A new push‐pull sample design for microscale mode 1 fracture toughness measurements under uniaxial tension

A sample geometry is proposed for performing microscale tensile experiments based on a push‐pull design. It allows measuring mode 1 fracture toughness under uniform far‐field loading. Finite element simulations were performed to determine the geometry factor, which was nearly constant for Young's moduli spanning 2 orders of magnitude. It was further verified that mode 1 stress intensity factor K_I is nearly constant over the width of the tension rods and an order of magnitude higher than K_II and K_III. Notched samples with different a/w ratios were prepared in (100)‐oriented Si by a combination of reactive ion etching and focused ion beam milling. The mode 1 fracture toughness K_I,q was constant with a/w and in average 1.02 ± 0.06 MPa√m in good agreement with existing literature. The geometry was characterized and experimentally validated and may be used for fracture toughness measurements of all material classes. It is especially interesting when a uniaxial, homogeneous stress field is desired, if crack tip plasticity is important, or when positioning of the indenter is difficult.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

Investigation of fatigue and fracture behaviour of sensitized marine grade aluminium alloy AA 5754

In the present study, fatigue and fracture characteristics of sensitized marine grade Al‐Mg (AA 5754) alloy are experimentally evaluated. Received alloy is sensitized at temperatures of 150°C (SENS50) and 175°C (SENS75) for 100 hours. Fracture parameters, K_Ic and J_Ic, are experimentally evaluated. Slow strain rate tensile tests at a crosshead speed of 0.004, 0.006, and 0.01 mm/min; fatigue crack growth tests at load ratios (R = P_min/P_max) of 0.1, 0.2, and 0.5; and low cycle fatigue tests at four strain amplitudes of (0.3‐0.6)% are performed for SENS50 and SENS75 alloys. Relatively lower magnitude of fracture toughness values are observed for SENS75 specimen. Severe degradation in tensile properties, fatigue crack growth characteristics, and low cycle fatigue lives are observed for SENS75 samples. Extended finite element method is adopted to simulate the elasto‐plastic crack growth during fracture toughness evaluation. Scanning electron microscopy (SEM) is used to understand the failure mechanism of sensitized alloys.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Fracture toughness of CaO-P2O5-B2O3 glasses and glass-ceramics determined by indentation

The fracture toughness, (K _IC) of CaO-P₂O₅-B₂O₃ glasses and glass-ceramics was investigated using both Vickers indentation and the notched beam technique (NBT). Five representative equations were applied and it was found that for the variation of K _IC with B₂O₃ content, the Lawn and Fuller equation showed the best correspondence with the NBT. The values of fracture toughness obtained from the Lawn and Fuller equation showed the same trend with B₂O₃ content as that determined by NBT, although the values from indentation were on average 33% lower. The determination of absolute fracture toughness by indentation requires a correction factor which can be obtained by calibration using NBT. A significant increase in K _IC occurred after a 37CaO-37P₂O₅-20B₂O₃-6Al₂O₃ (mol%) glass was converted to a glass-ceramic. The much higher K _IC for the glass-ceramic measured by NBT (1.32 MN m^–3/2) compared with that from indentation (0.89 MN m^–3/2) is attributed to internal stresses due to thermal expansion differences between the crystalline and residual glass phases leading to additional microcrack toughening.     

Evaluation of Fracture Parameters by Double-G,Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (K_Ic^c), unstable fracture toughness (K_Ic^un) and initiation fracture toughness (K_Icⁱⁿⁱ) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K_Ic^un of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.     

Indentation-induced subsurface tunneling cracks as a means for evaluating fracture toughness of brittle coatings

When a plate glued to a compliant substrate is subject to indentation, cracks may initiate from its subsurface due to flexure. Upon increasing the load, the damage develops into a set of tunnel radial cracks which propagate stably under a diminishing stress field. This phenomenon is utilized here to extract fracture toughness K _C for brittle materials in the form of thin plates or films. Experiments show that the SIF at the tip of the subsurface radial cracks is well approximated as K ~ P/c ^3/2, where P is the indentation load and c the mean length of the crack fragments. Using a transparent substrate, c can be easily determined after unloading, from which K _C is found. This simple and economic concept is applied to a wide variety of thin ceramic coatings, yielding toughness data consistent with literature values. Because the tip of the tunneling cracks are well removed from the contact site, the method circumvents certain complications encountered in common top-surface radial cracking techniques such as the effect of plastic deformation, residual stresses and crack extension after unloading. Although the present tests are limited to coating thicknesses >150 μm, it is believed that thinner coatings may be studied as well provided that the indenter radius is kept sufficiently small to insure that subsurface radial cracking dominates over all other failure modes.     

Effect of residual stress on cleavage fracture toughness by using cohesive zone model

This study presents the effect of residual stresses on cleavage fracture toughness by using the cohesive zone model under mode I, plane stain conditions. Modified boundary layer simulations were performed with the remote boundary conditions governed by the elastic K‐field and T‐stress. The eigenstrain method was used to introduce residual stresses into the finite element model. A layer of cohesive elements was deployed ahead of the crack tip to simulate the fracture process zone. A bilinear traction–separation‐law was used to characterize the behaviour of the cohesive elements. It was assumed that the initiation of the crack occurs when the opening stress drops to zero at the first integration point of the first cohesive element ahead of the crack tip. Results show that tensile residual stresses can decrease the cleavage fracture toughness significantly. The effect of the weld zone size on cleavage fracture toughness was also investigated, and it has been found that the initiation toughness is the linear function of the size of the geometrically similar weld. Results also show that the effect of the residual stress is stronger for negative T‐stress while its effect is relatively smaller for positive T‐stress. The influence of damage parameters and material hardening was also studied.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

Fracture toughness and evaluation of coating strength with an initial residual stress field

The effect of residual elastic stresses on the geometry of cracks which arise with contact and spontaneous failure of brittle coatings made of high-strength compounds is studied. Conditions are established for the correctness of fracture toughness K_Ic tests with indentation of a standard Vickers pyramid as applied to surface layers with an inhomogeneous structure and an initial residual stress field. Taking account of the anisotropy of fracture toughness established by experiment a reliable approach is suggested for evaluating the brittle strength of coatings in the presence of residual stresses.Translated from Problemy Prochnosti, No. 1, pp. 51–61, January, 1994.     

Fracture toughness of selectively reinforced Al2124 alloy: precrack tip in the aluminium alloy side

Abstract

The fracture toughness of Al2124/Al2124+SiC bimaterials is affected by thermal residual stresses, elastic/plastic mismatch, precrack tip position, and failure mechanism. When the precrack tip is in the Al2124 side, final catastrophic failure occurs when ductile fracture of the Al2124 layer between the precrack tip and the composite side takes place, followed by fracture of the composite layer. For a precrack tip 2·0 mm from the interface, K _Q(5%) values are lower than the 'Al2124 only' value due to the near crack tip tensile residual stresses and higher stress triaxiality within the Al alloy ligament. At 0·5 mm from the interface, K _Q(5%) values increase and are usually as high as the 'Al2124 only' value due to the stronger shielding of the elastic/plastic mismatch. If the precrack tip is 2·0 mm from the interface, K _crit values of the bimaterial are higher than the 'Al2124 only' value and this is deduced to be due to the elastic/plastic mismatch shielding. At 0·5 mm from the interface, K _crit values are reduced because both the near tip tensile residual stress is higher and stress triaxiality levels of the ductile ligament are higher, although the elastic/plastic mismatch shielding is also higher at this position.     

The effect of binder thickness and residual stresses on the fracture toughness of cemented carbides

Much of the data on WC-Co cermets show that the fracture toughness,K _Ic, increases with increasing tungsten carbide grain size at fixed volume fraction of the cobalt binder phase. It is shown that the origin of this effect can be explained on the basis of the plane stress fracture of constrained cobalt phase and the periodic internal stresses arising due to differential thermal contraction of the two phases. Quantitative models have been derived which take these two effects into account. The effect of macroscopic residual stresses, such as those generated by milling WC-Co drilling inserts, on the apparent toughness has also been analysed. It is shown that for the chevron-notched type specimen the macroscopic residual stress affects not only the maximum load but also the length of the crack at which the maximum occurs. A graphical method is presented which permits the evaluation of the true K_Ic.     

Residual stresses in particle-reinforced ceramic composites using synchrotron radiation

Residual stresses were determined in particle-reinforced ceramic composites using synchrotron based x-ray diffraction. The baseline Si₃N₄ and the Si₃N₄-TiN composites were processed by turbomilling, pressure casting, and isopressing. They were then continuously sintered to full density, under a pressureless, flowing nitrogen atmosphere. The flexural strength, fracture toughness, and residual stress were measured for as-machined samples and following quenching in water from 1000°C, 1100°C, and 1200°C. The residual stresses for both the baseline Si₃N₄ and the Si₃N₄-TiN composites were determined from the (441) and (531) reflections, by applying the 2-sin² method. The measured residual stresses were compared with the flexural strength and fracture toughness results to determine the effects of residual stress and thermal shocking on the mechanical properties of each material. In both the baseline Si₃N₄ and Si₃N₄-TiN composites, after thermal shocking, the compressive residual stresses were developed in directions both parallel and perpendicular to the sample surface. The residual compressive stresses for the Si₃N₄-TiN composites were much higher than the baseline Si₃N₄. As a result, both fracture toughness and flexural strength of the Si₃N₄-TiN composites were improved. In addition, the addition of the TiN appears to improve both the strength and toughness of the baseline Si₃N₄.     

Critical evaluation of indentation fracture toughness measurements with Vickers indenter on yttria‐stabilized zirconia dental ceramics

The purpose of this study was to investigate and analyze fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia (Y‐TZP) dental ceramics by the Vickers indentation fracture test. In order to determine fracture toughness, the Vickers indenter was used under the load of 294.20 N (HV30). The cracks, which occur from the corners of a Vickers indentation, were measured and used for fracture toughness determination, through five mathematical models according to (I) Anstis, (II) Evans and Charles, (III) Tanaka, (IV) Niihara, Morena and Hasselman and (V) Lankford. Morphology of indentation cracking was determined by scanning electron microscope. The most adequate model for determination of fracture toughness (K_Ic) of yttria stabilized tetragonal zirconia dental ceramics by the Vickers indentation fracture test is Lankford model.     

Enhancing mechanical and fracture properties of sandwich composites using nanoparticle reinforcement

Polyurethane (PU) foam is reinforced with SiC nanoparticles to develop core materials for sandwich composites. Isocyanate component (Part A) of PU foam was dispersed with SiC nanoparticles, and then mixed with polyol (Part B) to manufacture nanophased core materials. Nanoparticle reinforcement varied from 0.1 to 2.0 wt% of the total polymer. Both pristine and silane functionalized SiC nanoparticles were used in the investigation. Nanophased foams were tested in compression and flexure to determine the mechanical properties. Fracture toughnesses K _IC and G _IC were determined using the SENB test. Sandwich panels were fabricated and tested for face-core debond fracture toughness using the tilted sandwich debond test. The study has revealed that reinforcement of the foam by pristine nanoparticles substantially enhances mechanical properties but degrades fracture toughness. This loss in fracture toughness, however, may be recovered with the use of functionalized nanoparticles. Small concentrations (0.1–0.2 wt%) of functionalized nanoparticles provided large improvement in debond fracture toughness of sandwich specimens.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.     

Study of indentation induced cracks in MoSi2-reaction bonded SiC ceramics

MoSi₂-RBSC composite samples were prepared by infiltration of Si-2 at.% Mo melt into a preform of commercial SiC and petroleum coke powder. The infiltrated sample had a density > 92% of the theoretical density (TD) and microstructurally contained SiC, MoSi₂, residual Si and unreacted C. The material was tested for indentation fracture toughness at room temperature with a Vicker’s indenter andK _IC was found to be 4.42 MPa√m which is around 39% higher than the conventional RBSC material. Enhancement in indentation fracture toughness is explained in terms of bowing of propagating cracks through MoSi₂/SiC interface which is under high thermal stress arising from the thermal expansion mismatch between MoSi₂ and SiC.     

A study on the ASTM E1921 standard in determining the fracture toughness of ferritic steels

One of the most important aims of the fracture mechanics is to determine the fracture toughness of a material. Various methods were developed for this purpose and have been still used nowadays. In the J‐integral method that is one of them, providing of a dominant linear elastic condition on the specimen is not required. However, in ferritic steels, the fracture toughness values (K_JC) obtained by the J‐integral method show some inconsistencies. Therefore, the ASTM E1921 standard was developed on ferritic steels, which are instabilities in the values of elastic or elastoplastic fracture toughness. In this study, a new method was used to determine the fracture toughness (K_IC) of ferritic steels, and it was compared with the standard. Three steels with different mechanical properties and average grain size were investigated in this study.     

Mechanical properties of the solid Li-ion conducting electrolyte: Li0.33La0.57TiO3

Li_0.33La_0.57TiO₃ (LLTO) is a potential Li-ion conducting membrane for use in aqueous Li-air batteries. To be in this configuration its mechanical properties must be determined. Dense LLTO was prepared using a solid-state (SS) or sol–gel (SG) procedure and was hot-pressed to yield a high relative density material (>95 %). Young’s modulus, hardness, and fracture toughness of the LLTO-SS and sol–gel LLTO-SG materials was determined and compared to other solid Li-ion conducting electrolytes. The Young’s modulus for LLTO-SG and LLTO-SS was 186 ± 4 and 200 ± 3 GPa, respectively. The Vickers hardness of LLTO-SG and LLTO-SS was 9.7 ± 0.7 and 9.2 ± 0.2 GPa, respectively. The fracture toughness, K _IC, of both LLTO-SG and LLTO-SS was ~1 MPa m^1/2; the fracture toughness of LLTO-SG was slightly higher than that of LLTO-SS. Both LLTO-SG and LLTO-SS have a Young’s modulus and hardness greater than the other possible solid Li-ion conducting membranes; Li₇La₃Zr₂O₁₂ and Li_1+x+y Al _x Ti_2−x Si _y P_3−y O₁₂. Based on modulus and hardness hot-pressed LLTO exhibits sufficient mechanical integrity to be used as a solid Li-ion conducting membrane in aqueous Li-air batteries but, its fracture toughness needs to be improved without degrading its ionic conductivity.