluation for a Brittle Graphite Material

Abstract First, several disc-type test samples weakened by a central bean-shaped slit with two U-shaped ends, called U-notched Brazilian disc (UNBD) specimens, made of commercial graphite, were prepared. Four notch tip radii were considered in the tests. Then, a monotonic compressive load was diametrally applied to each sample along the slit, resulting in pure mode I loading. After sudden fracture, the fracture loads were recorded and converted into the corresponding values of the notch fracture toughness (NFT) KIρ,c. The main advantage of the UNBD specimen is that the NTF test can be easily conducted without using complicated fixtures. The well-established brittle fracture model, namely the strain energy density (SED) over a specified control volume, which embraces the notch edge, was employed to estimate the fracture loads theoretically. A good agreement was found between experimental and theoretical results. Under Mode I loading, the SED and the NFT are linked by a simple relationship providing a powerful tool for the fracture assessment of different specimens and structural components weakened by notches.

Formation and mechanical properties of La–Al(–Ga)–C bulk metallic glasses with high content of carbon

Rare earth metal-based bulk metallic glasses (BMGs) containing metalloid element are synthesized in La–Al(–Ga)–C alloy system by copper mold casting. The high glass-forming ability (GFA) of the La–Al–C alloys revealed by the critical diameters up to 3mm could be due to the large difference in atomic size besides the strong bonding among the constituent elements. By partial substitution of Al in the La–Al–C alloy with similar element Ga, the La–Al–Ga–C BMGs exhibited enhanced GFA and the critical diameters were up to 6mm. The mechanical properties including compressive mechanical behavior, hardness and notch fracture toughness of the La-based BMGs are investigated. The La60Al30C10 BMG exhibits compressive fracture strength of nearly 1GPa, which is the highest for the La-based BMGs. The mechanisms for the formation and mechanical properties of the La–Al(–Ga)–C BMGs are discussed. The La–Al(–Ga)–C BMGs with high content of element C and high strength could be model materials for fundamental research.

Closed-form expressions of mode I apparent notch fracture toughness for key-hole notches

Two closed-form expressions were developed in this research to estimate the mode I apparent notch fracture toughness of brittle materials weakened by key-hole notches based on the well-established brittle fracture criteria, namely, the point stress and the mean stress. The theoretical models were verified using the experimental results reported in open literature dealing with tensile fracture in rectangular isostatic graphite plates containing central key-hole notches of various notch tip radii. A very good agreement was found to exist between the predictions of both the models and the experimental results. The results showed that while the accuracy of each model was different for various notch tip radii, total accuracies of the two models were almost equal (both about 93%) demonstrating their effectiveness. Using such expressions, it is expected that one can simply estimate the load-carrying capacity of brittle and quasi-brittle components weakened by key-hole notches under mode I loading.

Stress-based criteria for brittle fracture in key-hole notches under mixed mode loading

Abstract Two stress-based failure criteria were developed in the present research to predict mixed mode I/II brittle fracture in engineering components weakened by a key-hole notch. The first criterion was based on the well-established maximum tangential stress (MTS) concept, successfully proposed and utilized several times in recent years for different notch features. The second one was on the basis of the mean-stress (MS) concept which has been frequently used for predicting pure mode I fracture in notched domains. The results of the criteria were represented in the form of fracture curves and the curves of fracture initiation angle in terms of the notch stress intensity factors. To verify the validity of the fracture models, the theoretical predictions were compared with a large bulk of experimental data, reported in literature, on the fracture of rectangular isostatic graphite plates weakened by central key-hole notches of five different tip radii. It was found that while the total accuracies of the criteria are very good, for small notch tip radii, the MTS criterion provides generally better mixed mode notch fracture toughness results than the MS criterion. Conversely, the MS criterion works much better than the MTS model for larger notch tip radii. Dealing with fracture initiation angle, both the criteria could estimate the experimental results successfully.

Brittle fracture in V-notches with end holes

In the present research, two brittle fracture criteria were developed in terms of the notch stress intensity factors to predict mode I fracture in engineering components weakened by V-notches with end holes (VO-notches). The criteria were based on the point stress and the mean stress failure concepts. To evaluate the validity of the criteria, first, 36 new fracture tests were conducted on a new notched specimen, namely the Brazilian disk containing central V-notch with end hole (VO-BD specimen) made of polymethyl-metacrylate. Three notch angles and four notch radii were considered in the experiments. Then, the experimentally obtained fracture loads were converted to the corresponding mode I notch fracture toughness values by mean of the finite element method in order to compare the test results with the theories. It was found that very good agreement exists generally between the experimental and theoretical results. Also, found in this research was that by increasing the VO-notch angle, the accuracy of the mean stress criterion decreases, particularly for larger notch radii. Although the accuracy of the criteria depends significantly on the notch geometry, except for the angle 90°, the average discrepancies of the mean stress criterion were less than 8.5% as well as those of the point stress criterion for the entire angles showing acceptable accuracy of the predictions.

Role of constraint on the shift of ductile–brittle transition temperature of subsize Charpy specimens

ABSTRACTThe ductile–brittle transition temperature is not intrinsic to steel but depends on the specimen type and loading mode used for the test. The influence of these parameters is related to the plastic constraint. Here, the constraint is evaluated by the effective T‐stress obtained by the stress difference method on the notch tip stress distribution. From Charpy energy values at different temperatures, it is possible to obtain a material failure master curve where the notch fracture toughness is plotted versus the shift of test temperature with the transition temperature corresponding to the effective T‐stress value. Values of the critical effective T‐stress are obtained for three subsize Charpy specimens (3/4, 1/2 and 1/3) and are reported on a material transition temperature master curve versus effective T‐stress. This allows obtaining the shift of transition temperature when comparing with those of a standard Charpy V specimen. The results do not confirm the prediction given by the empirical relation of the ASME.

Role of Constraint on Ductile Brittle Transition Temperature of Pipe Steel X65

The brittle–ductile transition temperature (DBTT) is not intrinsic to a material but depends on the specimen type and loading mode used for the test. The influence of these parameters is related to the plastic constraint. Here the constraint is evaluated by the effective T stress obtained by the stress different method on the notch tip stress distribution. From Charpy energy values at different temperatures, it is possible to get a material failure master curve (MFMC) where the notch fracture toughness is plotted versus the shift of test temperature with the transition temperature corresponding to the effective T stress value.

Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading

Fracture phenomenon was investigated both experimentally and theoretically for a type of coarse-grained polycrystalline graphite weakened by a U-shaped notch under mixed mode loading. First, 36 disc-type graphite specimens containing a central U-notch, so called in literature as the U-notched Brazilian disc (UNBD), were prepared for four different notch tip radii and the fracture tests were performed under mode I and mixed mode I/II loading conditions. Then, the experimentally obtained fracture loads and the fracture initiation angles were predicted by using the U-notched maximum tangential stress (UMTS) and the newly formulated U-notched mean stress (UMS) fracture criteria. Both the criteria were developed in the form of the fracture curves and the curves of fracture initiation angle, in terms of the notch stress intensity factors (NSIFs). The results showed that while the criteria could predict successfully the experimental notch fracture toughness values, the UMS criterion provides slightly better predictions than the UMTS criterion, particularly for shear-dominant deformations. Also, found in this research was that the curves of fracture initiation angle were almost identical for the two criteria which both could predict well the experimental results.